ABSTRACTS AND PRE-PROCEEDINGS Baia Mare September 25

Transcription

Technical University of Cluj-Napoca, Romania
North University Center at Baia Mare
Faculty of Science
Department of Mathematics and Computer Science
9
th
I
C
nternational
onference of
A
pplied
M
athematics
ABSTRACTS AND PRE-PROCEEDINGS
Baia Mare
September 25-28, 2013
9th International Conference on Applied Mathematics
September 25-28, 2013
organized by
Department of Mathematics and Computer Science, TUC-N, North University Center at Baia Mare,
Romanian Mathematical Society, Maramureş Branch,
SINUS Association
Organizing Committee: Gheorghe Ardelean, Vasile Berinde, Dan Bărbosu, Zoiţa Berinde, Andrei Horvat-Marc, Petrică Pop,
Nicolae Pop, Cosmin Sabo, Ioana Taşcu, Ioana Zelina
Conference Secretariat: Mihaela Petric
Abstracts volume technical editor: Andrei Horvat-Marc Web site of the Conference: Cosmin Sabo, Andrei Horvat-Marc
Scientific Committee:
Dumitru Acu, University ”L. Blaga”, Sibiu, Romania
Petru T. Mocanu, ”Babeş-Bolyai” University, Romania
Octavian Agratini, ”Babeş-Bolyai” University, Romania
Cristinel Mortici, ”Valahia” University Targovişte, Romania
Dorin Andrica, ”Babes-Bolyai” University, Romania
Gheorghe Munteanu, Transilvania University Brasov, Romania
Mircea Balaj, University of Oradea, Romania
Anton Mureşan, ”Babeş-Bolyai” University, Romania
Dan Bărbosu, TUC-N, CUNBM, Romania
Viorica Mureşan, Technical University Cluj-Napoca, Romania
Stefan Berezny, Technical University of Kosice, Slovakia
Costică Mustăţa, ”T. Popoviciu” Institute of Numerical Analy-
Vasile Berinde, TUC-N, CUNBM, Romania
sis, Cluj-Napoca, Romania
Zoita Berinde, TUC-N, CUNBM, Romania
Eugen Paltânea, Transilvania University Brao̧v, Romania
Lucian Beznea, Institue of Mathematics of Romanian Academy,
Marcin Paprzycki, Oklahoma State University, USA
Bucharest, Romania
Gheorghe Păun, Institute of Mathematics of Romanian Acad-
Daniel Breaz, ”1 Decembrie 1918” University, Romania
emy, Romania
Adrian Carabineanu, University of Bucharest, Romania
Ion Păvăloiu, ”T. Popoviciu” Institute of Numerical Analysis,
Emil Cătinaş, ”T. Popoviciu” Institute of Numerical Analysis,
Cluj-Napoca, Romania
Adrian Petruşel, ”Babeş-Bolyai” University, Romania
Aurelian Cernea, University of Bucharest, Romania
Cornel Pintea, ”Babeş-Bolyai” University, Romania
Mitrofan Choban, Univ.
Jan Plavka, Technical University of Kosice, Slovakia
of Tiraspol in Kishinev, Kishinev,
Moldova
Nicolae Pop, TUC-N, CUNBM, Romania
Ramesh Kumar Choudhary, APIIT SD , Panipat, India
Petrică Pop, TUC-N, CUNBM, Romania
Constantin Corduneanu, University of Texas at Arlington, USA
Constantin Popa, ”Ovidius” University of Constanta, Romania
Marius-Eduard Craciun, ”Ovidius” University of Constanta,
Dorian Popa, Tehnical University Cluj-Napoca, Romania
Romania
Radu Precup, ”Babes-Bolyai” University, Romania
Ioan Dzitac, University of Oradea, Romania
Vasile Preda, University of Bucharest, Romania
Dorel Duca, ”Babes-Bolyai” University Cluj-Napoca, Romania
Mihai Postolache, Politehnica University Bucharest, Romania
Sorin Gal, University of Oradea, Romania
Ioan Raşa, Tehnical University Cluj-Napoca, Romania
Ioan Gavrea, Technical University Cluj-Napoca, Romania
Miklos Ronto, University of Miskolc, Hungary
Vasile Glăvan, State University of Chişinău, Moldova
Ioan A. Rus, ”Babes-Bolyai” University, Romania
Radu Gologan, Politehnica University Bucharest, Romania
Tudor Sireteanu, Institute of Solid Mechanics of the Romanian
Ghiocel
Academy, Bucharest, Romania
Groza,
Technical
University
of
Civil
Building,
Bucharest, Romania
Mircea Sofonea, Université de Perpignan, France
Valeriu Guţu, State University of Chişinău, Moldova
Gheorghe Ştefănescu, University of Illinois, USA
Mircea Ivan, Technical University Cluj-Napoca, Romania
Damian Trif, ”Babeş-Bolyai” University Cluj-Napoca, Romania
Petar Kenderov, Bulgarian Academy of Sciences, Bulgaria
Ioan Tomescu, University of Bucharest, Romania
Marian Klesc, Technical University of Kosice, Slovakia
Luige Vladareanu, Institute of Solid Mechanics of the Romanian
Peter Kortesi, University of Miskolc, Hungary
Academy, Bucharest, Romania
Ştefan Măruşter, West University Timişoara, Romania
Cai Wen, Research Institute of Extenics and Innovation Meth-
Mihail Megan, West University Timişoara, Romania
ods, Guangdong University of Technology, Guangzhou, P.R
Dorel Mihet, West University Timişoara, Romania
China
Contents
1
Preface
Part 1.
Short Abstracts
3
Plenary Lectures
4
Boţ Radu Ioan
On primal-dual splitting algorihms for monotone inclusions with applications to
convex optimization
Choban Mitrofan
Fixed points for mappings defined on generalized pseudometric spaces
Corduneanu, Constantin
What’s in the Third stage of the Fourier Analysis?
Dzurina Josef
Properties of higher order differential equations
Păun Gheorghe
Numerical P Systems
Rus, Ioan A.
From a Dieudonné theorem concerning the Cauchy problem to an open problem in
weakly Picard operator theory
Rusu, Cristian
Software for Use: (Re)Defining Usability Heuristics
Sireteanu, Tudor and Ana Maria Mitu, Ovidiu Solomon, Claudia Meglea
Assessment of equivalent linear models for experimental hysteretic loops by
correlation method
Ştefănescu, Gheorghe
Open systems: modelling, programming, verification
Main and Regular lectures
1. Fixed Point Theory and Applications
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Berinde, Vasile
Fixed point theorems for nonself multi-valued almost contractions satisfying
property (M)
Bojor, Florin and Magnolia Tilca
Existence and uniqueness theorem for Fredholm integral equation, via Jachymski’s
Theorem
Bota, Monica-Felicia and Veronica Ilea, Oana Mleşniţe
Fixed point theorems for α − φ contractions in b-metric spaces
Chifu, Cristian and Gabriela Petruşel
Fixed point results for generalized multivalued contractions in b-metric spaces
endowed with a graph
Coroian Iulia
Fix point theorems for multivalued contractions with respect to two topologically
equivalent metrics
Dumitru, Dan
Generalizations of iterated function systems
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CONTENTS
Glăvan Vasile
Fixed points and viable sets in dynamics of relations and control
Guţu, Valeriu
How many contractions are needed to construct some kinds of plane compacta?
Horvat-Marc, Andrei
Fixed Point Theorems for Nonself Operators
Lauran, Monica
On a functional Fredholm integral equation, via nonexpansive operators
Lungu, Nicolaie and Dorian Popa
On Hyers-Ulam stability of some partial differential equations
Mureşan, Anton S.
The Theory of some Asymptotic Fixed Point Theorems
Mureşan, Viorica
A Volterra Functional - integral Equation, via Weakly Picard Operators’ Technique
Oprea, Anca
Fixed point theorems for contractions of rational type in metric spaces, for
multivalued operators
Otrocol, Diana and Veronica Ana Ilea
Qualitative properties of functional differential systems
Păcurar, Mădălina
Fixed point theorems for nonself Prešić type operators
Petric, Mihaela
Remarks on cyclic coupled fixed point theorems
Rus, Ioan A. and Marcel-Adrian Şerban
Some existence results for a system of operatorial equations
Viorel, Adrian
Fixed point results in cone metric spaces
2. Optimization Theory, Operations Research and Applications
Andreica Anca and Camelia Chira, Alexandru Agapie
Cellular Automata Topologies and Rules
Berežný, Štefan
Generalized Algorithm of Processes of the Winter Maintenance on Airports
-- see extended abstracts.
Draženská, Emı́lia
On the Crossing Numbers of Cartesian Products with Paths
Carp, Doina and Constantin Popa and Cristina Şerban
Modified Han algorithm for inconsistent linear inequalities
Chira, Camelia and Anca Andreica
Evolutionary Algorithms for Dynamic Complex Problems
Dănciulescu, Daniela
Systems of knowledge representation based on stratified graphs and their inference
process
Deaconu, Adrian and Mihai Iolu
Inverse Generalized Maximum Flow Algorithms
Enache-David, Nicoleta and Sangeorzan Livia
On a Markov Model for the Optimization of the Websites Structure
Marián Klešč
Minimal intersections in graph drawings
Kravecová, Daniela and Jana Petrillová
Determination of the crossing numbers of the Cartesian product of graphs
Levit, Vadim E. and Eugen Mandrescu
Greedoids on Vertex Sets of B-joins of Graphs
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CONTENTS
Parpalea, Mircea and Grigoraş, Nicoleta
The maximum parametric flow in discrete dynamic networks
Pintea Camelia
Pharaoh ants for Sensor Networks Security
Prusińska, A. and E. Szczepanik and A.A. Tret’yakov
High-order optimality conditions for degenerate calculus of variations problems
Pop, Petrică
On the multidimensional multi-way number partitioning problem
Sabo, Cosmin
Intelligent methods for making the best decisions using optimization techniques and
data mining
Scheiber, Ernest
On the Convexity of the Control Set of a Hybrid Optimal Control Problem
Stoilova, Krasimira. and Todor Stoilov
Bi-level definition of portfolio optimization problem
Staš, Michal
Axiomatic set theory for functional analysis
Süto, Jzsef and Ştefan Oniga
Testing artificial neural network for gesture recognition
Villar, José R., Silvia González, Javier Sedano, Camelia Chira and José M.
Trejo
Early diagnosis of Stroke: bridging the gap through wearable sensors and
computational models
Zelina, Ioana
Communication aspects in Fibonacci type topologies
3. Ordinary Differential Equations and Partial Differential Equations
Babuţia, Mihai Gabriel
Input-output methods in the study of nonuniform exponential dichotomy of
evolution families
Balint, Agneta M. and Ştefan Balint
Well posed problem in sense of Hadamard, for a source produced acoustic
perturbation propagation in a lined duct, carrying a gas flow
Curt, Paula
Some remarks on certain invariant geometric properties in Hele-Shaw flows
Cozma, Dumitru
Reversible cubic systems with centers
Groza G., M. Jianu and N. Pop
Infinitely differentiable functions represented into Newton interpolating series
Gil-Swiderska, Agnieszka
Second order partial differential equation of parabolic type in the cosmic rays
transport studies
Ionescu Adela
Mathematical models for repetitive phenomena in the excitable media. The case of
turbulent mixing
Klincsik, Mihály
Exact periodic patterns in quasi-linear reaction-diffusion systems with competitions
Perjan, Andrei
Limits of solutions to the singularly perturbed abstract hyperbolic-parabolic systems
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CONTENTS
Paţiuc, Vladimir and Galina Rı̂bacova
Numerical Approach for Solving Nonlinear Electromagnetic Problem
Perjan, A. and G. Rusu
Singularly perturbed problems for abstract linear differential equations with positive
powers of a positive defined operator
Pop Nicolae
The 3D elastic contact applied to robots control
Rontó, András and Miklós Rontó
Investigation of periodic solutions using interval halving
Sfetcu, Răzvan
Approximation of Köthe-Bochner spaces with subspaces of functions having finite
dimensional values
Siluszyk, Agnieszka
A new central configurations in the planar N -body problem and their linear stability
Şubă Alexandru, Vacaraş Olga
Cubic Systems with an Invariant Line at Infinity of the Maximal Geometric
Multiplicity
4. Advances in Numerical Analysis and Approximation Theory
Acu, Ana Maria and Sofonea Florin
Improvement of Grüss and Ostrowski Type Inequalities and Applications
Agratini Octavian
Approximation by Linear Discrete Operators on Weighted Spaces
Buša Ján
Identification of a Sum of Exponential Functions Using its Taylor Series
Baboş, Alina-Mihaela
Interpolation operators on a triangle with two and three curved edges
Bărbosu, Dan and Gheorghe Ardelean
The Bernstein quadrature formula revisited
Birou, Marius Mihai
Bernstein type operators which preserve some test functions
Cismaşiu, Cristina Sanda
Some properties of a Durrmeyer type operator associated with Bleimann-Butzer-Hahn
operator
Gavrea, Ioan and Bogdan Gavrea
About some inequalities in approximation theory
Indrea, Adrian
About a linear and positive operator of Stancu-type with fixed points e1 and e2
Gavrea, Ioan and Mircea Ivan
Optimal rate of convergence for sequences of a prescribed form
Miclăuş, Dan
On the Stancu type bivariate approximation formula
Mitrea Alexandru
Two-sided estimates for the norm of the linear operators used in the convergence of
some approximation processes
Popa, Dorian and Ioan Raşa
On the stability of some classical operators from approximation theory (II)
Radu, Voichita Adriana
On a Class of Linear and Positive Operators
Raşa, Ioan
Approximation processes and asymptotic relations
Sofonea Florin, Muraru Carmen Violeta, Acu Ana Maria
Note on Approximation Properties of q-Bernstein-Schurer Operators
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CONTENTS
Taşcu, Ioana and Andrei Horvat-Marc
Graphical reprezentations of mean square error of the bivariate operator of Stancu
type
5. Advances in Algebra
Botnaru, Dumitru and Elena Baeş
The Cocartesian Right Product
Botnaru, Dumitru and Olga Cerbu
Semireflexive Subcategories
Botnaru, Dumitru and Alina Ţurcan
The Right Product
Constantinescu, Adrian
Hilbert - Mumford - Nagata Theorem on invariants and some topological aspects of
the finite generation of subalgebras. (II)
Crivei Septimiu
Finitely accessible categories versus module categories
Körtesi, Péter
About separation axioms in semitopological and topological invers semigroups
Mureşan, Călin Alexe
New Methods for the Polynomial Roots Approximation
Olteanu, Gabriela
Semisimple group algebras: primitive idempotents and group codes
Pelea, Cosmin
On some particular equivalence relations of multialgebras
Pop, Adina and Maria S. Pop
A generalization of Hyers-Ulam-Rassias stability on m-semigroups
Pop, Vasile
Simultaneous extensions of polyadic groups
Szántó, Csaba
Extensions of modules over tame hereditary algebras
Teodor Dumitru Vălcan
Abelian groups in which any proper subgroup has the direct summand intersection
property
6. Software Engineering - Principles and Practices
Bérczes, Tamás and Attila Kuki, Béla Almási, János Sztrik and Pascal Moyal
A new model of finite-source retrial queues with multi-state server’s breakdown
Sárvári, Csaba
Constructing questions using Maple T. A.
Hajdu-Macelaru, Mara Diana
Metrics in software quality evaluation
Motogna, Simona and Florin Crăciun, Gabriel Glodean
fUML Formal Description
Ildikó Perjési-Hámori
On-Line Testing in Higher Mathematics Education - Maple T. A.
Imre Piller
Software Tools for Information Retrieval with Lattices
Petreanu, Emanuela and Livia Sângeorzan
The use of Java technologies for web e-commerce applications
Sângeorzan, Livia and Mihaela Parpalea, Mircea Parpalea
A functional sentence perspective approach to preflow algorithm in parametric
networks
Szilágyi, Szabolcs
The effects of different queuing techniques over VoIP performance: a simulation
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CONTENTS
approach
Szabó, Peter
A Max-Plus Algorithm and the Prime Numbers
Sztrik, János and Tamás Bérczes
Tool supported analysis of queueing systems with Future Internet applications
Veres Laura
Application of rough approximations in Group Technology problems
Gergely Kocsis, Imre Varga
Information spreading on declining social networks
7. Applications of Mathematics and Computer Science in Science, Arts and
Technology
Ardelean, Gheorghe
New graphical models for the basins of attraction of the real roots of a nonlinear
equation
Contraş, Diana and Alina Pintescu
Developing an ontology for automated scene creation
Berinde Ruxandra and Vasile Berinde
Using a spatial configuration mathematical model to study the inhabited area of a
Maramureş village
Berinde, Zoiţa
New quantitative structure-toxicity relationship for aliphatic carboxylic acids
Dippong, Thomas and Zoiţa Berinde
A topological study for a set of columnar liquid crystals
Mare Roşca, Oana, Lucia Mihalescu, Monica Marian, Zorica Voşgan
Analysis and Interpretation of Structure and Diversity of Some Macrozoobenthic
Communities Using Mathematics Indices
Marzec, Krzysztof
Applications of computer science in impingement cooling system design
Mihali, Cristina and Gabriela Oprea, Claudia Butean
Spatial distribution maps of microelements concentration in surface soil around soil
pollution sources
8. Mathematical Modelling with Applications in Economics
Boca, Graţiela Dana
Structural Optimization Model Design using TOSCA Program
Carstea, Claudia and Sangeorzan Livia
Algorithms implementation model for software optimization
Darabă, Dinu
Optimizing Investment Costs for Production Systems with Discontinuous Operation
Mode
Hordau, Anne Marie Andreea
An Questionnare Based Analyses on Labor Force in Maramureş County
Răbâea, Adrian
An Implementation of Monte Carlo Method for European Option Pricing
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CONTENTS
ix
Mihoc, Ion and Cristina-Ioana Fătu
On the comparison of Fisher informations of the some probability distributions
48
Sabou, Simona and Liliana Zima, Rita Toader, Corina Rădulescu, Florina Hahn,
Cristian Vele
The performance appraisal in human resources
48
Toader,Cezar, Rita Toader and Corina Rădulescu
Resource-Oriented Applications in Product Data Management
48
Vele, Cristian and Cristian Anghel and Rita Toader
Using statistical data to evaluate the strategic efforts of companies
48
Zima Liliana, Simona Sabou, Rita Toader, Cezar Toader
The calculation of human resource performance
48
9. Variational methods and applications to ODEs and PDEs
48
Breckner, Brigitte E.
Parameter-depending problems on fractals
48
Bogdan, Marcel
An application to quasi-linear variational inequalities
49
Faraci, Francesca
An existence result for a quasi-linear elliptic equation with dependence on the
gradient
49
Inoan Daniela, Kolumbán József
Existence theorems for intersection problems and equilibrium problems
50
Lisei, Hannelore
Stochastic Nonlinear Equations of Schrödinger Type
50
László, Szilárd
Multivalued variational inequalities and coincidence point results
50
10. Miscellanea
50
Cioruţa, Bogdan and Mirela Coman
Bézier Curves in GeoGebra and Computational Applications dedicated to
Environmental Informatics
50
Cioruţa, Bogdan and Mirela Coman
Fourier Series in GeoGebra - New Possibilities for Representation and Applications 51
T. V. Do, R. Chakka, J. Sztrik, T. Bérczes, D. Efrosinin
An efficient method to solve a two-server heterogeneous retrial queue with threshold
policy
51
Dana Debora Gliţia
Field extensions and Clifford theory
51
Körtesi, Péter
A divisibility problem of integers
52
Marian, Claudia and Monica Marian
Prognose and diagnosis in education by using statistical methods
52
Marian, Monica and Beatrice Agneta
Statistical Instruments Used in Environmental Assessment Validation of Newly
Introduced Species
52
Pişcoran, Laurian Ioan and Cătălin Ionel Barbu
Tzitzeica curves in a Minkowski space
52
Part 2.
Extended Abstracts
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x
CONTENTS
Ardelean, Gheorghe
New graphical models for the basins of attraction of the real roots of a nonlinear
equation
55
Balint, Agneta M. and Ştefan Balint
58
Berežný, Štefan
61
Bérczes, Tamás and Attila Kuki, Béla Almási, János Sztrik and Pascal Moyal
63
Boca, Graţiela Dana
66
Carstea, Claudia and Sangeorzan Livia
69
Dănciulescu, Daniela
Systems of knowledge representation based on stratified graphs and their inference
process
73
Darabă, Dinu
Optimizing Investment Costs for Production Systems with Discontinuous Operation
Mode
77
T. V. Do, R. Chakka, J. Sztrik, T. Bérczes, D. Efrosinin
An efficient method to solve a two-server heterogeneous retrial queue with threshold
policy
79
Enache-David, Nicoleta and Sangeorzan Livia
82
Gil-Swiderska, Agnieszka
Second order partial differential equation of parabolic type in the cosmic rays
transport studies
85
Hordău, Anne Marie Andreea
87
Kravecová, Daniela and Jana Petrillová
89
Kocsis Gergely and Imre Varga
92
Mare Roşca, Oana, Lucia Mihalescu, Monica Marian, Zorica Voşgan
Analysis and Interpretation of Structure and Diversity of Some Macrozoobenthic
Communities Using Mathematics Indices
95
Marian, Claudia and Monica Marian
97
Marian, Monica and Beatrice Agneta
Statistical Instruments Used in Environmental Assessment Validation of Newly
Introduced Species
100
Marzec, Krzysztof
102
Scheiber, Ernest
105
Sabou, Simona and Liliana Zima, Rita Toader, Corina Rădulescu, Florina Hahn,
Cristian Vele
108
Stoilova, Krasimira. and Todor Stoilov
111
Szilágyi, Szabolcs
The effects of different queuing techniques over VoIP performance: a simulation
approach
113
CONTENTS
Sztrik, János and Tamás Bérczes
Toader,Cezar, Rita Toader and Corina Rădulescu
Villar, José R., Silvia González, Javier Sedano, Camelia Chira and José M.
Trejo
Early diagnosis of Stroke: bridging the gap through wearable sensors and
computational models
Vele, Cristian and Cristian Anghel and Rita Toader
Zima Liliana, Simona Sabou, Rita Toader, Cezar Toader
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Preface
The Ninth International Conference on Applied Mathematics (ICAM 9) follows some successfully
international conferences organized in Baia Mare since 1996 (35 Years of Higher Mathematics Education
in Maramureş 1996, ICAM1: 1998; 135th Pannonian Applied Mathematics Meeting: 2001, ICAM2:
2000; ICAM3: 2002; ICAM4: 2004; ICAM5: 2006; ICAM6: 2008; ICAM7: 2010 and ICAM8:2011).
The general profile and scientific programme is mainly the same as at the previous ICAM editions.
Apart from Plenary Lectures (9 at ICAM9), the conference programme includes main and regular
lectures grouped on thematic minisymposia. The following symposia have been proposed for ICAM9:
• Fixed Point Theory and Applications
• Optimization Theory, Operations Research and Applications
• Numerical methods for Ordinary Differential Equations and Partial Differential Equations
• Advances in Numerical Analysis and Approximation Theory
• Advances in Algebra
• Advances in Geometry
• Software Engineering - Principles and Practices
• Applications of Mathematics and Computer Science in Science, Arts and Technology
• Mathematical Modelling with Applications in Economics
• Mathematics Education Advanced Intelligent Control Applied in Robotics and Mechatronics
• Variational methods and applications to ODEs and PDEs
• Applications of Mathematics and Computer Science in Chemistry and Biology
Due to the considerable number of submitted papers (more than 160), a rather important number
of papers have been accepted for presentation and some of them were included in the Poster session.
One new feature of ICAM9 is the fact that the Local Organizing Committee has decided to publish,
apart from the usual volume of short abstracts, several extended abstracts that form a Pre-Proceedings
section in the volume of Abstracts.
This is done in order to ensure a fast publication of those papers submitted by authors before the
conference.
Extended and improved versions of the papers presented at the conference will be included in
post-Proceedings volumes published as special issues of our journals:
Carpathian Journal of Mathematics (2012 Impact factor: 0.852)
Creative Mathematics and Informatics (B+ CNCSIS indexed journal)
after a rigorous peer-review process.
Both journals are cover-to-cover reviewed/indexed in: Zentralblatt MATH and Mathematical
Reviews.
Contributions to post-Proceedings will be submitted on-line using the submission and editorial
system SEMN of the two journals:
Carpathian Journal of Mathematics: http://radu.autoportret.ro/cjm/
Creative Mathematics and Informatics: http://radu.autoportret.ro/cmi/
The authors who will contribute to the post-Proceedings volumes have to select ”Special issue
ICAM9” for Article Type when submitting their contribution. More information about these journals
(Editorial Board, Aims and Scope, Instruction for Authors, etc.) may be found at the following
addresses:
http://carpathian.ubm.ro/
http://creative-mathematics.ubm.ro/
We thank all contributors to ICAM9 and hope they will enjoy their stay in Baia Mare and
Maramureş, where, exactly in the same period is organized the local festival ”Sărbătoarea Castanelor
(Chestnuts Festival)”.
Vasile BERINDE,
Chair of ICAM9
Part 1
Short Abstracts
Plenary Lectures
On primal-dual splitting algorihms for monotone inclusions with applications to convex optimization
Radu Ioan Boţ
University of Vienna, Austria
radu.bot@univie.ac.at
We consider the primal problem of finding the zeros of mixtures of linear compositions and parallel
sums of maximally monotone operators. By formulating its Attouch-Théra-type dual inclusion problem,
a class of primal-dual splitting algorithms which simultaneously solve the two problems is presented.
The proposed schemes process at each iteration individually the resolvents of the maximally monotone
operators involved and aim to overcome the shortcoming of classical splitting algorithms when dealing
with linear compositions of maximally monotone operators. The iterative algorithms are used for
solving nondifferentiable convex optimization problems arising in image and video processing. The
talk is based on the papers [1, 2, 3].
Bibliography
[1] Boţ, R.I., Csetnek, E.R., Heinrich, A., A primal-dual splitting algorithm for finding zeros of sums of maximal
monotone operators, to appear in SIAM Journal on Optimization
[2] Boţ, R.I., Hendrich, C., A Douglas-Rachford type primal-dual method for solving inclusions with mixtures of composite
and parallel-sum type monotone operators , arXiv:1212.0326 [math.OC], 2012
[3] Boţ, R.I., Hendrich, C., Convergence analysis for a primal-dual monotone + skew splitting algorithm with applications
to total variation minimization , arXiv:1211.1706 [math.OC], 2012
ICAM9
Fixed points for mappings defined on generalized pseudometric spaces
Mitrofan Choban
Tiraspol State University, Republic of Moldova
mmchoban@gmail.com
A generalized pseudometric space is a topological space X with a continuous pseudometric d with
values in a Banach reticulate lattice for which any Cauchy sequence has an accumulation point. If the
sets Z(x, d) = {y ∈ X : d(x, y) = 0} are compacta, then the pseudometric is called perfect. For spaces
with such pseudometrics there are proved the Bishop-Phelps, Takahashi, Caristi, Caristi-Browden
theorems.
ICAM9
Constantin Corduneanu
What’s in the Third stage of the Fourier Analysis?
University of Texas at Arlington, U.S.A
cordun@xchange.uta.edu
The aim of this paper is to present the state of the art in Fourier Analysis in its ”third stage”.
ICAM9
5
Properties of higher order differential equations
Josef Dzurina
Technical University of Kosice, Slovakia
jozef.dzurina@tuke.sk
In the talk we provide criteria for oscillation of the even order delay differential equation
y (n) (t) + p(t)y(ct) = 0
We provide detail analysis of the properties of this equation, we offer necessary and sufficient conditions
for oscillation of studied equation and we fulfill the gap in the oscillation theory.
ICAM9
Numerical P Systems
Gheorghe Păun
Institute of Mathematics of the Romanian Academy, Bucureşti, Romania,
Research Group on Natural Computing, Department of Computer Science and Artificial Intelligence, University of Sevilla, Sevilla, Spain
gpaun@us.es
Membrane computing is a branch of natural computing initiated fifteen years ago, in [1], and
already in 2003 considered by ISI a fast emerging research area in computer science. The goal is to
abstract computing ideas (data structures, operations with them, ways to control these operations,
computer architectures, computing models) from the structure and the functioning of the living cell
and for the way cells collaborate in tissues and other populations of cells, the brain included. The
obtained models are called P systems. Very shortly, they consist of cell-like or tissue-like arrangements
of membranes, delimiting compartments where multisets of objects (symbols in an alphabet, strings
or more complex objects) evolve according to various types of evolution rules; also the membranes can
evolve, by specific rules. The rules are used in a nondeterministic maximally parallel way. A very large
number of variants were considered, with mathematical, computational, or biological motivations.
These computing devices proved to be both computationally powerful (in many cases, equivalent
with Turing machines) and computationally efficient (by a space-time trade-off, polynomial solutions
to computationally hard problems, typically, NP-complete problems, were proposed). Also, a large
variety of applications were reported, especially in modeling biological processes, but also in other
areas.
Numerical P systems were introduced in [3] with motivations coming from economics. Such a
system consists of a cell-like membrane structure, in the compartment of which numerical variables
are placed; these variables evolve by means of programs, consisting of two parts, a production function
and a repartition protocol. Roughly speaking, in a computation step, depending on the current value
of variables, a “total production” is computed in each compartment, which is then distributed among
the variables in that compartment and in the neighboring compartments. A computation is a sequence
of such production-repartition steps. One of the variables is distinguished and its values form the set
of numbers generated by the computation.
The talk will present the basic classes of numerical P systems (catalytic and non-catalytic, sequential
and parallel, etc.), their computing power (Turing universality in most cases) and computational
complexity aspects. Applications in robot control will be mentioned, as well as a series of open
problems and research topics. A quick introduction to membrane computing will be provided.
Bibliography
[1] Gh. Păun: Computing with membranes. Journal of Computer and System Sciences, 61, 1 (2000), 108–143 (and
Turku Center for Computer Science-TUCS Report 208, November 1998, www.tucs.fi).
[2] Gh. Păun: Computing with Membranes: An Introduction, Springer, Berlin, 2002.
[3] Gh. Păun, R. Păun: Membrane computing and economics: Numerical P systems. Fundamenta Informaticae, 73
(2006), 213–227.
[4] Gh. Păun, G. Rozenberg, A. Salomaa, eds.: Handbook of Membrane Computing. Oxford University Press, 2010.
[5] The P Systems Website: http://ppage.psystems.eu.
6
ICAM9
From a Dieudonné theorem concerning the Cauchy problem to an open problem in weakly Picard
operator theory
Ioan A. Rus
Babeş-Bolyai Unversity Cluj-Napoca, Romania
iarus@math.ubbcluj.ro
Let f ∈ C[a, b] × Rn , Rn ). We consider the following Cauchy problem:
y 0 = f (x, y), y(a) = y0
(1)
and the corresponding sequence of successive approximations:
Z x
f (s, yn (s))ds.
(2)
yn+1 (x) = y0 +
a
The following result was given by J. Dieudonné in 1945 (see [1] and [2]):
Theorem 1. We suppose that the Cauchy problem (1.1) has a uniques solution. Then there exists
h ∈ (0, b − a) such that the sequence of successive approximations (2) converges to the unique solution
of (1), uniformly on [a, a + h] if and only if the sequence (yn+1 − yn )n∈N converges to 0 uniformly on
[a, a + h].
The aim of this talk is to study the following problem rose by the above theorem.
Problem. Let X be a Banach space and f : X → X be an operator. In which conditions the
following implication holds:
f n+1 (x) − f n (x) → 0 as n → +∞ =⇒ f n (x) → x∗ (x) ∈ Ff , ∀x ∈ X
or equivalently
f is asymptotically regular =⇒ f is a weakly Picard operator.
Bibliography
[1] I.A. Rus, On a theorem of Dieudonné, in Differential Equations and Control Theory (V. Barbu-Ed.), Longman, 1991,
296-298.
[2] I.A. Rus and M.-A. Şerban, Basic problems of the metric fixed point theory and the relevance of a metric fixed point
theorem, Carpathian J. Math., 29(2013), no.2, 239-258.
ICAM9
Software for Use: (Re)Defining Usability Heuristics
Cristian Rusu
Pontificia Universidad Catlica de Valparaso, Escuela de Ingeniera Informtica, Valparaso, Chile
cristian.rusu@ucv.cl
The Special Interest Group on Computer-Human Interaction (SIGCHI) of the Association for
Computing Machinery (ACM) defines Human-Computer Interaction (HCI) as the discipline concerned
with the design, evaluation and implementation of interactive computing systems for human use,
and with the study of major phenomena surrounding them. The ISO/IEC 9241 standard defines
the usability as the extent to which a product can be used by specified users to achieve specified
goals with effectiveness, efficiency and satisfaction in a specified context of use. Usability evaluation
for applications based on emerging information technology brings new challenges. Is it the classical
concept of usability still valid? Which are the dimensions of the (new) usability? How can it be
measured? How should we develop for (better) usability? There is a need for new evaluation methods
or at least for the use of traditional evaluations in novel ways.
Usability evaluation methods are commonly divided into inspection and testing methods. Inspection
methods find usability problems based on the expertise of usability professionals. Testing methods find
usability problems through the observation of the users while they use (and comment on) a system
7
interface. Heuristic evaluation is a widely used inspection method. A group of evaluators inspect the
interface design based on usability principles (heuristics), usually Nielsens ten heuristics.
Heuristic evaluation is easy to perform, cheap and able to find many usability problems (both
major and minor problems). However, it may miss domain specific problems. That is why the
use of appropriate heuristics is highly relevant. Sets of usability heuristics were developed by the
UseCV research group in HCI at Pontificia Universidad Catlica de Valparaso (Escuela de Ingeniera
Informtica), for specific applications: Grid Computing, Virtual Worlds, Interactive TV, Transactional
Web Applications, Mobiles (among others). Heuristics were validated by experiments and seems to
work better than general heuristics.
ICAM9
Assessment of equivalent linear models for experimental hysteretic loops by correlation method
Tudor Sireteanu*, Ana Maria Mitu*, Ovidiu Solomon**, Claudia Meglea***
*Institute of Solid Mechanics, Romanian Academy, 15 Constantin Mille, RO-010141, Bucharest
**Romanian-American University,1b Expozitiei Blvd., Bucharest
***Center of Technology and Engineering for Nuclear Projects, 409 Atomistilor, Bucharest - Magurele
Corresponding author: anamariamitu@yahoo.com
Cyclic stress-strain or force-displacement data are required for engineering application at all stages
in the design and assessment of future life prediction of materials and structures, or of stiffness and
damping properties of vibration control devices. In most practical cases the experimental data yield
hysteresis loops displaying highly non-linear behavior. The fitting of non-linear parametric models
to experimental data is not a simple task. Moreover, in many of the existing computing programs
for structural dynamic analysis only equivalent linear visco-elastic or linear differential models can
be used to approximate the hysteresis behavior of materials, structures or devices,. In this paper is
presented a linearization method based on correlation functions of force and displacement signals
recorded by cyclic tests, without need for analytical models of hysteresis behavior. The application of
the proposed method is illustrated for hysteresis loops obtained by testing several devices for vibration
control and anti-seismic protection. The effectiveness of linearization method based on correlation
approach is illustrated through comparative analysis of seismic response of systems with hysteresis
and linear equivalent characteristics.
ICAM9
Open systems: modelling, programming, verification
Gheorghe Ştefănescu
Department of Computer Science, University of Bucharest, Romania
gheorghe.stefanescu@fmi.unibuc.ro
Powerful algebraic techniques have been developed for classical sequential computation. Many of
them are based on regular expressions and the associated regular algebra. For parallel and interactive
computation, extensions to handle 2-dimensional patterns are often required. Finite interactive
systems, a 2-dimensional version of finite automata, may be used to recognize 2-dimensional languages.
In this talk we present a blueprint for getting a formal representation of parallel, interactive programs
and of their semantics. It is based on a new approach for getting regular expressions for 2-dimensional
patterns, particularly using words of arbitrary shapes and powerful control mechanisms on composition.
We extend the class of 2-dimensional expressions with new control features, progressively increasing the
expressive power of the formalism up to a level where a procedure for generating the words accepted
by finite interactive systems may be obtained. Targeted applications come from the area of modelling,
specification, analysis and verification of structured interactive programs via the associated scenario
semantics.
ICAM9
8
Main and Regular Lectures
1. Fixed Point Theory and Applications
Fixed point theorems for nonself multi-valued almost contractions satisfying property (M)
Vasile Berinde
Department of Mathematics and Computer Science, North University Center at Baia Mare, Technical University of Cluj-Napoca, Romania
vberinde@ubm.ro
Let X be a Banach space, K a non-empty closed subset of X and let T : K → B(X) be a non-self
multi-valued almost contraction. We extend the results established in [1] to non-self multi-valued
almost contractions satisfying property (M), thus also extending the results from [3] from single-valued
mappings to multi-valued ones.
Bibliography
[1] Alghamdi, Maryam A., Berinde, V. and Shahzad, N., Fixed points of multi-valued non-self almost contractions, J.
Appl. Math. Volume 2013, Article ID 621614, 6 pages http://dx.doi.org/10.1155/2013/621614
[2] Alghamdi, Maryam A., Berinde, V. and Shahzad, N., Fixed points of non-self almost contractions, Carpathian J.
Math. 33 (2014), No. 1 (in print)
[3] Berinde, V. and Păcurar, M., Fixed points of single-valued non-self almost contractions, Fixed Point Theory 14
(2013), No. 2 (in print)
ICAM9
Existence and uniqueness theorem for Fredholm integral equation, via Jachymski’s Theorem
Florin Bojor and Magnolia Tilca
florin.bojor@yahoo.com; magnolia.tilca@yahoo.com
The aim of this paper is to study the existence and uniqueness of the solutions of Fredholm integral
equation type. The main tools employed in this study are based on applications of the Jachymski
fixed point theorem on metric spaces endowed with a graph.
Bibliography
[1] Ionescu D.V. Ecuaţii diferenţiale şi integrale, Ed. Didactică şi pedagogică, Bucureşti, 1972.
[2] Jachymski J., The contraction principle for mappings on a metric space with a graph, Proc. Amer. Math. Soc. 1
(136) (2008) 1359–1373.
[3] Lungu N. Rus I.A., On a functional Volterra-Freduolm ecuation, via Picard operators, J.M.I. 3(4) (2009) 519-527.
ICAM9
Fixed point theorems for α − φ contractions in b-metric spaces
Monica-Felicia Bota*, Veronica Ilea*, Erdal Karapinar**, Oana Mleşniţe*
*Babesş-Bolyai University, Cluj-Napoca, Romania; **Atilim University, Ankara, Turkey
bmonica@math.ubbcluj.ro, vdarzu@math.ubbcluj.ro, erdalkarapinar@yahoo.com, oana.mlesnite@math.ubbcluj.ro
Very recently, Samet et al. [4] introduced the notion of α-ψ-contractive type mapping and proved
some fixed point results for such mappings. We give some fixed and strict fixed point results in
9
b-metric spaces. We consider both the singlevalued and the multivalued cases of α-ψ-contractions. As
applications we give some Ulam-Hyers stability results.
Bibliography
[1] M. Boriceanu, A. Petruşel, I.A. Rus, Fixed point theorems for some multivalued generalized contractions in b-metric
spaces, International Journal of Mathematics and Statistics, 6(2010), 65-76.
[2] S. Czerwik, Nonlinear set-valued contraction mappings in b-metric spaces, Atti Sem. Mat. Univ. Modena, 46(1998),
263-276;
[3] I. A. Rus, Remarks on Ulam stability of the operatorial equations, Fixed Point Theory, 10(2009), No. 2, 305-320.
[4] B. Samet, C. Vetro, P. Vetro, Fixed point theorems for α-ψ-contractive type mappings, Nonlinear Analysis 75 (2012),
2154-2165.
ICAM9
Fixed point results for generalized multivalued contractions in b-metric spaces endowed with a graph
Cristian Chifu and Gabriela Petruşel
Bbabeş-Bolyai Unversity Cluj-Napoca, Romania
Cristian.Chifu@tbs.ubbcluj.ro
Gabi.Petrusel@tbs.ubbcluj.ro
The purpose of this paper is to present some fixed point results on a b-metric space endowed with
a graph, using the contractive type conditions of Reich and Ćirić with respect to Hausdorff-Pompeiu
functional H. The data dependence of fixed point set is also studied.
Bibliography
[1] Bota, M., Dynamical Aspects in the Theory of Multivalued Operators, Cluj University Press, 2010.
[2] Czerwik S., Nonlinear set-valued contraction mappings in b-metric space, Atti Sem. Mat. Univ. Modena, 46(1998),
263-276.
[3] Jachymski J., The contraction principle for mappings on a metric space with a graph, Proc. Amer. Math. Soc.,
136(2008), 1359-1373
[4] Nicolae A., O’Regan D. and Petruşel A., Fixed point theorems for singlevalued and multivalued generalized contractions
in metric spaces endowed with a graph, J. Georgian Math. Soc., 18(2011), 307-327.
[5] Petruşel A., Rus I. A., Yao J.-C., Well-posedness in the generalized sense of the fixed point problems for multivalued
operators, Taiwanese J. Math., 11(2007), 903-914.
ICAM9
Fix point theorems for multivalued contractions with respect to two topologically equivalent metrics
Iulia Coroian
Babeş-Bolyai University, Faculty of Mathematics and Computer Science, Cluj-Napoca, Romania
coroian.iulia@gmail.com
Fix point theorems for multivalued contractions with respect to two topologically equivalent
metrics
In this paper, we will present some fixed point results for multivalued almost contractions with
respects to two topologically equivalent Hausdorff type metrics.
ICAM9
Generalizations of iterated function systems
Dan Dumitru
Spiru Haret University of Bucharest, Romania
dandumitru1984@yahoo.com
The aim of this article is to investigate infinite iterated function systems formed by contraction type
functions such as (ε, ϕ)-functions with ε > 0 and ϕ a comparation function, or by strong Meir-Keeler
10
functions and to prove the existence and uniqueness of the attractors of these kind of infinite iterated
function systems.
Bibliography
[1] J. Hutchinson, Fractals and self-similarity, Indiana Univ. Math. J., 30 (1981), No 5, 713-747
[2] K. Lesniak, Infinite iterated function systems: a multivalued approach, Bull. Pol. Acad. Sci. Math., 52 (2004), No 1,
1-8
ICAM9
Fixed points and viable sets in dynamics of relations and control
Vasile Glăvan
Siedlce University of Natural Sciences and Humanities, Siedlce, Poland,
Moldova State University, Chişinǎu, Republic of Moldova
vglavan@uph.edu.pl
We are concerned with the dynamics of closed relations in complete metric spaces and with the
iterations of set-valued functions F : X → P(X). A sequence (xn )n∈Z , such that xn+1 ∈ F (xn ) for all
n ∈ Z, is called a trajectory, or a chain. If instead of inclusion one has the inequality ρ(xn+1 , F (xn )) ≤ δ
for some δ ≥ 0, then one speaks about a δ-chain (here ρ denotes the Hausdorff-Pompeiu semi-distance).
A closed subset Y ⊆ X is called invariant, if F (Y ) = Y , and completely invariant, if F −1 (Y ) =
Y = F (Y ). The last equalities mean that given x ∈ Y , every chain (xn )n∈Z with x0 = x satisfies also
xn ∈ Y for all n ∈ Z. Such a subset is said to be viable on Z + (on Z) if for any x ∈ Y , there exists
a chain (xn )n∈Z+(Z) such that x0 = x and xn ∈ Y for all n ∈ Z + (respectively, n ∈ Z ). Obviously,
completely invariant subsets, fixed points and periodic chains, as well as their reunion, represent viable
sets. If the relation is contractive, then it has a unique attractor which coincides with the closure of
the set P er(F ) of periodic points [1] and, at least in the case of an affine IFS, this attractor represents
the smallest closed viable set, containing P er(F ).
In our report we will generalize this facts for some affine Iterated Function System (Rn ; f1 , f2 , . . . fm )
with fj (x) = Aj x + bj , where the linear operators Aj are not necessarily contractive. More precisely,
we assume, that the family of matrices Aj , j = 1, 2, . . . , m, satisfies the so called ”cone condition” (see,
e.g., [2]), which means that there are two cones, one of them invariant with respect to all Aj , and
another one being invariant with respect to all A−1
j , provided that all operators are invertible. This
implies that the matrices are hyperbolic and all their unstable subspaces are located in the first cone,
while the stable ones are included in the second cone.
Under the ”cone condition” most of the chains are unbounded, excepting, at least, fixed points
and periodic orbits. Denote by Λ the subset of points x ∈ Rn with the property, that there exists a
bounded chain (xn )n∈Z , satisfying x0 = x. We show, that Λ is non-empty, compact and viable on
Z. Moreover, we prove, that Λ is the maximal subset with these properties. At the same time Λ is
the smallest closed viable set, containing all periodic chains. We also prove, that the IFS has the
Shadowing Property on Λ: given ε > 0, there is δ > 0 such, that for every δ-chain (xn )n∈Z , staying in
a neighborhood of Λ, there exists a chain (yn )n∈Z ⊂ Λ, such that k xn − yn k≤ ε, n ∈ Z.
In the particular case of a two-dimensional affine IFS with common linear parts we give some
topological characteristics of the viable set Λ, depending on eigenvalues of the linear operator. We
give also some applications in control theory.
This work was partially supported by the SCSTD Grants 11.817.08.41F and 12.839.08.06F.
Bibliography
[1] Glavan, V., Guţu, V., On the dynamics of contracting relations.
In: Analysis and Optimization of Differential
Systems, Edited by V. Barbu et al., Kluwer Acad. Publ., 2003, pp.
179–188.
[2] Katok, A., Hasselblatt, B., Introduction to the Modern Theory of Dynamical Systems. Cambridge University Press,
1995.
ICAM9
11
How many contractions are needed to construct some kinds of plane compacta?
Valeriu Guţu
Moldova State University, Chişinău, Republic of Moldova
vgutu@yahoo.com
A hyperbolic Iterated Function System (IFS) is a finite collection of contractions, usually considered
in a complete metric space. It is known that any hyperbolic IFS possesses a unique invariant compact
set, called the attractor of this IFS.
The structure of attractors of hyperbolic IFS’s and their properties were studied by many authors.
M. Hata (1985), M. Barnsley (1988), P. F. Duvall and L. S. Husch (1992), M. Kwieciński (1999),
S. Crovisier and M. Rams (2006), M. J. Sanders (2009), M. Kulczycki and M. Nowak (2012), T. Banakh
and M. Nowak (2013) and others have studied the possibility of compacta to be obtained as attractors,
as well as some examples of compacta, which can not serve as attractor of any hyperbolic IFS (see,
e.g., [1] and the bibliography therein).
We study this problem from another side:
1. Which compacta can serve as attractors of hyperbolic IFS’s?
2. Given a compact set, what is the minimal number of contractions of a hyperbolic IFS (provided
it exists) needed to obtain this set as attractor?
Theorem 1. Any nonempty finite union of convex compacta in Rn can be realized as attractor of
a hyperbolic IFS.
Theorem 2. Any plane convex compact set can be realized as attractor of a hyperbolic IFS,
consisting of at most three contractions. If the given compact set can be embedded uniquely in a figure
of constant width, then this number of contractions is minimal possible.
Theorem 3. Any nonempty finite union of m plane convex compacta can be realized as attractor
of a hyperbolic IFS, consisting of at most 3m contractions.
Remark. There are examples when the number of contractions in Theorem 3 is minimal possible
and other examples when this number can be diminished.
Bibliography
[1] Banakh, T., Nowak, M., A 1-dimensional Peano continuum which is not an IFS attractor, Proc. Amer. Math. Soc.,
141(2013), no. 3, 931-935
ICAM9
Fixed Point Theorems for Nonself Operators
Andrei Horvat-Marc
andrei.horvatmarc@cunbm.utcluj.ro
Most of xed point theorem are established for self mappings. The transition from this results to
fixed point theorems for non-self mappings can be done via nonlinear alternative and the consequences
of this, i.e. Leray-Schauder alternative. In A. Granas and J. Dugundji [4] are presented some versions
of nonlinear, respectively Leray-Schauder, alternatives. In this work we present examples of non-self
operators satisfies some boundary conditions which ensure the existence of fixed points.
Bibliography
[1] V. Berinde, On the approximation of fixed points of weak contractive mappings, Carpathian J. Math. 19 (2003), no. 1,
7–22.
[2] V. Berinde and M. Păcurar, Fixed point theorems for nonself single-valued almost contractions, (2013).
[3] K. Deimling, Nonlinear functional analysis, Springer-Verlag, Berlin, 1985.
[4] A. Granas and J. Dugundji, Fixed point theory, Springer Monographs in Mathemetics, Springer, 2002.
[5] Donal O’Regan, A continuation theory for weakly inward maps, Glasgow Mathematical Journal 40 (1998), 311–321.
ICAM9
12
On a functional Fredholm integral equation, via nonexpansive operators
Monica Lauran
North University Center at Baia Mare, Technical University of Cluj-Napoca, Baia Mare, Romania
lauranmonica@yahoo.com
In this paper we present one result relative to existence of solutions of the functional Fredholm
integral equation with deviating argument in a subset of Banach space:
Zb Zb
K(x, y, s, t, u(s, t))dsdt, x, y ∈ [a, b]
u(x, y) = f (x, y, g(u)(x, y)) +
a
a
by nonexpansive operators technique.
Bibliography
[1] Berinde,V., Existence and approximation of solutions of some first order iterative differential equations, Miskolc
Math. Notes,Vol. 11 (2010), No. 1, pp. 1326
[2] Berinde, V.and M. Lauran, Nonexpansive fixed point technique used for solve boundary value problem for fractional differential equations, Analele St. ale Univ.Al.I. Cuza Iasi, Seria Matematica, Tomul LVII, Supliment,
DOI:10.2478/v10157-011-0009-0
[3] Goebel,K. and Kirk, W.A., Topics in Metric Fixed Point Theory, Cambridge University Press, Cambridge, 1990
[4] Ishikawa, S., Fixed point and iteration of a nonexpansive mapping in a Banach space, Proc. Amer. Math. Soc.,
59(1976), No. 1,65-71
[5] Lauran, M., Existence results for some nonlinear integral equations, Miskolc Math. Notes, vol. 13 (2012), No.1,
pp.67-74
[6] Lauran, M., Existence results for some differential equations with deviating argument, Filomat, 25 (2011), No. 2,
21-31.
[7] Pachpatte, B.G., On Fredholm type integral equation in two variables,Diff. Eq. and Appl., 1(2009), No.1, 27-39.
[8] Rus, I. A. and Petrusel, A.and Petrusel, G., Fixed point theory, Cluj University Press, 2008
ICAM9
On Hyers-Ulam stability of some partial differential equations
Nicolaie Lungu and Dorian Popa
Tecnical University of Cluj-Napoca, Romania
nlungu@math.utcluj.ro
In a recent paper we obtained a stability result for a partial differential equation of order one in
Banach spaces. In this paper we improve the result mentioned above and, as applications, we obtain
Hyers-Ulam stability results for some linear partial differential equations of second order and for some
nonlinear partial differential equations.
Bibliography
[1] Lungu, N. , Popa, D., Hyers-Ulam stability of a first order partial differential equation, J. Math. Anal. Appl.385(2012),
86-91.
ICAM9
13
The Theory of some Asymptotic Fixed Point Theorems
Anton S. Mureşan
Babeş-Bolyai Unversity of Cluj-Napoca, Romania
anton.muresan@econ.ubbcluj.ro
In this paper we give and study some problems about some asymptotic fixed point theorems like:
data dependence of fixed points, Ulam stability, sequences of operators and fixed points, well-posedness
of fixed point problem, and limit shadowing property.
Bibliography
[1] Andras, Sz., Fredholm-Volterra integral equations, Ed. Did. Ped., Bucureşti, 2005 (In Romanian)
[2] Filip, A.D., Fixed point theorems in Kasahara spaces with respect to an operetor and applications, Fixed Point Theory,
12(2011), No. 2, 329-340
[3] Mureşan, A.S., Graphic contactions, Proceedings - ICFPTA, Cluj-Napoca, July 2012 (to appear)
[4] Păcurar, M., Fixed point theory for cyclic Berinde operators, Fixed Point Theory, 12(2011), No. 2, 419-428
[5] Păcurar, M., Rus, I.A., Fixed point theory for cyclic ϕ-contractions, Nonlinear Analysis, 72 (2010), 1181-1187
[6] Rus, I.A., Maps with ϕ-contractive iterates, Studia Univ. Babeş-Bolyai, Mathematica,XXV,4, 1980, 47-51 (in
Romanian)
[7] Rus, I.A., The theory of a metrical fixed point theorem: theoretical and applicative relevances, Fixed Point Theory,
9(2004), No.2, 541-559
[8] Rus, I.A., Some nonlinear functional differential and integral equations, via weakly Picard operator theory: a survey,
Carpathian J. Math., 26(2010), 230-258
[9] Rus, I.A., Petruşel, A., Petruşel, G., Fixed Point Theory, Cluj University Press, Cluj-Napoca, 2008
ICAM9
A Volterra Functional - integral Equation, via Weakly Picard Operators Technique
Viorica Mureşan
Technical Unversity of Cluj-Napoca, Romania
vmuresan@math.utcluj.ro
In this paper we consider a Volterra functional - integral equation with linear modifications of the
arguments. By using Contraction principle and weakly Picard operators’ technique, we give existences,
uniqueness and data dependence results for the solution.
Bibliography
[1] Mureşan, V., Functional - Integral Equations, Mediamira, Cluj-Napoca, 2003
[2] Şerban, M.A., Rus, I.A. and Petruşel, A., A class of abstract Volterra equations, via weakly Picard operators’ technique,
Math. Ineq. & Appl. (Zagreb), 13(2010), No. 2, 255-269
ICAM9
Fixed point theorems for contractions of rational type in metric spaces, for multivalued operators
Anca Oprea
Babeş-Bolyai University, Faculty of Mathematics and Computer Science, Cluj-Napoca, Romania
anca.oprea@math.ubbcluj.ro
The purpose of this paper is to present a fixed point result, for multivalued operators, which
satises the contractive conditions of rational type on complete metric spaces.We extend the results
of I.Cabrera, J.Harjani and K.Sadarangan [2]to multivalued operators.The paper will contain also a
proof for the fixed point theorems for contractions of rational type in partially ordered metric spaces.
ICAM9
14
Qualitative properties of functional differential systems
Diana Otrocol and Veronica Ana Ilea
T. Popoviciu” Institute of Numerical Analysis and Babeş-Bolyai University, Romania
dotrocol@ictp.acad.ro, vdarzu@math.ubbcluj.ro
In this paper we study certain qualitative properties of functional differential systems using weakly
Picard operators techniques. In the end, some applications are given.
Bibliography
[1] V. Kolmanovskii, A. Mishkis, Applied theory of functional differential equations, Kluwer Academic Publisers, 1992
[2] D. Otrocol, Abstract Volterra operators, Carpathian J. Math., 24(2008) no. 3, 370-377
[3] J. Šremr, On the initial value problem for two-dimensional linear functional differential systems, Memoirs on Diff. Eq.
and Math. Physics, 50(2010), 1-127
[4] M.A. Şerban, I.A. Rus, A. Petruşel, A class of abstract Volterra equations, via weakly Picard operators technique,
Mathematical Inequalities & Applications, 13(2010), 255-269
ICAM9
Fixed point theorems for nonself Prešić type operators
Mădălina Păcurar
Babeş-Bolyai University of Cluj-Napoca, Romania;
madalina.pacurar@econ.ubbcluj.ro
In some previous papers, [1]-[4] the authors have studied the existence and approximation of fixed
points of single-valued self Prešić type operators f : X k → X, where k ≥ 1 is a positive integer.
The main aim of the present paper is to extend some of those results from self mappings to non
self mappings.
Bibliography
[1] Cirić, L.B., Prešić, S.B., On Prešić type generalization of the Banach contraction mapping principle, Acta Math.
Univ. Comenianae, 76 (2007), No. 2, 143-147
[2] Păcurar, M., Iterative Methods for Fixed Point Approximation, Risoprint, Cluj-Napoca, 2010
[3] Păcurar, M., A multi-step iterative method for approximating fixed points of Prešić-Kannan operators, Acta Math.
Univ. Comen. New Ser., 79 (2010), No. 1, 77-88
[4] Păcurar, M., Fixed points of almost Prešić operators by a k-step iterative method, An. Ştiint,. Univ. Al. I. Cuza Iaşi,
Ser. Noua, Mat. (to appear)
[5] Păcurar, M., Common fixed points for almost Prešć type operators. Carpathian J. Math. 28 (2012), no. 1, 117–126
ICAM9
Remarks on cyclic coupled fixed point theorems
Mihaela Petric
Technical University Cluj-Napoca, North Unversity Center Baia Mare, Romania
petricmihaela@yahoo.com
The objective of this lecture is to present some remarks concerning the concepts of coupled fixed
points and coupled best proximity points for cyclical contractions.
Bibliography
[1] Borcut, M., Berinde, V., Tripled fixed point theorems for contractive type mappings in partially ordered metric spaces,
Nonlinear Anal., 74 (2011), 48894897
[2] Sintunavarat, W., Kumam, P., Coupled best proximity point theorem in metric Spaces, Fixed Point Theory and
Applications 2012, 2012:93
ICAM9
15
Some existence results for a system of operatorial equations
Ioan A. Rus and Marcel-Adrian Şerban
Babeş-Bolyai Unversity Cluj-Napoca, Romania
iarus@math.ubbcluj.ro
mserban@math.ubbcluj.ro
In this paper we study a system of operatorial equations in terms of vectorial distances and vectorial
measures of noncompactness. The basic tools are some classical fixed point principles, the general
retraction operator principle and the cartesian hull of a subset of a cartesian product. Applications to
some systems of functional integral equations are also given.
Bibliography
[1] Rus, I.A., On the fixed points of the mappings defined on a cartesian product (III), (in Romanian), Studia Univ.
Babeş-Bolyai Math., 24(1979), 55-56.
[2] Rus, I.A., Petruşel, A., Petruşel, G. Fixed Point Theory, Cluj University Press, Cluj-Napoca, 2008.
[3] Şerban, M.A., Fixed point theorems on cartesian product, Fixed Point Theory, 9(2008), No. 1, 331-350.
[4] Şerban, M.A., Fixed Point Theory for Operators on Cartesian Product, (in Romanian), Cluj University Press,
Cluj-Napoca, 2002.
ICAM9
Fixed point results in cone metric spaces
Adrian Viorel
Department of Mathematics, Technical University of Cluj-Napoca, Romania
Adrian.Viorel@math.utcluj.ro
In this work we deal with cone metric spaces, generalizations of metric spaces wherein the metric
takes values in a cone rather than in R+ . Cone metric spaces were (re)introduced by Huang and Zhang
(2007), the authors being unaware of the fact that the concept existed under the name K-metric (or
K-normed) space. Following the article of Huang and Zhang, a great deal of interest has risen around
cone metric spaces and their corresponding fixed point theory. Recently, Amini-Harandi and Fakhar,
respectively Janković and coworkers, proved independently that the topology generated by the cone
metric coincides with the topology generated by a usual (scalar) metric. Based on this observation
some of the cone fixed point results obtained in the recent years were shown to be direct consequences
of standard metric fixed point theorems. The aim of this contribution is to extend these investigations
in the following directions: K-boundedness, compactness and K-nonexpansive operators, which are
relevant in fixed point theory.
ICAM9
2. Optimization Theory, Operations Research and Applications
Cellular Automata Topologies and Rules
Anca Andreica1 , Camelia Chira1 , Alexandru Agapie2
1 Babes-Bolyai
University of Cluj-Napoca, Romania and 2 University of Economic Studies, Bucharest, Romania
anca@cs.ubbcluj.ro, cchira@cs.ubbcluj.ro, agapie@csm.ro
Cellular Automata (CAs) represent useful and important tools in the study of complex systems
and interactions. CAs can generate a complex behavior based on the local interaction of simple
components that evolve according to some state change rule [3]. The detection of rules that exhibit
coordinated global information processing is a challenging task highly important in the study of
complex systems.
In this paper we investigate different CA topologies with probability-based rules for both asynchronous [1] and synchronous [2] Cellular Automata. Computational experiments focus on the
16
density classification task for the one-dimensional binary-state CA. This is a prototypical distributed
computational task with the objective of finding the density most present in the initial cellular state.
The discovery of rules exhibiting a high degree of global self-organization is not easily achieved since
coordinated global information processing must rise from the interactions of components with local
information and communication. The use of probability-based rules for the density task generates a
complex behavior with competitive performance in the correct classification of initial configurations.
Results are analysed in the context of various topologies for CA with binary states.
Bibliography
[1] Agapie, A., Hns, R., Mhlenbein, H., Markov Chain Analysis for One-Dimensional Asynchronous Cellular Automata,
Methodology And Computing In Applied Probability, Volume 6, Issue 2, pp 181-201 (2004)
[2] Chira, C., Gog, A., Lung, R. I., Iclanzan, D., Complex Systems and Cellular Automata Models in the Study of
Complexity, Studia Informatica series, Vol. LV, No. 4, pp. 33-49 (2010)
[3] Wolfram, S., Theory and Applications of Cellular Automata, Advanced series on complex systems, World Scientific
Publishing, 9128 (1986)
ICAM9
On the Crossing Numbers of Cartesian Products with Paths
Emı́lia Draženská
Technical university, Košice, Slovak Republic
emilia.drazenska@tuke.sk
In general, compute the crossing number for a given graph is a very difficult problem. It has been
proved that this problem is NP–complete. The crossing numbers of a few families of graphs are known.
Most of them are Cartesian products of special graphs.
The crossing numbers of Cartesian products of cycles, stars and paths with all graphs of order four
are given. The crossing numbers of Cartesian products of cycles with many graphs of order five are
given. Except for the star S5 , there are given the crossing numbers of G Cn for all five–edge trees G.
Values of crossing numbers of the Cartesian products G Cn , G Sn , G Pn with six–vertex graphs
G are known for several graphs G.
We extend these results by giving the exact values of crossing numbers of Cartesian products
G Pn for every tree G on seven vertices. There are 11 trees of order seven.
ICAM9
Modified Han algorithm for inconsistent linear inequalities
Doina Carp1 , Constantin Popa2 , Cristina Şerban3
1
Constanta Maritime University, Romania
2
Faculty of Mathematics and Computer Science, Ovidius University of Constanta, Romania
3
Faculty of Civil Engineering, Ovidius University of Constanta, Romania
doina.carp@gmail.com, cpopa1956@gmail.com, cgherghina@gmail.com
In the paper [2] the author described a finitely terminating algorithm for solving an inconsistent
system Ax ≤ b of linear inequalities in a least squares sense. His algorithm uses a singular value
decomposition of a submatrix of A om each iteration, making it impractical for all but only smaller
problems. The same disadvantages appear for the version of Hans method proposed in [1], where a
QR factorization with column pivoting is used. In order to overcome these difficulties, in this paper
we show that a modification of Han’s algorithm allows us to introduce a controlled (possible iterative)
approximation to the original singular value solution. We also present numerical experiments and
comparisons with the original methods from [1] and [2].
Bibliography
[1] R. Bramley, B. Winnicka, Solving linear inequalities in a least squares sense, SIAM J. Sci. Comp., 17(1) (1996),
275-286.
17
[2] S.-P. Han, Least squares solution of linear inequalities, tech. rep. TR-2141, Mathematics Research Center, University
of Wisconsin - Madison, 1980.
ICAM9
Evolutionary Algorithms for Dynamic Complex Problems
Camelia Chira, Anca Andreica
Babes-Bolyai University of Cluj-Napoca, Romania
cchira@cs.ubbcluj.ro, anca@cs.ubbcluj.ro
Evolutionary approaches to dynamic complex problems need to be able to continously adapt the
solution to a changing environment [1]. This study focuses on the detection of dynamic communities
in complex networks. Networks represent a central model for the description of complex phenomena
and they have been studied independently in many different fields such as mathematics, neuroscience,
biology, epidemiology, sociology, social-psychology and economy. The detection of communities in
complex networks is a challenging problem recognized to be NP-hard [2]. The dynamic version of
the problem is of great significance since most real-world networks change in time and this dynamic
behaviour should be reflected in the evolution of communities. For example, ad-hoc networks formed
by communication nodes constantly change and need to be grouped in order to be able to choose the
most efficient communication path. Clearly, the study of dynamic networks can facilitate predictions
about the evolution in time of networks from various different areas. Dynamics add another dimension
of complexity to the NP-hard problem of detecting communities. An extra mechanism is needed to
deal with the network at different timesteps and to include as necessary in the detection of the current
community structure, the community structure that existed at the previous timestep.
Online algorithms should be able to capture the dynamic aspect of network data and adjust
online the communities as the network evolves. These features are well described by the concept of
evolutionary clustering introduced in [3] and engaged in some of the existing methods for the detection
of evolving communities [4, 5, 6]. The strategy is to look for a trade-off between snapshot quality (a
measure of how good the current community structure is) and history cost (a measure of how different
the current community structure is compared to the previous one). In this paper, we investigate the
performance of evolutionary models for this dynamic complex problem by facilitating the adaptation
of solutions to the changes in network structure during their evolution.
Bibliography
[1] Branke, J., Evolutionary optimization in dynamic environments, 2001, Kluwer academic publishers.
[2] Fortunato, S., Community detection in graphs, arxiv 0906.0612, 2010.
[3] Chakrabarti, D., Kumar, R., Tomkins, A., Evolutionary clustering, Proceedings of the 12th ACM SIGKDD
international conference on Knowledge discovery and data mining, KDD ’06, ACM, 554-560, 2006.
[4] Lin, Y., Chi, Y., Zhu, S., Sundaram, H., Tseng, B., Facetnet: a framework for analyzing communities and their
evolutions in dynamic networks,Proceedings of the 17th international conference on World Wide Web, 685-694, ACM,
2008.
[5] Kim, M.-S., Han, J., A particle-and-density based evolutionary clustering method for dynamic networks, Proc. VLDB
Endow.,Vol. 2, No. 1, 622-633, 2009.
[6] Folino, F., Pizzuti, C., Multiobjective evolutionary community detection for dynamic networks, Proceedings of the
12th annual conference on Genetic and evolutionary computation, GECCO ’10, 535-536, ACM, 2010.
ICAM9
Systems of knowledge representation based on stratified graphs and their inference process
Daniela Dănciulescu
University of Craiova, Craiova, Romania
ddd 1307@yahoo.com
The concept of stratified graph introduces some method of knowledge representation ([8], [10]).
The inference process developed for this method uses the paths of the stratified graphs, an order
18
between the elementary arcs of a path and some results of universal algebras. The order is defined by
considering a structured path instead of a regular path. In this paper we define the concept of system
of knowledge representation as a tuple of the following components: a stratified graph G, a partial
algebra Y of real objects, an embedding mapping (an injective mapping that embeds the nodes of G
into objects of Y) and a set of algorithms such that each of them can combine two objects of Y to
get some other object of Y. We define also the concept of inference process performed by a system
of knowledge processing. The inference process is based on the concept of accepted structured path.
The set of all accepted structured paths of G is organized as a partial algebra ASP(G) such that
every accepted structured path d can be uniquely decomposed by means of two accepted structured
subpaths of d. We show that the inference process is a morphism of partial algebras.
Bibliography
[1] V. Boicescu, A. Filipoiu, G. Georgescu and S. Rudeanu, Lukasiewicz-Moisil Algebra, Annals of Discrete Mathematics
49 (North-Holland, 1991)
[2] Tudor (Preda) Irina-Valentina, Considerations Regarding Formal Languages Generation Using Labelled Stratified
Graphs, International Journal of Applied Mathematics and Informatics, University Press, Issue 2, Volume 5, pp.
101-108, 2011
[3] Tudor (Preda) Irina-Valentina, Generating Natural Language by Labelled Stratified Graphs, Scientific Bulletin University of Pitesti, Matematics and Informatics Series, pg. 89-100, Nr. 17 (2011)
[4] N. Tanareanu, Knowledge Bases with Output, Knowledge and Information Systems 2/4, 438460, 2000
[5] N. Tandareanu, Knowledge representation by labeled stratified graphs, Proceedings of the 8th World Multi Conference
on Systemics, Cybernetics and Informatics (2004), Vol. 5, 345-350.
ICAM9
Inverse Generalized Maximum Flow Algorithms
Adrian Deaconu and Mihai Iolu
University Transilvania of Braşov, Department of Computer Science, Brasov, Romania
a.deaconu@unitbv.ro, mihaiiolu@yahoo.com
In this paper we present algorithms for solving the inverse generalized maximum flow problem
(denoted IGMF). A generalized maximum flow problem takes into account the gain (loss) of flow on
each arc. An inverse generalized maximum flow problem is to change the capacities of the arcs so that
a given feasible flow becomes a maximum flow in the modified network and the distance between the
initial vector of capacities and the modified one is minimum.
The first problem we solve is the problem of inverse generalized maximum flow under max-type
distances (denoted IGMFM). We present an algorithm that solves this problem in O(mn · log(n))
time.
We study IGMFM and the inverse generalized maximum flow under sum-type distances (denoted
IGMFS) in lossy networks, in which every residual arc is lossy (the gain factor is less or equal
to one). In the case of lossy networks we show that the algorithm for IGMFM improves its time
complexity to O(m · log(n)). We also present an O(mn · log(n2 /m)) or O(min{n2/3 , m1/2 } · m ·
log(n2 /m) · log(max{n, U })) time algorithm for IGMFS (depending on the implementation, strongly
or, respectively, weakly polynomial).
For all algorithms we present an apriori fast test that tells us if the problem has feasible solution
or not.
Bibliography
[1] R.K. Ahuja, T.L. Magnanti, J.B. Orlin, Network Flows. Theory, Algorithms and Applications, Prentice Hall,
Englewood Cliffs, NJ, 1993
[2] R.K. Ahuja, J.B. Orlin: Combinatorial Algorithms for Inverse Network Flow Problems, Networks (2002).
[3] E. Ciurea, A. Deaconu, Inverse Minimum Flow Problem, Journal of Applied Mathematics and Computing, 23
(2007) 193-203.
[4] A. Deaconu, The Inverse Maximum Flow Problem Considering L∞ Norm, RAIRO, 42 (2008), No. 3, 401-414
[5] C. Heuberger, Inverse Combinatorial Optimization: A Survey on Problems, Methods, and Results, Journal of
Combinatorial Optimization, 8 (2004) 329-361
[6] L. Liu and J. Zhang, Inverse Maximum Flow Problems under Weighted Hamming Distance, J. Combin. Optim., 12
(2006) 395-408
19
[7] P.T. Sokkalingam, R.K. Ahuja, J.B. Orlin, Solving Inverse Spanning Tree Problems through Network Flow Techniques,
Oper. Res. 47 (1999) 291-298.
[8] C. Yang, X. Chen, An Inverse Maximum Capacity Path Problem with Lower Bound Constraints, Acta Math. Sci.,
Ser. B 22 (2002) 207-212.
[9] C. Yang, J. Zhang, Z. Ma, Inverse Maximum Flow and Minimum Cut Problems, Optimization, 40 (1997) 147-170
[10] J. Zhang, C. Cai, Inverse Problems of Minimum Cuts, ZOR-Math. Methods Oper. Res. 47 (1998) 51-58.
ICAM9
Minimal intersections in graph drawings
Marián Klešč
Technical Unversity of Košice, Slovakia
marian.klesc@tuke.sk
The visualized graph should be very effective in many research areas and technical applications. It
is known that the aesthetics and readability of graph-structures heavily depends on the number of
crossings, when the structures are visualized on a 2-dimensional medium.
The crossing number cr(G) of a graph G is the smallest number of edge crossings in any drawing
of G in the plane. It was introduced by Turán [6] during the World War II. The crossing number
problem has been vividly investigated for over 60 years, but there are only few infinite graph classes
for which the values of crossing number are known. Even for the complete and complete bipartite
graphs this invariant is known only for some few parameters. In general, computing the crossing
number is very difficult. It has been proved by Garey and Johnson [2] that computing the crossing
number of a graph is an NP-hard problem.
In 1973, Harary, Kainen, and Schwenk [4] established the crossing number of the Cartesian product
C3 × C3 and conjectured that cr(Cm × Cn ) = m(n − 2) for 3 ≤ m ≤ n. Recently has been proved by
Glebsky and Salazar [3] that for any fixed m ≥ 3, the conjecture holds for all n ≥ m(m + 1). Besides
the Cartesian products of two cycles, there are several other exact results. In 2007, Bokal [1] proved
the conjecture given by Jendrol’ and Ščerbová [5] that cr(K1,n × Pm ) = (m − 1)b n2 cb n−1
2 c for the
path Pm of length m. Applying the capped Cartesian product operation in combination with a newly
introduced π– subdivision, he established the crossing numbers for the Cartesian products of K1,n
with a tree of maximum degree 3 and for the product Wn × Pm , where Wn is the wheel on n + 1
vertices.
In the talk, we summarise new results concerning crossing numbers for the Cartesian products of
two graphs, for join products of two graphs as well as for some other operations on graphs.
Bibliography
[1] D. Bokal,On the crossing numbers of Cartesian products with trees, J. Graph Theory, 56 (2007), 287-300
[2] M.R. Garey, D.S. Johnson,Crossing number is NP-complete, SIAM J. Algebraic and Discrete Methods, 4 (1983),
312-316
[3] L.Y. Glebsky, G. Salazar, The crossing number of Cm × Cn is as conjectured for n ≥ m(m + 1), J. Graph Theory, 47
(2004), 53–72
[4] F. Harary, P.C. Kainen, A.J. Schwenk,Toroidal graphs with arbitrarily high crossing numbers, Nanta Math., 6 (1973),
58–67
[5] S. Jendrol’, M. Ščerbová, On the crossing numbers of Sm × Pn and Sm × Cn , Časopis pro pěstovánı́ matematiky, 107
(1982), 225-230
[6] P. Turán,A note of welcome, J. Graph Theory, 1 (1977), 79
ICAM9
.
Greedoids on Vertex Sets of B-joins of Graphs
Vadim E. Levit and Eugen Mandrescu
Ariel University and Holon Institute of Technology, Israel
levitv@ariel.ac.il and eugen m@hit.ac.il
20
Let G = (V (G), E(G)) denote a simple, finite, undirected graph. A subset A of V (G) is called
a local maximum stable set of if A is a maximum stable set in the subgraph induced by its closed
neighborhood [2]. The family of all local maximum stable sets of G is denoted by Ψ(G). Let G1 , G2
be two disjoint graphs, and let B = (V (G1 ), V (G2 ), E(B)) be a bipartite
S graph. By the B-join
of G1 and
G
we
mean
the
graph
B(G
,
G
),
whose
vertex
set
is
V
(G
)
V (G2 ) and edge set is
2 S
1
2
1
S
E(G1 ) E(G2 ) E(B).
In this talk we present various conditions for Ψ(B(G1 , G2 )) to be a greedoid [1], in terms of the
graphs G1 , G2 , and B, using some findings from [3, 4, 5].
Bibliography
[1] Korte,B., Lovsz, L., Schrader, R., Greedoids, Springer-Verlag (Berlin), 1991.
[2] Levit, E. V., Mandrescu, E., A new greedoid: the family of local maximum stable sets of a forest, Discrete Applied
Mathematics, 124 (2002), 91-101
[3] Levit, E. V., Mandrescu, E., Local maximum stable sets in bipartite graphs with uniquely restricted maximum
matchings, Discrete Applied Mathematics 132 (2004), 163-174
[4] Levit, E. V., Mandrescu, E., Graph operations that are good for greedoids, Discrete Applied Mathematics 158 (2010),
1418-1423
[5] Levit, E. V., Mandrescu, E., On local maximum stable set greedoids, Discrete Mathematics 312 (2012), 588-96
ICAM9
The maximum parametric flow in discrete dynamic networks
Mircea Parpalea and Nicoleta Grigoraş
National College ”Andrei Şaguna” Braşov, Romania; ”Cambridge School” of Constanţa, Romania
parpalea@gmail.com; nicole grigoras@yahoo.com
The aim of this paper is to present an approach for solving the maximum parametric flow over
time problem. The proposed algorithm consists in repeatedly finding a maximum dynamic flow for
a sequence of parameter values, in their increasing order. In each of its iterations, the algorithm
computes a new breakpoint for the maximum parametric flow value function. The complexity of the
algorithm is presented and also an example is given on how the algorithm works.
Bibliography
[1] Ahuja, R., Magnanti, T. and Orlin, J., Network Flows. Theory, algorithms and applications, Prentice Hall, Inc.,
Englewood Cliffs, New Jersey, 1993
[2] Ciurea, E., Ciupală, L., ALGORITMI Introducere ı̂n algoritmica fluxurilor ı̂n reţele Ed. MATRIX ROM. Bucureşti,
2006
[3] Ciurea, E., Parpalea, M., A sequential algorithm for finding the solution of the parametric minimum flow problem,
Carpathian Journal of Mathematics, 28(1) (2012), 47–58
[4] Hamacher, H. W. and L. R. Foulds, L. R., Algorithms for Flows with Parametric Capacities, ZOR - Methods Model.
Oper. Res. 33 (1989), 21–37
[5] Parpalea, M., Min-Max Algorithm for the Parametric Flow Problem, Bulletin of the Transilvania University of Braşov,
3(52) (2010), 191–198
[6] Parpalea, M., Ciurea, E., The quickest maximum dynamic flow of minimum cost, International Journal of Applied
Mathematics and Informatics, 3(5) (2011), 266–274
[7] Ruhe, G., Complexity Results for Multicriterial and Parametric Network Flows Using a Pathological Graph of Zadeh,
Zeitschrift für Oper. Res. 32 (1988), 9–27
ICAM9
Pharaoh ants for Sensor Networks Security
Camelia Pintea
cmpintea@yahoo.com
21
A new conceptual model based on Pharaoh ants is introduced to solve a complex problem: the
security of networks. Pharaoh ants with their specific features will influence positively the results of
the introduced algorithm.
Bibliography
[1] Pintea, C-M., Pop, P.C., Sensor networks security based on sensitive robots agents. A conceptual model, Advances in
Intelligent Systems and Computing, Springer, 189(2013), 47-56
[2] Pintea, C-M., Pop, P.C., Sensitive Ants for Denial Jamming Attack on Wireless Sensor Network, Advances in
Intelligent and Soft Computing Series, Springer, accepted.
[3] Banerjee, S., Grosan, C., Abraham, A. IDEAS: Intrusion Detection based on Emotional Ants for Sensors. In:
Intelligent Systems Design and Applications, 344349, IEEE C.S. (2005)
[4] Pintea, C-M., Dumitrescu D., Distributed Pharaoh System for Network Routing, Automat. Comput. Appl. Math.16(12)(2007), 27-34
ICAM9
High-order optimality conditions for degenerate calculus of variations problems
A. Prusińska1 , E. Szczepanik1 and A.A. Tret’yakov1,2
1
Siedlce University of Natural Sciences and Humanities, Siedlce, Poland
2
Russian Acad. Sci., Dorodnitsyn Comp. Ctr., Moscow, Russia
aprus@uph.edu.pl
The contribution is devoted to singular calculus of variations problems with constraint functional
not regular at the solution point in the sense that the first derivative is not surjective. We pursue an
approach based on the constructions of the p-regularity theory. For p-regular calculus of variations
problem we formulate and prove necessary and sufficient conditions for optimality in singular case
and illustrate our results by classical example of calculus of variations problem.
ICAM9
On the multidimensional multi-way number partitioning problem
Petrică Pop
Department of Mathematics and Computer Sciences, Faculty of Sciences, North University Center at Baia Mare, Technical University of
petrica.pop@mail.ubm.ro
In this paper, we consider a generalization of the two-way number partitioning problem, called
the multidimensional multi-way number partitioning problem (MDMWNPP), where a set of vectors
has to be partitioned into p sets (parts) such that the sums per every coordinate should be exactly
or approximately equal. We present a survey of the existiting techniques for solving this complex
problem.
Bibliography
[1] J. Kojic, Integer linear programming model for multidimensional two-way number partitioning problem, Comput.
Math. Appl. 60 (2010) 2302 - 2308.
[2] P.C.Pop and O. Matei, A memetic algorithm approach for solving the multidimensional multi-way number partitioning
problem, Appl. Math. Model. in press.
ICAM9
Intelligent methods for making the best decisions using optimization techniques and data mining
Cosmin Sabo
cosminsabo@gmail.com
The use of database technology to manage large volumes of business data is growing at an
exponential rate and leads to a phenomenon now referred to as Big Data. The size and the volume
22
data being managed by the companies raise the following interesting issue: can we use intelligent
methods wherein the data to help business achieve competitive advantage? This is the major goal of our
research and based on our expertise on managing large volumes of data, data mining and optimization
we will provide intelligent methods that will provide the capabilities to explore, summarize and model
the business data.
ICAM9
Axiomatic set theory for functional analysis
Michal Staš
Faculty of Electrical Engineering and Informatics, Technical University of Košice, Boženy Němcovej 32, 042 00 Košice, SR
michal.stas@tuke.sk
Mathematicians usually prefer to work in the Zermelo-Fraenkel axiomatic set theory ZF or ZF
with the Axiom of Choice AC denoted as ZFC. A lot of them often do not notice when they have used
AC, even in an essential way. However the common proofs of many results especially in functional
analysis usually exploit the Axiom of Choice in spite of the fact that one can prove them in ZF or
in ZF with a weak form of AC. We shall try to indicate that a weaker form of an axiom of choice is
sufficient for proving a statement, e.g., important results in functional analysis as the Hahn-Banach
Theorem or the Baire Category Theorem with its consequences for Banach spaces.
Bibliography
[1] Bell J.L., Fremlin D.H., Geometric form of the axiom of choice, Fund. Math. 77 (1972), no. 2, 167170.
[2] Blair C. E., The Baire category theorem implies the principle of dependent choices, Bull. Acad. Polon. Sci. Sér. Sci.
Math. Astronom. Phys. 25 (1977), 933–934.
[3] Bukovský L., The Structure of the Real Line, Monografie Matematyczne, Vol. 71 2011.
[4] M. Foreman and F. Wehrung, The Hahn-Banach Theorem implies the existence of a non-Lebesgue measurable set,
Fundamenta Mathematicae 138, no. 1 (1991), 13–19.
[5] H. Garnir, M. de Wilde and J. Schmets, Analyse fonctionelle I, Birkhuser, Basel, (1968).
[6] Halpern, J.D., Levy, A., The Boolean prime ideal theorem does not imply the axiom of choice, Axiomatic Set Theory,
Proceedings of Symposia in Pure Mathematics 13 (1971) part 1, D. Scott ed., American Math. Soc., Providence,
83-134.
[7] Howard P. and Rubin J.E., The Boolean prime ideal theorem+countable choice do not imply dependent choice, Math.
Logic Quarterly 42 (1996) 410-420.
[8] Luxemburg, W., Two applications of the method of construction by ultrapowers to analysis, Bull. Amer. Math. Soc.
68, (1962)416-419.
[9] Luxemburg, W., Beweis des Satzes von Hahn-Banach, Arch. Math (Basel) 18, (1967a) 271-272.
[10] Luxemburg, W., Reduced powers of the real number system and equivalents of the Hahn-Banach theorem, Technical
Report 2, Cal. Inst. Tech. (1967b)
[11] Pincus, D., Independence of the prime ideal theorem from the Banach theorem, Bull. Amer. Math. Soc. 78, (1972),
766-770.
[12] Pincus, D. The strength of the Hahn-Banach theorem, Proc. Victoria Symposium on Nonstandard Analysis, SpringerVerlag, New York, (1974), 203-208.
[13] Pincus D. and Solovay R.M., Definability of measures and ultrafiltersh. Journal of Symbolic Logic 42, (1977), n. 2,
179-190.
[14] Solovay R. M., A model of set theory in which every set of reals is Lebesgue measurable, Ann. of Math. 92 (1970),
156.
ICAM9
Testing artificial neural network for gesture recognition
József Süto and Ştefan Oniga
University of Debrecen, Hungary
sutojozsef90@gmail.com
oniga.istvan@inf.unideb.hu
Neural networks are well applicable for gesture recognition. In this article we want to present the
result of a feed forward network for a simplified gesture recognition problem.
23
In neural networks, the learning algorithm is very important, because the performance of neural
network depends on it. One of the most known learning algorithm is the backpropagation. There are
some mathematical software which provides acceptable result for a given problem by a backpropagation
based network, but in some cases a high-level programming language implemented program can provide
better solution.
Acknowledgement The research was supported by the European Union and the State of
Hungary, co-financed by the European Social Fund in the framework of TMOP 4.2.4.A/2-11-1-20120001 ”National Excellence Program - Elaborating and operating an inland student and researcher
personal support system convergence program”.
The used devices and development accessories was financed by TAMOP-4.2.2.C-11/1/KONV-20120001 project. The acquisition of used devices and development accessories has been supported by the
European Union, co-financed by the European Social Fund.
Bibliography
[1] Martin T. Hagan, Howard B. Demuth, Mark Beale, Neural Network Design, ISBN 7-111-10841-8, 1996
[2] Ben Krse, Patrick van der Smagt, An introduction to Neural Networks, Eight edition, University of Amsterdam,
November 1996
[3] S.Oniga, I.Orha, Hardware Implemented Neural Networks used for Hand Gestures Recognition, Carpathian Journal of
Electronic and Computer Engineering, vol. 4, 11/2011
[4] James A. Freeman, David M. Skapura, Algorithms, Applications, and Programming Techniques, ISBN 0-201-51376-5,
1991
[5] Kouichi Murakami, Hitomi Taguchi, Gesture recognition using recurrent neural networks, CHI’91 Proceedings of the
SIGCHI Conference on Human Factors in Computing Systems, 1991
[6] G. Sebestyen, A. Tirea and R. Albert, Monitoring Human Activity through Portable Devices, Carpathian Journal of
Electronic and Computer Engineering, vol. 5, (2012)
[7] Analog devices, ADXL345 3 axis digital accelerometer, Rev. D, 2009
Inc.,
Chipkit
Max32
Board
Reference
Manual,
Revision:
July
25,
2011,
[8] Digilent
http://www.digilentinc.com/Data/Products/CHIPKIT-MAX32/chipKIT%20Max32 rm.pdf, 2013
[9] C.G. Gavrincea, A.S. Tisan, Real time EMG pattern recognition system for hand postures, Carpathian Journal of
Electronic and Computer Engineering, vol. 1, 2008
[10] A.
Pavelka
and
A.
Prochzka,
Algorithms
for
Initialization
of
Neural
Networks,
http://dsp.vscht.cz/konference matlab/matlab04/pavelka.pdf, 2013
[11] Bjarne Stroustrup, The C++ Programming Language, ISBN 9789639301191, Copyright 1997 by AT&T
ICAM9
Communication aspects in Fibonacci type topologies
Ioana Zelina
Department of Mathematics and Computer Science, Technical University of Cluj-Napoca, North University Center at Baia Mare, Romania
ioanazelina@yahoo.com
The communication is a very important issue in interconnection networks for distributed systems
because the exchange of information is based on message exchange. In the case of direct interconnection
network a processor communicates using direct links only with its neighbors that means the network
topology is of a great importance. The interconnection network can be seen as a graph and the
properties of a network can be studied using the graph theory. The Fibonacci cube, extended Fibonacci
cube and Lucas cube are topologies based on the sequence of Fibonacci numbers which provide good
properties for an interconnection network regarding diameter, node degree, recursive decomposition,
embeddability and communication algorithms. In this paper we present a survey on the algorithms
for routing and for broadcasting a message in Fibonacci type topologies.
Bibliography
[1] W.J. Hsu, Fibonacci cubes-new interconnection technology, IEEE Transactions on Parallel and Distributed Systems
4(1)(1993), 312
[2] E. Munarini, C.P. Cippo, N. Zagaglia Salvi, On the Lucas cubes, Fibonacci Quarterly 39(1)(2001), 1221
24
[3] I. Zelina, G. Moldovan, P.C. Pop, Some Communication Aspects in Extended Fibonacci Cubes, IEEE Proc. of
SAINT2008, Workshop HEUNET08, Turku, Finland, publisher IEEE Computer Society Press, 2008, 245-248
ICAM9
3. Ordinary Differential Equations and Partial Differential Equations
Input-output methods in the study of nonuniform exponential dichotomy of evolution families
Mihai Gabriel Babuţia
West University of Timisoara, Romania
mbabutia@math.uvt.ro
This talk presents one of our recent results from [4] concerning the nonuniform exponential
dichotomy in the light of (Cb , Lp ) admissibility. We discuss our results by making a parallel to those
obtained by M. Megan, A. L. Sasu and B. Sasu [3] in 2002 and to the recent developments of L.
Barreira and C. Valls in [1] and [2] and Jiang and Liao in [5]. Overall, our results are extended
from the admissibility of spaces of continuous functions to the admissibility of Lp spaces, without
constructing auxiliary Lebesgue spaces.
Bibliography
[1] L. Barreira, C. Valls, Admissibility for nonuniform exponential contractions, J. Differential Equations 249 (2010),
2889-2904.
[2] L. Barreira, C. Valls, Nonuniform exponential dichotomies and admissibility, Discrete Contin. Dynam. Systems 30
(2011), 39-53.
[3] M. Megan, A. L. Sasu, B. Sasu, On nonuniform exponential dichotomy of evolution operators in Banach spaces,
Integral Equations and Operator Theory 44 (2002), 71-78.
[4] A. L. Sasu, M. G. Babuţia, B. Sasu, Admissibility and nonuniform exponential dichotomy on the half-line, Bull. Sci.
Math. 137 (2013), 466-484.
[5] Y. Jiang and F. Liao, Admissibility for Nonuniform (µ, ν) Contraction and Dichotomy, Abstract and Applied
Analysis Volume 2012, Article ID 741696, doi:10.1155/2012/741696
ICAM9
Some remarks on certain invariant geometric properties in Hele-Shaw flows
Paula Curt
Babeş-Bolyai Unversity of Cluj-Napoca, Romania
paula.curt@econ.ubbcluj.ro
We study the time evolution of the free boundary of a viscous fluid for planar flows in Hele-Shaw
cells under injection. We analyze the geometrical properties of the moving frontier for bounded and
unbounded (with bounded complement) domains and discuss both zero and non-zero surface tension
models. Applying methods from the theory of univalent functions, we prove the invariance in time
of Φ-likeness property (a geometric property which includes starlikeness and spirallikeness) and of
α-convexity (a geometric property which makes a continuous passage from the starlike functions to
the convex functions). In the case of bounded domains we get an upper bound α0 (α0 > 0) for α, such
that the α-convexity property of the moving boundary is preserved in time for each α ≤ α0 . In the
case of unbounded domains we generalize the fact that the convex dynamics is preserved in time, by
obtaining the invariance in time of α-convexity for α sufficiently close to 1. Moreover, we establish an
upper bound for the order of strongly starlikeness of the classical solution in the Hele-Shaw problem
which starts with a starlike bounded domain.
Bibliography
[1] Curt, P., Fericeanu, D., A special class of univalent in Hele-Shaw flow problems, Abstr. Appl. Anal., Vol. 2011, Art.
ID 948236, 10 pp.
25
[2] Curt, P., Fericean, D., Groşan, T., φ-like functions in two-dimensions free boundary problems, Mathematica,
63(76)(2011), no. 2, 121-130.
[3] Fericean, D., Strongly φ-like functions of order α in two-dimensions free boundary problems, Applied Math. and
Comp., 218(15)(2012), 7856-7863.
[4] Gustafsson, B., Prokhorov, D., Vasil’ev, A., Infinite lifetime for the starlike dynamics in Hele-Shaw cells, Proc. of the
American Math. Soc., 132(2004), no. 9, 2661-2669.
[5] Gustafsson, B., Vasil’ev, A., Conformal and Potential Analysis in Hele-Shaw Cells, Birkhäuser Verlag, 2006, 231 pp.
[6] Miller, S.S., Mocanu, P.T., The theory and applications of second-order differential subordinations, Studia Univ.
Babeş-Bolyai, Math., 34(1989), no. 4, 3-33.
[7] Polubarinova-Kochina, P. Ya., On a problem of the motion of the contour of a petroleum shell, Dokl. Akad. Nauk
USSR, 47(1945), no. 4, 254-257 (in Russian).
ICAM9
Reversible cubic systems with centers
Dumitru Cozma
Tiraspol State University, Republic of Moldova
dcozma@gmail.com
By using a nondegenerate transformation of variables and a time rescaling, a cubic system with a
singular point with pure imaginary eigenvalues (λ1,2 = ±i, i2 = −1) can be brought to the form
ẋ = y + ax2 + cxy + f y 2 + kx3 + mx2 y + pxy 2 + ry 3 ,
ẏ = −(x + gx2 + dxy + by 2 + sx3 + qx2 y + nxy 2 + ly 3 ),
(1)
where the variables and coefficients in (1) are assumed to be real. Then the origin O(0, 0) is a singular
point of a center or a focus type for (1). It arises the problem of distinguishing between a center and
a focus, i.e. of finding the coefficient conditions under which O(0, 0) is, for example, a center. We
obtain the center conditions for system (1) by using the method of rational reversibility.
An algorithm for checking whether it is possible to transform a given system to one which is
time-reversible by means of a bilinear transformation was described in [1] and an algorithm for finding
all time-reversible systems within a given family of 2-dim systems of ODE’s whose right-hand sides
are polynomials was presented in [2]. The relation between time-reversibility and the center-focus
problem was discussed in [3]. The center conditions for cubic system (1) with two invariant straight
lines was obtained in [4] by using the method of rational reversibility.
Bibliography
[1]
[2]
[3]
[4]
Lloyd, N.G., Pearson, J.M., Symmetry in planar dynamical systems, J. Symbolic Computation, 33 (2002), 357-366.
Romanovski V.G., Time-reversibility in 2-dimensional systems, Open Sys. & Infor. Dyn., 15 (2008), no.4, 359–370.
Teixeira, M.A., Yang Jiazhong, The center-focus problem and reversibility, J. of Diff. Equations, 174 (2001), 237–251.
Cozma D., Darboux integrability and rational reversibility in cubic systems with two invariant straight lines,
Electronic Journal of Differential Equations, Vol. 2013 (2013), no.23, 1–19.
ICAM9
Infinitely differentiable functions represented into Newton interpolating series
G. Groza1 , M. Jianu1 and N. Pop2
1 Dept.
2 Dept.
of Math. and Comp. Science, Technical University of Civil Eng. of Bucharest, Romania
of Math. and Comp. Science, North University Center at Baia Mare, Technical University of Cluj-Napoca, Baia Mare,
Romania,
grozag@utcb.ro, marilena jianu@yahoo.com, nicpop@gmail.com
Given the interpolating sequence defined by α1 = 0, α2 = 1, α3 = 12 , and for k ≥ 4,
αk =
2s + 1
, when k ∈ (2m + 1, 2m+1 + 1], s = k − 2m − 2,
2m+1
26
we construct the polynomials u0 (x) = 1,
uk (x) =
k
Y
(x − αj ), k ≥ 1.
j=1
By extending the results of [1] and [2] we study infinitely differentiable functions f : [0, 1] → R which
can be represented into Newton interpolating series at {αk }k≥1 , that is
f (x) =
∞
X
ak uk (x).
k=0
The results are used to obtain approximate solutions of boundary value problems for ODEs.
Bibliography
[1] G. Groza, N. Pop, A numerical method for solving of the boundary value problems for ordinary differential equations,
Result. Math., 53(2009), No. 3-4, 295-302.
[2] G. Groza, S. M. Ali Khan, N. Pop, Approximate solutions of boundary value problems for ODEs using Newton
interpolating series, Carpathian. J. Math., 25(2009), No. 1, 73-81.
ICAM9
Mathematical models for repetitive phenomena in the excitable media. The case of turbulent mixing
Adela Ionescu
Department of Applied Mathematics, University of Craiova, Romania
adelajaneta@yahoo.com
This paper focuses on some new trends in CFD (computational fluid dynamics), an exciting and
attractive discipline which nowadays becomes more and more mature. It concerns the turbulence
problem in mixing media. The mixing theory appears in an area with far from complete solving
problems: the flow kinematics. Its methods and techniques developed the significant relation between
turbulence and chaos. The turbulence is an important feature of dynamic systems with few freedom
degrees, the so-called “far from equilibrium systems”. These are widespread between the models of
excitable media, and a recent challenge is to find a consistent and coherent theory to stand up that a
mixing model in excitable media leads to a far from equilibrium model.
Studying a mixing for a flow implies the analysis of successive stretching and folding phenomena
for its particles, the influence of parameters and initial conditions. In the previous works, the study of
the 3D non-periodic models exhibited a quite complicated behavior. In agreement with experiments,
they involved some significant events - the so-called “rare events”. The variation of parameters had a
great influence on the length and surface deformations.
In this paper there is continued the author’s work started in recent years on turbulent mixing.
The 3D mixing flow phenomena had very few analytical and experimental tests, in order to prove
that this model has a far from equilibrium behavior and it is very sensitive to the variation of its
parameters and orientation versors. The comparisons of deformation (in length and surface) efficiency
of 3D versus 2D case brought a very rich panel of random distributed events. An important partial
conclusion was that the mixing, and especially the turbulent mixing, is introduced at irrational values
of length and surface versors.
There is used a modern mathematical soft, MAPLE11, which has a lot of computational
appliances. Crossing over from 2D to 3D case, it is easy to deduce the requirement of a special analysis
of the influence of parameters on the behavior of this complex mixing flow. Since in the precedent
work there were obtained numeric plots standing for the images of the deformation efficiency, in this
paper the standpoint is a little changed. Using specific computational appliances, from “DEplot”
package, there is started a computational comparison analysis of the flow behavior in 2D and 3D case.
Two analysis directions are followed:
a) The widespread isochoric 2D (non-periodic) flow model, versus the 3D mixing flow model;
b) The general 2D (non-periodic) flow model versus the 2D perturbed model.
27
Thus, the panel of random distributed events would be completed with new special events and
new data would be collected for the qualitative analysis of the mixing phenomena.
Bibliography
[1] A. Ionescu, Recent trends in computational modeling of excitable media dynamics, Lambert Academic Press 2010,
Saarbrucken, Germany
[2] A. Ionescu, Recent challenges in turbulence: computational features of turbulent mixing, Recent advances in Continuum
Mechanics (Proceedings of the 4th IASME/WSEAS Int. Conference on Continuum Mechanics), Mathematics and
Computers in Science and Engineering, Cambridge, UK, 24-26 feb 2009, 29-38
[3] J.M. Ottino, The kinematics of mixing: stretching, chaos and transport. Cambridge University Press. 1989
[4] A. Ionescu, New approach for the turbulent mixing study – the behavior of vortic flows from computational standpoint,
Acta Universitatis Apulensis Journal, Special Issue – Proceedings of the International Conference on Theory and
Applications of Mathematics and Informatics ICTAMI 2009, Aeternitatis Publishing House, Alba Iulia 2009, 13-22
ICAM9
Exact periodic patterns in quasi-linear reaction-diffusion systems with competitions
Mihály Klincsik
Unversity of Pécs, Hungary
klincsikm@gmail.com
Modeling of some real biological pattern formations often leads to different reaction-diffusion
systems. All models for spatial pattern generation are necessarily nonlinear practical applications
require numerical solutions since no non-trivial analytical solutions are available in general. We
shall present some periodic non-constant stationary solutions to the simplified Shigesada-TeramotoKawasaki PDE system (see in [1] and [2]), which describes the population density of two competitive
species. The solution exhibits specific periodic spatial segregation behavior of the species in case of
one space dimension.
Bibliography
[1] Shigesada N., Kawasaki K., Teramoto E., Spatial segregation of interacting species, J. Theor. Biology 79(1979), 83-99.
[2] Murray J. D., Mathematical Biology, Springer Verlag, Berlin, 1989.
ICAM9
Limits of solutions to the singularly perturbed abstract hyperbolic-parabolic systems
Andrei Perjan
Moldova State University, Chişinău, Moldova
perjan@usm.md
Let H and V be two real Hilbert spaces such that V ⊂ H continuously and densely. Let
A(t) : D(A) ⊂ H → H be a family of self-adjoint positive defined operators and let B : D(B) ⊂ H → H
be a nonlinear operator.
We study the behavior of solutions uε to the following abstract hyperbolic system
ε u00ε (t) + u0ε (t) + A(t) uε (t) + B uε (t) = fε (t), t ∈ (0, T ),
uε (0) = v0ε , u0ε (0) = v1ε ,
as ε → 0. Under some conditions on operators A(t) and B, we prove that uε → v, when v0 ε → v0 and
fε → f in some topologies, where v is the solution to the following abstract parabolic system
0
v (t) + A0 v(t) + B v(t) = f (t), t ∈ (0, T ),
v(0) = v0 .
ICAM9
28
Numerical Approach for Solving Nonlinear Electromagnetic Problem
Vladimir Paţiuc, Galina Rı̂bacova
Moldova State University, Republic of Moldova
patsiuk@mail.ru, ribacus@yahoo.com
We consider the nonlinear problem for semiconductor diode based on drift-diffusion equations
[1]. The proposed numerical approach consists of the finite volume method [2] in combination with
some iterative procedure (Gummel’s algorithm) and Newton’s method for internal linearization. Some
results of numerical simulation are presented.
Bibliography
[1] Numerical Methods in Electromagnetics, Special Volume (W.H.A. Schilders and E.J.W. ter Maten, Guest Editors) of
Handbook of Numerical Analysis, Vol. XIII. Elsevier, Amsterdam, 2005
[2] Li R., Chen Z., Wu W., Generalized Difference Methods for Differential Equations. Numerical Analysis of Finite
Volume Methods, Marcel Dekker Inc., New York-Basel, 2000
ICAM9
Singularly perturbed problems for abstract linear differential equations with positive powers of a
positive defined operator
A. Perjan1 , G. Rusu2
Moldova State University, Chişinău, Moldova
aperjan1248@gmail.com and rusugalinamoldova@gmail.com
Let H be a real Hilbert space endowed with the scalar product (·, ·) and the norm | · |. Let
Ai : D(Ai ) ⊂ H → H, i = 0, 1, be two linear self-adjoint operators.
Consider the following Cauchy problem:
( ε u00ε (t) + A1 uε (t) + u0ε (t) + A0 uε (t) = fε (t), t ∈ (0, T ),
(Pε )
uε (0) = u0ε , u0ε (0) = u1ε ,
where ε > 0 is a small parameter(ε 1), uε , fε : [0, T ) → H.
Supposing that the operator A1 is subordinated to a positive power of the operator A0 , we
investigate the behavior of solutions uε to the problems (Pε ) when u0ε → u0 , fε → f as ε → 0. We
establish a relationship between solutions to the problems (Pε ) and the corresponding solution to the
following unperturbed problem:
0
v (t) + A0 v(t) = f (t), t ∈ (0, T ),
(P0 )
v(0) = u0 .
ICAM9
The 3D elastic contact applied to robots control
Nicolae Pop
This paper proposes an algorithm for the condition detection in which the slip state transitions
in a stick-slip motion, or the solution breaks down and also to study the state transition of nodes
belonging to the contact area: stick, slip or open contact state. The Coulomb friction laws on the
contact boundary in 3D elastic contact problems applied to robots control are analyzed.
Bibliography
[1] Oden, J. T. and Pires, E., Nonlocal and nonlinear friction laws and variational principles for contact problems in
elasticity, ASME J. Appl. Mech. 50 (1983), 67–76
[2] Cocu, M., Existence of solutions of Signorini problems with friction, Int. J. Eng. Sci 22, No. 10, 567–575
[3] Klarbring, A., Exemples of non-uniqueness and non-existence of solutions to quasi-static contact problems with
friction, Ingineur-Archiv. 60 (1990), 529–541
29
[4] Cho, H. and Barber, J. R., Dynamic behavior and stability of simple frictional systems, Math. Comput. Modeling
28 (1998), 37–53
[5] Cho, H. and Barber, J. R., Stability of the three-dimensional Coulomb friction law, Proc. R. Soc. Lond. A 455
(1999), 839–861
ICAM9
Investigation of periodic solutions using interval halving
András Rontó and Miklós Rontó
Institute of Mathematics of the Academy of Sciences of the Czech Republic and University of Miskolc, Hungary
ronto@math.cas.cz, matronto@uni-miskolc.hu
Based on [1, 2], we show how a suitable interval halving and parametrisation technique can help
to essentially improve the sufficient convergence condition for the periodic successive approximations
dealing with periodic solutions of nonlinear non-autonomous systems of ordinary differential equations.
Bibliography
[1] A. Rontó and M. Rontó, Periodic successive approximations and interval halving, Miskolc Math. Notes 13(2), 459–482.
[2] A. Rontó, M. Rontó, and N. Shchobak, Constructive analysis of periodic solutions with interval halving, Boundary
Value Problems 2013, 2013:57, 1–34
ICAM9
Approximation of Köthe-Bochner spaces with subspaces of functions having finite dimensional values
Răzvan Sfetcu
Faculty of Mathematics and Computer Science, University of Bucharest, Romania
razvan michael@yahoo.com
We consider Köthe-Bochner spaces LX (ρ) (X Banach space, ρ function norm) where X has
Schauder basis. With the help of the Schauder basis, we consider finite dimensional spaces Y ⊂ X
and the corresponding spaces LY (ρ) which approximate the space LX (ρ).
Bibliography
[1] Chiţescu I., Function Spaces (in Romanian), Ed. Şt. Encicl., Bucureşti, 1983
[2] Lin P. K., Sun H., Extremal structure in Köthe function spaces, J. Math. Analysis and Applications 218 (1998),
2315-2322
[3] Zaanen A. C., Integration, Nord Holland Publishing Co., Amsterdam, Interscience Publishers John Wiley & Sons,
Inc., New York, 1967
ICAM9
A new central configurations in the planar N -body problem and their linear stability
Agnieszka Siluszyk
University of Natural Sciences and Humanities, Siedlce, Poland
sil a@uph.edu.pl
In [1] has proved necessary condition for the stability the Lagrange’s triangle of the three bodies
problem as the configuration. In [2,3] the authors have shown the stability of permanent configurations
in the problem of four bodies. In this paper we establish the existence a planar configuraion which is
consisted with N bodies situated on two different circular orbits. We show necessary and sufficient
conditions for existing this configuration. Additionally, we study the problem (the condtitions) linear
stability for such configuration.
Bibliography
[1] Routh E.I. Proceedings of the London Mathematical Society, v.6, 1875
[2] Macmilian W.D., Bartky W. Configurations in the Problem of Four Bodies, Trans.Amer.Math.Soc.,34, 838-875,
(1932).
30
[3] Roberts G.E. Stability of Relative Equilibria in the Planar n-Vortex Problem, SIAM Journal on Applied Dynamical
Systems, 12, no. 2, 1114-1134 (2013).
ICAM9
Cubic Systems with an Invariant Line at Infinity of the Maximal Geometric Multiplicity
Alexandru Şubă, Olga Vacaraş
Institute of Mathematics and Computer Science of ASM, Republic of Moldova
suba@math.md, vacaras olga@mail.md
In the work [1] for polynomial differential systems there are introduced the following definitions
of the multiplicity of an invariant algebraic curve: algebraic multiplicity, geometric multiplicity,
integrable multiplicity, infinitesimal multiplicity, holonomic multiplicity and the relations between
these definitions are established.
The main aim of this lecture is to show that for cubic systems the geometric multiplicity of a line
at infinite is at most seven. Any cubic system having a line at infinite of the geometric multiplicity
seven via affine transformations and time rescaling can be written as one of the following two forms:
ẋ = 1, ẏ = a + bx + cx2 + x3 and ẋ = −x, ẏ = ax + x3 + 2y, a, b, c ∈ R.
Bibliography
[1] Christopher C., Llibre J. and Pereira J.V., Multiplicity of invariant algebraic curves in polynomial vector fields,
Pacific Journal of Mathematics, 329 (2007), no. 1, 63–117.
ICAM9
4. Advances in Numerical Analysis and Approximation Theory
Improvement of Grüss and Ostrowski Type Inequalities and Applications
Ana Maria Acu, Florin Sofonea
”Lucian Blaga” University of Sibiu, Romania
acuana77@yahoo.com, sofoneaflorin@yahoo.com
Several inequalities of Grüss and Ostrowski type available in the literature are generalized and
improved. A estimation of cumulative distribution function is given. The inequality of Grüss type
proved by P. Cerone and S.S. Dragomir [1] is extended for the weighted case.
Bibliography
[1] Cerone, P., Dragomir, S.S, New bounds for the Čebyšev functional, Applied Mathematics Letters, 18 (2005), 603-611.
ICAM9
Approximation by Linear Discrete Operators on Weighted Spaces
Octavian Agratini
Babeş-Bolyai University, Cluj-Napoca, Romania
agratini@math.ubbcluj.ro
The talk aimed at two aspects relative to linear approximation processes.
We consider some sequences of positive linear operators expressed by series and we modify them
into finite sums investigating their approximation properties in weighted spaces of continuous functions.
Special cases are revealed.
Beside this research, a new property of moduli of smoothness associated to certain spaces of
functions is proven. In terms of statistical convergence we determine the behavior of these special
functions at the point δ = 0. In this respect, Peetre’s K-functional is also investigated.
31
ICAM9
Identification of a Sum of Exponential Functions Using its Taylor Series
Ján Buša
Department of Mathematics and Theoretical Informatics, FEI Technical University in Košice
jan.busa@tuke.sk
In the talk a problem of the correspondence between parameters of a sum of exponential functions
and its Taylor series coefficients is considered. If the coefficients of the Taylor expansion of a function
(supposed to be a sum of exponential functions) are given, it is shown that parameters in exponents are
solutions to the algebraic equation, which coefficients are the solutions of a system of linear algebraic
equations. This system is constructed using Taylor coefficients.
In the talk a problem
of the correspondence between parameters of a sum of exponential functions
P
of the form f (x) = nk=1 Ak exp(αk ·x) and its Taylor series coefficients is considered. If the coefficients
of the Taylor expansion of the function f (x) are given, it is shown that parameters αk of exponents are
solutions to the algebraic equation, which coefficients are the solutions of a system of linear algebraic
equations. This system is constructed using Taylor coefficients.
ICAM9
Interpolation operators on a triangle with two and three curved edges
Alina-Mihaela Baboş
Land Forces Academy ”Nicolae Bălcescu”, Sibiu, Romania
alina babos 24@yahoo.com
We construct Lagrange, Hermite and Birkhoff-type operators, which interpolate a given function
and some of its derivatives on the border of a triangle with two and three curved edges. We also
consider some of their product and boolean sum operators. We study the interpolation properties and
the degree of exactness of the constructed operators.
Bibliography
[1] Barnhil, R.E., Gregory, J.A., Polynomial interpolation to boundary data on triangles, Math. Comput. 29(131),726-735
(1975).
[2] Barnhil, R.E., Birkoff, G., Gordon, W.J., Smooth interpolation in triangle, J. Approx. Theory. 8,114-128 (1973).
[3] Coman, Gh., Cătinaş, T., Interpolation operators on a triangle with one curved side, BIT Numer Math 47, (2010).
[4] Blaga, P., Cătinaş, T., Coman, Gh., Bernstein-type operators on triangle with all curved sides, Mediterr. J. Math. 9
(2012), 833-845.
ICAM9
The Bernstein quadrature formula revisited
Dan Bărbosu and Gheorghe Ardelean
barbosudan@yahoo.com
Starting with the Bernstein approximation formula on the interval [a, b] a corresponding quadrature
formula is obtained. Its coefficients an an upper bound for the remainder term is obtained. Next, the
composite quadrature formula of Bernstein-type on [a, b] is constructed. Some numerical examples are
also presented.
Bibliography
[1] Acu,A., M., Sofonea, D.,F., Some numerical integration methods based on interpolation polynomials, Carpathian J.
Math.,29(2013), No.1, 1-8
[2] Arama, O., Some properties concerning thesequence of S.N.Bernstein (Romanian), Studii şi Cerc. Mat., 8(1957),
195-210
[3] Bărbosu, D., A Schurer-Stancu type quadrature formula, Carpathian J. Math., 23(2007), No.1-2, 27-31
32
[4] Bărbosu, D., Miclăus, D., On the composite Bernstein type quadrature formula, Rev. Anal. Numer. Theor. Approx.,
39(2010), 3-7
[5] Bernstein,S.,N., Demonstration du theoreme de Weierstrass fondee sur le calcul de probabilites, Commun. Math.
Kharkow, 13 (1912-19130, no.2, 1-2
[6] Stancu, D.,D., Quadrature formulas constructed by using certain linear positive operators, Numerical Integration(proc.
Conf. Math. Res. Inst. Oberwolffach)(G.Hammerlin,ed.), Birkhauser (1982), 241-251
[7] Stancu, D.D., Vernescu, A., On some remarkable positive polynomial operators of approximation, Rev. Anal. Numer.
Theor. Approx., 28(1999), 85-95
ICAM9
Bernstein type operators which preserve some test functions
Marius Mihai Birou
Technical University of Cluj Napoca, România
marius.birou@math.utcluj.ro
In this paper we construct a sequence of Bernstein type operators which fix some polynomials. We
study the convergence of this sequence and establish a result of Vornovskaya type. Also, we present a
comparison of these operators with the classical Bernstein operator related to the approximation error.
ICAM9
Some properties of a Durrmeyer type operator associated with Bleimann-Butzer-Hahn operator
Cristina Sanda Cismaşiu
Transilvania University of Braşov, Romania
c.cismasiu@unitbv.ro
2000 Mathematics Subject Classification: 41A36, 41A35.
Keywords and phrases: Positive linear operators, Bleimann - Butzer - Hahn operators, approximation properties.
Our lecture refers to a new linear positive operator of Durrmeyer type which is associated with
Bleimann-Butzer-Hahn operator
R∞
f (t)pn+2,k−1 (t)dt
n−1
X
0
Cn (f ; x) = pn,0 (x)f (0) +
pn,k (x) · ∞
+ pn,n (x)f (n)
R
k=1
pn+2,k−1 (t)dt
0
= pn,0 (x)f (0) +
n−1
X
k=1
1
pn,k (x) ·
B(k, n − k + 2)
Z∞
f (t)
tk−1
dt + pn,n (x)f (n),
(1 + t)n+2
0
defined for any function f ∈ CB [0, +∞) and x ≥ 0, with pn,k (x) =
n
k
xk
, x ≥ 0, 0 ≤ k ≤ n,
(1 + x)n
n ∈ N. We studied some of its approximation properties.
Bibliography
[1] Adell, J. A., De la Cal, J., San Miguel, M., Inverse Beta and Generalized Bleimann Butzer - Hahn Operators, J.
Approx. Theory 76 ( 1994), 54-64.
[2] Agratini, O., Approximation properties of a generalization of Bleimann, Butzer and Hahn operators, Mathematica
Pannonica 9 (1998)2, 165-171.
[3] Bleimann, G., Butzer, P. L., Hahn, L. A., Bernstein - type operator approximating continuous functions on the
semi-axis, Indag. Math. 42 (1980), 255-262.
[4] Cismaşiu, C. S., A new linear positive operator of Durrmeyer type associated with Bleimann-Butzer-Hahn oprator,
Bull. Of Transilvania Univ. Braşov, Vol 6(55), No. 1 2013, Series III: Mathematics, Informatics, Physics, 1-8.
[5] Ivan, M., A note on the Bleimann - Butzer - Hahn operator, Automat. Comput. Appl. Math. 6 (1997), 11-15.
ICAM9
33
About some inequalities in approximation theory
Ioan Gavrea and Bogdan Gavrea
Technical University Cluj-Napoca, Romania
ioan.gavrea@math.utcluj.ro
We present some inequalities that appear in approximation theory. Some improvements and
generalizations of Chebysev-Gruss type inequalities are given.
ICAM9
About a linear and positive operator of Stancu-type with fixed points e1 and e2
Adrian Indrea
Technological High School of Tarna Mare, Romania
adrian.indrea@yahoo.com
The objective of this paper is to introduce an operator of Stancu-type, with the properties that
the test functions e1 and e2 are reproduced. Also, in our approach, a theorem of error approximation
and a Voronovskaja-type theorem for this operator is obtained.
In this paper, we introduce a general class which preserves the test functions e1 and e2 . For our
operators approximation properties, a convergence theorem and a Voronovskaja-type theorem are
obtained.
The paper is organized as follows. In section 2 we recall some results obtained in [?] which are
essentially used for obtaining the main results of this paper. Section 3 is devoted to the construction
of the general class of a new linear and positive operators. In Section 4 we obtain a Stancu type
operator which is an operator that preserves the test functions e1 and e2 .
Bibliography
[1] Agratini, O., An asymptotic formula for a class of approximation processes of King’s type, Studia Sci. Math. Hungar.,
47 (2010), Number 4, 435-444
[2] Bărbosu, D., Introduction in numerical analysis and approximation theory, Ed. Univ. de Nord Baia Mare, 2009
[3] Braica, P.I., Pop, O.T., Bărbosu, D. and Pişcoran, L., About a linear and positive operator of Stancu-type with
fixed points e0 and e1 (submitted)
[4] Braica, P.I., Pop, O.T. and Indrea, A.D., About a King-type operator, Appl. Math. Inf. Sci, No. 6 (1)(2012), 191-197
[5] Gadjiev, A.D., Ghobanalizadeh, A.M., Approximation properties of a new type Berstein - Stancu polynomials of one
and two variables, Appl. Math. Comp., (2010), No. 216, 890-901
[6] Indrea, A.D., A particular class of linear and positive Stancu-type operators, Acta Univ. Apulensis, No. 31(2012),
249-256
[7] King, J. P., Positive linear operators which preserve x2 , Acta Math. Hungar., 99 (2003), No. 3, 203-208
[8] Oancea, Ingrid A., Berstein - Stancu type operator wich preserves e2 , An. Şt. Univ. Ovidius Constanţa, Vol. 17(1)
(2009), 145-152
[9] Pop, O. T., The generalization of Voronovskaja’s theorem for a class of liniar and positive operators, Rev. Anal.
Numer. Théor. Approx., 34 (2005), No. 1, 79-91
[10] Pop, O.T., Indrea, A.D. and Braica, P.I., Durrmeyer operators of King-type, Annals of the University of Craiova,
Math.Comp.Sci.Ser. 39(2), (2012), 288-298
[11] Stancu, D.D., On a generalization of the Bernstein polynomials, Studia Univ. ”Babeş - Bolyai”, Scr. Math - Phis 14,
(1969), 31-45 (in Romanian)
ICAM9
Optimal rate of convergence for sequences of a prescribed form
Ioan Gavrea and Mircea Ivan
mircea.ivan@math.utcluj.ro
We provide a highly convergent version of the generalized Euler sequence and we determine the
element with the optimal rate of convergence in several classes of sequences of a prescribed form. The
34
new approach extends and unifies many previous efforts in this direction. In addition, we answer an
open problem on the asymptotic expansion of the Harmonic number sequence.
ICAM9
On the Stancu type bivariate approximation formula
Dan Miclăuş
Technical University of Cluj-Napoca
North Unversity Center at Baia Mare, Romania
danmiclausrz@yahoo.com
In the present paper we establish the form of remainder term associated to the bivariate approximation formula for Stancu type operators, using the bivariate divided differences. We also shall
establish an upper bound estimation for the remainder term, in the case when approximated function
fulfills some given properties.
Bibliography
[1] Lupaş, L. and Lupaş, A., Polynomials of binomial type and approximation operators, Studia Univ. Babeş-Bolyai,
Mathematica 32 (1987), No. 4, 61–69
[2] Miclăuş, D., The revision of some results for Bernstein-Stancu type operators, Carpathian J. Math., 28 (2012), no. 2,
273–284
[3] Stancu, D. D., Approximation of functions by a new class of linear polynomial operators, Rev. Roum. Math. Pures et
Appl. 13 (1968), 1173–1194
ICAM9
Two-sided estimates for the norm of the linear operators used in the convergence of some
approximation processes
Alexandru Mitrea
alexandru.ioan.mitrea@math.utcluj.ro
Two-sided estimates concerning the norm of some linear operators involved in approximation
processes are obtained. Further, based on these estimates, we derive convergence-type results and we
establish the topological structure of the set of unbounded divergence for some particular approximation
procedures, such as quadrature formulas of product-type on Legendre nodes, numerical differentiation
formulas associated to a Chebyshev node matrix and numerical differentiation on Sturm-Liouville
type node matrix.
ICAM9
On the stability of some classical operators from approximation theory (II)
Dorian Popa and Ioan Raşa
Tecnical University of Cluj-Napoca, Romania
popa.dorian@math.utcluj.ro, ioan.rasa@math.utcluj.ro
Let C[0, 1] be endowed with the supremum norm. For 0 ≤ a ≤ b, consider the Stancu operators
Sn : C[0, 1] → C[0, 1]
n X
n k
k+a
n−k
Sn f (x) =
x (1 − x)
f
.
k
n+b
k=0
we investigate the Hyers-Ulam stability of the operators Sn and prove that the HUS constant of Sn is
2n
n
n / n .
2 2
2
35
This corrects, generalizes and improves a result in our paper [1] concerning the Bernstein operator Bn ,
which is obtained when a = b = 0.
We consider also the case when C[0, 1] is endowed with the L1 −norm.
Moreover, we discuss an extremal property of the Bernstein operators concerning the Hyers-Ulam
stability constants.
Bibliography
[1] D. Popa, I. Raşa, On the stability of some classical operators from approximation theory, Expo. Math., in press,
http://dx.doi.org/10.1016/j.exmath.2013.01.007.
ICAM9
On a Class of Linear and Positive Operators
Voichita Adriana Radu
”Babeş-Bolyai” University, FSEGA, Deparment of Statistics-Forecasts-Mathematics, Cluj-Napoca, Romania
voichita.radu@econ.ubbcluj.ro
The focus of this paper is to gather the most significant properties of the Bernstein-Stancu
operators:
C n : Y → Πn
n
X
(an )k n
k
1
C n f (x) =
0, , ..., ; f xk .
n
n
k
nk
k=0
ICAM9
Approximation processes and asymptotic relations
Ioan Raşa
ioan.rasa@math.utcluj.ro
We discuss two approximation processes: general King operators and Campiti-Metafune operators.
They are related by similar Voronovskaja formulas. Their shape preserving and global smoothness
preserving properties are investigated and compared.
ICAM9
Note on Approximation Properties of q-Bernstein-Schurer Operators
Florin Sofonea1 , Carmen Violeta Muraru2 , Ana Maria Acu1
1
”Lucian Blaga” University of Sibiu, Romania;
2
”Vasile Alecsandri” University of Bacău
sofoneaflorin@yahoo.com; carmen 7419@yahoo.com; acuana77@yahoo.com;
In 2011, C. Muraru [1] introduced a generalization of the Bernstein-Schurer operators based on
q-integers. In this paper we will propose a new variant of q-Bernstein-Schurer operators which preserve
the linear function. A Bohman-Korovkin type approximation theorem of these operators is considered.
The rate of convergence by using the first modulus of smoothness is computed. Also, a Durrmeyer
variant of q-Bernstein-Schurer operators is considered.
Bibliography
[1] Muraru, C.V., Note on q-Bernstein-Schurer operators, Stud. Univ. Babeş-Bolyai Math. 56 (2011), No.2, 489-495.
ICAM9
36
Graphical representations of mean square error of the bivariate operator of Stancu type
Ioana Taşcu and Andrei Horvat-Marc
itascu@yahoo.com; andrei.horvatmarc@cunbm.utcluj.ro
In this paper are represented the errors obtained from approximation of a continuous function by a
bivariate operator. Starting from [1], we represent some quantitative estimation of approximation. We
take the definition of the Stancu bivariate operator obtained by the tensorial product of parametric
extensions.
Bibliography
[1] I. Taşu and I. Zelina, On the mean square error of the bivariate operator of Stancu type, Carpathian J. Math.,
19(2003), No. 2, 141-146
[2] Stancu D.D., Vernescu A., On some remarkable positive polynomial operators of approximation, Revue dAnalyse
Numérique et de Théorie de lApproximation, Tome 28, 1(1999), 85-95
ICAM9
5. Advances in Algebra
The Cocartesian Right Product
Dumitru Botnaru, Elena Baeş
State University from Tiraspol, Technical University of Moldova, Chişinău
dumitru.botnaru@gmail.com, baeselena@yahoo.it
We examine a construction that allows to obtain new reflective subcategories. For notions and
notation see [1]. Let K be a coreflective subcategory, and R be a reflective subcategory in the category
C2 V of the locally convex topological vector Hausdorff spaces. For an arbitrary object X of the
category C2 V we consider the following constructions: k X : kX −→ X, that is the K-coreplique;
rkX : kX −→ rkX, that is R-replique; v X · k X = uX · rkX , that is the cocartesian square.
Full subcategory of all objects isomorphic to objects of type vX is called the cocartesian right
product of subcategories K and R, and is denoted by V = K ∗dc R.
Theorem. Let (K, R) be a pairs of conjugate subcategories and R a reflective subcategory of the
category C2 V. Then: 1. K ∗dc R = QεL (R), QεL (R) is the full subcategory of all (εL)-factorobiects
of the objects of the R subcategory; 2. K ∗dc R is a reflective subcategory of the category C2 V; 3.
The subcategory K ∗dc R is closed under εL-factorobjects; 4. v · k = r · k; 5. If r(K) ⊂ K, then the
coreflector functor k : C2 V −→ K and the reflector one v : C2 V −→ K ∗dc R commute: k · v = v · k.
Bibliography
[1] Botnaru D., Structures bicatégorielles complémentaires, ROMAI J., 2009, v.5, nr.2, p.5-27.
ICAM9
Semireflexive Subcategories
Dumitru Botnaru, Olga Cerbu
State University from Tiraspol, State University Moldova, Chişinău
dumitru.botnaru@gmail.com, olga.cerbu@gmail.com
In the category C2 V of the locally convex topological vector Hausdorff spaces are introduced the
notions: semireflexive subcategories [2], the right product of two subcategories [3] and pairs of the
conjugate subcategories [1]. The relations between semireflexive subcategories via the right product of
37
two subcategories and pairs of the conjugate subcategories are examined. We construct and describe
some old and new examples.
Bibliography
[1] Botnaru D., Structures bicatégorielles complémentaires, ROMAI J., 2009, v.5, nr.2, p.5-27.
[2] Botnaru D., Cerbu O., Semireflexive product of two subcategories, Proceedings of the Sixth Congress of Romanian
Mathematicians, Bucharest, 2007, v.1, p.5-19.
[3] Botnaru D., Ţurcanu A., The factorization of the right product of two subcategories, ROMAI Journal, 2010, v. VI N
2, p.41-53.
ICAM9
The Right Product
Dumitru Botnaru, Alina Ţurcan
State University from Tiraspol, Technical University of Moldova, Chişinău
dumitru.botnaru@gmail.com, alina.turcanu@gmail.com
In the category of the locally convex topological vector Hausdorff spaces are introduced the notions:
the right product of two subcategories, where one is coreflective and the other is reflective [1]. This
product is never a reflective subcategory. There are highlighted the properties of the right product and
are indicated the conditions where this product is a reflective subcategory. We construct examples.
Bibliography
[1] Botnaru D., Ţurcanu A., The factorization of the right product of two subcategories, ROMAI Journal, 2010, v. VI N
2, p.41-53.
ICAM9
Hilbert - Mumford - Nagata Theorem on invariants and some topological aspects of the finite
generation of subalgebras. (II)
Adrian Constantinescu
”Simion Stoilow” Institute of Mathematics of the Romanian Academy, Bucharest, Romania
Adrian.Constantinescu@imar.ro
Recall the well known central Theorem of the Invariant Theory:
Theorem[Hilbert - Mumford - Nagata] Let k be an algebraically closed field, A a k-algebra of finite
type and G a reductive ( in particular linearly reductive ) algebraic Lie group over k acting rationally
on A. Then the subalgebra of invariants AG = {a ∈ A|ga = a for each g ∈ G} is finitely generated
over k.
In this talk we will use the universally 1-equicodimensional rings and schemes - a class of objects
defined by us by means of a universally topological property , as well as a class of scheme morphisms
defined also by a universally topological property to establish the Theorem above, at least in the
situation when G is linearly reductive. For a subalgebra of an algebra of finite type over a field k,
the property of universally 1-equicodimensionality control completely the finite generation of the
subalgebra.
Some variants of this class of scheme morphisms, defined also in a universally topologically manner,
will be discussed in relation to other situations of finite generation of subalgebras of algebras of finite
type over a field k.
Bibliography
[1] A. Constantinescu, Schemes dominated by algebraic varieties and some classes of scheme morphisms.II, Preprints
Series of ”Simion Stoilow” Institute of Mathematics of the Romanian Academy, ISSN 0250 3638, Preprint nr.8/2010,
36 p.
[2] D. Mumford, Geometric Invariant Theory, Springer Verlag, 1965.
[3] M. Nagata, A theorem on finite generation of a ring, Nagoya Math. 27 (1966), p. 193-205.
ICAM9
38
Finitely accessible categories versus module categories
Septimiu Crivei
crivei@math.ubbcluj.ro
An additive category is called finitely accessible if it has direct limits, the class of finitely presented
objects is skeletally small, and every object is a direct limit of finitely presented objects. Any finitely
accessible category C may be embedded via the covariant Yoneda functor as a full subcategory of the
category Mod(A) of unitary right modules over a certain ring with enough idempotents A, called the
functor ring of C. This allows one to relate properties of C with properties of the module category
Mod(A). We shall review the main connections between them, and present some new ones, especially
related to purity and approximations.
Bibliography
[1] S. Crivei, M. Prest and B. Torrecillas, Covers in finitely accessible categories, Proc. Amer. Math. Soc. 138 (2010),
1213–1221.
[2] M. Prest, Definable additive categories: purity and model theory, Mem. Amer. Math. Soc. 210, No. 987 (2011).
ICAM9
About separation axioms in semitopological and topological invers semigroups
Péter Körtesi
Institute of Mathematics, University of Miskolc, Hungary
matkp@uni-miskolc.hu; pkortesi@gmail.com
It is well-known that T0 separation aximoms are equivalent to Hausdorf fseparation in toőpological
groups. However, if we weaken the relation between the two structures - semitopolocal case, or we
take more general algebraic structures - invers semigroups, this property disappears. We will study
some separation axioms for inverse semigroups, and some shadow separation properties as well.
ICAM9
New Methods for the Polynomial Roots Approximation
Călin Alexe Mureşan
University of Petroleum and Gas, Romania
c1a2muresan@yahoo.com
Our results, about one of the product of distances between the polynomial roots, in complex
space, can be used for the polynomial roots isolation. These, conduce as to many evaluations of the
complexity of the isolation, located in the finest class known.
ICAM9
Semisimple group algebras: primitive idempotents and group codes
Gabriela Olteanu
Department of Statistics-Forecasts-Mathematics
Babeş-Bolyai University
gabriela.olteanu@econ.ubbcluj.ro
In [3, 4, 6, 7], Jespers, Olteanu, del Rı́o and Van Gelder described a complete set of orthogonal
primitive idempotents in each Wedderburn component of a semisimple group algebra F G for various
classes of finite groups G and F being the field of rational numbers or a finite field, using strong Shoda
pairs and the description of the Wedderburn decomposition of F G given by Olivieri, del Rı́o and
39
Simón in [5] and [2]. We shall describe some of these methods to compute complete sets of orthogonal
primitive idempotents in semisimple group algebras F G.
In [6], the computation of primitive idempotents in finite group algebras is used in order to provide
algorithms to construct minimal left group codes for a large class of groups and fields. To illustrate
these methods, we provide alternative constructions to some best linear codes over F2 and F3 . We
shall present some examples of best linear codes. The methods to construct minimal left group codes
were implemented using the programming language provided by the computer algebra system GAP
and we included them in the GAP package Wedderga [1].
Bibliography
[1] O. Broche, A. Konovalov, A. Olivieri, G. Olteanu, Á. del Rı́o, I. Van Gelder, Wedderga - Wedderburn Decomposition
of Group Algebras, Version 4.5.1 (2013). http://www.gap-system.org/Packages/wedderga.html
[2] O. Broche, Á. del Rı́o, Wedderburn decomposition of finite group algebras, Finite Fields and their Applications 13
(2007), no. 1, 71–79.
[3] E. Jespers, G. Olteanu, Á. del Rı́o, Rational group algebras of finite groups: from idempotents to units of integral
group rings, Algebr. Represent. Theor. 15 (2012), 359–377. http://arxiv.org/abs/1001.1236
[4] E. Jespers, G. Olteanu, Á del Rı́o, I. Van Gelder, Group rings of finite strongly monomial groups: central units and
primitive idempotents, J. Algebra 387 (2013), 99–116. http://arxiv.org/abs/1209.1269
[5] A. Olivieri, Á. del Rı́o, J.J. Simón, On monomial characters and central idempotents of rational group algebras,
Comm. Algebra 32 (4), 1531–1550 (2004).
[6] G. Olteanu, I. Van Gelder, Construction of inimal non-abelian left group codes, submitted.
http://arxiv.org/abs/1302.3747
[7] I. Van Gelder, G. Olteanu, Finite group algebras of nilpotent groups: a complete set of orthogonal primitive idempotents,
Finite Fields Appl. 17 (2011), 157–165. http://arxiv.org/abs/1302.3882
ICAM9
On some particular equivalence relations of multialgebras
Cosmin Pelea
cpelea@math.ubbcluj.ro
The equivalence relations of a multialgebra which determine universal algebras are important
tools in multialgebra theory. Our talk is a survey (based on [1] and [2]) on the class of these relations
of a given multialgebra hA, F i. We give a special attention to the image α(θ) of a binary relation θ
of A through the closure operator they determine. We will discuss some problems concerning the
construction of α(R) for particular relations R and special cases of multialgebras.
Bibliography
[1] Pelea, C., Hyperrings and α∗ -relations. A general approach, J. Algebra 383 (2013), 104–128
[2] Pelea, C., Purdea, I., Stanca, L., Fundamental relations in multialgebras. Applications, preprint, arXiv:1305.6141
ICAM9
A generalization of Hyers-Ulam-Rassias stability on m-semigroups
Adina Pop and Maria S. Pop
Technical University of Cluj Napoca, North Univ Center of Baia Mare, Department of Mathematics and Computer Science, Baia Mare,
Romania
adina p 2006@yahoo.com; maria sanziana@yahoo.com
In this paper we investigate the generalized Hyers-Ulam-Rassias stability of mappings of m−semigroups
m ∈ N; m ≥ 3 into Banach spaces. For m = 3 the results can be found in Amyari and Moslehian
[ Approximately ternary semigroup homomorphisms, Lett. Math. Phys. 77(2006), 1-9 ] with the
mention that they are true in the class of normal m−semigroups which is larger than the class of
commutative m−semigroups. For m = 2 we find certain results of Hyers [ On the stability of the
linear functional equation, Proc. Nat. Acad. Sci. USA, 27 (1941), 222-224 ], Rassias, Th. M. [On
the stability of the linear mapping in Banach space, Proc. Amer. Math, Soc. 72 (1978), 297-300 ]
40
and Rassias, J. M. [ Solution of a Problem of Ulam, J. Approx. Theory Math. 57 (1989), 268-273 ].
In addition, we establish the superstability of m−ary homomorphims into Banach algebras endowed
with multiplicative norms, generalizing the results of Szekelyhidi [ On a theorem of Baker, Lawrence
and Zorzitto, Proc. Amer. Math. Soc., 84 (1982), 95-96 ] and Amyari and Moslehian (2006) .
Bibliography
[1] Amyari, M. and Moslechian, M.S., Approximately ternary semigroup homomorphisms, Lett. Math. Phys. 77(2006),
1-9
[2] Dehghanian, M. and Modarres, M.S., Ternary Weighted Function and Beurling Ternary Banach Algebra l1ω (S), Abs.
and Appl. Analysis, (2011), doi:10.1155/2011 206165
[3] Găvruţa, P.,A generalization of the Hyers-Ulam-Rassian stability of approximately additive mappings, J. Math. Anal.
Appl. 184 (1994), 431-436
[4] Hyers, D.H.,On the stability of the linear functional equation, Proc. Nat. Acad. Sci. USA, 27 (1941), 222-224
[5] Kerner, R., Ternary and non-associative algebraic structures and their applications in physics, Univ. P. and M.
Curie, 2000
[6] Moslehian, M. S., Szekelyhidi, L., Stability of ternary homomorphisms via generalized Jensen equation , Result.
Math. 49 (2006) 286-300, doi: 101007/s00025-006-0225-1
[7] Post, E. L., Polyadic groups, Trans. Amer. Math. Soc. 18(1940), 208-350
[8] Rassias, Th. M., On the stability of the linear mapping in Banach space, Proc. Amer. Math, Soc. 72 (1978), 297-300
[9] Rassias, Th. M., The Problem of S.M. Ulam for Approximately Multiplicative Mappings, J. Math. Anal. Appl. 246,
(2000), 352-378
[10] Rassias, J. M., Solution of a Problem of Ulam, J. Approx. Theory Math. 57 (1989), 268-273
[11] Szekelyhidi, L. On a theorem of Baker, Lawrence and Zorzitto, Proc. Amer. Math. Soc., 84 (1982), 95-96
[12] Ulam, S. M., A Collection of Mathematical Problems, Interscience Tracts in Pure and Applied Mathematics, no. 8,
Interscience Publishers, New York, NY, USA, 1960.
[13] Zettl, H., A characterization of ternary rings of operators, Adv. Math. 48 (1983), 117-143
ICAM9
Simultaneous extensions of polyadic groups
Vasile Pop
Technical University of Cluj-Napoca, Department of Mathematics, Cluj-Napoca, Romania
vasile.pop@math.utcluj.ro
The reduction of two polyadic groups of arbitrary arity to the same group was studied by I.
Corovei, I. Purdea and V. Pop. In this paper we give necessary and sufficient conditions under which
two polyadic groups of (m + 1) and (n + 1)-arity can be extended to the same (k + 1)-group, where k
is multiple of m and n.
Bibliography
[1] Corovei, I., Purdea, I., The reduction of (m + 1)-groups and its extensions to the same group, Preprint sem. of
algebra 5(1988), Babeş-Bolyai Univ., 63-68.
[2] Dörnte, W., Untersuchungen über einen verallgemeinderten Gruppenbegrieff, Math. Z., 29(1929), 1-19.
[3] Dudek, W.A., Michalski, J., On a generalization of Hosszu Theorem, Dem. Math., 3(1982), 783-805.
[4] Hosszu, M., On explicit form of n-group operation, Publ. Math. Debrecen, 10(1963), 88-92.
[5] Pop, V., Reduction of two polyadic groups to a group, Aut. Comput. Appl. Math., 14(2005), no. 1, 9-16.
ICAM9
Extensions of modules over tame hereditary algebras
Csaba Szántó
UBB Cluj, Faculty of Mathematics and Computer Science, Romania
szanto.cs@gmail.com
Consider a finite dimensional tame hereditary algebra (path algebra of a noncyclic affine quiver)
and its finite dimensional right modules. An indecomposable module is called exceptional if it has
no self extensions. Two modules X, Y are called orthogonal if Hom(X, Y ) = Hom(Y, X) = 0. An
orthogonal exceptional pair to an indecomposable M is a pair of orthogonal exceptional modules
(Y, X) such that there is a short exact sequence 0 → uX → M → vY → 0 with Ext1 (X, Y ) = 0 (here
41
uX = X ⊕ · · · ⊕ X u-times). Schofields theorem tells us that if M is exceptional then there exists
orthogonal exceptional pairs to M , however there is no convenient method to determine these pairs.
In case the quiver is Dynkin (not affine) Bo Chens theorem shows that the pair (M/T, T ), where T is
the Gabriel-Roiter submodule of M , is orthogonal exceptional to M . We generalize this result for
tame cases using Ringel-Hall algebras.
ICAM9
Abelian groups in which any proper subgroup has the direct summand intersection property
Teodor Dumitru Vălcan
”Babeş-Bolyai” University of Cluj-Napoca, Romania
tdvalcan@yahoo.ca
We say that an R-module (abelian group) M has the direct summand intersection property (in
short D.S.I.P.) if the intersection of any two direct summands of M is again a direct summand in M .
In this work we will present three classes of abelian groups (torsion, divisible, respectively torsion-free)
which have the property that any proper subgroup has D.S.I.P. and we are going to show that there
are not such mixed groups.
Bibliography
[1] Albrecht, U., Hausen, J., Modules with the quasi-summand intersection property, Bull. Austr. Math. Soc., 44, 1991,
189-201
[2] Albrecht, U., Hausen, J., Mixed Abelian Groups with the Summand Intersection Property, Lecture Notes in Pure and
Applied Math., 182, Aekker, New York, 1996, 123-132
[3] Arnold, D.M., Hausen, J., A characterization of modules with the summand intersection property, Comm. Algebra,
18(2), 1990, 519-528
[4] Fuchs, L., Infinite Abelian Groups Theory, Vol.I, Academic Press, New York and London, Pure and Applied
Mathematics, 36, 1970
[5] Hausen, J., Modules with the summand intersection property, Comm. Algebra, 17, 1989, 135-148
[6] Kamalov, F.F., Intersection of direct summands of abelian groups, (in Russian), Izv, Vyssh. Uchebn. Zaved. Mat. 5,
1977, 45-56
[7] Kuroş, A., The Groups Theory, (in Russian), Ed. Nauka, 1967
[8] Vălcan, D., Abelian groups with the direct summand intersection property, (in Romanian), The Annual Conference of
the Romanian Society of Mathematical Sciences, 1977, May 29 - June 1, Bucharest, Romania, 111-120
ICAM9
6. Software Engineering - Principles and Practices
Constructing questions using Maple T. A.
Csaba Sárvári
University of Pécs, Polláck Mihály Faculty of Engineering and Information Technology, Hungary
sarvari.cs@gmail.com
Under an EU project two English-language collections of exercises are being developed at the
University of Pécs. The titles of the exercise books are: Algebra and number theory, Multivariate
functions and series. For the development the MAPLE T.A test and assessment system [1], [2] is
used. Using this system not only multiple choice questions can be framed, but there are possibilities
to check the partial results as well. During the evaluation of the answers the Maple computer algebra
system runs in the background, thus the system automatically evaluates the variously formulated
answers of the person completing test and compares it to the correct solution.
In our presentation we cover some mathematical didactic issues raised by the task development.
Our examples are selected from themes of differential equations and linear algebra and multivariate
42
functions. We investigate the process of constructing questions and present some special forms of
questions, e.g. questions based on relation analysis.
Bibliography
[1] André Heck, Leendert van Gastel, Diagnostic Testing with Maple T.A. , In: M. Seppällä, O. Xambo, O. Caprotti
(eds.) WebALT 2006 Proceedings. pp 37 - 51.
[2] Stefanie Winkler, Andreas Körner, Vilma Urbonaite, Maple T.A. in Engineering Educations, 7th Vienna Conference
on Mathematics Modelling Febr. 15-17, 2012
ICAM9
Metrics in software quality evaluation
Mara Diana Hajdu-Macelaru
mara.macelaru@mail.ubm.ro
Software metrics can be classified into three categories: product metrics, process metrics, and
project metrics. In current paper we will detail the existing software quality metrics , their importance
and accuracy . We will also improve some of the existing metrics and state which of the metrics counts
more when evaluating the software quality.
ICAM9
fUML Formal Description
Simona Motogna, Florin Crăciun and Gabriel Glodean
Department of Computer Science, Babes Bolyai University, Cluj-Napoca, Romania
motogna@cs.ubbcluj.ro; craciunf@cs.ubbcluj.ro
Constructing software automatically from high-level models is one of the challenges in software
engineering nowadays. There is an urgent need for adequate methods to ensure high quality of models.
The Executable Foundational UML (fUML) has been proposed as a computationally complete and
compact subset of UML. A fUML model is supposed to be executed and tested in the early stage of
the software development process. A complete and sound formalization of fUML operational semantics
is still in its early stages, and although several proposals to execute and verify fUML models have been
issued, this problem is still open. Our project aims to develop a novel K-based approach for executing
and verifying fUML models. K is a rewrite-based executable semantic framework. This paper focuses
on the formalization of the fUML activities execution. We define an intermediate language to describe
fUML activity graphical components and we introduce a fully concurrent K-based execution model of
the fUML activities and actions. Initial set of experiments have shown that our K-based approach is
feasible.
Bibliography
[1] OMG, Concrete Syntax for UML Action Language (Action Language for Foundational UML - ALF), OMG, 2010.
[2] E. Planas, J. Cabot, and C. Gomez, Lightweight verification of executable models, in ER, 2011, pp. 467475.
[3] G. Rosu and T. F. Serbanuta, An overview of the K semantic framework, Journal of Logic and Algebraic Programming,2010.
[4] V. Rusu and D. Lucanu, A k-based formal framework for domain-specific modelling languages, in FoVeOOS, 2011,
pp. 214231.
ICAM9
43
On-Line Testing in Higher Mathematics Education - Maple T. A.
Ildikó Perjési-Hámori
University of Pécs, Polláck Mihály Faculty of Engineering and Information Technology, Hungary
perjesi@pmmik.pte.hu
Under a EU project two English-language collections of exercises are being developed at the
University of Pécs. The titles of the exercise books are: Algebra and number theory, Multivariate
functions and series. For the development the MAPLE T.A test and assessment system [1], [2] is
used. With the help of this system not only multiple choice questions can be framed, but there are
possibilities to check the partial results as well. During the evaluation of the answers the Maple
computer algebra system runs in the background, thus the system automatically evaluates the variously
formulated answers of the person completing test and compares it to the correct solution. (For example
if the question is about the comparison test of series convergence there are infinite number of correct
answers, the system is able to check whether the answer is correct or not.)
In our presentation we cover some mathematical didactic issues raised by the task development.
Our examples are selected from themes of numerical and function series, and from the integration of
multivariate functions.
Bibliography
[1] André Heck, Leendert van Gastel, Diagnostic Testing with Maple T.A. , In: M. Seppällä, O. Xambo, O. Caprotti
(eds.) WebALT 2006 Proceedings. pp 37 - 51.
[2] Stefanie Winkler, Andreas Körner, Vilma Urbonaite, Maple T.A. in Engineering Educations, 7th Vienna Conference
on Mathematics Modelling Febr. 15-17, 2012
ICAM9
Software Tools for Information Retrieval with Lattices
Imre Piller
University of Miskolc, Hungary
piller.imre@gmail.com
The information retrieval became one of the most important topic in informatics in the last decade.
There are various structures and methods for representing the information and store as a data in
efficient way, this work shows some of them from the simpler structures to the more general ones. In
this consideration the lattice is the preferred structure because it is able to describe complex relations
between objects in a hierarchical manner [2].
There are many possible structures for representing information. The key-value pair is a well
known elementary structure which appears almost in all informational systems. The relational model
is more flexible and closer to the human thinking in complicated cases. Where the hierarchy has a
key role we need to create trees or lattices. It is important to provide tools which are able to present
these structures and help to emphasize their advantages and disadvantages.
The theory of formal concept analysis is an arising area of mathematics and computer science. It
has a pure theoretical foundation and has many real world application [1]. There are many research
which shows the importance of the theory in information retrieval [3].
The aim of this work is to present available software tools for the examination of conceptual
structures. There are many advantages of the integration of special topics in a common platform. It
helps to solve the common tasks (for example visualization) in an easier way and the users can use a
familiar interface. The GeoGebra is a widely used educational software but has a minimal support for
the mentioned structures. This work makes steps to extend the functionality in this direction in the
hope that the theory of formal concept analysis will be a popular area in the future.
Bibliography
[1] Bernhard Ganter, Gerd Stumme, Rudolf Wille, Formal Concept Analysis, Foundations and Applications, SpringerVerlag Berlin Heidelberg 2005
[2] Uta Priss Lattice-based Information Retrieval., Knowledge Organization, Vol. 27, 3, 2000, p. 132-142.
44
[3] Uta Priss, Formal Concept Analysis in Information Science., Cronin, Blaise (ed.), Annual Review of Information
Science and Technology. Vol 40, 2006, p. 521-543.
ICAM9
The use of Java technologies for web e-commerce applications
Emanuela Petreanu and Livia Sângeorzan
Department of Mathematic and Computer Science, Transilvania University of Braşov, Romania
sangeorzan@unitbv.ro
The e-commerce sector, in the century of speed and information, must find an answer for everybody
who wants to solve their shopping needs as quickly as possible, if possible by just giving a mouse click.
The Internet is providing a range of solutions and useful information in all fields, including a large
variety of online shops. The Internet became an important environment for presenting and marketing
of the company products in real time that is available to everyone. The web applications offer people
the possibility to buy products for every activity in their life, work or spending their vacations..
The paper presents a structure of a site, using Java web technologies, which permits access the web
application Mountain Expert in order to buy sport products. Through this application when you leave
in a trip in nature, you might want to buy sport clothes and accessories, and if you are in a hurry and
dont have time, a web shop is the best solution. The web application Mountain Expert has applied
rules and techniques of accessibility from WAI (Web Accessibility Initiative). The server application
is implemented using Java JSF and Primefaces libraries. Java web technologies has a great flexibility
allowing to be used with other technologies and also using these languages /technologies makes possible
the obtaining of remarkable results. This paper will present a new development approach of the web
applications implementation based on MVC pattern with JavaServer Faces technology. This approach
is based on the separation of the user presentation part and business logic behind the application.
Bibliography
[1] June Cohen, The Unusually Useful Web Book, New Riders , ISBN-10: 0735712069, ISBN-13: 978-0735712065, 2003
[2] David R. Heffelfinger, Java EE 6 Development with NetBeans 7, Packt Publishing, ISBN 978-1-84951-270-1, 2011
[3] Bill Dudney, Jonathan Lehr, Bill Willis, LeRoy Mattingly Mastering JavaServer Faces Wiley, ISBN: 978-0-47146207-1, 2004
[4] Ian Hlavats JSF 1.2 Components, Packt Publishing, ISBN 978-1-847197-62-7, 2009
[5] Damiano Distante, Model Driven Development of Web Application with UWA,MVC and JavaServer Faces, Proceeding
ICWE’07 Proceedings of the 7th international conference on Web engineering, pages 457-472
[6] http://en.wikipedia.org/wiki/NetBeans
[7] http://db.apache.org/derby/
[8] http://en.wikipedia.org/wiki/Object diagram
[9] http://www.w3.org/standards/webdesign/accessibility
ICAM9
A functional sentence perspective approach to preflow algorithm in parametric networks
Livia Sângeorzan1 , Mihaela Parpalea2 , Mircea Parpalea3
1 Department
of Mathematic and Computer Science, Transilvania University of Braşov, Romania
2 Department
of Foreign Languages, Transilvania University of Braşov, Romania
3 National
College Andrei Saguna, Braşov, Romania
parpalea@gmail.com; sangeorzan@unitbv.ro; parpalea@yahoo.com
The present paper proposes a fractal-like approach to the parametric flow problem, derived from
the rules and recursion of generative linguistics, based on the Functional Sentence Perspective (FSP)
which describes the German word order. The same as any sentence can be analysed in terms of
theme of the sentence (that which is spoken about in the sentence) and rheme of the sentence (that
which is said about the theme in the sentence), in a preflow-push algorithm, a partitioning push (a
non-cancelling push of flow in the parametric residual network) might leave the node unbalanced
for only a subinterval of the range of the values of the parameter. This will lead to separating the
45
problem for the two disjoints subintervals, which allows the algorithm to continue after the same
rules, independently, on each of the partitioned subintervals. The algorithm runs as the template-like
structure of a dialogue act which reveals a design where information about the items (part-of-speech)
is a two sections vector with one segment for each of the used part of speech categories.
Bibliography
[1] Ahuja, R., Orlin, J., Distance-directed augmenting path algorithms for maximum flow and parametric maximum
flow problems, Naval Research Logistics, 38(1990), 413-430.
[2] Brill, E., A simple rule-based part of speech tagger. Proceedings of the Third Conference on Applied Natural
Language Processing, 1992, 152155.
[3] Hamacher, H.W., Foulds, L.R., Algorithms for Flows with Parametric Capacities. ZOR - Methods and Models of
Operations Research, 33(1989), 21-37.
[4] Parpalea, MM., German Word Order. Bulletin of the Transilvania University of Braşov, Series IV, Vol.2, 51(2009),
175-182.
[5] Parpalea, M., Min-Max algorithm for the parametric flow problem, Bulletin of the Transilvania University of Brasov,
Series III: Mathematics, Informatics, Physics, Vol.3, 52(2010), 191-198.
[6] Ruhe, G., Complexity Results for Multicriterial and Parametric Network Flows Using a Pathological Graph of Zadeh,
Zeitschrift fr Operations Research, 32(1988), 9- 27.
[7] Ruhe, G., Algorithmic Aspects of Flows in Networks, Kluwer Academic Publishers, Dordrecht, The Netherlands,
1991.
[8] Sangeorzan, L., Kiss-Iakab, K., Parpalea, M., Runtimes for Parallel Fractals. Proceedings On the 31st Annual
Congress of the American Romanian Academy of Arts and Sciences, 5(2007), 549-552.
[9] Tarjan, R., Ward, J., Zhang, B., Zhou, Y., Mao, J., Balancing Applied to Maximum Network Flow Problems.
AlgorithmsESA, Springer 4168(2006), 612-623.
ICAM9
A Max-Plus Algorithm and the Prime Numbers
Peter Szabó
Technical University of Košice, Department of Aerodynamics and Simulations, Slovakia
peter.szabo@tuke.sk
Let us consider the following task:
max{ti−1 + x1 , ti−2 + x2 , · · · , t0 + xi , xi+1 , · · · , xn } = λ + xi
for all i = 1, 2, · · · , n. It is assumed that input values ti are nonnegative real numbers for all
i = 0, 1, · · · , n − 1. The λ, x1 , · · · , xn ∈ R values are the solutions of the equations. One of the
effective solution of this problem is based on using special partitions of number n, see [1]. This
property enables to investigate different partition problems. In this work, we examine the possibility
to prove the Goldbach conjecture.
Keywords : Goldbach conjecture, max-plus algebra, Toeplitz matrix.
Bibliography
[1] Szabó,P. : An Iterative Algorithm for Computing the Cycle Mean of a Toeplitz Matrix in Special Form, Kybernetika,
2013 in press.
ICAM9
Application of rough approximations in Group Technology problems
Laura Veres
University of Miskolc, Hungary
matvlaura@gmail.com
The notion of rough sets was introduced by Z. Pawlak in the early eighties deals with incomplete
information about objects. As an application to Group Technology problems, I developed a new
method and an algorithm, based on rough approximations and modal operators defined on a context,
for determinig the master parts corresponding to a manufacturing process.
46
ICAM9
7. Applications of Mathematics and Computer Science in Science, Arts and
Technology
Developing an ontology for automated scene creation
Diana Contraş and Alina Pintescu
Automation Department, Technical University of Cluj-Napoca
pdia17@yahoo.com
This article presents an ontology meant to be used by algorithms for automated creation of scenes.
At any time and in any place we encounter scenes: in plays, in paintings, in film frames, at hospitals,
at police stations, at schools, at restaurants, at stores, everywhere. Depending on where it is located,
a scene can contain more types of elements: backgrounds, objects, characters connected through their
spatial relationships. Our intention is to offer the possibility of realizing many combinations of the
chosen elements in order to obtain the waned scene. In practice is difficult to obtain such a result,
that is why we intend to design an automatic system, which will automatically generate the scenes.
The possible elements of scenes together with their relationships are grouped in an ontology which is
presented in this article.
Bibliography
[1] Gruber, Thomas R. A Translation Approach to Portable Ontology Specifications, 1993
[2] Sowa, John Knowledge Representation: Logical, Philosophical and Computational Foundations, 1999
[3] Gmez-Prez, Asuncion; Fernndez-Lpez, Mariano; Corcho, Oscal Ontological Engineering: With Examples from the
Areas of Knowledge Management, E-commerce and the Semantic Web, Springer, 2004
[4] Gmez-Prez, Asuncion; Fernndez-Lpez, Marianol Overview and analysis of methodologies for building ontologies, 2002
[5] Noy, Natalya F.; McGuinness, Deborah L. Ontology Development 101: A Guide to Creating Your First Ontology,
Technical Report KSL0105, Stanford Knowledge Systems Laboratory, 2001
[6] Alatrish, Emhimed Salem Comparison of Ontology Editors, e-RAF Journal on Computing, Volume no. 4, 2012
[7] Matei, Oliviu Ontology-Based Knowledge Organization for the Radiograph Images Segmentation, Advances in
Electrical and Computer Engineering, 8(15), 2008
[8] Panagi, P.; Dasiopoulou, S.; Papadopoulos, G.T.; Kompatsiaris, I.; Strintzis, M.G. A Genetic Algorithm Approach
to Ontology-driven Semantic Image Analysis, Visual Information Engineering, 2006
[9] Matei, Oliviu Defining an Ontology for the Radiograph Images Segmentation, 9th International Conference on
Development and Application Systems, 2008
[10] O. Matei, Evolutionary Computation: Principles and Practices, Risoprint, 2008.
ICAM9
Using a spatial configuration mathematical model to study the inhabited area of a Maramureş village
Ruxandra Berindea and Vasile Berindeb
a School
of Architecture, University of Sheffield, United Kingdom;
b Department
of Mathematics and Computer Science, North University Center at Baia Mare, Technical University of Cluj-Napoca, Roma-
nia;
ruxandra.berinde@sheffield.ac.uk; vberinde@ubm.ro
We use the Space Syntax theory, i.e., the concept of JPG (Justified Plan Graph) as surveyed in
[1], in order to mathematically describe and analyze the configuration aspects of the inhabited area of
the Maramureş village Budeşti.
Bibliography
[1] Ostwald, M.J., The mathematics of spatial configuration: revisiting, revising and critiquing Plan Graph Theory,
Nexus Network J., 13 (2011), 445–470
ICAM9
47
New quantitative structure-toxicity relationship for aliphatic carboxylic acids
Zoiţa Berinde
Department of Chemistry and Biology, North University Center at Baia Mare, Technical University of Cluj-Napoca, Romania
zoitaberinde@ubm.ro
The paper reports on a quantitative structure-activity relationship (QSAR) study of the toxicity
of 38 aliphatic carboxilic acids. This is done by modelling as molecular graphs the chemical structure
of the compounds and then by extracting several topological indices from the corresponding weighted
connectivity matrices, which are then correlated with some biological properties of aliphatic carboxilic
acids, amongst which the most important is their toxicity.
ICAM9
A topological study for a set of columnar liquid crystals
Thomas Dippong and Zoiţa Berinde
Department of Chemistry and Biology, North University Center at Baia Mare, Technical University of Cluj-Napoca, Romania;
th0mas2004@yahoo.com; zoitaberinde@ubm.ro
The paper reports on a study that searches for a possible relationship between the chemical
structure of a class of columnar liquid crystals and some of their physico-chemical properties.
Monovariable as well multivariable correlation studies between the transition temperature and
one or more molecular descriptors (like topological indices or Van der Waals parameters) have been
performed
ICAM9
Spatial distribution maps of microelements concentration in surface soil around soil pollution sources
Cristina Mihali, Gabriela Oprea, Claudia Butean
Technical University of Cluj Napoca, North University Center at Baia Mare, Romania
mihali.cristina@gmail.com
Spatial distribution maps of pollutant microelements in the soil are important tools for the
assessment of pollution degree around the pollution sources. The concentrations of microelements (Pb,
Cd, Zn and Cu) were measured for sampling points distributed around the main soil pollution sources
in Baia Mare area. The pollution sources were a lead smelter and tailing ponds [1]. The sampling
point coordinates (latitude and longitude) were registered with a GPS (Global Positioning System)
instrument. Considering the coordinates of each sampling point and the corresponding concentration
of the considered microelement in the sampling point, a matrix XYZ was obtained where X was the
longitude; Y was the latitude and Z the concentration of the microelements [2]. A continuous surface
was generated beginning with each sampling point. Origin program was applied for gridding with
correlation method. The spatial distribution maps of the microelements indicated some area high
polluted around the lead smelter especially for Pb and Cd.
Bibliography
[1] Mihali, C., Michnea, A., Oprea, G., Gogoaşă, I., Pop, C., Şenilă, M., Grigor, L., Trace element transfer from soil
to vegetables around the lead smelter in Baia Mare, NW Romania, Journal of Food, Agriculture & Environment,
10(2012), 828-834.
[2] Levei, E.A., Freniu, T., Ponta, M., Şenilă, M., Miclean, M., Roman, C., Cordo, E., Characterization of soil quality
and mobility of Cd, Cu, Pb, and Zn in the Baia Mare area Northwest Romania following the historical pollution,
International Journal of Environmental Analytical Chemistry, 89(2009), 635-649
ICAM9
48
8. Mathematical Modelling with Applications in Economics
An Implementation of Monte Carlo Method for European Option Pricing
Adrian Răbâea
TUCN-NUCBM, Romania
arabaea@gmail.com
Pricing options[1] often requires use of parallel computing and Monte Carlo methods[2] in financial
industries. We describe and analyze the performance of a multi-core processors of personal computers
dedicated to Monte Carlo simulation[3] on the evaluation of financial derivatives.
Bibliography
[1] Black, F., Scholes, M.: The pricing of Options and Corporate Liabilities, Journal of Political Economics 81, 1973,
637-659
[2] Jenny X. Li, Gary L. Mullen, Parallel computing of a quasi-Monte Carlo algorithm for valuing derivatives, Parallel
Computing 26, 641-653, 2000
[3] Rabaea A., Rabaea M. - Experiments with Parallel Monte Carlo Simulation for Pricing Options using PVM, Lecture
Notes in Computer Science 1908 - Recent Advances in Parallel Virtual Machine and Message Passing Interface,
Springer-Verlag Berlin Heidelberg, 330-337, 2000.
ICAM9
On the comparison of Fisher informations of the some probability distributions
Ion Mihoc(1) and Cristina-Ioana Fătu(2)
(1) Faculty
(2)
of Mathematics and Computer Science, ”Babes-Bolyai” University of Cluj-Napoca,
Faculty of Economics, Christian University ”Dimitrie Cantemir”, Cluj-Napoca, Romania
imihoc@math.ubbcluj.ro, cristina.fatu@cantemircluj.ro
Fisher information plays an important role in the statistical inference connection with the
properties of the estimators for an unknown vector parameter θ which lie in some parameter space
Dθ , Dθ ⊂ Rk , k ≥ 1.
In this paper, we study some properties of the Fisher information for some probability distributions
which belong to an exponential family.
Bibliography
[1] Gupta, R.D. and Kundu, D. Generalized exponential distrinutions, Australian and New Zealand Journal of
Statistics, 41 (2002), 173-188
[2] Mihoc, I., Fătu, C.I., About some properties of the F isher inf ormation in the sample theory, Automation
Computers Applied Mathematics, ISSN 1221-437X, 19 (2010) No. 2, 97-108
ICAM9
9. Variational methods and applications to ODEs and PDEs
Parameter-depending problems on fractals
Brigitte E. Breckner
Babeş-Bolyai Unversity, Cluj-Napoca, Romania
brigitte@math.ubbcluj.ro
The talk is based on the recent papers [1] and [2], jointly written with Csaba Varga. There are
treated nonlinear elliptic problems defined on the Sierpinski gasket, a highly non-smooth fractal set.
Even if the structure of this fractal differs considerably from that of (open) domains of Euclidean
spaces, the talk emphasizes that PDEs and systems of PDEs defined on it may be studied (as in the
49
Euclidian case) by means of certain variational methods, involving also some abstract multiplicity
theorems by B. Ricceri (see [3] and [4]).
Bibliography
[1] Breckner, B.E., Varga, Cs., Multiple solutions of Dirichlet problems on the Sierpinski gasket, submitted
[2] Breckner, B.E., Varga, Cs., A note on gradient-type systems on fractals, submitted
[3] Ricceri, B., A class of nonlinear eigenvalue problems with four solutions, J. Nonlinear Convex Anal., 11 (2010),
503–511
[4] Ricceri, B., A further refinement of a three critical points theorem, Nonlinear Anal., 74 (2011), 7446–7454
ICAM9
An application to quasi-linear variational inequalities
Marcel Bogdan
”Petru Maior ”Unversity of Tı̂rgu Mureş, Romania
marcel.bogdan@science.upm.ro
In the present exposition we consider a variational inequality coming from a boundary value
problem, governed by a topological pseudomonotone operator in the Brezis’s sense, classified as
quasi-linear [3].
Our purpose is to relate a Ritz-Galerkin scheme type by our approach in [1, 2] that involves a
sequence of operators.
Bibliography
[1] Bogdan, M., Kolumbán, J., Some regularities for parametric equilibrium problems, J. of Global Optimization, 44(2009),
481-492
[2] Bogdan, M., On parametric quasivariational inequalities, Scientific Bulletin of the Petru Maior University of Tı̂rgu
Mureş, 9(2012), 26-27
[3] Zeidler, E., Nonlinear Functional Analysis and its Applications, Vol. III, Springer Verlag, Berlin, Germany, 1990.
ICAM9
An existence result for a quasi-linear elliptic equation with dependence on the gradient
Francesca Faraci
University of Catania, Italy
ffaraci@dmi.unict.it
In this lecture we present an existence theorem for a quasilinear elliptic problem with dependence
on the gradient of the following type
−∆p u = f (x, u, ∇u) in Ω
u=0
on ∂Ω,
under general growth conditions of the nonlinearity on u and ∇u. Our aim is to combine variational
techniques with fixed point methods in order to prove the existence of a solution. More precisely our
approach is based on sub-supersolution techniques, extremal solutions for an auxiliary parametric
problem and Schaefer’s fixed point theorem. A multiplicity theorem is also obtained.
Based on a joint work with D. Motreanu and D. Puglisi (see [1]).
Bibliography
[1] Faraci F., Motranu D., Puglisi D., Quasi-linear elliptic equations with dependence on the gradient, preprint.
ICAM9
Existence theorems for intersection problems and equilibrium problems
Daniela Inoan, József Kolumbán
Technical University of Cluj-Napoca, Babeş Bolyai University of Cluj-Napoca
50
Daniela.Inoan@math.utcluj.ro, jokolumban@yahoo.com
Necessary and sufficient conditions for the existence of an x̄ ∈ X such that f (x̄, y) ≥ 0, for all
y ∈ Y , are given. Here X is a subset of a Hausdorff topological vector space, Y is an arbitrary
set independent of X, and f : X × Y → R is a given function. Our results extend the KnasterKuratowski-Mazurkiewicz Lemma, Ky Fan’s minimax inequality and Brézis-Nirenberg-Stampacchia
Theorem.
ICAM9
Stochastic Nonlinear Equations of Schrödinger Type
Hannelore Lisei
hanne@math.ubbcluj.ro
We consider a stochastic nonlinear equation of Schrödinger type, which is perturbed by an infinite
dimensional Wiener process. The existence of the solution is proved by using the Galerkin method. We
also construct a splitting method for these equations: we approximate the solution of our problem by
a sequence of solutions of two types of equations: one without stochastic integral term, but containing
the Laplace operator and the nonlinear term, and the other one containing only the stochastic integral
term. The two types of equations are connected to each other by their initial values. We prove that the
solutions of these equations both converge strongly to the solution of the Schrödinger type equation.
ICAM9
Multivalued variational inequalities and coincidence point results
Szilárd László
laszlosziszi@yahoo.com
In this paper, we establish some existence results of the solutions for several multivalued variational
inequalities involving elements belonging to a class of operators that was recently introduced in
the literature. As applications we obtain some new coincidence point results in Hilbert spaces.
Bibliography
[1] László, S., Multivalued variational inequalities and coincidence point results, J.Math.Anal.Appl., 404(2013), 105-114
[2] László, S., Some existence results of solutions for general variational inequalities, J.Optim.TheoryAppl., 150(2011),
425-443
ICAM9
10. Miscellanea
Bézier Curves in GeoGebra and Computational Applications dedicated to Environmental Informatics
Bogdan Cioruţa, Mirela Coman
bciorutza@yahoo.com; comanmirela2000@yahoo.com
Bézier is one of the influent polynomial and important tool for interpolation. The Bézier interpolating curve always lies within the convex hull and it never oscillates wildly away from the control
points. Bézier polynomial has several applications in the fields of engineering, science and technology
such as highway or railway rout designing, networks, Computer Aided Design system, animation,
environment design, robotics, communications, Environmental Informatics and many other disciplines
51
or areas of interest because it is easy to compute and is also very stable. One of the main approaches
to robot motion, for example, is through the use of Quadratic and Cubic Bézier spline functions.
In CAD systems and in Environmental Information (Computational) Systems, parametric representation of curves and surfaces and its shape control are under wide consideration and research,
and it is very important to choose the appropriate basis functions. Based on their good properties,
the classical Bézier curves play a significant role in CAD system, so in recent years, the parametric
representation of curves and surfaces with shape parameters has received attention especially in
Environmental Informatics for the landslide geomorphology, the simulation of a waste deposit / landfill
compactation, contours and mapping.
The purpose of this workpaper is to introduce the possibilities to represent in a particular way,
using GeoGebra open-source mathematic software, some types of the generalized Bernstein basis
functions associated with the shape parameters and Bézier curves and surfaces which seems to be
entirely new in environmental science and engineering domain, but for perspective in the long-term
research because the curves and surfaces have simpler form and geometric meaning.
ICAM9
Fourier Series in GeoGebra - New Possibilities for Representation and Applications
Bogdan Cioruţa, Mirela Coman
bciorutza@yahoo.com; comanmirela2000@yahoo.com
The Fourier series have long provided one of the principal methods of analysis for mathematical
physics, engineering and signal processing; it has also spurred generalizations and applications that
continue to develop right up to the present. While the original theory of Fourier series applies
to periodic functions occurring in wave motion, such as with light and sound, its generalizations
often relate to wider settings, such as the time-frequency analysis underlying the recent theories
of trigonometric analysis. Methods based on the Fourier series are used in virtually all areas of
engineering and science, and by the circuit designers, spectroscopists, crystallographers and anyone
working in signal processing and communications.
In this paper we try to give an introduction to the Fourier series (or trigonometric series) that
could be suitable for students with the calculus and graphical representation specific to the open-source
math software GeoGebra. Without getting too hung up on details we present the useful terminology
and start to analyse and apply our knowledge in finding different possibilities to represent, use and
develop Fourier analysis for concrete functions that could be occur in many domain of activities
connected to mathematics and informatics.
ICAM9
Field extensions and Clifford theory
Dana Debora Gliţia
Babeş-Bolyai Unversity of Cluj Napoca, Romania
dana.glitia@ubbcluj.ro
We study Clifford theory in connection with the action of the Galois group of a field extension in
the context of group graded algebras.
L
Let G be a finite group, let K/F be an algebraic field extension, and let R = g∈G Rg be a finite
dimensional strongly G-graded F -algebra. A simple R1 -module, as well as a simple K ⊗F R1 -module,
define a “Clifford theory”. The main idea is that the R-module induced from a simple R1 -module
generates an abelian subcategory of the category of R-module which is equivalent to the category
of modules over its endomorphism algebra. The author investigates the relationships between these
theories. One of the main results says that a G-graded derived equivalence over F preserves the
52
Clifford theory defined by corresponding simple modules, and also preserves Galois actions and Schur
indices.
Bibliography
[1]
[2]
[3]
[4]
[5]
[6]
Dade, E.C., Clifford theory for group-graded rings. J. Reine Angew. Math., 369 (1986), 40–86.
Dade, E.C., Clifford theory for group-graded rings. II. J. Reine Angew. Math. 387 (1988), 148–181.
Gliţia, D.D., Group graded bimodules over a commutative G-ring, (2013), to appear.
Karpilovsky, G., Projective representations of finite groups. Marcel Dekker, 1985.
Marcus, A., Representation theory of group graded algebras. Nova Science Publishers, 1999.
Marcus, A., Characters and equivalence classes of central simple group graded algebras. Commun. Algebra, 36 (2008),
1394–1412.
[7] Marcus, A., Derived invariance of Clifford classes, J. Group Theory, 12 (2009), 83–94.
[8] Turull, A., The Brauer-Clifford group. J. Algebra 321 (2009), 3620–3642.
[9] Turull, A., Clifford theory and endoisomorphisms. J. Algebra 371 (2012), 510–520.
ICAM9
A divisibility problem of integers
Péter Körtesi
Institute of Mathematics, University of Miskolc, Hungary
matkp@uni-miskolc.hu; pkortesi@gmail.com
We will show the way how a nice property of divisibility of integers, equivalent to Fermat’s small
theorem has been studied in the Self-Made Mathematics Group of the University of Miskolc, and we
will emphasize the way how Computer Algebra tools influenced the findings related to the property.
ICAM9
Tzitzeica curves in a Minkowski space
Laurian Ioan Pişcoran1 and Cătălin Ionel Barbu2
1 Technical
2 ”Vasile
University of Cluj-Napoca, North University Center of Baia Mare, Romania
Alecsandri” National College, Bacău, Romania
plaurian@yahoo.com; kafka mate@yahoo.com
Using the Minkowski-Pythagorean hodograph, or short MPH-curves, in this paper we will study
the existence of Tzitzeica-MPH curves in the Minkowski space R2,1 .
ICAM9
Part 2
Extended Abstracts
Proceedings of
Pre-
9
I
C
th
nternational
onference
on
A
M
pplied
athematics
25-28 September, 2013
Baia Mare, Romania
Editor: Petrica Pop Sitar
Baia Mare
2013
E DITURA B IBLIO P HIL
ISBN 978-606-93094-8-3
55
New graphical models for the basins of attraction of the real roots of a nonlinear equation
Gheorghe Ardelean
Department of Mathematics and Computer Science, Technical University of Cluj-Napoca, North University Center at Baia Mare, Romania
ardelean g@yahoo.com
Abstract. In this paper we present two new graphical models for the basins of attraction of real roots,
generated by iterative methods for solving nonlinear equations. Even if the images generated are not as
spectacular as in the complex case, this shows some behaviors of iterative methods for solving nonlinear
equations (such range of convergence and speed of convergence).
1.1. Introduction. Newton’s method is the best known iterative method for solving nonlinear
equations. Let f : R → R be a function and α a root of the equation f (x) = 0, that is f (α) = 0. It is
known that if f 0 (α) 6= 0, x0 is sufficiently close to α and under some conditions, the classical Newton’s
method defined by
(1)
xn+1 = xn −
f (xn )
,
f 0 (xn )
n = 0, 1, 2, . . .
generates a sequence {xn }∞
n=0 that converges to α.
The mapping
Φ(x) = x −
(2)
f (x)
f 0 (x)
is called the Iteration Function (abbrev. I. F.) [9] of the method defined by (1).
It is known that Newton’s method converges quadratically in a sufficiently small neighborhood of
the root α.
The fractal pictures of the basins of attraction generated by Newton’s method for complex
polynomials are well known [2,3,5,7,8,10].
A new third-order newton-type iterative method for solving nonlinear equations we introduce in
[1].
In this paper we present graphical representations for the basins of attraction of real roots for two
examples of nonlinear equations and two Newton-type methods.
1.2. The basin of attraction and sample methods and equations. Let f : [a, b] → R be a
function and α a root of the equation f (x) = 0, that is f (α) = 0, α ∈ [a, b] and let x0 ∈ [a, b].
If starting from x0 the sequence generated by the iterative relation (1) converges to α then we say
that x0 is attracted to α.
The basin of attraction of the root α is the set of all starting points x0 ∈ [a, b] which are attracted
to α.
To show the graphical view of the basins of attraction, we considered the classical Newton’s method
defined by the relation (1) and the harmonic mean Newton’s method [4,6] defined by
(3)
xn+1 = xn −
f (xn )(f 0 (xn ) + f 0 (yn ))
,
2f 0 (xn )f 0 (yn )
n = 0, 1, 2, . . .
n)
where yn = xn − ff0(x
(xn ) ,
and two nonlinear equations f1 (x) = 0 and f2 (x) = 0 , where
(4)
f1 : [−8, 8] → R, f1 (x) = 2xsinx − 2
(5)
f2 : [−1, 3] → R, f2 (x) = x4 − 4x3 + 6x2 − 4x
The roots of the equation f1 (x) = 0 in the interval I1 = [−8, 8] are α1 ≈ −6.439, α2 ≈ −2.773,
α3 ≈ −1.114, α4 ≈ 1.114, α5 ≈ 2.773 and α6 ≈ 6.439, and the roots of the equation f2 (x) = 0 in the
interval I2 = [−1, 3] are β1 = 0 and β2 = 2.
We present two versions for graphical view of the basins of attraction.
56
1.3. Graphical views of the basins of attraction. a) The ”sinusoidal” model for the basins
of attraction
To generate, for example, the basins of attraction for the roots of the equation f1 (x) = 0 on the
interval I1 = [−8, 8] using classical Newton’s method, we divide the interval I1 into n+1equidistant
points {ti }ni=0 (in this case n = 500, t0 = −8 and t500 = 8). We solve the equation (4), by using
classical Newton’s method, starting from each point {ti }ni=0 .
If ti attempts a root α of the equation, α ∈ I1 ,with a tolerance ε = 10−5 in a maximum of 14
iterations, then we draw a line between the points (ti , 0) and (ti , f1 (ti ) in a color associated to the
root α.
Nothing to draw if ti is not attracted by any root α ∈ I1 . So, the white regions means that here
the method does not converges to any root in I1 .
Figure 1.”Sinusoidal” view for Newton’s method and the equation f1 (x) = 0
In the Figure 1, we can see that some values are not attracted by the nearest root. We say that
these are out of the base basin of attraction of any root in the interval I1 . If we denote B(α) to be
the basin of attraction of the root α, then we define the base basin of attraction B ∗ (α) to be the
largest open interval such that α ∈ B ∗ (α) ⊆ B(α). As one can see in Figure 1, from starting point
x0 = −7.712 the next point is x1 = Φ(x0 ) = −4.254 and then x2 = Φ(x1 ) = −1.547. Because x2 is in
the base basin of α3 ≈ −1.114 it results that x0 ∈ B(α3 ). (Geometrically, the tangent in(x0 , f1 (x0 ))
intercept Ox axes in x1 and the tangent in(x1 , f1 (x1 )) intercept Ox axes in x2 ).
To generate the basins of attraction we used Mathcad 14.0 package.
b) The”bars” model for the basins of attraction
To generate, for example, the basins of attraction for the roots of the equation f1 (x) = 0 on the
interval I1 = [−8, 8] using classical Newton’s method, we divide the interval I1 into n+1 equidistant
points {ti }ni=0 (n = 500). We solve the equation (4), by using classical Newton’s method, starting from
each point {ti }ni=0 . If ti attempts a root α of the equation, α ∈ I1 ,with a tolerance ε = 10−5 in k ≤ 14
iterations then we draw in ti a vertical bar with height equal to k and in a color associated to the root
α.
If ti is not attracted by any root α ∈ I1 , then we draw at ti a red bar under the Ox axes.
In fact, in this case, ti is attracted by a root out of the interval I1 (the equation f1 (x) = 0 has an
infinity of roots!).
57
Figure 2 .”Bars” view for Newton’s method and the equation f1 (x) = 0
This kind of representation is more relevant as the ”sinusoidal” one because it shows us the number
of iterations. So, using this representation for the basins of attraction, we can compare some iterative
methods for solving nonlinear equations.
1.4. Conclusions. Our graphical representations allow us to see the behavior of iterative methods
for solving nonlinear equations and compare them.
Bibliography
[1] G. Ardelean, A new third-order newton-type iterative method for solving nonlinear equations, Appl. Math. and
Comp., 219 (2013) 9856–9864.
[2] G. Ardelean, A comparison between iterative methods by using the basins of attraction, Appl. Math. and Comp., 218
(2011) 88–95.
[3] B. Kalantari, Polinomiography and applications in art, education and science, Computers&Graphics, 28 (2004)
417–430.
[4] H.H.H. Homeier, On Newton-type methods with cubic convergence, J. Comp. Appl. Math., 176 (2005) 425–432.
[5] Şt. Măruşter, Numerical experiments on attraction basins, Annals Computer Science Series, 2nd Tome 1st Fasc.,
(2004) 167–171.
[6] A. Y. Ozban, Some new variant of Newton’s Method, Appl. Math. Lett., 17 (2004) 677–682.
[7] M. L. Sahari, I. Djellit, Fractal Newton basins, Discrete Dynamics in Nature and Society (2006) Article ID 28756.
[8] H. Susanto, N. Karjanto, Newton’s method basin of attraction revisited, Appl. Math. and Comp., 215 (2009)
1084–1090.
[9] J. F. Traub, Iterative Methods for the Solution of Equations, Chelsea publishing company, New York, 1997.
[10] J. L. Varona, Graphic and numerical comparison between iterative methods, Math. Intell., 24 (2002) 37–46.
ICAM9
58
Agneta M. Balint1 and Ştefan Balint2
1 Physics
Faculty West University of Timişoara, Romania
2 Mathematics
and Computer Science Faculty, West University of Timişoara, Romania
balint@physics.uvt.ro, balint@balint.uvt.ro
Abstract. The purpose of this paper is to replace Brambley’s concept of ”well posed differential equation”
[1] related to the source produced acoustic perturbation propagation in a rectangular lined duct carrying
a gas flow with that of ”well posed problem in Hadamard sense”. The reason is that the concept
introduced by Brambley is confusing, i.e. the same equation can be well posed or ill posed depending on
the functional framework. For the source produced acoustic perturbation (SPAP) propagation problem
the concept of ”well posed problem in Hadamard sense” is defined as follows: for any SPAP, from a given
set of SPAP-s, there exists a unique solution to the problem of propagation and the solution depends
continuously on the SPAP. Necessary and sufficient conditions are derived for that the propagation
problem be well posed in sense of Hadamard.
1.1. Introduction. In the context of a large number of published results concerning acoustic
perturbation propagation in a lined duct carrying a gas flow, in this section the mathematical
considerations made in this paper are motivated.
1.2. Preliminary results. The propagation problem of the SPAP (described by the functions
F (x, y, t), G(x, y, t), H(x, y, t)) is: find u0 (x, y, t), v 0 (x, y, t), p0 (x, y, t) which satisfy equations
∂u0
dU0
1 ∂p0
∂u0
+ U0 (y) ·
+ v0 ·
+
·
= F (x, y, t)
∂t
∂x
dy
ρ0 ∂x
0
0
0
∂v
∂v
1 ∂p
+ U0 (y) ·
+
·
= G(x, y, t)
∂t
∂x
ρ0 ∂y
∂p0
∂u0
∂v 0
∂p0
+ γ · p0 ·
+ γ · p0 ·
+ U0 (y) ·
= H(x, y, t)
∂t
∂x
∂y
∂x
(1)
boundary conditions
∂ 2v0
∂v 0
∂p0
0
+
b
·
+
c
·
v
=
∓
f or y = −h
∂t2
∂t
∂t
and ”initial” condition:
(2)
(3)
a·
u0 (x, y, t) = 0
v 0 (x, y, t) = 0
p0 (x, y, t) = 0
and y = h
f or any t negative
Definition. Following the usage of Hadamard, we will say that the propagation problem (1), (2), (3)
is well set if:
(i) for any SPAP from a given class of SPAP-s, there is a unique solution to the problem;
(ii) the solution varies continuously with the SPAP.
The mathematical treatment of the propagation problem (1), (2), (3) in this paper is made under the
following assumptions :
I. the set B of SPAP-s is that of the functions which satisfy :
1. are identically equal to zero for t non positive,
2. are bounded and infinitely differentiable
3. for any t fixed the functions have compact support with respect to the spatial variables x,y and
their support is included in Ω = (−∞, +∞) × (−h, h) .
II. the solution of the problem (1), (2), (3) (if exists) belongs to the set S of system of functions
0
0
0
0
0
0
u = u (x, y, t), v = v (x, y, t), p = p (x, y, t) which are continuously differentiable and rapidly
decreasing with respect to x .
Under the above assumptions the magnitude of a SPAP from B at the moment of time t can be
evaluated by k F (◦, ◦, t) k = sup sup |F (x, y, t) | and so on;
x∈R0 y∈[−h,h]
59
and the magnitude of the corresponding solution (if exists) at the moment of time t can be evaluated
by k u0 (◦, ◦, t) k = sup sup | u0 (x, y, t) | and so on.
x∈R0 y∈[−h,h]
1.3. Existence, uniqueness and continuity. The following result holds:
Proposition 3.1. If for an SPAP from B the following conditions hold:
0
0
0
0
0
(i) the propagation problem (1) ,(2) ,(3) has a solution u = u (x, y, t), v = v (x, y, t), p =
0
p (x, y, t) in S .
(ii) for any (x, y) ∈ (−∞, +∞) × [−h, h] the solution possesses Laplace transform Lt with respect
to t
(iii) the Fourier transform with respect to x, Fx , of the solution commutes with its Laplace
0
0
transform, Lt , i.e. u (α, y, ω) = Fx ◦ Lt · u (x, y, t) = Lt ◦ Fx · u (x, y, t) and so on,
then there exists a real number µ such that for any α ∈ R0 and any ω ∈ C with Im ω > µ for the
Fx ◦ Lt transforms u (α, y, ω), v (α, y, ω), p (α, y, ω) (of the solution) the following equalities hold:
(4)
"
#
d2 p
2α
dU0 dp
(ω−α · U0 (y))2
2
+
·
· +
−α · p = i·ρ0 ·α· F̄ (α, y, ω)+
dy 2 ω−α·U0 (y) dy dy
c20
dU0
dḠ i (ω−α · U0 (y))
2·ρ0 ·α
·
· Ḡ (α, y, ω)+ρ0 ·
+
· H̄ (α, y, ω)
+
ω−α·U0 (y) dy
dy
c20
(5)
α
1
dU0 dp
· p (α, y, ω) −
· +
·
2
ρ0 (ω − α · U0 (y))
dy dy
ρ0 (ω − α · U0 (y))
i
1
dU0
+
· F̄ (α, y, ω) +
2 · dy · Ḡ (α, y, ω)
ω − α · U0 (y)
(ω − α · U0 (y))
u (α, y, ω) =
(6)
v (α, y, ω) = −
i
dp
i
·
+
· Ḡ (α, y, ω)
ρ0 (ω − α · U0 (y)) dy ω − α · U0 (y)
v (α, ∓h, ω) = ∓
(7)
1
· p (α, ∓h, ω)
Z (ω)
Here: ω = i · z and z is the Lt transform variable; α is the Fx transform variable; F̄ (α, y, ω),
c
Ḡ (α, y, ω), H̄ (α, y, ω) are the Fx ◦ Lt transforms of the SPAP (F, G, H); Z (ω) = −a · i · ω + b −
i·ω
is the wall impedance.
Proposition 3.2. If there exists a real number µ such that for α ∈ R0 and ω ∈ C with Im ω > µ the
boundary value problem:
(8)
"
#
d2 p
2α
dU0 dp
(ω − α · U0 (y))2
+
·
·
+
− α2 · p = 0
dy 2 ω − α · U0 (y) dy dy
c20
i · ρ0 · ω · p (α, ∓h, ω) ± Z (ω) ·
(9)
dp
(α, ∓h, ω) = 0
dy
possesses only the zero solution, then if exists a solution to the problem of propagation (1), (2), (3)
having the properties i), ii), iii) (from Proposition 3.1), it is unique.
Proposition 3.3. If the set of the imaginary parts Imω of the zero’s ω of the dispersion relations is
bounded from above by µ, then the B.V.P. (4), (9) has a unique solution given by:
Z
(10)
h
p (α, y, ω) =
I y, y 0 ; α, ω · f α, y 0 , ω dy 0
−h
(α, y 0 , ω)
where: f
the right hand member of (4); I (y, y 0 ; α, ω) is the Green’s function defined for
0
y ∈ [−h, h], y ∈ [−h, h], α ∈ R0 , ω ∈ C with Im ω > µ , by the formula:
60
(11)

[ω − α · U0 (0)] 2


· p1 α, y 0 , ω · p2 (α, y, ω)

E0 (α, ω)
I y, y 0 ; α, ω =

[ω
−
α · U0 (0)] 2


· p1 (α, y, ω) · p2 α, y 0 , ω
E0 (α, ω)
f or
− h ≤ y0 ≤ y ≤ h
f or
− h ≤ y ≤ y0 ≤ h
with:
dp2
dp1
(α, 0, ω) − p2 (α, 0, ω) ·
(α, 0, ω)
dy
dy
and p1 (α, y, ω), p2 (α, y, ω) are solutions of the eq. (8) which satisfy the conditions:
(12)
(13)
(14)
E0 (α, ω) = p1 (α, 0, ω) ·
p1 (α, −h, ω) = 1 and
p2 (α, h, ω) = 1 and
dp1
i · ρ0 · ω
(α, −h, ω) = −
dy
Z (ω)
dp2
i · ρ0 · ω
(α, h, ω) =
dy
Z (ω)
respectively.
Proposition 3.4. If the set of the imaginary parts Im ω of the zero’s ωof the dispersion relations is
bounded from above by a real number µ and the Green function satisfies
(15)
I y, y 0 ; α, ω ≤ | P (α) |
(16)
ω · I y, y 0 ; α, ω → 0 f or
α ∈ R0 and Im ω > µ
| ω | → ∞ and Im ω > µ
then for every SPAP (F, G, H) from B, the propagation problem (1), (2), (3) has a unique solution
having the properties i), ii), iii).
1.4. Acknowledgement. This work was supported by a grant of the Romanian National Authority for Scientific Research, CNCS-UEFISCDI, project number PN-II-ID-PCE-2011-3-0171.
Bibliography
[1] Brambley, E. J., Fundamental problems with the model of uniform flow over acoustic liner, J. Sound and Vibrations,
322 (2009) 1026-1037
ICAM9
61
Štefan Berežný
Department of Mathematics and Theoretical Informatics, Faculty of Electrical Engineering and Informatics, Technical University of Košice,
Košice, Slovak Republic
Stefan.Berezny@tuke.sk
Abstract. The paper describes a generalized algorithm, which describes the simulation of winter maintenance of airports. It is a model of the winter maintenance of airport motion areas. Purpose of this
algorithm is a simulation of snow cover at the airport movement areas with respect at varying weather
conditions. This algorithm was created, based on the data and algorithms that have been developed for
Košice airport. The result of this work is a flowchart of the algorithm, according to which it is possible
to create a program that can simulate winter maintenance of motion areas on any airport with respect
to the initial limitations.
1.1. Introduction. First algorithm which generalizes given problem of winter maintenance was
published in [2]. This algorithm generalizes the algorithm, which was published in the proceedings
[1]. The basic scheme was published in the work [3], that used the methodology of work [6]. Basic
parameters used for Košice airport are included in the work [5]. Optimization operations of winter
maintenance was published in the journal [4].
1.2. The inputs of the algorithm. The main difference generalization of this algorithm is that
the model can be used universally on almost any airport and not just the particular specified airfields
of airports. Input data for the algorithm are represented by basic parameters:
Parameters airport:
Runway
j ∈ {1, . . . , k1 }
PjR = WjR × LR
j
Taxiway
j ∈ {1, . . . , k2 }
PjT = WjT × LTj
Connecting roads
j ∈ {1, . . . , k3 }
PjC = WjC × LC
j
Apron
j ∈ {1, . . . , k4 }
PjA = WjA × LA
j
Parameters and variables of the
Name
Type
HSC
Matrix of real numbers
ISnow
Series of real numbers
CHSnow
Etime
Etimex
QSnow
HSnow
MP
Timer
CCSc
NSc
N
SSnow
hr
min
k1
k2
k3
k4
Wjx
Lxj
algorithm:
Description
Snow depth at defined parts of the airfields
Intensity of snow
Current snow depth
Estimated time of clean-up airfields
Estimated time of clean-up airfield x of the airport,
where x ∈ {R, T, C, A}
Quality of snow
Real number
Snow depth obtained from the sensor
The performance of the mechanization means
Integer
Timer clock
Integer
Current cleaned of aerodrome surface
Integer
Number of aerodrome surface
Integer
Number of dividing the movement area of the airport
Real number
Amount of snow
Integer
Hour
Integer
Minute
Integer
Number of runways
Integer
Number of taxiways
Integer
Number of connecting roads
Integer
Number of aprons
Real number
Width of the airfield x, where
x ∈ {R, T, C, A}
Real number
Length of the airfield x, where
62
Pjx
Real number
StartT imex Integer
x ∈ {R, T, C, A}
Surface area of the airfield x, where
x ∈ {R, T, C, A}
Starting time: Number of time cycle, in which
began winter maintenance of airfields x, where
x ∈ {R, T, C, A}
1.3. The outputs of the algorithm. Estimated Time of clean-up the airport movement area
x ∈ {R, T, C, A} is given by:
(QSnow · CHSnow · P x · 0.01)
MP
The total estimate of the time of clean-up the aerodrome movement area of airport is given by:
1
x
x
Etime :=
max
· StartT ime + ET ime
x∈{R,T,C,A} 6
ET imax :=
Parameters and variables are updated in ten minute intervals. Snow depth due to the intensity
of snowfall and running of cleaning airfields is updated. Based on these changes of variables, the
expected time of completion of maintenance of airport movement areas is modified.
Based on the well-established schema of algorithm for processes of winter maintenance would be
created realistic simulator of these processes and software solutions for winter maintenance. Such
realistic simulator would be provide timely and properly respond to the situation and minimize
catastrophe risk in aviation safety at the airport, which are associated with closing the airport or the
event of poor maintenance of airport runway.
Bibliography
[1] BEREŽNÝ Štefan: Algorithms of Processes of the Winter Maintenance on Koice Airport, In: MOSATT 2011: proceedings of the International Scientific Conference Modern Safety Technologies in Transportation: 20. - 22.September
2011, Zlat Idka, Slovakia - Koice: Suprema Ltd, 2011 S. 24-29. - ISBN 978-80-970772-0-4 - ISSN 1338-5232.
[2] BEREŽNÝ Štefan: Generalized Algorithm of Processes of the Winter Maintenance on Košice Airport, In: ICAM8:
Proceedings of the International Conference of Applied Mathematics: October 27-30, 2011, Baia Mare – Romania
[3] KLAČANSKÝ Matúš: Mathematical Model Design of Simulation of 24-hours Cycle of Maintenance of Airport Area,
Bachelor thesis, Koice, Technical University of Koice, Faculty of Electrical Engineering and Informatics, Slovak
Republic, 2011, 36 p.
[4] KOŠČÁK Peter BEREŽNÝ Štefan - FERENC Ján: Optimization operations of winter maintenance of airport, In:
International Journal of Traffic and Transportation Engineering. Vol. 1, no. 3 ,(2012), p. 40-45. - ISSN 2325-0062
[5] KOŠČÁK Peter BEREŽNÝ Štefan: Optimal Attaching Means Winter Maintenance of Airport, Proceeding of The
9th International Scientific Conference: New Trends in Aviation Development, Gerlachov High Tatras, September
16. - 17. 2010, Slovak Republic, ISBN: 978-80-555-0475-5.
[6] PŠENČÍKOVÁ Jana: Algoritmizace, Computer Media s. r. o., Czech Republic, 2009, 128 p. ISBN: 978-80-7402-34-6
ICAM9
63
Tamás Bérczes1 , Attila Kuki1 , Béla Almási1 , János Sztrik1 and Pascal Moyal2
1 Department
2 Universite
of Informatics Systems and Networks at the Faculty of Informatics, University of Debrecen, Hungary
de Technologie de Compiegne, Compiegne, France
berczes.tamas@inf.unideb.hu; kuki@inf.unideb.hu; almasi.bela@inf.unideb.hu; sztrik.janos@inf.unideb.hu, pascal.moyal@utc.fr
Abstract.This paper deals with unreliable systems, where the performance of the system can be experienced in different levels of health between the perfect and the failed states.
The underlying model is a single server retrial queue with a finite number of homogeneous sources of
requests and a single non-reliable server. The server is subject to random deteriorations and breakdowns
depending on whether it is busy or idle. The operations of the system might be blocked or unblocked
by the failure of the server and the service of the interrupted request may be resumed or the request
can be transmitted to the orbit. All random variables involved in the model constructions are supposed
to be exponentially distributed and totally independent of each other.
The novelty of the investigation is the levels of goodness of a system in case of finite sources of
requests. The transitions of states of the server depend on its working status (ie., busy or idle), which
makes the system rather complicated. The MOSEL-2 tool was used to formulate and solve the problem.
The main performance and reliability measures were calculated.
1.1. Introduction. Retrial queues have been widely investigated and used to model many
problems arising in telephone switching systems, telecommunication networks, computer networks,
optical networks, etc. The main characteristic of a retrial queue is that a customer who finds the
service facility busy upon arrival is obliged to leave the service area, but some time later he comes
back to re-initiate his demand. Between the trials a customer is said to be in the orbit. The literature
on retrial queueing systems is very extensive. For a recent account, readers may refer to the recent
books of Falin and Templeton [1], Artalejo and Gomez-Corral [7] that summarize the main models
and methods. Since in practice some components of the systems are subject to random breakdowns
(see for example [2], [3],[4]) it is basically importan to study the reliability of retrial queues with server
breakdowns and repairs because of limited ability of repairs and heavy influence of the breakdowns on
the performance measures of the system. However, so far the repairable retrial queues were analyzed
only in the case when the server could be in two states: operable or failed. For related literature the
reader is referred to the works [5], [6] where infinite-source non-reliable retrial queues were treated.
In general, systems used in industries always suffer from stochastical deterioration and may undergo
many deteriorating states before failure.
In this paper, a finite-source system is investigated with the following assumptions. Consider a
single server queueing system, where the primary calls are generated by K, 1 < K < ∞ homogeneous
sources. We assume that the system deterioration condition can be described by a finite number of
levels 1, 2.., m + 1. Level 1 denotes the best health condition meaning that the system is as good as a
new one, while m denotes the most deteriorated condition. Finally, m + 1 indicates that the system
has failed.
The server can be in three states:
• idle state: The server level is between 1..m and the server can start serving the arriving
requests.
• busy state: The server is in busy state, when the server is in available state (the server level
is between 1..m) and one request is under service.
• failed state: The server is in failed state, when the server level is m + 1. It can not start
serving any arriving requests until it is repaired.
We assume, that the service times are exponential distributed with parameters µ1 ,· · · ,µm , corresponding to server levels 1,· · · ,m
If a source is free at time t, it can generate a primary call during interval (t, t + dt) with probability
λdt + o(dt). If the server is idle at the time of arrival of a call, then the servive of the call starts
immediately, the source moves into the under service state and the server moves into busy state. The
service is finished during the interval (t, t + dt) with probability µi dt + o(td), i = 1..m, according to the
server level. If the server is busy, then the source starts generation of a Poisson flow of repeated calls
with rate ν until it finds the server idle. After service the source becomes free, and it can generate a
64
new primary call, and the server becomes idle so it can serve a new call. The server can step into the
next level during the interval (t, t + dt) with probability δdt + o(dt) if it is idle, and with probability
γdt + o(dt) if it is busy. If δ = 0, γ > 0 or δ = γ > 0 active or independent breakdowns can be
discussed, respectively. If the server step reaches the level m + 1, that is the server is failed, two
different cases can be treated. The first one is the blocked sources case, when all the operations are
stopped, that is no new calls are generated. The second one is the unblocked sources case, when only
the service is interrupted but all the other operations are continued. In this paper we investigate only
the unblocked sources case. If the server fails in a busy state, the interrupted request returns to the
sources. The repair times are exponentially distributed with a finite mean 1/τ . All the times involved
in the model are assumed to be mutually independent of each other.
Because of the fact, that the state space of the describing Markov chain is very large, it is rather
difficult to calculate the system measures in the traditional way of writing down and solving the
underlying steady-state equations. To simplify this procedure we used the software tool MOSEL
(Modeling, Specification and Evaluation Language), see Begail et al. [8], to formulate the model and
to obtain the performance measures.
1.2. The M/M/1//K retrial queueing model with multi-state unreliable server. To
maintain theoretical manageability, the distributions of inter-event times (i.e., request generation
time, service time, retrial time, available state time, failed state time) presented in the network are by
assumption exponential and totally independent.
We introduce the following notations:
• y(t) represents the server states at time t, y(t) = 1 · · · m if the server is up with the
corresponding service rates µ1 ,· · · ,µm and y(t) = m + 1 if the server is failed.
• c(t) = 0 if the server is idle, c(t) = 1 if the server is busy
• o(t) is the number of jobs in the orbit at time t.
The system state at a time t corresponds to a Continuous Time Markov Chain (CTMC) with 3
dimensions:
X(t) = (y(t); c(t); o(t))
The steady-state distributions are denoted by
P (y; c; o) = lim P (y(t) = q, c(t) = r, o(t) = j),
q = 1..m + 1,
t→∞
r = 0, 1,
j = 0, ..., K − 1.
Note, that the state space of this Continuous Time Markovian Chain is finite, so the steady-state
probabilities surely exist. For computing the steady-state probabilities and the system characteristics,
we use the MOSEL software tool in this paper.
As soon as we have calculated the distributions defined above, the most important steady-state
system characteristics can be obtained in the following way:
• Utilization of the server
US =
m K−1
X
X
P (y, 1, o)
y=1 o=0
• Availability of the server
AS =
m X
1 K−1
X
X
P (y, c, o)
y=1 c=0 o=0
• Average number of jobs in the orbit
O = E(o(t)) =
=
m+1
1 X
K
XX
y=1 c=0 o=0
oP (y, c, o)
65
• The mean number of calls staying in the orbit or in service
M = E[o(t) + c(t)] = O +
m+1
X K−1
X
P (q, 1, j).
q=1 o=0
• The mean rate of generation of primary calls
(
λE[K − c(t) − o(t); y(t)in(1, .., m)],
λ=
λE[K − c(t) − o(t)],
• The mean response time
for blocked case,
for unblocked case.
E[T ] = M/λ.
• The mean waiting time
E[W ] = N/λ.
Acknowledgment. The publication was supported by the TÁMOP-4.2.2.C-11/1/KONV-20120001 project. The project has been supported by the European Union, co-financed by the European
Social Fund. The research was also supported by the European Union with the help of the GOP-1.3.208-2009-0007 program.
This research was partially granted by the Hungarian Science and Technology Foundation, HungarianFrench Bilateral Cooperation under grant TeT 10-1- 2011-0741, FR- 25/2010. The work of János
Sztrik was realized in the frames of TÁMOP 4.2.4. A/2-11-1-2012-0001 National Excellence Program Elaborating and operating an inland student and researcher personal support system. The project
was subsidized by the European Union and co-financed by the European Social Fund.
The work of Tamás Bérczes was realized in the frames of TÁMOP 4.2.4. A/2-11-1-2012-0001 National
Excellence Program Elaborating and operating an inland student and researcher personal support
system The project was subsidized by the European Union and co-financed by the European Social
Fund.
Bibliography
[1] Falin G.I. and Templeton J.G.C. Retrial queues, Chapman and Hall, London, 1997.
[2] Kovalenko I.N., Kuznetsov N.Yu. and Pegg P.A. Mathematical theory of reliability of time dependent systems with
practical applications, John Wiley and Sons, Chichester, 1997.
[3] Ravichandran N. Stochastic methods in reliability theory, John Wiley and Sons, New York, 1990.
[4] Trivedi K. S. Probability and statistics with reliability, queueing and computer science applications, Prentice-Hall,
Englewood Cliffs, 1982.
[5] Artalejo J.R. New results in retrial queueing systems with breakdown of the servers, Statistica Neerlandica 48(1994),
23–36.
[6] Aissani A. and Artalejo J. R. On the single server retrial queue subject to breakdowns, Queueing Systems Theory
and Applications 30(1998), 309–321.
[7] Artalejo, J.R. and Gomez-Corral, A. Information theoretic analysis for queueing systems with quasi-random input,
Mathematical and Computer Modelling 22(1995) 65–76.
[8] Begain K., Bolch G. and Herold H. Practical performance modeling, application of the MOSEL language, Kluwer
Academic Publisher, Boston, 2001.
ICAM9
66
Graţiela Dana Boca
Technical University of Cluj Napoca, North Unversity Center of Baia Mare, Romania
bocagratiela@yahoo.com
Abstract.The present work shows some of the typical computational tools and algorithms which are
often applied in industrial optimization.
The industry usually has existing CAD and CAE procedures that can handle large-scale finite
element calculations for complex geometries. Structural optimization using TOSCA structure helps to
find optimized design proposals in a very early phase of the product development cycle and dramatically
reduces the overall development costs and time. In the industry structural calculations is often done by
finite element modeling. Normally, the degrees freedom of the finite element models is constrained by
the capacity of computer power available for solving the model. Frequently, an industrial designer will
also prefer to use his daily preprocessor for constructing the finite element models for the optimization.
The purpose of the present paper is to show that optimization allows to be conducted in an already
existing CAD flow for large-scale models having a high number of degrees freedom, a realistic geometry
and boundary conditions, which finally can be done in an earlier faze of design product which assure
the robustness reliability of product.
1.1. Introduction. The general Robust Optimization formulation is:
(
Minimize f0 (x)
Subject to fi (x; ui ) ≤ 0; ∀ui ∈ Ui ; i = 1 . . . m (1)
here x ∈ Rn is a vector of decision variables, f0 , fi are as before, ui are disturbance vectors or
parameter uncertainties, and Ui are uncertainty sets, which, for our purposes, will always be closed.
By introducing a new constraint if necessary, we can always take the objective function to have
no uncertainty. The goal of (1) is to compute minimum cost solutions x among all those solutions
which are feasible for all realizations of the disturbances ui within Ui . If Ui is a singleton, then the
corresponding constraint has no uncertainty. Intuitively, this problem offers some measure of feasibility,
protection for optimization problems containing parameters which are not known exactly.
Frequently, an industrial designer will prefer to use his daily preprocessor for constructing the
finite element models for the optimization. Normally, the degrees freedom of the finite element models
is constrained by the capacity of computer power available for solving the model. The purpose of the
present paper is to show that non-parametric optimization allows the optimization to be conducted
in an already existing CAD flow for large-scale models having a high number of degrees freedom, a
realistic geometry and boundary conditions. This also allows an efficient handling of the definition of
the optimization problem. Following the total quality management we must to start from the data and
information, especially for our industry which still uses old generation machine and tools. The quality
is the only factor who can assure the top market competition and also the customers expectation.
FE DESIGN - proven partner for industrial manufacturers and suppliers.
Demands for state of-the -art product development are stronger than ever. Nowadays all industries are
subject to accelerating changes in production and development and increasing aggressive competition.
Complex demands can be fulfilled by applying simulation and optimization technologies in a virtual
product developing process. The use of structural optimization in the early design phase leads to
optimal design proposal that eliminate the need to perform numerous design variations.
The FE DESIGN approach goes beyond the usual analysis of single engineering problems. Therefore
customers are able to make better product development decisions in the earlier design phase using a
multi-disciplinary approach which includes the combination of static and dynamic FE analyses with
simulation, with durability analyses, or calculation with life cycle predictions. Using existing CAE
solvers for solving optimization problems is essential in the industry. It ensures that the important
know-how regarding the CAE-solvers and their results are reserved in the optimization computations.
Additionally, standard pre and post-processors can be used in the optimization process. Figure 1. The
virtual simulation of product can be done to different torques and materials and factors which can
present the future work activity and work condition considering the real parameters from industry.
67
Figure 1 Optimization added to an existing CAD and CAE workflow [6]
Modeling and design quality product.
Having the solutions a specialist will consider the results as a suggestion for a future optimize of flank
profile of the teeth a problem which can be solve with the help of TOSCA program, by using the
similar mathematical model realize with the FEM method who is consider the base of data.
In this way we can discover earlier the possible factors and the parameters which can improve
the quality. That solution brings benefits from economical point of view, material; reduce the cost,
increasing the quality and the optimization of technological process. The present work shows some of
the typical computational tools and algorithms which are often applied in industrial optimization.
The industry usually has existing CAD and CAE procedures that can handle large-scale finite element
calculations for complex geometries.
Structural optimization using TOSCA Structure helps to find optimized design proposals in a very
early phase of the product development cycle and dramatically reduces the overall development costs
and time. In the industry structural calculations is often done by finite element modeling. Element
groups, node groups, sets, property numbers and/or material numbers defined in your preferred
CAE preprocessor can directly be applied in optimization solutions, discussing and distributing 3D
optimization results without restraints using freely distributed 3D plug-in viewer and post processing
of optimization results in personal preferred. Normally, the degrees freedom of the finite element
models is constrained by the capacity of computer power available for solving the model. Frequently,
an industrial designer will also prefer to use his daily preprocessor for constructing the finite element
models for the optimization. The purpose of the present paper is to show that optimization allows to
be conducted in an already existing CAD flow for large-scale models having a high number of degrees
freedom, a realistic geometry and boundary conditions, which finally can be done in an earlier faze of
design product which assure the robustness reliability of product
1.2. Conclusion. The rapid development of models or prototypes may largely reduce the development cost and the product development cycle. Since it is based on technological changes or
improvements, the development of such models or prototypes is usually conducted by technologist,
who has no regard for the cost of such a development.
Using the new programs as ANSYS, TOSCA, FEMFAT, the future for quality product it is a reality,
in this way we can improve quality from the first stage of life cycle of the product. Each individual
issue requires typically dedicated analyses and modeling tools, which leads to the introduction of
various fields of application and corresponding domain and research. The use of structural robust
optimization tools in the early stage of the development process offers new potential in the process
chain. This method in design product will help customers to: make early decision in the design cycle,
reduce the product development cycle, improve time-to market and reduce design and manufacturing
cost: reduce design cycle, reduce cost of materials, reduce number of prototypes and physical testes.
The algorithm identify the life cycle of the product design and the evolution of specific elements which
68
can influence the robust design of the product but the economical and trust solution it is the FE
solution, which mean reduce costs, robust design from the first stage of product design.
The benefits are: fast improvement of existing FE models, reduction of stress calculation, increase
durability, no need to run nonlinear analysis after optimization, robust reliability, practical conceptual
designing for weight reduction considering manufacturing constraints → material savings
- fast conceptual designing for Eigen frequency optimization → sound reduction and avoiding
frequency interactions
- reliable conceptual designing considering different structural constraints in each load case →
feasible design for several load scenarios without time consuming trial and error process
- combined conceptual designing for both static and dynamic properties → obtaining new
design which is not intuitive
- straightforward maximal stress reduction for complex surfaces and geometries → increasing
life-span
- increase of durability using shape optimization → fatigue resistant design
- combined stress reduction and increase of durability → design fulfilling misuse load cases
and long life excitations
- general reduction of the development time and development cycles → cost saving
The equation of flexibility and knowledge product can be written in function of following variables
for our improvement product matrix were: Qp represent quality perception, Qa = quality action, Qd =
quality decision, Pq ,-quality perception , Pa -action perception, Pp - precision perception, T -technology,
M -man, manufacture power, A-affect variable.
(1)
EKP = f (Qp , Qa , Qd , Pq , Pa , Pd , T, M, A)
Bibliography
[1] Albers, A. and Weiler, H., (2009) Impact of Distribution Functions of Input Parameters on the Quality of Robustness
Analysis in Simulation. Nafems Seminar: VIRTUAL TESTING, Simulations verfahren als integrierter Baustein einer
effizienten Produktentwicklung, 10-11.05.06, Wiesbaden, ISBN 1-874376-14-X
[2] Bangert, C.and Jiang, J.(2006), Optimization and robustness analysis with deep drawing simulation, INPRO Workshop
”Robust Processes with Modern Steels”, Berlin
[3] Bendsoe, M.P. and Sigmund, O.(2003), Topology optimization: Theory, Methods and Applications. Springer-Verlag,
Berlin Heidelberg New York
[4] Emmrich, E., (2004), Entwicklung einer FEM-basierten Methode zur Gesaltung von Sicken fr biegebeanspruchte Leitsttzstrukturen im Konstruktionsprozess, Forschungsberichte des Instituts fr Produktentwicklung, Band 13, Karlsruhe
[5] W. Huber, W., Fischer and M. and Himmler, G., ( 2003), Stress Reduction in an Inter stage Air Seal using TOSCA
(MSC.Construct) for Increasing the LCF Fatigue Life, MSC Virtual Product Development Conference, Bad Neuenahr
[6] Pedersen, C.B.W. and Allinger, P., (2005), Recent Developments in the Commercial Implementation of Topology
Optimization, TopoptSYMP2005 - IUTAM-Symposium- Topological design optimization of structures, machines and
material status and perspectives, Copenhagen, Denmark, pp:123-132
ICAM9
69
Carstea Claudia1 , Sangeorzan Livia2
1 Departament
2 Faculty
of Informatics and Mathematic, George Bariţiu University from Braşov, Romania
of Mathematics and Computer Science, University Transilvania of Braşov, Romania
carstea.claudia@unitbv.ro; livia.sangeorzan@gmail.com
This paper deals with significant aspects of the process of making an evaluation system for the
information system project management and optimize the software with genetic algorithms. This
new era requires a new breed of software, service and support solutions. It is critical to be able to
visualize what is going on in your IT infrastructure and implement solutions that not only monitor,
but deliver proactive management capabilities. Over time, those elements have become dispersed and
distributed across wide networks. As the complexity of infrastructures increased, so did the need for
management software to handle this complexity, anticipate problems and resolve them before they
impact the business.
1.1. Introduction. The ESSENCE of mathematics is not to make simple things - complicated,
but making complicated things SIMPLE. In the computer science field of artificial intelligence, a genetic
algorithm (GA) is a search heuristic that mimics the process of natural selection. This heuristic is
routinely used to generate useful solutions to optimization and search problems. In a genetic algorithm,
a population of candidate solutions (called individuals, creatures, or phenotypes) to an optimization
problem is evolved toward better solutions. [2,15] Each candidate solution has a set of properties (its
chromosomes or genotype) which can be mutated and altered; traditionally, solutions are represented in
binary as strings of 0 s and 1s, but other encodings are also possible. The evolution usually starts from
a population of randomly generated individuals, and is an iterative process, with the population in
each iteration called a generation. In each generation, the fitness of every individual in the population
is evaluated; the fitness is usually the value of the objective function in the optimization problem
being solved.
Figure 1 Iterative cycle for genetics algorithms
The more fit individuals are stochastically selected from the current population, and each individual’s genome is modified (recombined and possibly randomly mutated) to form a new generation. [3]
The new generation of candidate solutions is then used in the next iteration of the algorithm. Commonly, the algorithm terminates when either a maximum number of generations has been produced, or
a satisfactory fitness level has been reached for the population. (Figure 1) A typical genetic algorithm
requires:
• a genetic representation of the solution domain,
• a fitness function to evaluate the solution domain.
1.2. Why Genetic Algorithms? Genetic algorithms tend to thrive in an environment in which
there is a very large set of candidate solutions and in which the search space is uneven and has many
hills and valleys. True, genetic algorithms will do well in any environment, but they will be greatly
outclassed by more situation specific algorithms in the simpler search spaces. Therefore you must
70
keep in mind that genetic algorithms are not always the best choice. Sometimes they can take quite a
while to run and are therefore not always feasible for real time use. They are, however, one of the
most powerful methods with which to (relatively) quickly create high quality solutions to a problem.
Now, before we start, I’m going to provide you with some key terms so that this article makes sense.
[7, 8, 11] Genetic algorithms are a very effective way of quickly finding a reasonable solution to a
complex problem. Granted they aren’t instantaneous, or even close, but they do an excellent job of
searching through a large and complex search space. Genetic algorithms are most effective in a search
space for which little is known. You may know exactly what you want a solution to do but have no
idea how you want it to go about doing it. This is where genetic algorithms thrive. They produce
solutions that solve the problem in ways you may never have even considered. Then again, they can
also produce solutions that only work within the test environment and flounder once you try to use
them in the real world. Put simply: use genetic algorithms for everything you cannot easily do with
another algorithm. (Figure 2)
Figure 2 GA concepts
Genetic algorithms were formally introduced in the United States in the 1970s by John Holland at
University of Michigan. The continuing price/performance improvements of computational systems
has made them attractive for some types of optimization. In particular, genetic algorithms work very
well on mixed (continuous and discrete), combinatorial problems. They are less susceptible to getting
stuck at local optima than gradient search methods. But they tend to be computationally expensive.
Genetic algorithms are one of the best ways to solve a problem for which little is known. They are a
very general algorithm and so will work well in any search space. All you need to know is what you
need the solution to be able to do well, and a genetic algorithm will be able to create a high quality
solution. Genetic algorithms use the principles of selection and evolution to produce several solutions
to a given problem. You have to remember that f and d functions depend by particularity of problem
to have resolve. (Figure 3)
Figure 3 Performance function
Some examples of Genetic Algorithm Software are:
GENOCOP III Genetic Algorithm for Constrained Problems in C (by Zbigniew Michalewicz)
DE Differential Evolution Genetic Algorithm in C and Matlab (by Rainer Storn). DE has won the
third place at the 1st International Contest on Evolutionary Computation on a real-valued function
testsuite
71
Figure 4 Activities Diagram
PGAPack - Parallel Genetic Algorithm in Fortran and C (from Argonne National Laboratory)
PIKAIA - Genetic algorithm in Fortran 77/90 (by Charbonneau, Knapp and Miller)
GAGA = Genetic Algorithm for General Application in C (by Ian Poole)
GAS Genetic Algorithm in C++ (by Jelasity and Dombi)
GAlib C++ Genetic Algorithm Library (by Matthew Wall)
GADS Genetic Algorithm and Direct Search Toolbox in
Matlab - (from MathWorks)
GEATbx - Genetic and Evolutionary Algorithm Toolbox for Matlab
GAOT Genetic Algorithms Optimization Toolbox in
The software development process is usually affected by many risk factors that may cause the loss
of control and failure, thus which need to be identified and mitigated by project managers. Software
development companies are currently improving their process by adopting internationally accepted
practices, with the aim of avoiding risks and demonstrating the quality of their work. [12]
The optimization method was tested with several software risk prediction models that have been
developed based on the literature and using data from a survey which collected information from
in-house and outsourced software development projects in the Chilean software industry. These
models predict the probability of success of a project based on the activities undertaken by the project
manager and development team. The results show that the proposed method is very useful to identify
those activities needing greater allocation of resources, and which of these will have a higher impact
on the projects success probability.
1.3. Activities Diagram. The managerial philosophy and the leading manner affect the way
in which any company is administrated, no matter the field of operation. We can include in this
category factors such as: taking the risks, instituted politics and procedures, giving responsibilities,
the attitude in regard of financial reports. The control medium is strongly influenced by the degree
in which the employees are aware of their role in reaching the companys targets. But the employees
ethical manner is not enough. Their abilities are another essential element of the control medium.
The ability, that is knowledge and aptitudes necessary in every line of work, must be mentioned by
the leaders. It is in the interest of every company to have the best employees. (Figure 4)
72
Figure 5 The evaluation model diagrame
A regular monitoring assures a dynamic reaction to the changes that appear, so that the project
manager has pertinent information for the politics of the companys implementations (Figure 5).
Bibliography
[1] Baker, D., Bridges, D., Hunter, R., Johnson, G., Krupa, J., Murphy, J. and Sorenson, K. Guidebook to DecisionMaking Methods, WSRC-IM-2002-00002, Department of Energy, 2002
[2] Buchmann Robert, Mocean Loredan, Xml Connectivity within Flash Presentations, in Information And Knowledge
Age Proceedings Of The 7th International Conference On EInformatics Bucharest, 2012
[3] Claudia Cârstea, Plesea Doru, The future in marketing tests and management programs, International Conference,
Plovdiv, 2003, pag.462, ISSN 0477-0250
[4] Jeffrey L. Whitten, Lonnie D.Bentley, Systems analyses and Design Methods, McGrow-Hill Companies Inc, 1998
[5] J. McGovern, Enterprise Service Oriented Architectures: Concepts, Challenges, Recommendations, Springer, 2006
[6] B. Henderson-Sellers, P. Giorgini, Agent- Oriented Methodologies, Idea Group Publishing, USA, 2005
[7] W. H. Immon, Building the Data Warehouse, John Wiley & Sons, 1996
[8] M. Roost et al, A Model of Information Systems Development for Learning Virtual Organizations, Information
Systems Development: Advances in Theory, Practice and Education, O. Vasilecas etc., Ed. Springer, 2010
[9] N.L. Russo, Expanding the horizont of information systems development, Organizational and social perspectives of
information technology: Proceedings of the IFIP TC8/WG8.2 International Working Conference, Aalborg, Denmark,
2000
ICAM9
73
Daniela Dănciulescu
University of Craiova, Department of Computer Science, A.I.Cuza Street 13, 200585, Craiova, Romania
danadanciulescu@gmail.com
Abstract. The concept of stratified graph introduces some method of knowledge representation ([8],
[10]). The inference process developed for this method uses the paths of the stratified graphs, an order
between the elementary arcs of a path and some results of universal algebras. The order is defined by
considering a structured path instead of a regular path. In this paper we define the concept of system of
knowledge representation as a tuple of the following components: a stratified graph G, a partial algebra
Y of real objects, an embedding mapping (an injective mapping that embeds the nodes of G into objects
of Y ) and a set of algorithms such that each of them can combine two objects of Y to get some other
object of Y .
1.1. Introduction. The concept of stratified graph provides a method of knowledge representation. This concept was introduced in [8], where the intuitive aspect is presented. The mathematical
proof of the existence of this structure was given in [10]. The method of knowledge representation
based on stratified graphs uses:
• concepts from graph theory redefined in the new framework (especially the concepts of labeled
path);
• elements of universal algebra (Peano algebra, partial algebra, morphism of partial algebras).
Intuitively, a stratified graph is built over a labeled graph G0 , placing on top a subset of a Peano
algebra generated by the label set of G0 .
The main goal is to define the concept of knowledge processing system based on stratified graphs
and its corresponding inference process.
1.2. Basic concepts. We consider a symbol σ of arity 2 and take the sets defined recursively as
follows:
B0 = M 0
Bn+1 = Bn ∪ {σ(x1 , x2 ) | (x1 , x2 ) ∈ Bn × Bn }, n ≥ 0
where M0 is a finite set that the description of an element of M0 does not contain the symbol σ. Thus
the set M0 = {σab, c, d} can not be taken into consideration. The set
[
B=
Bn
n≥0
is the Peano σ -algebra ([1]) generated by M0 . We can suppose that σ(x, y) is the word σxy over the
alphabet M0 ∪ {σ}. Often this algebra is denoted by M0 .
By Initial(M0 ) we denote the collection of all subsets of B satisfying the following conditions:
K ∈ Initial(M0 ) if
• M0 ⊆ K ⊆ B
• if σ(u, v) ∈ K, u ∈ M0 , v ∈ M0 then u ∈ K and v ∈ K
We consider a finite set S and denote by 2S×S the collection of all subsets of S × S. We define the
mapping prodS : dom(prodS ) −→ 2S×S as follows:
dom(prodS ) = {(ρ1 , ρ2 ) ∈ 2S×S × 2S×S | ρ1 ◦ ρ2 6= ∅}
prodS (ρ1 , ρ2 ) = ρ1 ◦ ρ2
where ◦ is the usual operation between the binary relations:
ρ1 ◦ ρ2 = {(x, y) ∈ S × S | ∃z ∈ S : (x, z) ∈ ρ1 , (z, y) ∈ ρ2 }
We denote by R(prodS ) the set of all the restrictions of the mapping prodS :
R(prodS ) = {u | u ≺ prodS }
where u ≺ prodS means that dom(u) ⊆ prodS and u(ρ1 , ρ2 ) = prodS (ρ1 , ρ2 ) for (ρ1 , ρ2 ) ∈ dom(u).
74
Let us consider a nonempty set T0 ⊆ S × S. If u is an element of R(prodS ) then we denote by
S×S
Clu (T0 ) the closure of T0 in the partial algebra (2S×S , {u}). This is the smallest
S subset Q of 2
such that T0 ⊆ Q and Q is closed under u. It is known that this is the union n≥0 Xn , where
X0 = T0
Xn+1 = Xn ∪ {u(ρ1 , ρ2 ) | (ρ1 , ρ2 ) ∈ dom(u) ∩ (Xn × Xn )}, n ≥ 0
If L ∈ Initial(M0 ) then the pair (L, {σL }), where
• dom(σL ) = {(x, y) ∈ L × L | σ(x, y) ∈ L}
• σL (x, y) = σ(x, y) for every (x, y) ∈ dom(σL )
is a partial algebra.
By alabeled graph we understand a tuple G = (S0 , L0 , T0 , f0 ), where S0 is a finite set of nodes, L0
is a set of elements named labels, T0 is a set of binary relations on S0 and f0 : L0 −→ T0 is a surjective
function. Because the empty set is not used in knowledge representation we suppose that the empty
set is not an element of T0 . Such a structure admits a graphical representation. Each element of S0
is represented by a rectangle specifying the corresponding node. We draw an arc from x1 ∈ S0 to
x2 ∈ S0 and this arc is labeled by a ∈ L0 if (x1 , x2 ) ∈ f0 (a).
Consider a labeled graph G0 = (S, L0 , T0 , f0 ). A stratified graph ([10]) G over G0 is a tuple
(G0 , L, T, u, f ) where
• L ∈ Initial(L0 )
• u ∈ R(prodS ) and T = Clu (T0 )
• f : (L, {σL }) −→ (2S×S , {u}) is a morphism of partial algebras such that f0 ≺ f , f (L) = T
and if (f (x), f (y)) ∈ dom(u) then (x, y) ∈ dom(σL )
The existence of this structure, as well as the uniqueness is proved in [10]: For every labeled graph
G0 = (S0 , L0 , T0 , f0 ) and every u ∈ R(prodS ) there is just one stratified graph (G0 , L, T, u, f ) over
G0 .
1.3. Accepted structured paths. We consider a labeled graph G0 = (S, L0 , T0 , f0 ). A regular
path over G0 is a pair ([x1 , . . . , xn+1 ], [a1 , . . . , an ]) such that (xi , xi+1 ) ∈ f0 (ai ) for every i ∈ {1, . . . , n}.
We denote by ST R(G0 ) the smallest set satisfying the following conditions:
• For every a ∈ L0 and (x, y) ∈ f0 (a) we have ([x, y], a) ∈ ST R(G0 ).
• If ([x1 , . . . , xk ], u) ∈ ST R(G0 ) and ([xk , . . . , xn ], v) ∈ ST R(G0 ) then ([x1 , . . . , xk , . . . , xn ], [u, v]) ∈
ST R(G0 ).
An element of the set ST R(G0 ) is a structured path of G0 .
Let us consider the set
L(X) = {[x1 , . . . , xn ] | n ≥ 1, xi ∈ X, i = 1, . . . , n}
This is the set of all nonempty lists over X. We denote f irst([x1 , . . . , xn ]) = x1 and last([x1 , . . . , xn ])
= xn .
We define the mapping
⊗ : ST R(G0 ) × ST R(G0 ) −→ ST R(G0 )
as follows:
• dom(⊗) = {((α1 , u1 ), (α2 , u2 )) | (α1 , u1 ) ∈ ST R(G0 ), (α2 , u2 ) ∈ ST R(G0 ),
last(α1 ) = f irst(α2 )}
• If ([x1 , . . . , xk ], u) ∈ ST R(G0 ) and ([xk , . . . , xn ], v) ∈ ST R(G0 ) then
([x1 , . . . , xk ], u) ⊗ ([xk , . . . , xn ], v) = ([x1 , . . . , xn ], [u, v])
Consider a labeled graph G0 = (S, L0 , T0 , f0 ) and the set
(1)
K(G0 ) = {([x, y], a) | a ∈ L0 , (x, y) ∈ f0 (a)}
The set ST R(G0 ) is the ⊗-Peano algebra generated by K(G0 ).
We define
ST R2 (G0 ) = {w | ∃(α, w) ∈ ST R(G0 )}
75
In fact, ST R2 (G0 ) represents the projection of the set ST R(G0 ) on the second axis: in a classical
notation we write ST R2 (G0 ) = pr2 (ST R(G0 )).
We define the mapping ∗ : ST R2 (G0 ) × ST R2 (G0 ) −→ ST R2 (G0 ) as follows:
• dom(∗) = {(β1 , β2 ) | ∃α1 , α2 : (α1 , β1 ) ∈ ST R(G0 ), (α2 , β2 ) ∈ ST R(G0 ),
last(α1 ) = f irst(α2 )}
• If (β1 , β2 ) ∈ dom(∗) then β1 ∗ β2 = [β1 , β2 ]
The pair (ST R2 (G0 ), ∗) becomes a partial algebra.
The mapping h : (ST R2 (G0 ), ∗) −→ ((L0 )σ , σ) defined by

 p if p ∈ L0
h(p) =

σ(h(u), h(v)) if p = [u, v], u ∈ ST R2 (G0 ), v ∈ ST R2 (G0 )
is a morphism of partial algebras.
We define the set ASP (G) as follows: ([x1 , . . . , xn+1 ], c) ∈ ASP (G) if and only if ([x1 , . . . , xn+1 ], c) ∈
ST R(G0 ) and h(c) ∈ L.
An element of ASP (G) is named accepted structured path over G.
1.4. Splitting properties. In this section we obtain two splitting properties: one of them refers
to the decomposition of a structured path; the other gives the decomposition of an accepted structured
path. The first splitting property is used to prove the second property.
(splitting property I)
If ([x1 , . . . , xn+1 ], c) ∈ ST R(G0 ) and n ≥ 2 then there are u, v ∈ ST R2 (G0 ) and k ∈ {2, . . . , n},
uniquely determined, such that
c = [u, v]
([x1 , . . . , xk ], u) ∈ ST R(G0 )
([xk , . . . , xn+1 ], v) ∈ ST R(G0 )
(splitting property II)
If ([x1 , . . . , xn+1 ], c) ∈ ASP (G) \ K(G0 ) then there are u, v ∈ ST R2 (G0 ) and k ∈ {2, . . . , n}, uniquely
determined, such that
c = [u, v]
([x1 , . . . , xk ], u) ∈ ASP (G)
([xk , . . . , xn+1 ], v) ∈ ASP (G)
1.5. Inference process based on accepted structured paths. We consider a stratified graph
G = (G0 , L, T, u, f ) over G0 = (S0 , L0 , T0 , f0 ). Let Y = (Y, ) be a binary algebra and an injective
mapping ob : S −→ Y . We suppose that for each u ∈ L we have an algorithm Algu : Y × Y −→ Y .
This means that Algu is a partial mapping. In other words dom(Algu ) ⊆ Y × Y and for every pair
(x, y) ∈ dom(Algu ) given as input for Algu this algorithm gives as output some element of Y . A
system of knowledge based on stratified graphs is a tuple
SKP = (G, (Y, ), ob, {Algu }u∈L )
where
•
•
•
•
G = (G0 , L, T, u, f ) is a stratified graph over G0 = (S, L0 , T0 , f0 );
(Y, ) is a binary partial algebra;
ob : S −→ Y is an injective mapping;
For each u ∈ L the entity Algu is an algorithm that defines a mapping
Algu : dom(Algu ) −→ Y
where dom(Algu ) ⊆ Y × Y .
For a knowledge processing system based on stratified graphs we can define the inference process
as in the next definition.
76
1.6. Conclusions. In this paper we treat from the mathematical point of view the concept of
inference based on stratified graphs. We define the concept of knowledge processing system with
stratified graphs.
Bibliography
[1] V. Boicescu, A. Filipoiu, G. Georgescu and S. Rudeanu, ”Lukasiewicz-Moisil Algebra”, Annals of Discrete Mathematics 49 (North-Holland, 1991)
[2] Tudor (Preda) Irina-Valentina, Labelled Stratified Graphs can Generate Formal Languages, European Conference
for the Applied Mathematics and Informatics, Athens, Greece, 29–31 December, 2010, p.184–189, ISBN 978-960-474260-8, 2010
[3] Tudor (Preda) Irina-Valentina, Considerations Regarding Formal Languages Generation Using Labelled Stratified
Graphs, International Journal of Applied Mathematics and Informatics, University Press, Issue 2, Volume 5, pp.
101-108, 2011
[4] Tudor (Preda) Irina-Valentina, Generating Natural Language by Labelled Stratified Graphs, Scientific Bulletin University of Pitesti, Matematics and Informatics Series, pg. 89-100, Nr. 17 (2011)
[5] N. Ţăndăreanu, Knowledge Bases with Output, Knowledge and Information Systems 2/4, 438–460, 2000
[6] N. Ţăndăreanu, Collaborations between distinguished representatives for labelled stratified graphs, Annals of the
University of Craiova, Mathematics and Computer Science Series, 30 (2003), no.2, 184-192.
[7] N. Ţăndăreanu, Distinguished Representatives for Equivalent Labelled Stratified Graphs and Applications, Discrete
Applied Mathematics, 144 (2004), no.1-2, 183-208.
[8] N. Ţăndăreanu, Knowledge representation by labeled stratified graphs, Proceedings of the 8th World Multi-Conference
on Systemics, Cybernetics and Informatics (2004), Vol. 5, 345-350.
[9] N. Ţăndăreanu, M. Ghindeanu, Hierarchical Reasoning Based on Stratified Graphs. Application in Image Synthesis.,
15th International Workshop on Database and Expert Systems Applications, Proceedings of DEXA2004, Zaragoza,
Spania, IEEE Computer Society, Los Alamitos California, p.498–502, 2004(3)
[10] N. Ţăndăreanu, Proving the Existence of Labelled Stratified Graphs, Annals of the University of Craiova, Vol.
XXVII (2000), 81-92
[11] Nicolae Ţăndăreanu, Cristina Zamfir, Slices and extensions of ω-trees, Annals of the University of Craiova,
Mathematics and Computer Science Series, 38 (2011), no.1, 72-82.
[12] Nicolae Ţăndăreanu, Irina Tudor (Preda), Dana Dănciulescu, Applications of stratified graphs in optimal planning,
12th International Conference on Artificial Intelligence and Digital Communications, October 5-7, 2012, 7-24
ICAM9
77
Optimizing Investment Costs for Production Systems with Discontinuous Operation Mode
Dinu Darabă
Department of Engineering and Technological Management, Technical University of Cluj-Napoca, North University Center at Baia Mare,
Baia Mare, Romania
dinu.daraba@ubm.ro
Abstract.In case of the investment process, the optimization is based on a mathematical model or a range
of mathematical models which describe the process. The Choice of the most appropriate mathematical
model is the guarantee to obtain useful information for investors. This paper presents a classic analytical
method of decreasing the investment cost in the batch production systems that are specific to the
engineering industry.
1.1. Introduction. For the efficient use of the investment resources, the investment process
in the field of technical systems requires the use of the mathematical optimization methods based
on static linear programming (geometric methods, analytical methods and sequential methods) and
dynamic linear programming, when taking into account the influence of the time factor. Depending
on the potential of the mathematical model, the concept of optimum could have a double meaning:
a permanent or relative one. The closest to the optimum variant, resulting from the application of
mathematical methods, provides the investors with useful information to adopt the solution with
the lowest investment risk, in order to achieve the closest economic efficiency to the proposed one.
Modeling and solving the optimization problems involve the following sequential steps [2]:
(1) Choice of the aimed function - usually it is the criterion of economic efficiency to be achieved
and which is to meet some specific, immediate and prospective needs. A benchmark to be
maximized or minimized will be selected accordingly.
(2) The main and secondary restrictions are determined the minimum level for some economic
effects to be achieved, the minimum level of the production costs, the minimum amount of
the resources.
(3) The objective function is created, starting from its dependence on the variables of the solutions
underlying the formulated alternatives.
(4) Solving the algorithm formed by the system of equations and inequalities as well as the aimed
function.
(5) Verifying the stability of the optimal solution identified in relation to the adopted hypotheses
and considering whether there are other alternative variants that would provide suitable
results with fewer risks under those hypotheses.
(6) Recommendation for investors on the variant that would be adopted, presenting its advantages
over other alternatives.
(7) Recommendation for investors on the variant that would be adopted, presenting its advantages
over other alternatives.
1.2. Mathematical model. Considering that a batch of products is manufactured by a production system comprised of some technological equipment operating in discontinuous mode and others in
semi-continuous mode. Mathematically, it is assumed that the production system made up of a string
of X technological equipment in batch operation mode and Y equipment in semi-continuous operation
mode, to form the G group of equipment. The total manufacturing time of a batch of parts will be [1]:
D=
X
X
i=1
ti +
Y
X
dj
j=1
where: ti and dj are durations of the manufacturing processes.
Denoting with Q the production task of a batch of parts, the manufacturing system productivity
could be expressed as [1]:
Q
W = .
D
The imposed restrictions also refer to the cost of the technological equipment. To determine the cost
of the technological equipment, their number is considered, corresponding to various technological
78
operations i with discontinuous operation mode, which are necessary to meet the production task
Q, are different but proportional to Q; expressions to determine the cost of their purchase can be
expressed in the form [1]:
Ci = ui Xiαi = ui · (Ki · Q)αi = ai · Qαi , i = 1, , X
where : ai and αi are specific constants of the batch mode operating equipment;
ui - unit cost of the equipment;
Ki - constant of proportionality.
Using the same rationale for the batch mode operating equipment we could assume[1]:
βk
Q
, k = 1, ., Y.
Ck = bk ·
θk
where: bk and βk are the specific constants of the semi-continuous mode operating equipment;
θk the operation time that is necessary to manufacture a batch of products.
The total investment cost, which also represents the aimed function, will be:
(1)
CT =
X
X
αi
ai · Q
+
Y
X
bk ·
i=1
i=1
Q
θk
βk
Minimizing this expression with respect to the variables ti and dj should be done by respecting the
restrictions relative to the respective production, expressed by the relation:
Q
Q
= X
(2)
W =
G
D
P
P
ti +
dj
i=1
j=1
Using the substitution of the Q (2), production task into the aimed function (1), an equivalent equation
without restrictions is obtained:
βk
X
Y
X
X
D
αi
αi
αi
CT =
ai · W · D +
bk · W
θk
i=1
k=1
Finally we obtain a system whose solution will offer the best solution. This allows the investor the
choice of equipment with the features needed productive activity.
Bibliography
[1] Loorkar, Y. and Robinson, J.D., Minimization of Capital Investment for Batch Proceses. Calculation of Optimum
Equipment Sizes, Industrial Engineering Chemistry and Process. Design Development, Vol. 9, No. 4, (1970), pp.
625-629
[2] Stancu, F., Prvu, D., Dumitru, M., Stoian, M. and Vasilescu, I., Eficienţa economică a investiţiilor, Ed. D. P.,
Bucureşti, 1995.
ICAM9
79
An efficient method to solve a two-server heterogeneous retrial queue with threshold policy
T. V. Do1 , R. Chakka1 , J. Sztrik2 , T. Bérczes2 , D. Efrosinin3
1 Department
2 Faculty
of Networked Systems and Services, Budapest University of Technology and Economics, Hungary
of Informatics, University of Debrecen, Hungary
3 Johannes
Kepler University, Linz, Austria
do@hit.bme.hu, jsztrik@inf.unideb.hu
Efrosinin and Sztrik [1] considered a two-server heterogeneous retrial queue with threshold policy.
They model the system as a quasi-birth-and-death (QBD) process with threshold dependent blocktridiagonal infinitesimal matrix and apply the general theory of matrix-geometric solutions. Thus, the
computation of the rate matrix R (the minimal non-negative solution to the matrix equation) is based
on the iteration algorithm. However, R can be expressed in a closed formula.
1.1. Level-dependent Band-QBD Solution. From the form of Λ (see page 214 of [1]) we
observe that has two QBD-bands (see [2]):
• In band 1, we have the balance equations
πi−1 A01 + πi A10 + πi+1 A21 = 0, 1 ≤ i ≤ q2 − 2.
(1)
• the balance equations of band 2 is expressed as follows.
πi−1 A02 + πi A12 + πi+1 A22 = 0, i ≥ q2 + 1.
(2)
Note that if the size of the orbit is finite, then the range of index i in equation (2) is upper bounded
by N − 1. That is, q2 + 1 ≤ i ≤ N − 1.
1.2. Infinite Orbit Size. The boundary balance equations are
(3)
π0 A00 + π1 A21 = 0,
(4)
πq2 −2 A01 + πq2 −1 A11 + πq2 A22 = 0.
MGM (Matrix Geometric Method):
From eq. (1), we obtain (see [3, 4])
πi = π0 R1i + πq2 −1 R2q2 −1−i , ∀i = 0, . . . , q2 − 1,
(5)
where R1 and R2 are the minimal non-negative solution of the quadratic matrix equations
(6)
A01 + R1 A10 + R12 A21 = 0,
(7)
A21 + R2 A10 + R22 A01 = 0,
respectively.
The matrix geometric solution for πi , i ≥ q2 is given by
πi = πq2 Ri−q2 , i ≥ q2 ,
(8)
where R is the minimal non-negative solution of the quadratic matrix equation
A02 + RA12 + R2 A22 = 0.
(9)
SE (Spectral Expansion):
Following [2], we obtain the expression for πi , 0 ≤ i ≤ q2 − 1, from equation (1)
(10)
πi =
4
X
k=1
a1,k ψ 1,k xi1,k
+
4
X
q2 −1−i
b1,k φ1,k y1,k
, ∀i = 0, . . . , q2 − 1,
k=1
where a1,k ’s and b1,k ’s are the coefficients to be determined, and (x1,k , ψ 1,k ) (k = 1, 2, 3, 4)
are the eigenvalue, left-eigenvector solution pairs of the matrix equations
(11)
ψ 1,. [A01 + A10 x1,. + A21 x21,. ] = 0,
80
and (y1,k , φ1,k ) (k = 1, 2, 3, 4) are the eigenvalue, left-eigenvector solution pairs of the matrix
equation
2
φ1,. [A21 + A10 y1,. + A01 y1,.
] = 0.
(12)
The probability πi , i ≥ q2 , is given by
(13)
πi =
4
X
2
a2,k ψ 2,k xi−q
2,k , ∀i ≥ q2 ,
k=1
where (x2,k , ψ 2,k ) (k = 1, 2, 3, 4) are the eigenvalue, left-eigenvector solution pairs of the
matrix equations
ψ 2,. [A02 + A12 x2,. + A22 x22,. ] = 0.
(14)
Note that |x2,k | < 1 for k = 1, 2, 3, 4.
The R matrix. Following [5], the characteristic matrix polynomial associated
Q(x) = A02 + xA12 + x2 A22 (note that we use the same notations of [1]). We obtain

−(γ + λ)x
x(λ + γx)
0
0

µ
x
−(γ
+
λ
+
µ
)x
0
x(λ
+
γx)
1
1
(15)
Q(x) = 

µ2 x
0
−(γ + λ + µ2 )x
x(λ + γx)
0
µ2 x
µ1 x
λ − (λ + µ1 + µ2 )x
to eq. (2) is


.

It yields
Det[Q(x)]
= x3 (x − 1)[λ((γ + λ)2 + γµ1 )(γ + λ + µ2 )
−γ(µ1 (γ 2 + 2λ2 + γ(3λ + µ1 )) + ((γ + λ)2 + 2(γ + 2λ)µ1 + µ21 )µ2 + (γ + λ + µ1 )µ22 )x
+γ 2 µ1 (µ1 − µ2 )x2 ]
= x3 (x − 1)[ω0 − ω1 x + ω2 x2 ]
(16)
where
ω0 = λ((γ + λ)2 + γµ1 )(γ + λ + µ2 ),
ω1 = γ(µ1 (γ 2 + 2λ2 + γ(3λ + µ1 )) + ((γ + λ)2 + 2(γ + 2λ)µ1 + µ21 )µ2 + (γ + λ + µ1 )µ22 ),
ω2 = γ 2 µ1 (µ1 − µ2 ).
As a consequence, Det[Q(x)] has three zero roots (x2,1 = x2,2 = x2,3 = 0), one root equal to 1. In
addition,
γ 2 λ+2γλ2 +λ3 +γλµ2
if
γµ2√
(2γ+3λ+2µ2 )
2
ω − ω1 −4ω0 ω2
x2,4 = 1
and
2ω2
• Det[Q(x)] has one root x∗2,4 =
µ1 = µ2 .
• Det[Q(x)] has two roots
x2,5 =
√
ω1 +
ω12 −4ω0 ω2
2ω2
if µ1 6= µ2 .
Note that the eigenvalues of eq. (14) are the roots of Det[Q(x)]. Following the same argument as
in [5], if the QBD process is ergodic, Q(x) should have four eigenvalues inside the unit circle. As a
consequence, |x∗2,4 | < 1 (for µ1 = µ2 ) and |x2,4 | < 1 (for µ1 6= µ2 ). In what follows, we also use x2,4 to
refer to x∗2,4 when µ1 = µ2 .
It is easy to check that independent left-eigenvectors corresponding to three null-eigenvalues are
ψ 2,1 = [1, 0, 0, 0], ψ 2,2 = [0, 1, 0, 0],. . . ,ψ 2,3 = [0, 0, 1, 0].
Let ψ 2,4 = [ψ2,4,1 , ψ2,4,2 , ψ2,4,3 , 1] be the eigenvector corresponding to x2,4 . Utilizing ψ 2,4 Q(x2,4 ) =
0, we get
ψ2,4,1 =
2γµ1 µ2 + 2λµ1 µ2 + µ21 µ2 + µ1 µ22
,
(γ + λ + µ2 )(γ 2 + 2γλ + λ2 + γµ1 − γµ1 x2,4 )
−γ 2 µ2 − 2γλµ2 − λ2 µ2 − λµ1 µ2 − γµ22 − λµ22 − γµ1 µ2 x2,4
,
(γ + λ + µ2 )(γ 2 + 2γλ + λ2 + γµ1 − γµ1 x2,4 )
µ1
.
γ + λ + µ2
ψ2,4,2 = −
ψ2,4,3 =
81
Following [5], we get R = Ψ−1 · diag(0, 0, 0, x2,4 ) · Ψ, where Ψ = [ψ 2,1 , ψ 2,2 , ψ 2,3 , ψ 2,4 ]T . Hence,


0
0
0
0
 0
0
0
0 
.
(17)
R = x4 
 0
0
0
0 
ψ2,4,1 ψ2,4,2 ψ2,4,3 1
1.3. Finite Orbit Size. The matrix geometric solution for πi , i ≥ q2 is given by
πi = πq2 R3i−q2 + πN R4N −i , q2 ≤ i ≤ N,
(18)
where R3 and R4 is the minimal non-negative solution of the quadratic matrix equations
(19)
A02 + R3 A12 + R32 A22 = 0,
(20)
A22 + R4 A12 + R42 A02 = 0,
respectively.
The alternative expression for πi , i ≥ q2 , is given by
(21)
πi =
4
X
k=1
2
a2,k ψ 2,k xi−q
2,k
+
4
X
N −i
b2,k φ2,k y2,k
, ∀q2 ≤ i ≤ N,
k=1
where (x2,k , ψ 2,k ) (k = 1, 2, 3, 4) are the eigenvalue (of least absolute value), left-eigenvector solution
pairs of the matrix equations
(22)
ψ 2,. [A02 + A12 x2,. + A22 x22,. ] = 0,
and (y2,k , φ2,k ) (k = 1, 2, 3, 4) are the eigenvalue (of least absolute value), left-eigenvector solution
pairs of the matrix equation
(23)
2
φ2,. [A22 + A12 y2,. + A02 y2,.
] = 0.
Acknowledgement
The publication was supported by the TÁMOP-4.2.2.C-11/1/KONV-2012-0001 project. The
project has been supported by the European Union, co-financed by the European Social Fund.
The work of Támas Bérczes was funded in the frames of TÁMOP 4.2.4.A/2-11-1-2012-0001
“National Excellence Program Elaborating and operating an inland student and researcher personal
support system”. The project was subsidized by the European Union and co-financed by the European
Social Fund.
Bibliography
[1] Dmitry Efrosinin and Janos Sztrik. Performance analysis of a two-server heterogeneous retrial queue with threshold
policy. Quality Technology and Quantitative Management, 8(3):211–236, 2011.
[2] Tien V Do, Ram Chakka, Orhan Gemikonakli, and Denes Papp. Level dependent band-QBD processes: Steady state
solution and applications. In Second International Working Conference on Performance Modelling and Evaluation of
Heterogeneous Networks, pages WP8/1–6, Ilkley, United Kingdom, 2004.
[3] N. Akar and K. Sohraby. Finite and Infinite QBD Chains: A Simple and Unifying Algorithmic Approach. In
Proceedings of IEEE INFOCOM, pages 1105–1113, 1997.
[4] Nail Akar, Nihat Cem Oguz, and Khosrow Sohraby. A Novel Computational Method for Solving Finite QBD processes.
Commun. Statst.- Stochastic Models, 16(2):273–311, 2000.
[5] Tien Van Do and Ram Chakka. An Efficient Method to Compute the Rate Matrix for Retrial Queues with Large
Number of Servers. Applied Mathematics Letters, 23:638–643, 2010.
ICAM9
82
Nicoleta Enache-David and Livia Sangeorzan
Faculty of Mathematics and Informatics, Transilvania University of Brasov, Romania
nicoleta.enache@unitbv.ro, sangeorzan@unitbv.ro
Abstract.In this paper we propose a Markov model for a web site. We introduce the typical navigation
trail notion and we determine the length of the typical navigation trails in a web site, using the entropy
of the Markov chain that we have considered. Finally, we propose a method for the optimization of the
structure of a web site, based on the length of the typical navigation trails.
1.1. Introduction. The websites have a hierarchical organization of content. Logical information
architecture makes a website more interesting to both search engines and visitors by ensuring that the
content is accessible in a logical way. In this paper we propose a method for the optimization of the
structure of a website.
Log files provide a list of the page requests made to a given web server in which a request is
characterized by the IP address of the machine placing the request, the date and time of the request
and the URL of the page requested. From this information it is possible to reconstruct the user
navigation sessions within a website, where a session consists of a sequence of web pages viewed by a
user in a given period of time.
1.2. A Markov Model for a Website. Let us consider a Markov chain M = (X, P, µ) defined
by a set of states X = (Xi )i=1,n , a transition matrix P = (pij )ij=1,n and a vector of initial probabilities
µ = (µi )i=1,n . The states Xi , i = 1, n are represented by the pages in website [1].
The transition matrix P contains the transition probabilities which are estimated as the proportion
of times the corresponding link was traversed from the anchor. The initial probability of a state is
estimated as the proportion of times the corresponding page was requested by the user.
Definition 1. A trail in M is a finite sequence T = {X1 , X2 , . . . , Xt } of states in M such that
(Xi , Xi+1 ), i ∈ {1, . . . , t − 1} are consecutive pages in the web site.
The probability p (T ) of a trail T of length t is given by:
(1)
p (T ) = Pk1 Pk1 k2 Pk2 k3 · Pki−1 ki ,
where k1 , . . . , kt is a permutation of 1, 2, . . . t, [2].
Definition 2. A typical trail in a web site is a trail T whose estimated probability is above a
specified cut-point λ ∈ (0, 1).
We denote by Tλ the estimated length of a trail T and we obtain:
(2)
tλ ≤ −
ln λ
H (M ) ln 2
where H (M ) is the entropy of the Markov chain M .
1.3. Website Structure Optimization. In order to optimize the structure of a website, we
use the FBT (Finding Backtrack Pages) algorithm that we have presented in [6]. FBT has as input
the pages of the website, the transition matrix, a collection of navigation trails and the target page
T P , and as output the set of backtrack pages M and the target page T P .
The main idea is to create additional links between the pages from the set M and the target page
T P . This way, the visitors can have an easier access to the target page.
Let us consider the set of backtrack pages M returned by the FBT algorithm. We propose the
SSO (Site Structure Optimization) algorithm that will consider only those pages from the set M that
are on a typical trail that have the length less or equal with tλ , λ ≤ 1 from (2).
SSO algorithm has as input the set of backtrack pages M , the target page T P , the start page and
the length of the typical trails, and as output we obtain an optimized structure of the website.
83
Figure 1 The initial structure of the website
Figure 2 The optimized structure of the website
1.4. Experimental Results. Our experimental results have been obtained on an ecommerce
website having 10 pages denoted by X1 , X2 , . . . , X10 , where the start page is X1 . We apply the SSO
algorithm for the website structure optimization and we conclude that we must create a new link
between the pages X9 and X1 . In figure 1 we present the initial structure of the site and in figure 2
we present the optimized structure of the site.
1.5. Conclusion. Our key insight is that visitors of a website will backtrack if they do not find
information where they expect it. The page from where they backtrack is the expected location for
84
the page. This way we can improve the structure of the website by creating an additional link from
homepage to the expected location for the page and one can offer an easier access to the information.
Bibliography
[1] Borges, J., Levene, M., An Average Linear Time Algorithm for Web Usage Mining, International Journal of
Information Technology and Decision Making, Vol. 3, 2004.
[2] Cover, T. M., Thomas J. A., Elements of Information Theory, John Wiley and Sons, Inc., 2006.
[3] Haggstrom, 0., Finite Markov Chains and Algorithmic Applications, Cambridge University Press, ISBN: 0-51101941-6, 2002
[4] Borges, J., Levene, M., Evaluating Variable-Length Markov Chain Models for Analysis of User Web Navigation
Sessions, IEEE Transactions on Knowledge and Data Engineering, 19(4): 441-452, 2007
[5] Wu, X. et al, Top 10 algorithms in data mining, Knowledge and Information Systems, 14:1-37, Springer, 2008
[6] David, N., Consideraţii asupra entropiei şi aplicaţii, International Session of Scientific Papers Scientific Research
and Education in the Air Force, Henri Coanda Air Force Academy, May 16-17, Brasov, Romania, 699-704, ISBN:
978-973-8415-56-0, 2008
[7] David, N., Aspects Regarding the Length of Typical Trails in a Web Site, Proceedings of the 10th WSEAS International
Conference on Mathematical Methods, Computational Techniques and Intelligent Systems (MAMECTIS 08), October
26-28, Corfu, Greece, 203-207, ISBN: 978-960-474-012-2, ISSN: 1790-2769, 2008
ICAM9
85
Second order partial differential equation of parabolic type in the cosmic rays transport studies
Agnieszka Gil-Swiderska
Institute of Mathematics and Physics, Siedlce University, Siedlce, Poland
gila@uph.edu.pl
Abstract. The propagation of cosmic rays is described by Parker’s transport equation (Parker, 1965),
which is a second order parabolic type partial differential equation. It is time-dependent 4- variables
(with ρ, θ, ϕ, R, meaning: distance from the Sun, heliolatitudes, heliolongitudes, and particles’ rigidity,
respectively) equation, which is a well-known instrument for studying problems connected with solar
modulation of cosmic rays. Transport equation contains all basic processes taking place in the heliosphere’s vicinity. In our paper we investigate a topic of the 27-day variation of the galactic cosmic rays
intensity, which is connected with solar rotation. We numerically solve the Parker’s transport equation
involving in situ measurements of solar wind speed and heliospheric magnetic field.
1.1. Parker’s transport equation. Galactic cosmic rays (GCR) are highly energetic nuclei of
extra solar source. When they are propagating through the heliosphere (being a region totally driven
by the Sun’s magnetic activity), they are partially modulated by the solar wind and heliospheric
magnetic field (HMF). Moreover, heliosphere changes in time and those changes influence GCR in
different time scales (e.g. [1]).
The Parker’s transport equation [2] contains all elementary processes taking place in the heliosphere:
convection, diffusion, energy changes of the GCR particles owing to the interaction with solar wind’s
inhomogeneities, drift due to the gradient and curvature of the regular HMF and on the heliospheric
current sheet (HCS):
∇i (κij ∇j f ) − ∇i (Ui f ) +
(1)
1 ∂(f R3 )
∂f
(∇i Ui ) =
2
3R
∂R
∂t
where f is the omnidirectional distribution function, R is the rigidity of the GCR particles, U is the
solar wind velocity and t - time. The anisotropic diffusion tensor κij for the 3-D magnetic field is
taken in to account as in ([3, 4]).
The GCR intensity in the interstellar space is taken according to [5] as:
I=
21.1T −2.8
,
(1 + 5.85T −1.22 + 1.18T −2.54 )
where T is the particles’ kinetic energy.
In article by Moraal [6] is presented a noteworthy review regarding Parker’s transport equation. It
is impossible to solve analytically, in general, Parker’s equation without the substantial simplifications
which makes the mathematical model to paltry to represent the processes in the heliosphere. Thus, it
needs to be solved numerically. Many methods have been developed to solve this equation numerically,
most of them employing the finite difference technique (e.g. [7] ). The other approach is stochastic,
where Parker’s transport equation is considered as the Fokker-Planck equation equivalent to a set of
first-order ordinary stochastic differential equations of the Ito’s type containing a speedily fluctuating
random term (e.g. [8]). First attempt to apply this method to this problem was done by [9] and [10].
In our paper Eq. (1) is reduced to the linear algebraic system of equations by finite difference scheme
and numerically solved using the Gauss - Seidel iteration method (e.g. [11]) for one rotation of the
Sun, i.e. for instant state of the heliosphere, when the distribution of the GCR density is determined
by the time independent parameters included in Eq. (1). The current sheet drift is taken into account
according to the boundary condition method [12].
Bibliography
[1] Kudela K., Space weather near Earth and energetic particles: selected results, Journal of Physics: Conference Series,
409, 1, 012017, DOI: 10.1088/1742-596/409/1/012017 (2013)
[2] Parker, E.N., The passage of energetic charged particles through interplanetary space, Planetary and Space Science,
Vol. 13, 9-49 (1965)
86
[3] Alania, M.V., Dzhapiashvili, T. V., The Expected Features of Cosmic Ray Anisotropy due to Hall-Type Diffusion
and the Comparison with the Experiment, In Proceedings of 16th International Cosmic Rays Conference, Vol. 3,
19-24 (1979)
[4] Alania, M.V., Stochastic variations of galactic cosmic rays, Acta Physica Polonica B, Vol.33, 1149-1166 (2002)
[5] Webber, W.R., Lockwood, J.A., Voyager and Pioneer spacecraft measurements of cosmic ray intensities in the
outer heliosphere: Toward a new paradigm for understanding the global solar modulation process: 1. Minimum solar
modulation (1987 and 1997), Journal of Geophysical Research, Vol. 106, 29323-29332 (2001)
[6] Moraal, H., Cosmic-Ray Modulation Equations, Space Science Reviews, Vol. 176, 299-319 (2013)
[7] Jokipii, J.R., Levy, E. H. , Effects of Particle Drifts on the Solar Modulation of Galactic Cosmic Rays, Astrophysical
Journal, Vol. 213, 85 -88 (1977)
[8] Gardiner, C. W., Handbook of Stochastic Methods, Springer Verlag, Berlin, 1989
[9] Zhang, M., , A Markov stochastic process theory of cosmic-ray modulation, Astrophysical Journal, Vol. 513, 409-420
(1999)
[10] Gervasi, M., Rancoita, P. G., Usoskin, I. G., Kovaltsov, G. A., Monte-Carlo approach to Galactic Cosmic Ray
propagation in the Heliosphere, Nuclear Physics B , Vol. 78, 26-31 (1999)
[11] Kincaid, D.R., Cheney, E.W., Numerical analysis: mathematics of scientific computing, AMS Bookstore, 2009
[12] Jokipii, J.R., Kopriva, D. A., Effects of particle drift on the transport of cosmic rays. III - Numerical models of
galactic cosmic-ray modulation, Astrophysical Journal, Vol. 234, 384-392 (1979)
ICAM9
87
Anne Marie Andreea Hordău
Technical University of Cluj-Napoca, North University Centre of Baia Mare, Romania
annemariehordau@yahoo.com
This article is part of a major research on labour market in Romania after 1990. During this
research, analyses of labour market and unemployment, in Romania and in Maramures County, were
made on the basis of official data. To present a real picture of the situation at the county level,
as representative, we considered necessary also the application of a questionnaire among managers
from economic area. The main goal was to capture the characteristics of the decisions related to
employees and hiring process and redundancy. In addition to introductory questions relating to
the organization’s properties (size, type, industry), questionnaire includes ideas related to hiring,
unemployment process, involving economic areas in the process of continuous training of employees,
etc. Random, 100 companies of different size were selected by businesses in Maramures county, to
whom were sent questionnaires. Of these 74 responded. We consider this response rate satisfactory,
especially since, as you can see from the results presented below, the characteristics of the labour
market in the county from the standpoint of the economic agent are very clear-cut. Additional
companies examined would lead only to a confirmation of these results. First, we were interested in
demographic characteristics of the companies analyzed. The majority of these, 92% are private, only
5.5% of public institutions (city halls, hospitals, etc.). Two of the responding firms are under other
forms of organization.
Of great importance for developing analysis is to establish the size of the organization. In our
studycase the majority of firms are small, with fewer than 10 employees. They represent nearly 50
percent of all firms surveyed. The remaining firms are divided roughly equally into two groups-between
10 and 49 employees, and over 50 employees (even with a larger share of the latter).
Before the actual analysis of the hiring process-dismissal, another important aspect is linked to
the skill level of employees. It knows very well that the labour market in Romania is poor at their
jobs for persons with higher education. The majority of publications ”Labour Exchange” organised
across the country are seeking predominantly persons with secondary education, with secondary-school
studies or post-graduate. Unlike other issues analysed before, which have differentiated Maramures
County attribute, in this case the analysis proves that economic agents in this county have the same
preferences as those in the rest of the country. Thus, 44 of the firms surveyed, representing 60% most
employees with secondary education graduated. Almost 40% (28 companies) have several employees
with higher education and only 1 operator working in the field of provision of services has the majority
of employees with completed master degree studies.
Starting 2008, the international financial crisis began to feel and in Romania. To be able to
capture its effects, we asked the operators in the county where people have committed over the past
three years and how many people have been fired over the past three years. Most of them have hired
less than 5 people . What is interesting, however, is that, even in times of crisis, there were companies
that have hired more consistent-13 companies from the 74 hirred on average10 people in the past
three years, while the 19 companies have pledged around 15 people. Analyzing the activity field, it
emerged that most of the hires have made businesses related to trade. Another specificity is that
they have hired more people in manufacturing than in services. These results, and the tests applied,
they found a meaningful connection between local labour market activity and the number of persons
employed in the past three years, characterized by international and national economic crisis. Very
gratifying is the fact that most businesses have not fired any person in the last 3 years. Among those
who fired, majority have fired less than 5 people.
It is very important to be seen and which is the distribution of firms based on the number of new
people engaged and the number of people laid off in the past three years. In fact, we wanted to see if
those who have fired or dismissed people have hired other people for the available positions.
It seems that most companies have employed but also dismissed people in the same three-year
period. This shows that the layoffs were not based on the financial and economic situation precarious
found nationally, but the reasoning more on characteristics of employees. And, as will be seen later
in the analysis, the lack of interest, skills of employees are considered by employers as main reasons
88
for the determination of obtaining the status of unemployed. However, statistical analysis revealed
the existence of a link between persons employed and those laid off, the number. We were interested
then why employees were sent into unemployment. Unfortunately, half of the businesses surveyed
have avoided to answer this question. As we expected, in most cases, the main reason was linked to
financial problems (for those who have chosen a reason).
Employees sent in unemployment were evaluated on different criteria. In the questionnaire were
included criteria which referred to issues relating to their level of training, labour costs or punctuality
and other criteria. Most employers have framed the reasons in the fourth group-other criteria. Actually,
as this group is followed by the employers ’ group which were based on the level of training in the
choice of people to be laid off. Few have had as main criteria-outs or punctuality of employees wage
costs. In recent years, discussions of increasingly are worn on the correlation of University studies with
labour market requirements. For this reason, we wanted to see employers ’ opinion of the issues that
should put greater emphasis on the higher education institutions in Romania with an overwhelming
majority is apparent that employers prefer creative people who come up with new ideas for their
business. Higher level education institutions should, therefore, to think about the study programmes
so as to develop the creative ability of the future employee. In this way we have, from the point
of view of the business environment in Maramures County, a better integration of recent graduates
on the labour market. The effect would be extremely important, taking into account the results of
the analysis of the labour market at national level, showing an unemployment rate extremely high
(over 20% in recent years) among young people. Keeping higher education department, we analyzed
the degree of collaboration between business and academic area in Maramures. The most important
aspect of this collaboration, which discerned the effects on labour market relates to students ’ practice.
Unfortunately, a large majority of companies do not have any kind of collaboration on this very path
with institutions of higher education. It appears so, a lack of communication between employer and
educator that is not only detrimental to employees.
Bibliography
[1] Matei, L & Matei, A, (2010) Local employment policies in the context of the economic crisis:Influences of the European
Community structural instruments,Online at http://mpra.ub.uni-muenchen.de/23086/ MPRA Paper No. 23086.
[2] Nstase C & Kajanus M (2009), The impact of the global crisis on SME and entrepreneurship behavior Romania
and Finland cases, Article provided by Academy of Economic Studies - Bucharest, Romania in its journal The
AMFITEATRU ECONOMIC journal, number 3, 2009, pages 751-762
[3] Newberry, D., (2006), The role of small and medium sized enterprises in the futures of emerging economies, World
Resource Institute
[4] Roman, M. (2010), The effciency analysis applied for the evaluation of labour market policies: Study case for Romania,
Online at http://mpra.ub.uni-muenchen.de/20332/ MPRA Paper No. 20332.
ICAM9
89
Daniela Kravecová and Jana Petrillová
Department of Mathematics and Theoretical Informatics, Faculty of Electrical Engineering and Informatics, Technical University of Košice,
Košice, Slovakia
daniela.kravecova@tuke.sk, jana.petrillova@tuke.sk
Abstract. The problem of determination and reducing the number of crossings in a graph is studied
not only in the theory of graphs, but also in computer science. It is well known that the problem
of determination of the crossing numbers of graphs is NP-complete. The exact values of the crossing
numbers are known only for some graphs or some families of graphs. Some Cartesian products of special
graphs are one of few graph classes for which the exact values of crossing numbers were obtained. There
are known several exact results of the crossing numbers of the Cartesian product of a some special graphs
with paths, cycles and stars.
In this paper we determine exact value of the crossing numbers of the Cartesian product of graphs
on six vertices with the path.
1.1. Introduction. Let G be a simple graph with vertex set V and edge set E. A drawing of
a graph is a mapping of a graph into a surface. We assume that in a drawing (a) no edge passes
through any vertex other than its end-points, (b) no two edges touch each other (i.e., if two edges
have a common interior point, then they properly cross at this point), and (c) no three edges cross
at the same point. It is easy to see that a drawing with minimum number of crossings (an optimal
drawing) is always a good drawing, meaning that no edge crosses itself, no two edges cross more than
once, and no two edges incident with the same vertex cross each other. The crossing number cr(G) of
a graph G is the number of edge crossings in an optimal drawing of G in the plane. The Cartesian
product G1 G2 of two graphs G1 and G2 has vertex set V (G1 ) × V (G2 ) and two vertices (u, u0 ) and
(v, v 0 ) are adjacent in G1 G2 if and only if u = v and u0 v 0 ∈ E(G2 ) or u0 = v 0 and uv ∈ E(G1 ).
According to their special structure, Cartesian products of special graphs are one of few graph
classes for which the exact values of crossing numbers were obtained. Let Cn be the cycle of length n,
Pn be the path of length n, and Sn be the star isomorphic to K1,n .
Several authors have been researched the crossing numbers of the Cartesian products GCn ,
GPn and GSn for some specific graphs G. Beineke and Ringeisen [1] started to study the crossing
numbers of Cartesian products of cycles with all graphs on at most four vertices. Jendrol’, Sčerbová
in [2] and Klešč in [3], [4], [5] continued with determination of the crossing numbers of Cartesian
products of cycles, paths and stars with all 4-vertex graphs. The crossing numbers of Cartesian
products of paths with all graphs of order five are collected in [6]. It seems natural to enquire about
crossing numbers of Cartesian products of paths with other graphs. There are known the crossing
numbers of products GPn for some 6-vertex graphs G, see [8], [9], [10], [11], [12] and the crossing
numbers of Cartesian products of paths with 40 graphs of order six are collected in [7]. In this paper
we extend the results given in [7] by determining the crossing numbers of the Cartesian products of
other three graphs on six vertices with the path.
1.2. Main results. Let us consider three graphs G, H, and J in Figure 1.
c
a
f
e
b
e
d
c
a
b
f
f
c
d
G
a
H
b
e
d
J
Figure 1 The graphs G, H, and J.
Let be n ≥ 1. First we determine the crossing number of the graph GPn . We find it convenient
to consider the graph GPn in the following way. It has 6(n + 1) vertices, which we denote xi
for x = a, b, c, d, e, f and i = 0, 1, . . . , n. The edges belong to n + 1 copies of the subgraphs isomorphic
to G and six paths of length n, see Figure 2(a). We will denote each of subgraphs isomorphic to G
by G(i) , i = 0, 1, . . . , n. For i = 0, 1, . . . , n, let bi and ei be the vertices of G(i) of degree three, ci and
di the vertices of degree two and let ai , fi be the vertices of degree one.
90
(a)
(b)
Figure 2 The drawing of the graph GPn with 2(n − 1) crossings and HPn with 2(n − 2)
crossings.
The next lemma help us to prove that the crossing number of the graph GPn is 2(n − 1) for
n ≥ 1.
LemmaIf D is a good drawing of the graph GPn , n ≥ 3, in which every subgraph G(i) , i =
0, 1, . . . , n, has at most one crossing on its edges, then there are at least 2(n − 1) crossings in D.
Theorem cr(GPn ) = 2(n − 1) for n ≥ 1.
Figure 2(a) shows the good drawing of the graph GPn with 2 crossings on every copy G(i) ,
i = 1, 2, . . . , n − 1. Clearly, cr(GPn ) ≤ 2(n − 1). The reverse inequality is proved by induction with
respect n.
Now we determine the crossing number of the graph HPn . We find it convenient to consider
the graph HPn in the following way: it has 6(n + 1) vertices and edges that the edges are in n + 1
copies of H (i) , i = 0, 1, . . . , n, and in six paths of length n. For i = 0, 1, . . . , n, let ai , bi , ci and ei be
the vertices of H (i) of degree two, di the vertex of degree three and let fi be the vertex of degree one.
The graph HP1 is planar. The crossing number of the graph HP2 is at least one, because
the graph S3 P2 is its subgraph and cr(S3 P2 ) = 1 (see [2]). The reverse inequality cr(HP2 ) ≤ 1
follows from the drawing in Figure 2(b). The next lemma help us to prove that the crossing number
of the graph HPn is 2(n − 2) for n ≥ 3.
Lemma If D is a good drawing of the graph HPn , n ≥ 3, in which every of the subgraphs H (i) ,
i = 0, 1, 2, ..., n, has at most one crossing on its edges, then there are at least 2(n − 2) crossings in D.
Theorem cr(HPn ) = 2(n − 2) for n ≥ 3.
The drawing in Figure 2(b) shows that cr(HPn ) ≤ 2(n − 2), because every copy of H (i) ,
i = 2, 3, ..., n − 2, is crossed two times, H (1) and H (n−1) are crossed once and there is no other crossings
in the drawing. The proof of the reverse inequality proceeds by the induction on n.
In the last case we determine the crossing number of the graph JPn . We find it convenient to
consider the graph JPn in the following way: it has 6(n + 1) vertices and edges that the edges are in
n + 1 copies of J (i) , i = 0, 1, . . . , n, and in six paths of length n. For i = 0, 1, . . . , n, let bi , ci and di be
the vertices of J (i) of degree three and ai , ei and fi the vertices of degree one.
Figure 3 The drawing of the graph JPn with 3(n − 1) crossings.
The next result help us to prove that the crossing number of the graph JPn is 3(n − 1) for n ≥ 1.
Lemma If D is a good drawing of the graph JPn , n ≥ 3, in which every of the subgraphs J (i) ,
i = 0, 1, 2, ..., n, has at most two crossing on its edges, then there are at least 3(n − 1) crossings in D.
Theorem cr(JPn ) = 3(n − 1) for n ≥ 1.
91
The drawing in Figure 3 shows that cr(JPn ) ≤ 3(n − 1), because every copy of J (i) , i =
1, 2, ..., n − 1, is crossed three times and there is no other crossings in the drawing. The proof of the
reverse inequality proceeds by the induction on n.
Acknowledgment. This work was supported by the Slovak VEGA grant No. 1/0309/11.
Bibliography
[1] L. W. Beineke, R. D. Ringeisen, On the crossing numbers of products of cycles and graphs of order four, J. Graph
Theory, 4, 145–155 (1980)
[2] S. Jendrol’, M. Ščerbová, On the crossing numbers of Sm × Pn and Sm × Cn , Časopis pro pěstovánı́ matematiky,
107, 225–230 (1982)
[3] M. Klešč, The crossing numbers of Cartesian products of stars and paths or cycles, Mathematica Slovaca, 41, 113–120
(1991)
[4] M. Klešč, The crossing numbers of products of paths and stars with 4-vertex graphs, J. Graph Theory, 18, 605–614,
(1994)
[5] M. Klešč, The crossing numbers of products of 4-vertex graphs with paths and cycles, Discuss. Math Graph Theory,
19, 59–669 (1999)
[6] M. Klešč, The crossing numbers of Cartesian products of paths with 5-vertex graphs, Discrete Math., 233, 353–359
(2001)
[7] M. Klešč, J. Petrillová, The crossing numbers of products of path with graphs of order six, Discuss. Math Graph
Theory (to appear).
[8] D. Kravecová, The crossing number of P52 × Pn , Creative Mathematics and Informatics, 21, 1, 65–72 (2012)
[9] Y. H. Peng, Y. C. Yiew, The crossing number of P (3, 1) × Pn , Discr. math., 306, 1941–1946 (2006)
[10] J. Wang, Y. Huang, The crossing number of K2,4 × Pn , Acta Math. Sci., Ser A, Chin Ed., 28, 251–255 (2008)
[11] L. Zhao, W. He, Y. Liu, X. Ren, The crossing number of two Cartesian products, International J. Math. Combin., 1,
120–127 (2007)
[12] W. Zheng, X. Lin, Y. Yang, Ch. Cui, On the crossing number of Km Pn , Graphs Combin., 23, 327–336 (2007)
ICAM9
92
Gergely Kocsis and Imre Varga
Faculty of Informatics, University of Debrecen, Hungary
kocsis.gergely@inf.unideb.hu, varga.imre@inf.unideb.hu
Abstract. In this paper we examine the spreading of information on on-line social networks that are
in their final phase of their life. In this state a number of users (nodes) have left the network making
it less connected, and after a while, breaking it into separate pieces. Our final question is if it worth
to advertise on these networks or not. Using a previous model of ours we executed simulations on
a real sample network of more than 5 ∗ 107 nodes and many generated networks. Results were found
highlighting the way how social networks loose their users, and even some first findings are presented
answering the main question of ours.
1.1. Introduction and motivation. The life cycle of an online social network (such as Facebook,
Myspace, etc.) can be described by 4 distinct states (see Fig. A ). First when it is introduced, the
amount of users starts to increase slowly because of the low awareness of the network. After a while –
as more and more users are connected to the network – this increasing speeds up. This phase is called
the growing of the network. After a while the network reaches its possible maximum number of users.
The growing slows down and for a more or less long time the social network stays in its mature state.
History shows however that this state is not the last in the life of a social network. With time a new
rival always appears and sooner or later the network enters to its final phase of declining [3].
It is easy to understand that advertising in
social networks in their first 3 states – especially in the middle 2 – is very worthy. These
networks have almost clean scale free topology [2]. This property makes the spreading
of information very rapid. However the same
is not proven to be true for declining social
networks.
Fig. A
Life cycle of a social network [3]
In the followings first we try to find a method to reproduce real networks based on a huge set
sample of Facebook data. After that we examine the effect of attacking the network on the spreading
of information.
1.2. Real, generated and attacked networks. From the work of M. Gjoka et al. [5] we got a
set of data from a real piece of the global Facebook social network. Besides this network we also tried
to reproduce the network by generation. In this way we can produce networks with similar structure
as real networks, but in smaller size than in our sample data. Later these networks can be attacked
in order to represent networks in the declining phase. Nevertheless starting examinations on these
networks makes it possible to find out what will happen later on the real network.
Examining the degree distribution of our sample network it turns out that it has a power law
degree distribution with a slightly lower degree distribution exponent as the theoretical one γ = 3.
To generate scale-free networks with variable degree distribution exponent we used the model of Lee
et al. [1]. This is a mixture of the popularity-driven BA algorithm and the fitness-driven algorithm.
In this each new node connect to the network according to BA model with probability p and the
fitness-driven connection has 1 − p probability. Using this mixed algorithm we were able to produce a
similar network as the sample.
Using the above process we became able to generate networks having almost the same degree
distribution exponent as our sample network. To simulate a declining network we have to use a
so called attack process. We used three different ways to attack the network based on the degree
of nodes. Namely i.) removing nodes with the same probability (general attack), ii.) removing the
high degree nodes more likely (central attack) and iii.) removing the low degree nodes more likely
(peripheral attack). In addition the attack can be described by the attack rate η = N − /N0 , where
93
N − is the number of removed nodes. Finally the parameters of these model networks at each attack
types are the original number of nodes N0 , the dominance of BA model p and the attack rate η. As
it is well-known, the scale-free networks are very resistant against general attack [2]. The degree
distribution has almost the same exponent γ even if the attack rate η is close to 0.5, only the range
of the distribution is shrinking. The exponent γ seems to be constant also in case of significant size
peripheral attack. It is understandable while removing recently joined nodes with small k leads to a
state which is similar to an earlier and smaller one if the BA based system is large enough. When
the nodes with larger number of link are damaged frequently the slope of the degree distribution of
centrally attacked network is decreasing very fast.
1.3. Information spreading. In a previous work Kocsis and Kun proposed a model for information spreading on complex networks [4]. In our current work the simulations are based on this
model. The model in short builds up as the following:
The socio-economic system is represented by a set of agents which have a complex topology of
social contacts. Agents take place on the nodes of the underlying network topology and the social
contacts are represented by the edges. The state of agents during the time evolution of the system
is characterized by an integer variable Si , which takes the value 0 if the agent is informed and 1 in
the opposite case. Initially all agents are in the state Si = 1, i = 1, . . . , N0 , where N0 denotes the
total number of agents. In the model the primary source of information is a homogeneous external
driving field E. For simplicity this strength is set to E = 1. The sensitivity of agents to the external
information field is described by a parameter β. The information can be also transmitted between
interacting agents resulting in a horizontal flow of information. The sensitivity of agents to this source
of information is presented by α that is a real value. We cast the total amount of information Ii agent
i receives through the information channels into following form
(1)
ki
X
Ii = αSi
(1 − Sj ) + βSi ,
j=1
where ki denotes the number of social contacts of agent i. Agents get informed with a certain
probability A, which is a monotonically increasing function of the available information Ii
(2)
A(Ii ) = 1 − e−Ii /λ ,
where λ is a scale parameter. Note that Ii is the total amount of new information received by agent i.
Since the surroundings of a selected agent changes due to the agents which have become aware of the
innovation, the total amount of new information Ii and the resulting awareness probability A(Ii ) are
both functions of time.
1.4. Results of simulations. To prove that the way of spreading is size-independent we ran
simulations of networks of different sizes for all three types of attack. The parameters of the model
were set to the values proven to be the closest to the real world scenarios previously [4]. Namely we
set α = 0.01 and β = 0.001 in order to balance the effect of the two channels. During the simulations
we chose the ratio of informed agents as the key indicator of the spreading. The results are presented
on Fig. 1/a). Note that the spreading process behaves the same way independently of the size of the
network.
As a next step we compared our results on the real network with the ones on a simple unattacked
generated network. Slightly surprisingly the results proven to be different in these two cases indicating
that the sample Facebook network which we are using is not any more a simple scale-free graph rather
an attacked one. This implies the interesting fact, that it is currently about to enter to its declining
phase.
Because of this, we tried all three attack methods, to get a parameter set, that results a network
with about the same degree distribution and spreading properties as the real graph. Technically we
ran the same simulations on both networks and compared the trends of the informed agents as a
function of time. Our results are presented on Fig. 1/b). As we found all three ways of attack may
results in a network that is close to have the same behavior as the real network. The amount of nodes
to be removed in each case are the followings: about 46% in the peripheral case, about 16% in the
94
Figure 1
a) Ratio of informed nodes in the system as a function of time t. Networks attacked in the same way show the same
fashion of spreading independent of the size of the network. b) The effect of attack on the spreading. The direction of the arrow shows
the increase of the number removed nodes (10%, 20%, 30%, 40%, 50%).
general phase and less than 1% in the case of the central attack. These numbers mean that the future
of spreading highly depend on the way how the network declines.
Knowing how to generate a network that coincides with the real social network we can examine
how our model reflects if we attack the network in several different ways. What became clear directly
from our previous simulations is that the different ways of attacking have different consequences on
the spreading. Naturally in all cases with the increase of the number of removed nodes the spreading
becomes slower. However the same amount of removed nodes affect the spreading in different ways.
As it was seen above, if low degree nodes are removed from the network, the structure of it does not
change. This is why we see on Fig. 1/b) that even if we remove 50% of the lowest degree nodes, the
behavior of spreading does not change too much. Focusing on the case of general attack shows, that in
this case a smaller amount of removed nodes can imply the same effect. The third case however even
if we remove only a few nodes from the network following this rule, the spreading slows dramatically.
1.5. Summary. In our work we tried to find an aswer to the question ”How information spreads
on a declining social network?”. In order to make our results as close as possible to the real networks
we used a set of data from real Facebook users. We generated scale-free networks with changeable
degree distribution exponent using a mixture of popularity-driven and fitness-driven models of growing
networks. Then the networks were attacked using three different ways of attack to model the effects
of declining. We examined the effect of three attacking methods. We found that while the peripheral
attack hardly changes the process, the equal attack affects it more while the central attack dramatically
changes it.
1.6. Acknowledgment. The publication was supported by the TMOP-4.2.2.C-11/1/KONV2012-0001 project. The project has been supported by the European Union, co-financed by the
European Social Fund.
Bibliography
[1] H. Y. Lee, H. Y. Chan, and P. M. Hui, Scale-free networks with tunable degree distribution exponents, Phys. Rev. E,
69, 067102 (2004)
[2] R. Albert and A.-L. Barabsi, Statistical mechanics of complex networks, Rev. Mod. Phys. 74, 47-97 (2002)
[3] B. M. Varghese, The Life Cycle of a Social Network, Techpedia (http://www.techipedia.com/2011/social-networklife-cycle/ - last visited: Juna20.2013) (2011)
[4] G. Kocsis and F. Kun, Competition of information channels in the spreading of innovations, Phys. Rev. E, 84,
026111 (2011)
[5] M. Gjoka, M. Kurant, C. T. Butts and A. Markopoulou, Walking in Facebook: A Case Study of Unbiased Sampling
of OSNs, Proc. of IEEE INFOCOM ’10, San Diego, CA, (2010)
ICAM9
95
Analysis and Interpretation of Structure and Diversity of Some Macrozoobenthic Communities Using
Mathematics Indices
Oana Mare Roşca, Lucia Mihalescu, Monica Marian, Zorica Voşgan
Cluj-Napoca Technical University, Baia Mare North University Center,
oanarosca76@yahoo.com
Abstract.Modification of the structure of aquatic communities occurs in response to different types of
stress, including anthropogenic pollution. In order to sense some aspects of the level of contamination
and the ecological status of rivers the following environmental indicators are often used: analytical
(abundance, frequency, dominance), synthetic (ecological significance index) and diversity (ShannonWiener index, Margalef index and Simpson index).
1.1. Introduction. Macrozoobenthic communities consist of small invertebrates that live on or
in the substrate on rivers bottoms (worms, crustaceans, insect larvae, mollusks). In order to capture
some aspects of the numerical weight of the contribution and role of macrozoobenthos taxa, the
analytical environmental indices (density, frequency, abundance) and synthetic (ecological significance
index) are often used. Diversity indices get the environmental instability affecting the life of the
aquatic communities. These are the most used diversity indices in the interpretation of such toxic
pollution: Shannon-Wiener-H index, Margalef -d1 index and Simpson index-D.
1.2. Methods. The overview of data structures and how they are distributed is obtained by
applying the analytical, synthetic and diversity ecologic indices.
1.3. Discussion. The zoobenthos community structure reflects the state of the entire aquatic
ecosystem. Changing specific richness and numerical abundance that occurs in response to pollution
(Tudorancea, 2004) can also be captured using analytical indices (abundance, frequency, dominance),
respectively, synthetic indices (index of ecological significance). Numerical abundance represents
the absolute number of individuals of a species present in a given area. Frequency (F), expresses
in percentage the presence of a certain species within the collected samples. Thus, it highlights the
density (abundance number), homogeneity or heterogeneity of a particular species within a particular
biocoenosis. The calculation is:
p
F =
· 100
P
where is p is the number of samples in which the considered species is present and P is the total
number of collected samples (Varvara et all., 2001).
Constancy (C) is the notion which expresses the continuity of species in a given habitat (Varvara
et al., 2001). The higher the indicator value, the better the species is adapted to the conditions offered
by the biotope.
Dominancy (D). Dominancy expresses the influence exercised by a species within a community
(Balogh, 1958, quoted by Stugren, 1982).
nA
· 100
N
where: nA- total number of individuals of the A species found in the checked samples,
N - total number of individuals of all the species found in all the checked samples
To highlight the role of species in coenosis, we used the ecological significance index (W).
This index expresses the ratio between the frequency and dominance, as follows:
FA
W =
· 100
DA
where: F A- frequency of A species,
DA- dominancy of A species.
Diversity indices focus the information in a numerical value that allows researchers to objectively
assess the state of the studied communities. These indices capture the instability of the environmental
factors affecting the aquatic invertebrate communities, being frequently used in elucidating the degree
of deterioration of lotic systems (Washington, 1984; Moldoveanu et al., 2011). But diversity indices do
not capture the changes in species composition and as a result they will be complemented by biotic
D=
96
indices (Moldoveanu et al, 2011). Basically, a diversity index of a high numerical value implies a
better structuring of the species that is a higher stability and implicitly balanced biotic relationships.
Among the many known diversity indices the following will be presented: Shannon-Wiener index,
Simpson index and Margalef diversity index.
Shannon Wiener diversity index (H) measures the degree of organization (or disorganization)
of a system.
s
X
H0 = −
pi ln (pi )
i=1
where: pi = nNi ; ni - number of individuals of the i species within a sample,
N - total number of individuals within the sample.
K- factor for converting base 10 logarithms to base 2, it is equal to 3, 321928.
Simpson index (D) summarizes the probability of occurrence of each species; it reflects how the
ecosystem is dominated by a small number or a large number of species.
X ni (n1 − 1)
D =1−
N (N − 1)
where: ni - number of individuals of the i species within a sample,
N - total number of individuals within the sample
Margalef index (d1 ) assesses the information from a sample of a certain size.
S−1
d1 =
ln N
where: S- total number of the species.
N - total number of individuals of all the species.
1.4. Conclusions. Environmental indices are relatively easy to use and provide useful information
about the state of degradation of lotic ecosystems. Interpretation of the overall ecological status lotic
ecosystems will be made linking all the values of the analyzed indicators, including the biotic ones,
and not by singularly analyzed values.
Bibliography
[1] Moldoveanu, M., Rnoveanu, G., Chiriac, G. Ecological indices for monitoring and assessing ecological status of lotic
system. Conferinţa ştiinţifică anuală, 1-3 Noiembrie INHGA, 2011.
[2] Stugren, B.,Bazele ecologiei generale, Ed. Ştiinţifică şi Enciclopedică, 1982, Bucureşti, 435 p.
[3] Tudorancea, M. M, Ecologia unor populaii de chironomidae (Diptera) din rul Someul Mic i bazinul de drenaj al
rului Criul Repede, Tez de doctorat, Cluj Napoca, 2004, 97.
[4] Varvara, M., Zamfirescu, t., Neacu, P.Lucrări practice de ecologie, Ed. Univ. Al. I. Cuza, Iai, 2001, p. 153.
[5] Washington, H., G., Diversity, Biotic and Similarity indices. A review with special relevance to aquatic ecosystems,
Water Res. Vol. V (6), 1984, 653-694.
ICAM9
97
Claudia Marian and Monica Marian
monicamarian17@gmail.com
Abstract.This paper aims to exemplify a concrete way in which the methods and statistical indicators can
help to direct a formative approach of adult education. Descriptive statistical methods, like media and
frequency, and comparative study methods - analysis of variance (ANOVA) one/ two way will be used
as tools for initial evaluation of the knowledge, the joint analysis of the types of mental maps, selection
of vulnerable groups and post-intervention assessment of the effectiveness of training program.
1.1. Introduction. Contemporary education is largely subordinated to the requirements of
ergonomics and competitiveness. In general, this requires a careful management of human resources,
of the methods used to achieve the stated objectives, of the expected results, a careful monitoring
of the cost / benefits, anticipating the evolutionary routes, assessing possible risks, etc. Statistical
instrument are a good means of achieving these objectives by forecasting and diagnostic continuous
evolution of the whole educational endeavor.
An example of this was the need to implement an educational programs which, in the long run, to
determine protection, conservation and fund raising of biodiversity in declared areas Natura 2000. To
optimize the formative approach of experimental design are required several steps:
1. an initial assessment to know, on the one hand, which is the local people’s knowledge
regarding the basic concepts of what a Natura 2000 site requires (attitudes that they have
towards the site, knowledge about resources of flora and fauna in the area, the impact that a
protected area has on economic development of the region) On the other hand, pragmatic
approach require criteria for predictions of groups vulnerability and also identifying cognitive
distortions that prevent proper assimilation and reporting the information taught.
2. the second step consists in implementing a training program, applied mainly on vulnerable
groups, the program takes into account the need to offset the distortions and deficiencies
found in the initial phase
3. final evaluation as a feedback of the whole project, which monitor the dynamics of the
post-outreach project and which constituted the starting point for necessary measures to be
taken on long term by those who manage the site.
The study group consisted of 1273 people, inhabitants of the Natura 2000 site, based on statistical
criteria of representativeness and heterogeneity; the group included people of ages and in different
genres from different backgrounds, different levels of education and different responsibilities within
communities.
Statistical methods of data collection were based on the Likert scale questionnaire with 10 levels
and items requesting choice of correct between answer or either completing them.
Statistical methods chosen for processing raw data were as follows:
-: Descriptive statistical methods - media and frequency
-: Comparative study methods - analysis of variance (ANOVA) one/ two way.
The independent variables used: age, gender, origin, place of belonging, schooling level and type
of activity, and the dependent variables are the awareness of the population and attitudes toward
biodiversity of the site. Statistical analysis was performed using SPSS version 17.
After processing the data has arrived at the following results: first of all, the initial outreach on
the particularities of a Natura 2000 site and a protected area looks like this: only 32.8% recognized
all three specific characteristic of an protected area, 30.9% admit only 2 marks characteristic, 28.8%
identifies a single feature and 7.5% seem to be foreign to the concept of protected area recognizing
nothing special. Of these, only 62.1% identified an area protected by his fundamental distinguishing
criteria (species of plants / animals, biogeographic formations, etc. of environmental, cultural scientific
importance.
Regarding the correlation between the concept of biodiversity and protected areas, the distribution
of correct answers / wrong is this: importance of protected areas for biodiversity conservation is
assumed by 90.3% of respondents. Major discrepancies between the two data types, logically connected
98
to each other, demonstrate the existence of ”mental maps” incomplete and fragmentary. In the same
registry, more than half of the population does not know even a plant species at the site, while only
3.3% can name 5 species! (with a mean of 0.96 species group). For animals the situation is better, but
far from ideal - and here 41% of the subjects do not know even one species fauna of the site, but 21%
were able to name five species. (with a mean of 2.27 species group)
Congruent with this finding, information concerned the economic impact of protected areas on
the economic development of the region is validated only by half of the respondents, which betrays
misunderstanding of the mechanisms behind these dynamics. It’s important to understand this
dynamic - the public awareness of the economic value that biodiversity implicitly protected area can
play in their own welfare could be a motivating factor for its preservation. When analyzing how
varying the information related to the concepts of protected areas and biodiversity according to age
groups and genders, it appears that there are significant differences between the three age groups
analyzed (under 20 years, 21-40 and over 41) on the one hand and between the awareness of women /
men on the oher. The average response of those under 20 year is the lowest comparable with that
of ages between 21-40 years (men and women alike) and with those over 41, which has the highest
average correct answers. Men over 41 years old have the highest level of information, significantly
higher than women of the same age. These differences are statistically significant (Fage = 17.008
with p = 0.000 and p = Fgen = 4.798 to 0.008), with a risk of error below 0.8%. Same distribution
analysis by level of education and area of origin - urban / rural does not indicate significant differences
between their benefits.. Also, subjects in all localities analyzed have a comparable level of information.
Similarly, the activities that peoples has in community does not induce significant differences in the
level of awareness of the general notion of a protected area.
Regarding the attitude that people have towards the presence of Natura 2000 site in their area,
recorded on a scale of 1 to 10, the average yield is 7.4 - a situation that will improve the final evaluation
statistically significantly (p = 0.007), reaching an average of 8.6. In addition, the trend registering
a significant decrease in the inferior (1-5 points) and polarization responses to positive attitudes
favorable to this site in their area.
Future directions in educational intervention suggested by these statistical trends are:
-: Educational interventions focusing on basic concepts and clarifying connections between
them
-: Increasing concrete information about the flora and fauna of the site
-: Explanations focus on emphasizing the economic benefits provided by the site
-: Inclusion in the training group mainly those aged under 41, regardless of gender, education
level, type of affiliation urban / rural and activity in the community
They were the basis for the batch application and implementation of educational approach
The results of the training process and post-intervention assessment records following progress:
-: Compared to the situation at the initial evaluation, it is observed that the final evaluation,
significantly increases the number of those who recognize two features of protected areas, and
also those that recognize all three basic features (it’s true, to an extent smaller), and diminish
the number of those that recognize a single feature or none. This increase is significant for a
significance threshold of p = 0.03. The most significant increases (for a significance threshold
of p = 0.009) are recorded at the extreme age categories, while the population aged 21-40
years remains stable as level information.
-: Further, those over 41 years have the highest level of knowledge (average correct answers is
2.5 - 2.7 of 3 possible). Another trend is to close the level of awareness of women to men in
the same age category.
-: Understanding the concept of biodiversity register significant progress as a result of public
awareness / information made under the project. The number of those who know this notion
increased significantly (p = 0.02) from 81.6% at baseline in 94.3% in the final evaluation.
-: Analyzing the correspondence between biodiversity and protected areas remains constant
between the two assessments, initial and final weight was not significantly different responses
(p = 0.427 for an increase of 90.3% correct responses in the initial evaluation to 91.2% in the
final evaluation).
99
-: constantly keeps the trend: despite the theoretical knowledge of the concept of biodiversity
and mental connection with the concept of protected area, this does not reflect a proportional
pragmatic recognition of its economic value, where even if percentage of correct responses
increased significantly (p = 0.014) from 52.6% to 63.7% it is still low This trend respect
the psychological dynamics of assimilation into a faster pace of information theory, followed
somewhat slower then by forming attitudes.
-: Knowing the specific protected areas included in the analyzed site made a statistically
significant progress (p <0.001) between the two assessments
If in the initial assessment, the knowledge concerning Sit protected areas vary significantly
depending on the type and age of subjects (F = 6.349 for age p = 0.002 and F = 4.785 a kind p =
0.009), (information increases with age, male gender beating the one female) for final evaluation, the
gender differences are insignificant, as well as the age groups records the uniformity of this cognitive
level, the general population average know a mean of over 2 sites from 5 presented
under
between
over
20 years old 21-40 years old 41 years old
Initial assessment Masculine gender
1,7
1,4
2
Feminine gender
1,3
1,3
1,8
Masculine gender
2,4
2,3
2,6
Feminine gender
2,1
2,2
2,4
Final assessment
1.2. Conclusions. The conclusions that can be made for the measures to be taken for long term
are that formative approach must be focus mainly on the pragmatic aspects and on attitudinal one,
and the focus group must be compose by young population under 40 years.
Bibliography
[1]
[2]
[3]
[4]
[5]
Howitt, D., Cramer D., 2006, Introducere in SPSS pentru psihologi, versiunile SPSS 10, 11, 12 si 13, Polirom , Iasi
Labar A. V., 2008, SPSS pentru stiintele educatiei, Polirom, Iasi
Radu, I., si colab, 1993, Metodologie psihologica si analiza datelor, Sincron, Cluj Napoca
Sava, F.A., 2004, Analiza datelor in cercetarea psihologica. Metode statistice complementare, ASCR Cluj Napoca
Stan, A., Clocotici V., 2000, Statistica aplicata in psihologie, Polirom, Iasi
ICAM9
100
Statistical Instruments Used in Environmental Assessment Validation of Newly Introduced Species
Monica Marian1 , Beatrice Agneta Szilagyi2
1 Technical
2 University
University of Cluj-Napoca, North University Center at Baia Mare, Romania
of Agricultural Sciences and Veterinary Medicine, Faculty of Horticulture, Cluj-Napoca, Romania
beatrisce16@yahoo.com, nitella ro@yahoo.com
Abstract.Introduction of the new species of plants in the context of environmentally is a challenge, both
in terms of acclimatization, as well as potential hazards on the statute invasively. The results of the
measurement of physiological parameters, as well as germination, the undercoat of germination, intensity
of photosynthesis, plant growth, are processed statistical summary, thus contributing to the validation
decision on whether introduction of the new species in a more environmentally sensitive again. Such
statistical procedures have been followed up for testing suitability for introduction in Romania of the
species Asimina triloba (L.) Dunal, a North American shrub well-trained fruit.
1.1. Introduction. In temperate climates, Asimina triloba (L.) Dunal is the only cultivated
member of the Annonaceae family, with its generally subtropical and tropical species, and is popularly
known as the banana of the north.
In order to arrive at a precise interpretation of results regarding the influence of experimental
factors and calculate growth predictions made on Asimina triloba (L.) Dunal plants used in the study,
seedlings were divided into multiple categories. The hypotheses from which we started in our collection
of experimental data are:
- the initial size of seedlings significantly affects stem length, distance between internodes,
diameter of main and secondary stems, the number of branches and leaves on the main and
secondary stems as well as their parameters (leaf length and width);
- the plant location has a significant predictive value for plant evolution in terms of the
parameters analyzed;
- the plant age significantly affects growth.
1.2. Materials and methods. Data analysis was accomplished with the aid of the statistical
program SPSS (Statistical Package for the Social Sciences), version 17. In the present work, we
used descriptive statistics as a working method for interpreting stochastic data. The statistical
apparatus used for confirming the initial hypotheses were uni and bifactorial variant analysis
(anova uni and bifactorial). The F indicator (variance report) that it generates indicates the existence
of differences between the various groups analyzed, starting with several selection criteria; the
hierarchical regression calculation permits evaluating the weight that one of more causal factors
contributes to the variation in the effect; the calculation of correlation coefficients was meant to define
extant links between growth in various vegetable organs of the Asimina triloba (L.) Dunal plant.
In the present work, we show the results obtained through a variance analysis of biological aspects
in Asimina triloba (L.) Dunal and its growth predictions.
1.3. Results and discussion. We combined the two analysis criteria, plant location (Lpuel and
Baia Mare) and their age (one, two or three years). The bifactorial anova calculation revealed whether
differences in stem length exist among the 5 (five) subgroupsin other words, if age and plant location
significantly influence growth in the main stem. An analysis of the variance report values (F) and the
p-values (p) leads to the following conclusions:
When comparing average stem lengths among the three subgroups of Asimina triloba (L.) Dunal
plants aged one, two and three years, one observes that these lengths differ significantly (F=117.603).
This allows us to state with certainty (error risk of 0, as p=0.000) that stem length increases
substantially every year. Thus, plant age as a variance factor is significant for main stem growth in
the Asimina triloba (L.) Dunal plant.
Likewise, if we analyze average main stem length in the Asimina triloba (L.) Dunal plant in terms
of location, we observe that the two subgroups (in Baia Mare and Lpuel) are significantly different
(F=21.760). The error risk we assume for this statement is 0 (p=0.000). This fact allows us to affirm
that plant location, along with age, is a significantly influential factor in terms of growth in length of
the main stem in Asimina triloba (L.) Dunal plants.
101
Combining the two variance factors of plant age and location and comparatively analyzing average
main stem lengths of the five (5) subgroups that they generate, we observe that these averages
significantly differ among themselves (m1 bm=5.850, m2 bm=9.207, m2 lpuel=8.203, m3 bm=34.130,
m3 lpuel=21.320). The value of the variation report F=16.006 indicates significant differences among
the subgroups (p=0.000).
Prediction model R2
r
p
1 age
0,453 0,676 0,000∗ ∗
2 age∗ location 0,541 0,780 0,000∗ ∗
Prediction of main stem length growth
in terms of age and location of the Asimina triloba (L.) Dunal plant
Calculating the variance analysis allowed us to conclude that the subgroups formed by combining
criteria of plant location and age generate differences in main stem length of the Asimina triloba (L.)
Dunal plant. A multiple regression analysis allows us to know and to quantify the weight that the two
factorslocation and agecontribute to growth of the main stem in the plants studied. To this purpose,
table 2 condenses values of the correlation coefficients (r) and of the determinant coefficients (R2),
together wth the associated p-values.
In our case, in order to predict growth in length of the main stem of the Asimina triloba (L.)
Dunal plant, we used two prediction models. The first calculates the extent to which plant age affects
modification of the main stem length. The second model analyzes the extent to which the two factors
of age and plant location, taken as a whole, affect main stem growth. The correlation coefficient values
for both models are significant (rmodel 1=0.676 p=0.000 and rmodel 2=0.780 p=0.000), meaning that
as the plant ages, length of the main stem will increase proportionally. Stem length is greater in Baia
Mare than in Lpuel.
1.4. Conclusions. Analyzing the data obtained following a statistical analysis, we found that for
Asimina triloba (L.) Dunal plants, conditions present in Baia Mare (temperature, exposure, wetness)
are significantly favorable for growth in length of the main stem. We can affirm that the two criteria
(plant age and location) taken together are significant in terms of main stem growth in the Asimina
triloba (L.) Dunal plant. We can also say, based on the results obtained, that in terms of importance
the two factors have in main stem growth, plant age has a weight of 45.3% in main stem growth of
the Asimina triloba (L.) Dunal plant (R2 model 1=0.453), while adding the location factor boosts
variation a further 8.8% (R2 model 2=0.541), so that model 2 contributes 54.1% of main stem growth.
Bibliography
[1] Desmond, R. Layne. (1996). The Pawpaw [Asimina triloba (L.)Dunal], A New Fruit Crop for Kentucky and the
United States, HortScience, Vol. 31(5), 777-784.
[2] Kral, R. (1960). A revision of Asimina and Deeringothamnus (Annonaceae) Brittonia, 12, 233-278.
[3] Layne, D. R. and R. N. Peterson. (1996) The pawpaw regional variety trial (RVT), Background, rationale and early
data HortScience 31:667.
ICAM9
102
Krzysztof Marzec
MTU Aero Engines Polska employee, Phd student at Rzeszw University of Technology, Department of Thermodynamics and Flow Mechanics, Poland
k.marzec@poczta.onet.pl
Abstract.Jet impingement heat transfer cooling systems plays significant role in many industrial applications. This is due to the fact that the impinged jet provides higher rate of heat and mass transfer.
Applications such as electronic chip cooling, cooling of photovoltaic cells, de-icing of aircraft wings, annealing of metals, heat exchangers in automotive and aeronautical applications, cooling of gas turbine
blades and other are a few examples of jet impingement cooling. Influence of the grid density, flow
mechanism and heat transfer, consisting of a numerical model of an impingement cooling jet directed to
the flat surface were investigated. The simulation were performed using Computational Fluid Dynamics
(CFD) code Ansys CFX that solves implicitly turbulent equations of continuity, momentum and energy
using the Reynolds Averaged Navier-Stokes approach. Numerical analysis of the different mesh density
resulted in good convergence of the GCI index what excluded mesh size dependency. The numerically
simulated values of the heat transfer coefficient and Nusselt number have also been compared with the
results obtained from the formulas coming from the physical experiments. The agreement was generally
good.
1.1. Introduction. The literature includes many investigations of a single impingement jets or
jet arrays. A variety of geometrical and physical parameters for the impingement cooling have been
studied. For example Goldstein [1] reported a fundamental analysis of heat transfer behavior under a
circular impingement jet. Present literature contain many numerical simulations of the impingement
cooling affecting both circular and slot types of the jets [2-4]. Zuckerman and Lior [5] presented review
of the various types of the geometries and designs of the impingement jet cooling. They also presented
comparison of different CFD turbulence models used in impingement jets problems.
An impingement jet is a jet of high velocity fluid which is made to strike a target surface. An
impinging jet can be classified as submerged jet or free jet. If the fluid issuing from the jet is of the
same density and nature as that of the surrounding fluid then the jet is called a submerged jet. If the
fluid issuing from the nozzle is of a different density and nature than that of the surrounding fluid
then the jet is called a free Jet. Fig. 1 describes these two different types of the jets configurations.
Figure 1 a) submerged jet, b) free jet
Further classification between jets can be made as confined and un-confined jets. In the case of
confined jets, the jet remains bounded between the two surfaces during its flow. There is very less
entrainment of air from the atmosphere. Un-confined jets are free to expand after they impinge on
the target surface.
1.2. Numerical Setup. In this section, an overview on the numerical setup investigated is
presented. The numerical grid density is taken into consideration.
Computational Domain
The chosen computational domain corresponded to a single cooling impingement jet directed to
a flat surface. In this study the nozzle diameter D=4mm was constant for all analysis. The nozzle
103
Figure 2 a) un-confined jet, b) confined jet
exit-plate distance y/D=20 mm and was also constant for all simulations. The total length of the
target plate measured L=15mm. This ensured that the outlet boundaries were far away from the
section of interest where the jet impinged onto the target plate.
The numerical calculations were carried out using unstructured grids with hexahedral elements
generated with Ansys CFX. The purpose of the simulation was to investigate the influence of the
numerical grid density on the results of the heat transfer coefficient and Nusselt number in stagnation
region. Therefore 4 analysis with cell size in the area of the interface (between air flow and flat surface)
was taken into consideration. For detail sizing of the mesh in area of the interface see table 1.
Table 1
parameters of the grids used in simulations
grid number number of cells cell size in interface area ∆X [mm]
1
28887
0,08
2
145559
0,04
3
265679
0,03
4
315679
0,025
1.3. Numerical Methods. In the following, the flow solver used for the present investigation is
presented. The accuracy of the results will be discussed in details.
Numerical solver
The simulation were performed using Computational Fluid Dynamics (CFD) code Ansys CFX,
that solves equations of continuity, momentum end energy using Reynolds-Averaged Navier-Stokes
approach.
In the present investigation the k ω shear stress transport (SST) turbulence model was
used. The SST model combines the k ω model near the wall and the k model farther from the wall
to utilize the strengths of each. Zuckerman and Lior [5] reported that SST model can produce better
predictions of fluid properties in impinging jet flows and are recommended as the best compromise
between solution speed and accuracy. Typical Nuo errors of 20-40%.
Numerical accuracy
To investigate the sensitivity of the results of the numerical analysis Grid Convergence Index
(GCI) was performed.
|
Uh2 −Uh1
|
U
GCI = rph1
· 100%
−1
In presented test for the grid number 3, a GCI value of 0,63% was obtained. Therefore further
changes of the grid density had no sense because of the extra time consumption with negligible quality
improvement. It can be concluded that numerical results on the fine grid are grid independent and
adequate grid density was chosen for the study.
104
Table 2
Grid Convergence Index
grid number density factor r Uh [K] GCI (%)
1
328,864
2
2,000
324,249 1,403316
3
1,333
324,78 0,631657
4
1,200
324,74 0,083973
1.4. Results and Discussion. This section provides analysis of the flow field behavior of the
impingement jet in the stagnation region with obtained GCI value of 0,63% . The results of heat
transfer coefficient and dimensionless Nusselt number are shown and compared to the results from
the literature.
This is interesting to note that, the impingement values of heat transfer have been
elaborated by Mohanty and Tawfek [6] in the experimental configurations and the stagnation point
Nusselt numbers have been correlated. This paper presents comparison of the Mohanty and Tawfek
[6] correlations based on experiments with numerical calculations. Comparison has given following
results:
• heat transfer coefficient h=19,2% discrepancy
• Nusselt number Nuo=15% discrepancy
Taking into account that numerical model was simplified by using steady state two-dimensional
analysis, the fluid physical properties were constant, and the effect of the gravity and radiation was
neglected we can assume that numerical experiments gives satisfying results and can be used to
describe physical phenomena and flow behavior in stagnation region. Moreover the obtained GCI
index 0,63% gave adequate grid resolution and excluded dependency of mesh density on the results of
the numerical experiment. Further analysis of the Nusselt number and heat transfer coefficient not
only in stagnation region can be made based on analyzed numerical model.
1.5. Conclusions. The aim of the work was the numerical simulation of the flow in stagnation
region based on an impinged cooling jet directed to the flat surface. Four analysis with different
mesh density using numerical solver Ansys CFX were done. Achieved GCI index 0,63% for the grid
with 0,03 mm in the interface region excluded mesh size dependency on the results. Obtained values
of the heat transfer coefficient and Nusselt number were compared with the correlations based on
physical experiments Mohanty and Tawfek [6]. Comparison of the mentioned correlations with values
from numerical experiments had given satisfying results of the flow characteristic in stagnation region.
Presented numerical model might be a basis for further researches for example of the average Nusselt
number along the impinged surface.
Bibliography
[1] Goldstein, R.J., Sobolik, K.A. and Seol, W.S. 1990., Effect of entrainment on the heat- transfer to a heated circular
air-jet impinging on a flat surface, ASME Journal of Heat Transfer, 112(3), Aug., pp. 608-611.
[2] Jian-Jun Shu, Heat transfer on a hot surface impinged by a cold circular liquid jet, V European Conference on CFD,
ECCOMAS CFD 2010.
[3] F. Ben Ahmed, B. Weigand, K. Meier, Heat transfer and pressure drop characteristics for a turbine casing
impingement cooling system, Proceedings of International Heat Transfer Conference, Aug. 2010, Washington, USA.
[4] Wael M. El-Maghany, Ahmed A. Hanafy, Khaled M. Abdou, Mohamed A. Teamah, Numerical simulation for
confined rectangular slot jets impingement on isothermal horizontal plate, European Journal of Scientific Research,
Vol. 76, pp. 553-566, 2012.
[5] N. Zuckerman, N. Lior, Jet impingement heat Transfer: Physics, Correlations and Numerical Modeling, Advanced
in Heat Transfer Vol 39, 2006.
[6] Mohanty, A.K.; Tawfek, A.A., Heat transfer due to a round jet impinging normal to a flat plate, Int. J. Heat Mass
Transfer 36 (1993) 1639-1647.
ICAM9
105
Scheiber Ernest
Department of Mathematics and Computer Science, Transilvania University, Braşov, Romania
scheiber@unitbv.ro
Abstract.The purpose of this paper is to state that the set of the control functions for a type of hybrid
optimal control problem may be not convex. In order to simulate a hybrid system, the main difficulty
is to generate admissible control functions, i.e. the corresponding trajectory of a control function
reaches the switching manifolds. For a test problem we compute a suboptimal solution using a heuristic
optimization procedure based on the parametrization of the problem data. The attention is focused on
the use of admissible control functions. The implementation is done within the Mathematica software.
1.1. Introduction. The purpose of this paper is to re-examine a hybrid optimal control sample
problem presented in [1]. We have found that the set of admissible control functions may be not
convex. We were interested to verify the numerical result reported in the above mentioned paper, too.
Unfortunately, this task is not a simple one. The details of used algorithm are only sketched. Even the
problem involves first order linear differential equations with constant coefficients, the computations
requires a computer program.
Numerical methods to solve hybrid optimal control problems are presented in [3], [2], but without
providing the implementations of the algorithms.
We have used heuristic methods based on the particular definition of the test problem. The
involved control functions will be admissible.
1.2. The hybrid optimal control problem. Following [1],[3] a hybrid control system (HS) is
defined by
• Q a finite set of discrete states;
• U ∈ Rm the set of admissible control values;
• fq : [0, 1] × Rn × U → Rn , q ∈ Q, setting the right hand side of ordinary differential equations;
• (Iq )q∈Q a family of subintervals of [0, 1]. The length of each subinterval is less than 1;
• There exists r ∈ N∗ and the unknown switching times
0 = t0 < t1 < . . . < tr < tr+1 = 1
such that
(1) [ti−1 , ti ) ⊆ Iqi ;
(2)
(3)
ẋ(t) = fqi (t, x(t), u(t)),
t ∈ [ti−1 , ti ),
qi ∈ Q;
for i ∈ {1, 2, . . . , r + 1} and x(0) = x0 .
We suppose that a switching time ti occurs when the trajectory of (3) reaches a switching
manifold Mi,i+1 , i ∈ {1, 2, . . . , r}.
The vector Rr+1 = (q1 , . . . , qr+1 ), q1 , . . . , qr+1 ∈ Q is called discrete trajectory and it
will be prescribed.
• U = {u ∈ L∞
m [0, 1] : u(t) ∈ U, a.e.[0, 1]; inducing the discrete trajectory
Rr+1 } the set of admissible control functions;
There is supposed that for any u ∈ U there exists a continuous trajectory xu (t) such that
xu |[ti−1 ,ti ) is the solution of (3).
Attaching to the HS a cost functional J(u) we obtained a hybrid optimal control problem (HOCP).
If J(u) = φ(xu (1)) then there is defined a Meyer type HOCP.
In order to simulate a HS, the main difficulty is to generate an admissible control function, i.e.
the corresponding trajectory reaches the switching manifolds. This constraint will be satisfied in the
case of controllable differentiable systems.
Further we suppose that
• fqi (t, x, u) = aqi x + bqi u, x, u, aqi , bqi ∈ R, i ∈ {1, 2, . . . , r + 1};
• the switching manifolds are Mi−1,i = {x ∈ R : x − x0i = 0}.
In other words, the switching time ti occurs when xu (ti ) = x0i .
106
If
2aqi eaqi (ti−1 −ti ) x0i − x0i−1 aq (ti−1 −t)
e i
,
bqi
1 − e2aqi (ti−1 −ti )
then the solution of the differential equation
(4)
u(t) =
t ∈ [ti−1 , ti ),
ẋ(t) = aqi x(t) + bqi u(t)
will satisfy the equalities x(ti−1 ) = x0i−1 and x(ti ) = x0i . The solution is given by
Z t
aqi (t−ti−1 ) 0
xi−1 + bqi
eaqi (t−s) u(s)ds.
(5)
x(t) = e
ti−1
It results that in this case U 6= ∅. As for the convexity of this set we state that:
Theorem. The set of admissible controls U may not be convex.
To prove this statement, let be r = 1, R2 = {1, 2} and the switching manifold M1,2 = {x ∈ R :
x − x01 = 0}.
Let u1 , u2 ∈ U be two control functions and t11 < t21 such that xu1 (t11 ) = xu2 (t21 ) = x01 .
We suppose that xu1 (t), xu2 (t) are increasing, 0 < x0 < x01 and that t11 , t21 are the smallest reaching
times. If follows that xu2 (t) 6= x01 , ∀t ∈ [t11 , t21 ).
Now we define
u1 (t), t ∈ [0, t11 ]
u1 (t) =
.
u2 (t), t ∈ (t11 , 1]
Then u1 ∈ U.
For 0 ≤ λ ≤ 1, we consider the control function
λu1 (t) + (1 − λ)u2 (t), t ∈ [0, t11 ]
.
uλ (t) = λu1 (t) + (1 − λ)u2 (t) =
u2 (t),
t ∈ (t11 , 1]
uλ ∈ U if and only if the corresponding trajectory xλu1 +(1−λ)u2 (t) reaches the manifold M1,2 , ie.
there exists tλ1 ∈ (0, 1) such that xλu1 +(1−λ)u2 (tλ1 ) = x01 .
For t ∈ [0, t11 ] we shall have x0 ≤ xu1 (t) ≤ x01 , x0 ≤ xu2 (t) < x01 and consequently xλu1 +(1−λ)u2 (t) =
u
1
λx (t) + (1 − λ)xu2 (t) < x01 .
Let us suppose the existence of tλ1 ∈ (t11 , 1]. For t11 < t ≤ tλ1 we have
xλu1 +(1−λ)u2 (t) = λxu1 (t) + (1 − λ)xu2 (t) =
!
!
Z t
Z t
u1 1
a1 (t−s)
u2 1
a1 (t−s)
= λ x (t1 ) + b1
e
u2 (s)ds + (1 − λ) x (t1 ) + b1
e
u2 (s)ds =
t11
t11
= λx01 + (1 − λ)xu2 (t11 ) + b1
Z
t
t11
ea1 (t−s) u2 (s)ds =
= λ(x01 − xu2 (t11 )) + xu2 (t).
For t = tλ1 , from the equality λ(x01 − xu2 (t11 )) + xu2 (tλ1 ) = x01 we obtain the contradiction
λ=
xu2 (t) − x01
> 1.
xu2 (t11 ) − x01
1.3. The test problem. The test HOCP is
Z t1
Z t2
Z 1
1
2
2
2
2
2
2
minimize J(u) =
(x1 + u1 )dt +
(x2 + u2 )dt +
(x1 + u1 )dt
2
0
t1
t2
subject to
ẋ1 (t) = −x1 (t) + 4u1 (t) t ∈ [0, t1 )
ẋ2 (t) = −2x2 (t) + 2u2 (t) t ∈ [t1 , t2 )
ẋ3 (t) = −4x3 (t) − 5u3 (t) t ∈ [t2 , 1]
107
with x1 (0) = x0 = 5. The control functions must satisfy the inequalities |uk (t)| ≤ 40, k ∈ {1, 2, 3}.
The switching times t1 < t2 are unknown and the switching occurs when the trajectory reaches the
manifolds
M1,2 = x + 3
M2,3 = x − 8.
The controls functions must involve the reaching of the switching manifolds.
In this case the discrete trajectory is prescribed as R = {1, 2, 3}.
Here we present only the obtained numerical results: x03 = 3.5 (the final state), t1 = 1/3, t2 =
0.854167, J(u) = 64.72.
The plot of the control function shows that the boundary constrain is satisfied, too.
Finally, we mention that the plots of the optimal control function and the corresponding state
have similarities with that given in [1].
Bibliography
[1] Azhmyakov V., A gradient-type algorithm for a class of optimal control processes governed by hybrid dynamical
systems. IMA J. of Mathematical Control and Information, 28(2011), 291-307.
[2] Silva J.M.E., Computational Methods for Dynamic Optimization of Hybrid Systems: a Survey., 2008.
[3] Zhang H., James M.R., Optimal Control for a Class of Hybrid Systems Under Mixed Costs. Proceedings of the 44th
IEEE Conference on Decision and Control, and the European Control Conference, Seville, Spain, December 12-15,
2005.
ICAM9
108
Simona Sabou, Liliana Zima, Rita Toader, Corina Rădulescu, Florina Hahn, Cristian
Vele
simona sabou@yahoo.com
Abstract.This paper presents a new models of performance assessment, performance assessment objectives and the problem of performance evaluation. A performance management system needs to be based
on the organisations business strategy and human resources strategy. The potential problems that need
consideration in approaching performance assessment as a component of the performance management
system. Implementing a performance management strategy involves adopting a management style that
encourages continuous communication between employee and management, feed-back often in both directions and fostering teamwork. The main purpose of the adoption of such strategies is to bring added
value to the organization by promoting and encouraging the development of performance skills. Performance management involves: defining and clarifying the responsibilities associated with each post;
defining and tracking of performance standards; communication roles, indexes and standards; assessing and documenting the performance level of each employee; tracking the evolution of the skills and
knowledge of each employee.
1.1. The mathematical model of performance assessment. From the mathematical modeling point of view, its about a non-linear regression with an independent variable
f (x) = b0 + b1 x + b2 x2 + . . . + bn xn
This problem can be reduced at a multiple linear regression problem, but this thing necessitates
to many calculations. The use of orthogonal Tchebashevs polynomials is more indicated to find the
searched polynomial and its optimum degree.
The working algorithm is specified below:
• It must be specified the number of the values N , the counter k = 1, 2...N and the index
j = 0, 1..n, where n is the maximum degree of the polynomial it depends of N , [3].
• Determination of the average xm of x variable:
xm =
N
1 X
xk
N
k=1
• It must be determined the step h of the x variable;
• The variable x is changed with variable u:
x − xm
h
of the y values are determined:
u=
• The average ym
ym
N
1 X
=
yk
N
k=1
• By recurrence, the values of the report Hj and Hj−1 are determined :
Hj
j 2 (N 2 − j 2 )
=
Hj−1
4 (4j 2 − 1)
, j = 1, 2 . . . n
• By recurrence, the values of the terms Hj are calculated:
H0 = N,
Hj = Hj−1
Hj
,
Hj−1
j = 1, 2 . . . n
109
• The orthogonal Tchebashevs polynomials are determined, by recurrence:
p(u)0 = 1 , p(u)1 = u,
p(u)j+1 = u p(u)j −
Hj
p(u)j−1 ,
Hj−1
j = 1, 2 . . . n
• It must be determined the coefficients cj of the polynomial f (u):
c0 = ym ,
cj =
N
1 X
yk p(u)k ,
Hj
j = 1, 2 . . . n
k=1
• It must be determined the optimum degree of the f polynomial by calculating the terms Sj :
S0 =
N
X
(yk − ym)2 ,
Sj = Sj−1 − c2j Hj ,
j = 1, 2 . . . n
k=1
If the calculated values Sj have the same size order, starting with a certain index j0,
then we can consider that j0 is the optimum degree of the f polynomial. Otherwise, the
degree of the polynomial is n.
• It must be formed the expression in u variable of the f polynomial having j0 degree:
f (u) = c0 + c1 u + c2 u2 + . . . + cj0 uj0
• Knowing that the u variable u = u(x), then f (u) must be replaced with f (x) by replacing
u(x) in f (u)s expression. So, it will be obtained the polynomial f (x) = f (u(x)) as following:
f (x) = b0 + b1 x + b2 x2 + . . . + bj0 xj0
The algorithm of calculation presented above can be implemented in any high level programming .
The evaluation criteria of individual performance are the following:
• the level of meeting the performance standards;
• assume responsibility;
• adequate labour complexity;
• initiative and creativity.
The regression equation obtained according to the proposed model is the following:
y1 = 65, 7 − 1, 25x1 − 0, 5x2 − 4x3
1.2. Conclusions. I think it is very important to adapt the performance indicators of the fiecari
people at personal development plan and framing in the development strategy of the company.
The professional performance evaluation constitutes an undisputable motivational element with
regard to the professional activity of every employee.
Performance assessment has a special influence upon the social-economical activity, the organizational environment in any business organisation.
An important aspect of human resources management is represented by performance assessment
within the organisation, because through evaluation we can better understand the dynamic nature of
professional development.
It is very important to establish criteria for evaluating performance.
Tracking the evolution of performances by referencing the data and results for multiple campaigns
through evaluation using multiple assessment tools, among which the evaluation forms The advantage
of an informal performance assessment system resides in the fact that it requires a smaller amount
of time for designing and administering, as compared to a formal assessment programme. This is
why informal performance assessment is used especially in those situations when the available time is
limited or when an interruption of the employees activity is not possible.
Bibliography
[1]
[2]
[3]
[4]
Burloiu, Petre, Human Resources Management, Editura LUMINA LEX, Bucureşti, 1997, pg. 612;
Certo C. Samuel, Modern Managemen, Editura Teora, Bucureşti, 2001;
Cole G. A. Personnel Management, Editura CODECS, Bucureşti, 2000;
Cole G. A. Management. Theory and Prcatice, Editura Ştiinţa, Chişinău, 2004.
110
[5] Chişu Ana Viorica, The Human Resources Specialists Manual, Casa de editură IRECSON, Bucureşti, 2002;
[6] Manolescu Aurel, Human Resources Management, Editura Economică, Bucureşti, 1999;
[7] Mathis L. Robert, Panait C. Nica, Rusu Costache, Human Resources Management, Editura Economică, Bucureşti,
1999;
[8] Pănişoară Georgeta, Pănişoară I. Ovidiu, Human Resources Management, Editura Polirom, 2004;
[9] Pitriu H. D., Human Resources Management Professional Performance Assessment, Editura All Beck, 2000;
ICAM9
111
Krasimira Stoilova, Todor Stoilov
Institute of Information and Communication Technologies-Bulgarian Academy of Sciences, Bulgaria
todor@hsi.iccs.bas.bg
Abstract.The investment process is formalized by hierarchical coordination for solving bi-level optimization problem. The optimal resource allocation of sets of securities, available at the financial market can
be done by solving multi-criterion optimization task, leading to maximization of portfolio return and
minimization of portfolio risk. Two-level hierarchical approach for solving the portfolio optimization
problem is applied. The optimal Sharp ratio of risk versus return is minimized at the upper level. As a
result is determined the investors preferences for taking risk on the basis of objective considerations.
1.1. Introduction. An investment process targets the maximization of the portfolio return and
minimization of the investment risk [2, 3, 4, 5, 7, 8]. The term risk reflects the undetermined and
non-predictable future. The financial risk cannot be predicted because of the dynamical and stochastic
market behaviour. In order to formalize the investment process, allocation of the financial resources
has to be done.
For the finance modelling and risk assessment essential contribution has the theory of Markowitz
[6]. This theory is based on both optimization and probability theory. For the practical utilization of
the portfolio theory, the relation between the return and risk is the main parameter for the investor.
The portfolio risk is minimized according to two types of arguments: the portfolio content and the
parameter of the investors risk preference. The last usually is done by subjective investors assumptions
for the relation portfolio risk/return. The paper targets the decrease of the subjective influences in the
investment process. The unknown investors coefficient for undertaking risk is determined according to
optimization problem. The portfolio investment is formalized by a bi-level optimization problem. The
parameter of the investors risk preference is evaluated at the upper level. This parameter is used for
optimal resource allocation of the portfolio optimization problem by minimizing risk and maximizing
return. As a result the definition of the portfolio problem is performed without subjective influences.
1.2. Portfolio Optimization Problem. The portfolio theory is developed to support decision
making for allocation of investment to financial assets by selling and buying securities/bounds at the
stock exchange [1]. The resource allocation means to invest financial resources per different assets or
goods. Later these assets will give return to the investor after a period of time. The portfolio contains
a set of securities. For the investment process the target is to maximize the return and to minimize
the risk of the portfolio [8]. The analytical relations among the portfolio risk Vp , portfolio return Ep
and the values of the investment per type of assets xi , according to the portfolio theory, are [9]
Ep =
n
X
i=1
Ei xi = E T xVp =
n X
n
X
j
xi xj cov (i, j) = xT cov (·) x,
i=1
where xi - the relative amount of the investment, allocated for buying asset i; Ei - the average value
of the return of asset i; E T = (E1 , E2 , . . . , En )T - a vector with dimension 1 × n; cov (i, j) - the
co-variation coefficient between the assets i and j.
The component Vp = xT cov (·) x formalizes the quantitative assessment of the portfolio risk. The
component Ep = E T x is the quantitative evaluation of the portfolio return. The portfolio problem
solutions xi , i = 1, n determine the relative amounts of the investment per security i.
The portfolio theory defines the so called standard optimization problem by [9]:
(
min 21 xT cov (·) x − σE T x
xT .1 = 1
where
cov (·) x is a symmetric positively defined square matrix n × n;
E is a (n × 1) vector of the average profits of the assets for the period of time T = [1, 2, . . . , N ];
1 = |1 . . . 1|T is the unity vector, n × 1;
σ - is a parameter of the investors preferences to undertake risk in the investment process.
112
1.3. Hierarchical bi-level optimization problem. For the bi-level optimization problems
the upper level solves optimization problem, which solutions influence the lower level optimization
problems. The lower level solutions influence on its turn a set of parameters for the upper level
problem. Because of this mutual interrelation between the upper and lower level optimization problems
with their solutions, the resulting global problem is a bi-level one. From application considerations,
the solution of such problem is a difficult task. The complexity of the bi-level optimization problems
requires its solution to be made with numerical iterative calculations.
Currently, the portfolio problem is solved by quantitative assessment of σ ∗ in advance, without
applying interconnected hierarchical optimization. The value of σ ∗ is estimated intuitively or empirically
by an expert. The paper suggests the solution of the bi-level portfolio problem to be performed using
the concept of the non-iterative coordination [10, 12]. The concept of the non-iterative coordination
in hierarchical systems defines analytical approximations of the inexplicit functions, used by the
upper and lower optimization problems. In that manner, analytical relations between the investors
preferences for the risk σ and the solutions xi are derived [11]. Such relations support fast solution of
the bi-level problem and respectively allow real time decision making. The upper level problem is
defined with a goal function, which minimizes the Sharp ratio: portfolio risk versus portfolio return.
The argument of this optimization problem is the investors preferences for taking risk σ. Applying the
noniterative methodology [10, 12], analytical relations between the portfolio problems parameters
Ep (σ) Vp (σ), the portfolio solutions xi (σ) from the parameter of the investors preference σ are derived.
These relations allow speeding up the decision making process and the investment decisions can be
done in real time.
1.4. Conclusions. The process of decision making is presented as a two-level optimization system.
The upper level defines the optimal value of the parameter of risk preferences of the investor σ by
minimizing Sharp ratio (portfolio risk versus portfolio return). The lower optimization level uses σ
and solves the portfolio optimization problem. The bi-level formalism in a unique way defines the most
appropriate value of σ by optimizing the Sharp ratio. In that manner, the bi-level formalism achieves
two benefits: it reduces the subjective assessment of the investors risk preferences and it applies the
optimal value of σ by minimizing the Sharp ratio. These two outcomes considerably improve the
content of the portfolio problem with the bi-level definition in comparison with the classical definition
of one level portfolio optimization problem. The paper develops and applies a special method for
solving the optimization problem, titled non-iterative coordination. It allows to be defined explicitly
in analytical way the upper level optimization problem for solving and to derive explicit analytical
relations between the portfolio problem solutions and σ, x(σ).
ACKNOWLEDGEMENT This work is partly supported by project AComIn-Advanced Computing for Innovation, Grant Agreement: 316087, 2012-2016
Bibliography
[1] Bodie, Z., Kane, A., Marcus, A., Investments. Naturela, Sofia (2000)
[2] Kohlmann, M., Tang, S., Minimization of risk and linear quadratic optimal control theory, SIAM J. Control optim,
Vol. 42, No. 3 (2003) 11181142
[3] Korn, R., Continuous-Time Portfolio Optimization Under Terminal Wealth Constraints, ZOP-Mathematical Methods
of Operations Research, Vol. 42 (1995) 69-92
[4] Magiera, P., Karbowski, A., Dynamic portfolio optimization with expected value-variance criteria, Bucharest (2001)
308-313
[5] Markowitz, H. M., Portfolio selection, J. of finance, Vol. 7 (1952) 77-91
[6] Mateev, M., Analysis and assessment of investment risk, University publisher Economy, Sofia (2000) In Bulg.
[7] Sharpe W., Alexander, G., Bailey J., Investments, Prentice Hall, England Cliffs, New Jersey (1999)
[8] Sharpe, W., Portfolio theory & Capital markets, Mc Grow Hill, No4 (2000)
[9] Stoilov, T., Stoilova, K., Noniterative Coordination in Multilevel Systems, Kluwer Academic Publisher, Dordrecht/Boston/London (1999)
[10] Stoilova K., Stoilov, T., Noniterative Coordination Application in Solving Portfolio Optimisation Problems, Proceedings of the International Conference Automatics and Informatics, Vol. 1. Sofia (2003) 159-162.
[11] Stoilova, K., Predictive Noniterative Coordination in Hierarchical Two-level Systems, Comptes rendus de lAcadmie
bulgare des Sciences, Vol. 58, 5 (2005) 523-530
ICAM9
113
The effects of different queuing techniques over VoIP performance: a simulation approach
Szabolcs Szilágyi
Department of Computer Science, University of Oradea, Oradea, Romania
sszilagyi@uoradea.ro
Abstract. This paper presents one of the features of DS (Differentiated Services) architecture, namely
the queuing or congestion management. Packets can be placed into separate buffer queues, on the basis
of the DS value. Several forwarding policies can be used to favor high priority packets in different
ways. The major reason for queuing is that the router must hold the packet in its memory while the
outgoing interface is busy with sending another packet. Our main goal is to compare the performance
of the following queueing mechanisms: FIFO (First-In First-Out), CQ (Custom Queuing), PQ (Priority
Queuing), WFQ (Weighted Fair Queuing), CBWFQ (Class Based Weighted Fair Queuing) and LLQ
(Low Latency Queuing).
1.1. Introduction. At the beginning computer networks were designed mainly for data transfer
such as FTP and email, where delay was considered to be unimportant. In most cases the delivery
service was effective, and the TCP protocol dealt with data losses. As the multimedia applications
became popular (voice transfer, video conferences), separate telephone and video communication
networks were set up. Nowadays, office and company networks are transformed into one converged
network (see [1]), in which the same network infrastructure is used to ensure all the requested services.
Although converged networks have many advantages, there are some disadvantages too, namely the
competition for network resources (buffers of routers), which leads to congestion. Delay in delivering
the packets, jitter, loss of packets are all consequences of congestion. Not each application is sensitive
to these issues. For example, FTP is not impacted by delay and jitter, whereas the multimedia
applications (video, voice) are very sensitive to them and the loss of packets too. QoS was introduced
to handle this problem, and it is able to provide better multimedia performance (see [2]).
In the IP header there are some fields which can be used to make distinction between the packets
of different applications, for example the Type of Service field. Different technics such as congestion
management (PQ, CQ, WFQ, CBWFQ, LLQ), prevention of congestion (WRED), resource efficiency
insurance (fragmenting the packets, and compressing), traffic shaping and traffic policing are used
by the QoS technology in order to control data traffic. This article focuses on the most important
component, the congestion management.
Speed mismatches and path aggregations (see [1]) are the main causes of congestion in computer
networks. There are different algorithms which can overcome the mentioned problematic situations.
Our purpose is to analyze and evaluate the efficiency of these algorithms using simulations. We are
going to examine the following methods: FIFO, PQ, CQ, CBWFQ, WFQ and LLQ. It is important to
note that these algorithms have real effect only in case of congestion (see [3]).
The OPNET IT Guru Academic Edition (see [4]-[6]) was used to perform the simulation. The
network topology for the testing is identical with the one occurred in former articles (see e.g. [6]-[8]).
In this paper we continue to study the queueing technologies for congestion management. In [7] and [8]
the authors considered three algorithms: FIFO, PQ and WFQ. The conclusion was that WFQ is the
most efficient for multimedia applications. In addition to these we investigate three new algorithms:
CQ, CBWFQ and LLQ. The main result of this paper is that for multimedia applications (mainly
voice transfer) LLQ is more efficient then WFQ.
The mentioned algorithms has been examined in several papers (see e.g. [10] ).
1.2. Simulation environment and settings. We used the following network topology in
OPNET IT Guru Academic Edition:
The measurement environment consists of 2 routers, 2 switches and 6 hosts. The routers are
connected with a point-to-point link, having the speed of ppp-DS1. The rest of the hosts are connected
with 10BaseT. The part between the two routers is actually a narrow cross-section where congestion
can happen. For this reason the congestion management algorithm is activated in this area (see
[11]-[12]).
114
Figure 1 Simulation network topology
1.3. Simulation results. Simulation makes possible to perform several measurements and
statistical analysis. The following main indicators are investigated: the packet loss rate, the number of
received packets, the delay of packets between the endpoints and jitter. The length of the simulation
was 5 minutes in each case. Congestion management algorithms are activated only in the case of
congestion. The graph below presents this fact: it is the 105th second when the congestion management
algorithm becomes active and its performance study can be started. Figures 2-7 show the results of
the simulation.
The highest rate of packet loss (see Fig.2.) was produced by the FIFO rule, as it could be expected.
In the case of PQ, the loss of audio packets is zero, due to the existence of the highest priority queue.
The loss of video and FTP packets is extremely high in this case (see Fig.3.), as the highest priority
queue (voice traffic) blocks the video and FTP communication. Using CQ we can get better results
than using PQ, concerning the packet loss, but it requires a lot of fine-tuning work. WFQ, CBWFQ
and LLQ are the most efficient mechanisms concerning the packet loss.
In the case of voice communication there were examined the following performance parameters:
the number of received voice packets, the delay of voice packets and the variation in the delay of voice
packets (see Fig.3-7). Concerning the number of received voice packets the performance of the PQ,
WFQ, CBWFQ and LLQ mechanisms is the most efficient. CQ and FIFO show a bit worse results
but they are acceptable too. Interactive voice communication requires a maximum of 150 ms delay for
voice packets (see [13]). FIFO and CQ cannot fulfill this criterion. QoS also requires that the jitter do
not exceed 30ms. FIFO and CQ didn’t fulfill this criterion too.
Finally, the four most efficient algorithms (PQ, WFQ, CBWFQ, LLQ) were compared in respect
of the delay of voice packets and jitter. The reason of choosing the voice packets is that they are
very sensitive to delay and jitter. The result is interesting (see Fig.5 and 7.). Previous articles (see
e.g. [6]-[7]) showed that WFQ is the most efficient for voice packets. It can be observed that WFQ
and CBWFQ have the highest dispersion for the delay. WFQ has the highest value for jitter, much
higher than in the case of PQ and LLQ. It is obvious (see Fig.5. and 7.) that LLQ has much better
performance for voice packets than WFQ.
1.4. Conclusions. In this paper ∗ we tried to present a short overview of congestion management
algorithms used by routers. We managed to evaluate three more algorithms beside the ones published
in former articles (see e.g. [6]-[7]). The simulation environment was provided by the OPNET IT Guru
Academic Edition application, based on mathematical models. We used a generalized, extendable and
factual network topology. The article concludes that LLQ is the most efficient algorithm for voice
∗
The work was supported by the TÁMOP-4.2.2.C-11/1/KONV-2012-0001 project. The project has been supported
by the European Union, co-financed by the European Social Fund.
115
[]
Packet loss (pkts)
Figure 2 IP packet loss
FIFO
PQ
CQ
WFQ
CBWFQ
LLQ
100
50
0
0
100
200
Time (s)
300
[]
Traffic received (pkts/s)
Figure 3 VoIP: Packet received
400
FIFO
PQ
CQ
WFQ
CBWFQ
LLQ
200
0
0
100
200
Time (s)
300
data transfer. Our next research topic is to examine and test the algorithms presented in the current
article in a real network environment, as it is also a widely used by reasearchers (see e.g. [14]) to
perform traffic measurements.
Bibliography
c
[1] QOS, Implementing Cisco Quality of Service, Student Guide, Vol. 1-2, Ver. 2.2, Cisco
Systems Inc., 2006
[2] A. S. Ranjbar, CCNP ONT Official Exam Certification Guide, Cisco Press, 2007
[3] B. Durand, J. Sommerville, M.Buchmann, R. Fuller, Administering Cisco QoS in IP Networks, Syngress Publishing,
Inc., 2001
[4] www.opnet.com
[5] T. Svensson, A. Popescu, Development of laboratory exercices based on OPNET Modeler, Master thesis, Blekinge
Institute of Technology, Department of Telecommunications and Signal Processing, 2003
[6] A. Kuki, Tools for Performance Evaluation and Modeling in Higher Education of Informatics, Informatics in the
Hungarian Higher Education, Debrecen, Hungary 70-77, 2010
[7] M. M. G. Rashed, M. Kabir, A Comparative Study of Different Queuing Techniques in VoIP, Video Conferencing
and FTP, Daffodil International University Journal of Science and Technology, Volume 5, Issue 1, January 2010
[8] S. Akhtar, E. Ahmed, A. k. Saka, K. S. Arefin Performance Analysis of Integrated Service over Differentiated Service
c
for Next GenerationInternet, JCIT,
ISSN 2078-5828 (print), ISSN 2218-5224 (online), Vol. 1, Issue 1, 2010
[9] S. Farhangi, S. Golmohammadi, A comparative study between combination of PQ and MWRR Queuing techniques
c
in IP network based on OPNET, Advances in Computer Science and its Applications, Vol. 1, No. 1, World
Science
Publisher, United States, March 2012
[10] Sz. Szilágyi, B. Almási, A Review of Congestion Management Algorithms on Cisco Routers, Journal of Computer
Science and Control Systems, University of Oradea, Vol.5, Nr.1, ISSN 1844-6043, 2012
[11] A. S. Sethi, V.Y. Hnatyshin, The Practical OPNET User Guide for Computer Network Simulation, CRC Press
Taylor & Francis Group, NW, 2012
[12] L. L. Peterson, B. S. Davie, Computer Networks: A System Approach - Network Simulation Experiments Manual,
c
3rd Edition, Elsevier
Inc., 2011
116
[]
Packet end-to-end delay (s)
Figure 4 VoIP: Traffic delay
1.5
1
0.5
FIFO
PQ
CQ
WFQ
CBWFQ
LLQ
0
0
100
200
Time (s)
300
[]
Packet end-to-end delay (s)
Figure 5 VoIP: Traffic delay for PQ, WFQ, CBWFQ and LLQ
·10−2
1
0.5
PQ
WFQ
CBWFQ
LLQ
0
0
100
200
Time (s)
300
[13] P. K. Verma, L. Wang, Voice over IP Networks - Quality of Service, Pricing and Security, Lecture Notes in Electrical
Engineering, Vol. 71, Springer, 2011
[14] B. Almási, A. Harman, An Overview of the Multipath Communication Technologies, Proceedings of the Advances in
Wireless Sensor Networks (AWSN), Debrecen, Hungary, 2013 (to appear)
ICAM9
[]
Packet delay variation (s)
Figure 6 VoIP: Traffic jitter
0.2
0.1
FIFO
PQ
CQ
WFQ
CBWFQ
LLQ
0
0
100
200
Time (s)
300
[]
Packet delay variation (s)
Figure 7 VoIP: Traffic jitter for PQ, WFQ, CBWFQ and LLQ
·10−5
8
6
PQ
WFQ
CBWFQ
LLQ
4
2
0
0
100
200
Time (s)
300
118
János Sztrik and Tamás Bérczes
Faculty of Informatics, University of Debrecen, Hungary
sztrik.janos@inf.unideb.hu, berczes.tamas@inf.unideb.hu
Abstract. This paper deals with the role of performance modeling tools for investigation of queueing
systems. Advantages and drawbacks are considered when modeling and analysis issues are treated. For
illustration the authors introduce 4 major tool developer centers. Due to the growing importance in
practical applications, for example in Future Internet engineering, the reliability analysis of finite-source
retrial queueing system is presented by using the MOdeling, Specification and Evaluation Language
(MOSEL) software. A sample numerical example is given demonstrating the effect of failure of server
on the mean response time of sources. Finally, investigating this model benchmarks to compare the
efficiency of MOSEL and PRobabIliStic Model Checker (PRISM) tools concerning execution time, model
construction time, model checking time are carried out.
1.1. Some recent modeling tools. In the following 4 major tool developer centers are introduced briefly.
Tools at Faculty of Informatics, University of Dortmund, Germany This traditionally
famous center has developed several software packages which can be downloaded from the site:
http://ls4-www.informatik.uni-dortmund.de/tools.html.
Parallel to their methodological work the center continuously developed and used tools for performance
evaluation and performability. Their intention is to provide facilities for a model description close to
the original system specification and hiding details of the analysis techniques. Such tools map the
model specification automatically to an analyzable model.
Möbius Tool Möbius is a software tool for modeling the behavior of complex systems. It is one
of the major research projects of the Performability Engineering Research Group (PERFORM) in
the Coordinated Science Laboratory at the University of Illinois at Urbana-Champaign, USA. Many
advanced modeling formalisms and innovative and powerful solution techniques have been integrated
in the Möbius framework.
The package can be found at http://www.mobius.uiuc.edu/.
MOSEL Tool
Performance modeling tools usually have their own textual or graphical specification language
which depends largely on the underlying modeling formalism. MOSEL ( MOdeling,Specification
and Evaluation Language) tool, developed at the University of Erlangen, Germany, is based on the
following idea: Instead of creating another tool with all the components needed for system description,
state space generation, stochastic process derivation, and numerical solution, it focuses on the formal
system description part and exploit the power of various existing and well tested packages for the
subsequent stages. In order to reuse existing tools for the system analysis, the environment is equipped
with a set of translators which transform the MOSEL model specification into various tool-specific
system descriptions. For further details see [2].
MOSEL-2 provides means by which many interesting performance or reliability measures and the
graphical presentation of them can be specified straightforwardly. All information can be found at
http://www4.informatik.uni-erlangen.de/Projects/MOSEL/.
PRISM Tool
The PRobabIliStic Model checker PRISM provides a high-level modeling language for describing
systems that exhibit probabilistic behavior, with models based on continuous-time Markov chains
(CTMCs) as well as discrete-time Markov chains (DTMCs) and Markov decision procedures (MDPs).
For specifying system properties, PRISM uses the continuous stochastic logic (CSL) for CTMCs and
probabilistic computation tree logic (PCTL) for DTMCs and MDPs, both logics being extensions of
computation tree logic (CTL), a temporal logic that is used in various classical model checkers for
specifying properties. For further details, see for example [7].
The package can be downloaded from http://www.prismmodelchecker.org.
1.2. Finite-source retrial queues with a single server subject breakdowns and repairs.
Due to the growing importance of using retrial queueing systems for modeling complex communication
119
systems in Future Internet applications we show an example for using MOSEL to analyze a retrial
queueing system with the following assumptions. Consider a single server queueing system, where
the primary calls are generated by K, 1 < K < ∞ homogeneous sources. The server can be in three
states: idle, busy and failed. If the server is idle, it can serve the calls of the sources. Each of the
sources can be in three states: free, sending repeated calls and under service. If a source is free at
time t it can generate a primary call during interval (t, t + dt) with probability λdt + o(dt). If the
server is free at the time of arrival of a call then the call starts to be served immediately, the source
moves into the under service state and the server moves into busy state. The service is finished during
the interval (t, t + dt) with probability µdt + o(dt) if the server is available. If the server is busy at
the time of arrival of a call, then the source starts generation of a Poisson flow of repeated calls with
rate ν until it finds the server free. After service the source becomes free, and it can generate a new
primary call, and the server becomes idle so it can serve a new call. The server can fail during the
interval (t, t + dt) with probability δdt + o(dt) if it is idle, and with probability γdt + o(dt) if it is busy.
If δ = 0, γ > 0 or δ = γ > 0 active or independent breakdowns can be discussed, respectively. If the
server fails in busy state, it either continues servicing the interrupted call after it has been repaired or
the interrupted request transmitted to the orbit. The repair time is exponentially distributed with a
finite mean 1/τ . If the server is failed two different cases can be treated. Namely, blocked sources case
when all the operations are stopped, that is neither new primary calls nor repeated calls are generated.
In the unblocked (intelligent) sources case only service is interrupted but all the other operations are
continued (primary and repeated calls can be generated). All the times involved in the model are
assumed to be mutually independent of each other. More information about retrial queueing systems
can be read, for example in [1], [4], [5, 6].
For illustration our main objective is to demonstrate how the mean response time of calls depend
on server’s failure rates. To achieve this goal MOSEL is used to formulate and solve the problem.
The system state at time t can be described by the process
X(t) = (Y (t); C(t); N (t)), where Y (t) = 0 if the server is up, Y (t) = 1 if the server is failed, C(t) = 0 if
the server is idle, C(t) = 1 if the server is busy, N (t) is the number of sources of repeated calls at time t.
Because of the exponentiality of the involved random variables this process is a Markov chain with a
finite state space. Since the state space of the process (X(t), t ≥ 0) is finite, the process is ergodic
for all reasonable values of the rates involved in the model construction, hence from now on we will
assume that the system is in the steady state.
We define the stationary probabilities:
P (q; r; j) = lim P (Y (t) = q, C(t) = r, N (t) = j),
t→∞
q = 0, 1, r = 0, 1, j = 0, ..., K ∗ ,
∗
where K =
K −1
K −r
for blocked case,
for unblocked case.
The advantage of using tools is that we do not have to deal with the numerical problems of finding
the steady-state probabilities. We have to concentrate how to formulate the problem by the help of a
describing language ( usually Petri nets ) and then the whole process is automatic. In our case, the
states and transition rates of the continuous time finite state Markov chain is constructed and the
stationary distribution is calculated by the help of a so-called solver. The problem arising in practical
problems is the state space explosion which causes numerical problems due to the large number of
unknowns. It should be noted that there is no closed form solution to this problem. However, as
usual an algorithmic approach could be used to get the steady-state probabilities, see [1],[8] . This
means an extra work in programming and displaying the results graphically which is in our case is an
built-in module that is why we can omit it.
120
1.3. Numerical examples. We used the tool SPNP which was able to handle the model with
up to 126 sources. In this case, on a computer containing a 1.1 GHz processor and 512 MB RAM,
the running time was approximately 1 second. A more detailed investigation was published in [3]
illustrating other effects as well.
Figure 1 E[T ] versus server’s failure rate
In Figure 1 we can see the mean response time for the reliable and the non-reliable retrial system
when the server’s failure rate increases. The input parameters are collected in Table 1.
Figure 1
Table 1
K λ
6 0.8
µ ν
4 0.5
δ, γ
x axis
τ
0.1
Input system parameters
Comments
In Figure 1, we can see that in the case when the request returns to the orbit at the breakdown
of the server, the sources will have always longer response times. Although the difference is not
considerable it increase as the failure rate increase. The almost linear increase in E[T ] can be explained
as follows. In the blocked (non-intelligent) case the failure of the server blocks all the operations and
the response time is the sum of the down time of the server, the service and repeated call generation
time of the request (which does not change during the failure) thus the failure has a linear effect on
this measure. In the intelligent case the difference is only that the sources send repeated calls during
the server is unavailable, so this is not an additional time.
Benchmarks In the following we give some comparisons between the MOSEL and PRISM tools
showing how the number of terminals (NT) influences the execution time and total execution time.
The following preliminary conclusions can be drawn from benchmark:
• The execution times of the MOSEL system almost stay constant independently of NT ;
121
Figure 2 Execution Time
• The execution times of the PRISM system increase rapidly with the increase of NT.
• The model construction time in PRISM dominates the execution time rather than the model
checking time.
While MOSEL is thus more efficient for smaller models, with PRISM also larger models can be
analyzed. Furthermore, once a PRISM model is constructed, it can be arbitrarily often model checked
with different parameter values. For such scenarios, the model checking time is more relevant than
the model construction time.
Acknowledgment: This research was partially granted by the Hungarian Science and Technology
Foundation, Hungarian- French Bilateral Cooperation under grant TeT 10-1-2011-0741, FR- 25/2010.
The publication was also supported by the TÁMOP-4.2.2.C-11/1/KONV-2012- 0001 project. The
project has been supported by the European Union, co- financed by the European Social Fund.
Bibliography
[1] Artalejo, J.R. and Gomez-Corral, A., Retrial Queueing Systems, Springer, 2008
[2] Begain, K. and Bolch, G. and Herold, H., Practical performance modeling, application of the MOSEL language,
Kluwer Academic Publisher , 2001
[3] Bérczes, T. and Guta, G. and Kusper, G. and Schreiner, W. and Sztrik, J., Evaluating a probabilistic model checker
for modeling and analyzing retrial queueing systems, Annales Mathematicae et Informaticae, Vol. 37, 51-75 (2010)
[4] Bérczes, T. and Orosz, P. and Moyal, P. and Limnios, N. and Georgiadis, S. and Sztrik, J., Tool supported modeling
of sensor communication networks by using finite-source priority retrial queues, Carpathian Journal of Electronic
and Computer Engineering, Vol. 5, 13-18 (2012)
[5] Do, V.T. , An efficient solution to a retrial queue for the performability evaluation of DHCP , Computers & OR,
Vol. 37, 1191-1198 (2010)
[6] Do, V.T. , A new computational algorithm for retrial queues to cellular mobile , Computers & Industrial Engineering,
Vol. 59, 865-872 (2010)
[7] Kwiatkowska, M. and Norman, G. and Parker D., PRISM: Probabilistic Model Checking for Performance and
Reliability Analysis, ACM Sigmetrics Performance Evaluation, Vol. 36, 40-45 (2009)
[8] Lakatos, L. and Szeidl, L. and Telek, M., Introduction to Queueing Systems with Telecommunication Applications,
Springer, 2012
ICAM9
122
Cezar Toader, Rita Toader and Corina Rădulescu
Department of Economics, Faculty of Sciences, Technical University of Cluj-Napoca, North University Centre of Baia Mare, Romania
cezar.toader@cunbm.utcluj.ro; rita.toader@cunbm.utcluj.ro; corina.radulescu@cunbm.utcluj.ro
Abstract.The increasing importance of better customization of industrial products has led to development
of configurable products. Description and management of a large variety of products within a single data
model is challenging and requires a solid conceptual basis. This paper refers to important aspects of the
evolution of Web applications architecture, according to the evolution of the Web, through creation of
new levels of abstracting, while a special importance to scalability and adaptability was given. Due to
a growing importance given to resource-oriented Web services, in the last years, this paper brings into
discussion the principle of organizing the algorithmic resources in multi-level hierarchy and the principle
of uniform access to resources. Finally, in order to implement these principles, the author promotes an
architectural model of Web Applications.
1.1. Introduction. Product families, product configuration and product data management are
research areas with great deal of practical importance for traditional products, i.e., mechanical and
electronic products. A configurable product, or a product family, is such that each product individual
is adapted to the requirements of a particular customer order on the basis of a predefined configuration
model, which describes the set of legal product variants.
One challenge is to find the correct concepts for modeling configurable products so that the
descriptions can be kept up to date as the product evolves. The challenge has not been adequately
answered by the research in product configuration, product modeling standards or commercial product
data management (PDM) systems [3].
Configuration modeling does not fit nicely into the data modeling view for various reasons. Firstly,
configuration models need new concepts, such as has-part relation with alternative parts, not available
as traditional data modeling concepts. Secondly, as companies develop their products, product family
descriptions are constantly changed. Thirdly, individuals of configurable products have long lifetimes
and histories of their own. They evolve independently since customers may change their products as
they please.
1.2. Product configuration concepts. Configurable products clearly make a separation between the process of designing a product family and the process of generating a product individual
according to the product configuration model. This places configurable products in between mass
products and one-of-a-kind products by enabling customer specific adaptation without losing all
the economic benefits of mass-products. Knowledge based systems for configuration tasks, product
configurators, have recently become an important application of artificial intelligence techniques for
companies selling products adapted to customer needs [5].
The difficulties in managing configuration models are widely recognized, the vast majority of the
models ignore all aspects related to the evolution of configuration models.
Versionis a concept for describing the evolution of products. Versions typically represent the
evolution of a generic object that, in turn, has a set of versions. A generic object is sometimes also
called a generic version or generic instance. There can be two kinds of component references to
versions: statically bound and dynamically bound [6].
Schema evolution is a relevant issue for databases. The approaches to schema evolution can be
classified to filtering, persistent screening and conversion. In filtering, a database manager needs to
provide filters so that an operation defined on a particular type version can be applied to any instance
of any version of the type [4].
1.3. Resource Oriented Architectures. The concept of Resource Oriented Architectures
(ROA) gradually developed and some authors made several comparisons between these architectures and those based on services or those based on activities. Resource oriented architectures
developed based on the concepts of: resources, their identification, their representation, and links
between them.
123
Figure 3 Layered architecture of a distributed application
The technology of Uniform Resource Identifiers is fundamental for the Web because allows the
interconnection of Web resources. The principles that URI technology is based on are described by
Tim Berners-Lee back in 1996, [1]. Resource oriented architectures follow several principles, described
below:
• Addressability. A Web application based on ROA exposes an URI for every resource.
• Statelessness. Every HTTP request is completely isolated from the other requests.
• Connectedness. The resources have to be interconnected in their representation and, as a
consequence, a Web service can be put in different states by calling different links.
• Uniform interfaces to resources. The access to any Web resource can be made using
standardized HTTP methods: GET, PUT, POST, DELETE, HEAD, and OPTIONS.
Two important characteristics must be emphasized here: the way a resource is addressed, and the
lack of state information between HTTP requests. The Web was developed by creating new levels of
abstracting, but its initial simplicity was necessary at that moment. The subsequent development
of the Web and development of Web services required a special attention given to scalability and
adaptability.
When Fielding published his doctoral thesis Architectural Styles and the Design of Network-based
Software Architectures, he promoted a set of principles defining a Web-based architectures programming
style named REST (Representational State Transfer), [5]. Since then, the architectures following those
principles have got the attribute RESTful.
A large Web application having a modularized interface, can be as shown in Fig.1. Different
areas in application interface are, basically, interfaces of specialized task-oriented applications running
behind the scene. On the highest level, these specialized Web applications are waiting for requests
from the network. In order to fulfill the requests, these applications need to access different kind of
resources: static or dynamic HTML, static XML, Web services based on XML, etc.
According to their role in a complex application, several layers can be defined in order to group
these resources. Starting from top to bottom, it is necessary to define these layers: Task Layer, Entity
Layer, and Utility Layer, as we can see in Figure 1.
The highest level of the proposed architecture is Task Layer. It contains several Web applications
which can be called by external software, for example by a Web browser. In order to fulfill specific
tasks, an application on this level executes a set of operations:
• it builds the URI of requested resource according to the established hierarchy;
• it accepts the redirection toward a certain resource situated on Entity Layer;
• it gets a representation of data, usually in a form of XML file;
• it builds the response in HTML format, according to a specific template.
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Figure 4 RESTful Multilayer architecture of a Web application
The Web applications situated on the higher level are oriented, by their design, to specific tasks.
Their reusing potential for other tasks is relatively low. According to the request made by the client,
the applications on the Task Layer access resources situated on Entity Layer.
The Entity Level is subordinated to the application on the Task Layer. This level contains various
software modules, specifically designed for the application, which are considered Web resources for the
higher level. The resources on the Entity Level can deal with RPC-style requests. Modern applications
use Web services in order to have a uniform type of access to data. Web services offer datasets in
XML format. Web resources on Entity Layer request data from the Web services offered by the lower
level, Utility Layer. Applications having such complex architecture are often developed during many
years, by many programmers, and using different technologies. It is very likely that these old resources
are RPC-style. If so, the applications situated on the highest level should use RPC-style URIs instead
of REST-style URIs.
1.4. Restful multilayer architectures. In this paper, the authors propose a solution for the
following issue: how to modify the application architecture in order to permit the highest level
applications to use RESTful URIs and, without their knowledge, the lowest level resources to be called
using RPC-style URIs?
One solution of this problem which consists in creation of a specific method to transform the
RPC-style URIs in REST-style URIs, with respect of existing resource hierarchy.
The proposed solution consists in inserting a new adapting layer between Task Layer and Entity
Layer. Hence a new architecture is created where the highest level applications can use only REST-style
URIs to access all resources on the lowest level, no matter that they are REST-style or RPC-style.
One appropriate name is RESTful Multilayer Architecture [7].
The goal of RESTful Multilayer Architecture is to permit the client applications to use the
REST-style URIs when accessing both, the new REST-style resources, and the existing old RPC-style
resources, without the need to redesign these resources, as it can be seen in Fig.2.
This adaptation of RESTful requests sent by client applications and arrived on Task Layer, to the
real resource identifiers used on Entity Layer is made by Resource Dispatcher.
Within this architecture, Resource Dispatcher can be treated as a new entity called URI Adapting
Layer [7]. Important actions take place on URI Adapting Layer:
• a REST-style request, pointing to a resource situated on a lower level, is received;
125
• the received URI is parsed and main entities are identified (elements, methods);
• a new request is build, either RPC-style or REST-style;
• the caller is redirected using the new URI.
The client application has no knowledge about these actions. The Resource Dispatcher operations
are influenced by the existing resource hierarchy within the distributed application. Many resources
called before in different styles can be now called according to a uniform identification principle.
The goal is to permit the client applications to use only REST-style identifiers when they send
requests to Web modules situated on Task Layer. The existence of new URI Adapting Layer permits
the implementation of two very important ROA principles:
• The principle of resource addressability;
• The principle of uniform interfaces to resources.
1.5. Final conclusions. The concepts used in traditional products modeling seem to be suitable
to product families modeling as well. Utilizing the concepts from traditional product families and
adapting them for representing the architecture and variation of software product families, could lead
to concise and manageable models.
It is safe to say that methods for modeling and management of variation of traditional products are
more advanced than that of software product families. Nevertheless, two major areas were identified
for transferring results from software product families to traditional configurable products.
This paper describe one possible approach of the problem of resources organization within a
modern distributed application, supporting Product Data Management implementation. Beyond that,
this paper shows a way of integration the old RPC-style resources in the new REST-style applications,
without heavy redesign of entire applications.
The authors propose a modern way to design and organize the algorithmic resources of Web
applications in order to implement the REST architectural principles, which further leads to a
better structure of resources, to an increased degree of uniformity in resources addressability, and to
advantageous utilization of HTTP.
Bibliography
[1] Berners-Lee, T., Universal Resource Identifiers - Axioms of Web Architecture, Accessible at:
http://www.w3.org/DesignIssues/Axioms.html, 1996.
[2] Fielding, R.T., Architectural Styles and the Design of Network-based Software Architectures, PhD Dissertation, USA,
University of California, Irvine, 2000.
[3] Mannisto, T., A conceptual modeling approach to product families and their evolution, Doctoral thesis, Helsinki
University of Technology, 2000.
[4] Mannisto, T., Peltonen, H., Sulonen, R., View to product configuration knowledge modeling and evolution,
Configuration-papers from the 1996 AAAI Fall Symposium, AAAI Press, 1996.
[5] Petrovan, A., Toader, C., Modern Concepts in Product Data Management, International Multidisciplinary Conference,
7th Edition, Univ. de Nord Baia Mare, 2007, pp. 609-612.
[6] Tiihonen, J., Soininen, T., Product Configurators Information system Support for Configurable Products, TAI
Research Centre and Laboratory of information Processing Science, Product Data Management Group, Helsinki
University of Technology, 1997.
[7] Toader, C., RESTful multilayer architectures for Web-based learning systems, Creative Mathematics and Informatics,
nr.18, pp. 208-216, 2009.
ICAM9
126
Early diagnosis of Stroke: bridging the gap through wearable sensors and computational models
José R. Villar1 , Silvia González2 , Javier Sedano2 , Camelia Chira2 and José M. Trejo3
1
Computer Science Department, University of Oviedo, Spain
2
Instituto Tecnológico de Castilla y León, Spain
3
Neurology Department of the Burgos Hospital, Spain
villarjose@uniovi.es, silvia.gonzalez@itcl.es, javier.sedano@itcl.es, camelia.chira@itcl.es, jtrejogyg@gmail.com
Abstract. Stroke is a cerebrovascular disease defined as a circulatory disorder that causes either a
temporary or a permanent disorder of one or more areas of the brain. The most common symptom of
stroke is loss of the ability to move voluntarily the limbs, either left, right or both. The hand is usually
more severely affected compared to the leg [6, 9]. For the more prevalent cerebral infarction (85% of
the cases) there existsa thrombolytic drug that disrupts the thrombus occluding a cerebral artery. In
the first one and a half ”golden hour”, one out of three patients treated will recover to his/her previous
life.
Unfortunately, only a minority (5-15% of people suffering a stroke) arrive early enough to actually
receive the treatment [2, 7]. Thus, a device that helps people notifying a rather possible stroke episode
can make a big difference in reducing death, disability and health costs in thousands of patients each
year. In addition, the algorithms to be implemented should be embedded in real hardware platforms so
they can be introduce in wearable products. In spite of the increasing computing power and internal
resources, the algorithms still have to be as light as possible and should constrain to scenarios of reduced
power consumption and small memory capacity.
In this study, a new specific algorithm for Human Activity Recognition (HAR) is presented and
compared with a well-known HAR technique [3, 13]. Moreover, a simple algorithm for generating
alarms due to possible stroke cases is presented. Furthermore, evidence of more complex models are
provided and left as future work. The obtained results are expected to be included in a specific device
for early stroke diagnosing.
Acknowledgments. This research has been supported through the Spanish Ministry of Science and
Innovation TIN2011-24302 project.
1.1. Introduction. As stated in [5], stroke is a cerebrovascular disease defined as a circulatory
disorder that causes either a temporary or a permanent disorder of one or more areas of the brain. As
the author stated, ”Stroke is the second most common cause of death and major cause of disability
worldwide. Because of the ageing population, the burden will increase greatly during the next 20
years, especially in developing countries.” Paralysis is the most common symptom of stroke, specially
the paralysis of the limbs. The paralysis could be either partial -one side of the body- or total -both
sides-, and the upper limbs are usually more severely affected than the lower limbs [6, 9].
Cerebral infarction makes up to around 85% of all strokes [1, 2]. For the rest 15% of cerebral
hemorrhages there is no approved treatment, but for the more prevalent cerebral infarction, there
is one that can make a big difference: a thrombolytic drug that disrupts the thrombus occluding a
cerebral artery. If successful, cerebral tissue will recover and so will function, but that depends on
how fast the treatment is given. In the first one and a half ”golden hour”, one out of three patients
treated will recover to his/her previous life.
In spite of this golden hour drug, only a minority (5-15% of people suffering a stroke) arrive early
enough to actually receive the treatment [2, 7]: the main concern is related with the identification of
the stroke episode by the relatives or because the episode occurs when the subject is alone. Thus,
a device that helps people notifying a rather possible stroke episode can make a big difference in
reducing death, disability and health costs in thousands of patients each year.
In this study a method for the early diagnosing of the stroke is introduced. Up to our knowledge,
this is the very first study that propose low cost wearable sensors in the identification of this disease.
For doing so, two wearable triaxial accelerometers -one in each wrist- would allow to identify the most
remarkable stroke symptoms. The method includes a human activity recognition (HAR) method and,
afterwards, a stroke paralysis alarm generator. As these algorithms should run in micro controllers
the lowest the computational costs the better. The improvements found in this study include a novel
light HAR method and the algorithm for early stroke diagnosing. Additionally, it is worth mentioning
the proposed adaptation of well-known time series representation for the focused problem.
127
This study is organized as follows. Next section outlines the most remarkable behaviour of the
subjects suffering a stroke episode. Then, the time series representation used in this paper are briefly
described. Sect. 1.4 deals with the HAR method proposed in this study, while Sect. 1.5 presents the
algorithm for alarm generation. These two latter sections also show experiment results and discussion.
Finally, some conclusions and future work are included as a final section.
1.2. A brief description of Stroke’s paralysis symptoms. The most common symptom of
stroke is loss of the ability to move voluntarily the limbs, either left, right or both. The hand is usually
more severely affected compared to the leg. In fact, arm paralysis is so common in stroke that it is
used in scales by paramedics such as the Prehospital Cincinatti Stroke Scale. It has also been included
in the FAST acronym, in public campaigns aimed at stroke early recognition (FAST stands for Face
drooping, Arm paralysis, Speech difficulties, Time to act) [9]. Hand paralysis is also non-subjective so
it can be monitored by a movement-detection device.
If we pay attention to these symptoms, they are usually described as an asymmetrical movements
between both sides of the subject body: one part moves as usual as possible while the other is rather
still. In addition, the main symptom is the collapse of the subject: this may occur after the subject
had sat in a chair or fell in a bed, but also the subject might suffer a falling and then a collapse.
Therefore, knowing the current human activity (cHA) could allow to differentiate between the collapse,
falling or body asymmetries.
In addition, each combination of these possible remarkable states and the cHA would require its
co-occurrence during a different amount of time. We must differentiate between the lack of movement
in one part of the body when walking, reading or resting -whether it can be having a nap or sleeping
or a collapse-; each of these combinations will take a different time to be consider worth alarming.
1.3. A light introduction to PAA and SAX. As detailed in [4], many techniques have been
presented in the literature for time series (TS) representation and distance measuring, the Piecewise
Aggregate Approximation (PAA) [11] and Symbolic Aggregate approXimation (SAX) [12] among
others. These two latter have shown the best performance on aperiodic TS. As far as the available
data from human activity is rather aperiodic, these two techniques are outlined.
Let X be a TS of length n previously normalized to zero mean and standard deviation of one.
bi = [b
Let the desired representation domain dimension w. PAA finds the w size vector X
x1 , . . . , x
bw ]
n
w Pwi
calculated as x
bi = n
n
(i−1)+1 xj : the overall process consists in splitting the X in w intervals and
w
each x
bi computed as the mean value within the corresponding interval.
Additionally, if the alphabet size is fixed to as, SAX divides the domain of the values of the X in as
statistically equiprobable intervals taking advantage of the previous data normalization, each interval
is assigned with one symbol. Whenever a PAA component falls within an interval the corresponding
symbol is assigned in the SAX vector component. Furthermore, SAX also provides with a distance
measure among SAX vectors.
1.4. A light human activity recognition method. Using triaxial accelerometers induces
that the measurement obtained from the sensors should be decomposed in the gravity acceleration
(G) andqthe body acceleration (BA) -which is due to the human movement, bxi , byi and bzi -. Let
2
BAi = bxi 2 + byi + bzi 2 measured for each sample of the TS.
In our approach, we make use of two wrist bracelets -each one with a triaxial accelerometer
sampled at 16 Hz-. Let mBA and sBA be the mean and standard deviation of the movements during
activities of daily living of the subject, both calculated by means of a initial test.
The algorithm proposed in this study for HAR is shown in Algorithm 1, though for the sake of
brevity it is shown rather schematically; our real implemented algorithms are a bit more complex. There
are some issues that need further study, like the learning of the membership functions and its tuning
to the focused subject as well as the method for measuring similarities between TS representation.
Interestingly enough, the computational cost and resources needed for implementing this algorithm
are kept rather small, which is one of the main enhancement of this technique. The last part of the
algorithm is related with the stroke episode alarm generation.
128
Algorithm 1 Simplified SAX based HAR algorithm: {µA /A, ∀A}
Require: X, a normalized TS of size n using mBA and sBA
Ensure: Computes the possible activities and their certainties
b = SAX(X)
Determine X
for each A ∈ Registered Activities do
for each Ymov ∈ RegisteredActivityMovement(A) do
b and Ymov → simXY
Compute similarity between X
b
Update the certainty of X of class A according to simXY
end for
end for
if Resting State is believed then
Determine the resting activity level HIGH, LOW, NONE
Increment the corresponding counters
end if
1.5. A simple algorithm for stroke diagnosing. Similarly to the previous algorithm, this
study proposes the use of the SAX representation and some quite simple algorithms to detect anomalous
human behaviors. The TS from both bracelets are used in this case, and the state of resting should be
previously detected independently for each hand. In case of resting state, the BA is normalized using
the muRBAh and sRBAh , the mean and standard deviation of the signal of the BA when the subject
is resting; the h subindex is related with the hand -left or right-. These values should be calculated in
an initial test.
Algorithm 2 briefly outlines the propose approach; as in the former section, the algorithms are
very roughly explained due to the space limitations. Firstly, some counters and the current resting
level are determined in the previous algorithm. Afterwards, the similarity of the signal from each
hand is compare with the typical sequences of inactivity. In case that the total inactivity keeps going
on, the certainty of generating the corresponding alarm for the partial or total paralysis, and even for
a falling detection alarm.
Algorithm 2 Simplified Alarm Generation Algorithm
Require: Xh , a normalized TS of size n with mRBAh and sRBAh , ∀h ∈ {lef t, right}
Require: STATES and CERTAINTIES of the subject
Require: RESTING LEVEL: {HIGH, LOW, N ON E}
Ensure: Generates the suitable alarms
ch = SAX(Xh )
Determine X
for each Ymov ∈ RegisteredAlarmSequences do
ch and Ymov → simXY
Compute similarity between X
if simXY is HIGH then
Mark the detection of a {inactivity, falling}
end if
end for
Update time of inactivity counters
if time of inactivity is HIGH for the corresponding RESTING LEVEL or a falling has been detected
then
Generate the corresponding alarm
end if
1.6. Experimentation and further discussion. Experiments carried out in this very preliminary study include two young subjects. Ten runs of the well-known stroke patients rehabilitation test
(for short, SRT) [10]. Moreover, more tests were carried out with the subjects sleeping during a night.
Neither tabular nor figures can be included in this extended abstract due to the length restrictions.
We test to discriminate between resting and walking and the results were really impressive, with a
perfect discrimination of the class, though this specific problem by itself is not very complex.
129
The algorithm for alarm generation seems to be coherent with the specifications given by the
medical staff, though more work is needed to identify the sequences for identifying activity while
resting. Furthermore, the results shows that the algorithms work as expected though the different
threshold and the simplifications as well as the distance measure should be greatly improved.
1.7. Conclusions and future work. This study proposes two novel algorithms: a former one
for human activity recognition, the latter for stroke early diagnosing. These algorithms require rather
low both computational costs and resources. Obtained results are really promising, even with the
simplifications of using only thresholds. Nevertheless, there are still plenty of research to carry out.
Firstly, several intelligent algorithms should be designed for learning the different simplified parameters.
Secondly, the algorithms should be refined. Thirdly, the experimentation should include the higher
objective population as possible, as well as should include young people. We do expect to start the
experiments by the final quarter of this year.
Bibliography
[1] R. D. Adams., Principles of Neurology, McGraw Hil, 1997
[2] H. P. Adams, G. del Zoppo, M. J. Alberts, D. L. Bhatt, L. Brass, A. Furlan, R. L. Grubb, R. T. Higashida, E. C.
Jauch, C. Kidwell, P. D. Lyden, L. B. Morgenstern, A. I. Qureshi, R. H. Rosenwasser, P. A. Scott and E. F.M.
Wijdicks. Guidelines for the Early Management of Adults With Ischemic Stroke, Stroke, 38(2007), 1655-1711
[3] A. Ávarez-Álvarez, G. Triviño, O. Cordón., Body posture recognition by means of a genetic fuzzy finite state machine,
IEEE 5th International Workshop on Genetic and Evolutionary Fuzzy Systems (GEFS), IEEE Conference Publisher,
Paris France, (2011), 409-413
[4] H. Ding, G. Trajcevski, P. Scheuermann, X. Wang and E. Keogh.Querying and mining of time series data: experimental
comparison of representations and distance measures, Proc. VLDB Endow. 1:2 (2008), 1542–1552
[5] G. A Donnan, M. Fisher, M. Macleod and S. M. Davis- Stroke, The Lancet, 371:9624 (2008), 1612-1623
[6] A.D. Dromerick and S. A. Khader., Medical complications during stroke rehabilitation, Advances in Neurology, 92
(2003), 409-413
[7] E. Duarte, B. Alonso, M.J. Fernández, J.M. Fernández, M. Flórez, I. Garcı́a-Montes, J. Gentil, L. Hernández, F.J.
Juan, J. Palomino, J. Vidal, E. Viosca, J.J. Aguilar, M. Bernabeu, I. Bori, F. Carrión, A. Déniz, I. Dı́az, E. Fernández,
P. Forastero, V. Iñigo, J. Junyent, N. Lizarraga, L. López de Munaı́n, I. Máñez, X. Miguéns, I. Sánchez and A. Soler.
Stroke rehabilitation: Care model, Rehabilitación, 44:1 (2010), 60-68
[8] F.J. Fernández-Gómez, F. Hernndez, L. Argandoa, M.F. Galindo, T. Segura and J. Jordn.Pharmacology of neuroprotection in acute ischemic stroke, Rev Neurol. 47:5 (2008), 253-60
[9] C.S. Hogdson. To FAST or not to FAST, Stroke, 38 (2007), 2631-2632
[10] K. HollandsWhole body coordination during turning while walking in stroke survivors, School of Health and Population
Sciences. Ph.D. thesis, University of Birmingham (2010)
[11] E. Keogh, K. Chakrabarti, M. Pazzani and S. MehrotraDimensionality Reduction for Fast Similarity Search in
Large Time Series Databases Journal of Knowledge and Information Systems 3 (2000), 263-286
[12] J. Lin, E. Keogh, L. Wei and S. Leonardi.Experiencing SAX: a Novel Symbolic Representation of Time Series, Data
Mining and Knowledge Discovery 15:2 (2007), 107-144
[13] S. González, J. R. Villar, J. Sedano and C. Chira. A preliminary study on early diagnosis of illnesses based on
activity disturbances, Distributed Computing and Artificial Intelligence, 10th International Conference, Berlin, 2013
ICAM9
130
Cristian Vele, Cristian Anghel and Rita Toader
cristian vele@yahoo.com
Abstract. Why some companies can manage to grow and develop, while other companies fail and go
bankrupt? What is the secret? The answers reside in the strategic efforts of every company and in
their specific actions and decision taken in order to overpass their competitors and become the market
leader. Following this, the present article whishes to present the main strategies used by companies in
the construction industry and analyze them with the help of specialized statistical models.
1.1. Introduction. Choosing the most efficient strategy represents, from many points of view,
the central elements of strategic management, the main concern being the companys future and the
actions through which will be able to face the many external influences. Also, it is very important, in
order to ensure their long term sustainability, for strategies to be realistic, not only in relation to their
external environment, but also with their internal capabilities (Johnson & Scholes, 1999: 255, Dikmen
et. Al, 2009, 291). In the opinion of Aras and Crowther (Aras & Crowther, 2010: 568) there are
four major aspects of sustainability which need to be recognized and analyzed: (1) the influence on
society, more specifically the companys impact in terms of social contracts, and also the influence of
its stakeholders, (2) the impact on the environment, which is comprised of all the companys actions on
the geophysical environment, (3) the corporate culture, comprised of the relations between employees
and (4) finances, evaluated based on the financial results registered by the company.
In order, for a company, to choose the best strategy, first of all it must understand the advantages
and disadvantages of every strategic option. That is why, the strategic planning process must be
explicit, transparent and participative (Karnani, 2008: 31) and also it must be focused on increasing
the organizational performance (Grant, 2003: 515). One of the most efficient models to manage the
strategic planning process is based on three major categories of factors: the structural conditions, in
which the company is conducting its business, its resources and capabilities and its strategic experience
(Kim & Mauborgne, 2009: 74). As a consequence, the strategic process is represented by those
decisions related to (Finlay, 2000: 341): product portfolio, strategic positioning, necessary resources,
ways to access the resources and financing sources.
The first step in formulating the competitive strategy is to establish what are the long term
goals that need to be met. Starting from the fact that short term maximization of profit does not
ensure long term sustainability and development, companies must pay great attention to establishing
strategic goals in relation with the following elements (Pearce & Robinson, 2007: 164): profitability,
productivity, competitive position, employee development, employee relations, technological leadership
and social responsibility.
In order to be successful, a strategy must be formulated in a very simple and clear manner, in
order for every employee to be able to understand it. Thus, the formulation of a competitive strategy
must be comprised of three major parts:the objective (where do you want to arrive), the purpose (the
industry in which the company is activating) and advantage (how will you reach the objective) (Collins
& Rukstad, 2008: 84 85). Also, the strategies need to be formulating in accordance with the different
organizational levels: at the corporate level, business unit level and functional level.
1.2. Empirical research regardubg the strategies used by companies in the construction undustry. Our research is focused on the construction industry and it is based on the answers
given by 220 companies in the North Western region of Romania, which is comprised of the counties
of Bihor, Bistrita Nasaud, Cluj, Maramures, Satu Mare and Salaj. The main goal of our research
is to identify and analyze the efforts of companies in the construction industry to gain sustainable
competitive advantages. In order to achieve this, a questionnaire, containing questions regarding the
implemented strategies, was given to construction companies to be filled. The answers were gathered
and, by using specialized statistical software, were analyzed in order to identify the importance given
by companies in the construction industry to specific competitive strategies, such as: the diversification
of products and services, the use of cutting edge technologies, the focus on a market niche or becoming
a cost leader.
131
Figure 1 The diversification of products and services.
Figure 2 The use of cutting edge technologies.
Based on the answers given we can observe that 81,8% of the companies are diversifying their
offer in order to expand their market coverage and to provide the customers with integrated services.
By doing this, the companies in the construction industry are trying to counteract the decreasing
market demand and ensure their long term sustainability.
Another key aspect noticed in our research, as shown in FIGURE 2, is the importance given to
technological innovation. 83,8% of the companies presented in our study consider important and very
important the use of cutting edge technologies both for offering high quality products and services
and for keeping the production costs at the lowest possible. In doing this, companies are seeking to
increase sales, lower production costs and grow the profits.
The significant decline of the construction industry, from 2008 until present, has pushed numerous
companies into bankruptcy, while the remaining ones struggled to survive. However, some companies
have found out that focusing on a market niche, such as wood constructions or industrial constructions,
can be profitable. During our study we discovered that half of the participants, as shown in FIHURE
3, consider important and very important to focus on a market niche, not only to survive, but to
develop and grow.
Not least, our study allowed us to observe and confirm the companies attention and importance
given to reducing the costs as much as possible and becoming the company with the lowest cost in the
industry. Of course, becoming a cost leader is a very difficult task, but companies do not need to
become the leader, but merely to reduce their cost as much as possible. By doing this, they can keep
the prices unchanged and increase the profit margins. As shown previously, the use of technological
innovation can be a very efficient way to reduce the costs, also, increasing work productivity, finding
better supply channels or using highly qualified work force, can be useful ways to keep costs down. As
shown in FIGURE 4, 92,3% of the participants declared that reducing the costs at the lowest level
possible in important and very important.
132
Figure 3 Focusing on a market niche.
Figure 4 The implementation of cost leadership.
1.3. Conclusions. The highly competitive business environment today forces companies, more
than ever, to seek and gain sustainable competitive advantages in order to ensure their survival and
long term development. However, to gain competitive advantages is a very complex process that
involves collecting data from numerous sources and analyzing it with the help of mathematical models
in order to formulate the most efficient business strategy. At the same time, specializes statistical
models can help researches build a complex framework of companies in a certain industry, and help
managers select the best path for their company in accordance with their characteristics.
Bibliography
[1] Aras, G. & Crowther, D. (2010), Sustaining Business Excellence, Total Quality Management, vol. 21, no.5: 565 576
[2] Collins, D.J., Rukstad, M.G. (2008), Can You Say What Your Strategy Is?, Harvard Business Review, April: 82 - 90
[3] Dikmen, I., Birgonul, M.T., Budayan, C. (2009), Strategic Group Analysis in the Construction Industry, Journal of
Construction Engineering and Management, April: 288 - 297
[4] Johnson, G. & Scholes, K. (1999), Exploring corporate strategy fifth edition, Prentice Hall, Londra
[5] Karnani, A. (2008), Controversy: The essence of strategy, Business Strategy Review, Winter: 28 34
[6] Grant, R.M. (2003), Strategic Planning In A Turbulent Environment: Evidence From The Oil Majors, Strategic
Management Journal, vol. 24: 491 517
[7] Finlay, P.N. (2000), Strategic management: an introduction to business and corporate strategy, Pearson Education,
England
[8] Kim, W.C., Mauborgne, R. (2009), How Strategy Shapes Structure, Harvard Business Review, September: 73 80
[9] Pearce, J.A. & Robinson Jr., R.B. (2007), Strategic Management: formulation, implementation and control,
McGraw-Hill Irwin, New York, USA
ICAM9
133
Liliana Zima, Simona Sabou, Rita Toader and Cezar Toader
lili zima@yahoo.com
Abstract.This paper presents some aspects of calculation of individual performance according to the
performance assessment criteria, the problem of performance evaluation and new models of performance
assessment.
1.1. Introduction. In the first part of the article, we describe the main objectives assessment
and evaluation criteria.
Performance assessment is an important component of the supervisor-employee relationship. It is
part of an ongoing process of performance planning, management, and improvement and represents
a culmination of past years discussions between the supervisor and employee about the employees
performance.
The actual performance assessment serves several purposes. It encourages employee involvement,
provides a formal mechanism for employees to receive feedback regarding job performance and
expectations, and allows the employee to work closely with the supervisor to establish goals and
priorities for the next year. Performance assessment also facilitates growth and development of
employees and results in a documented history of employee performance.
A correct assessment system has to meet the following conditions:
• careful preparation and dissemination of the value system and performance assessment
procedures with the aim of preventing adverse reactions or challenging the results;
• the existence of a formal assessment tool;
• using criteria that limit the absolute power of management;
• personally knowing the assessed person and permanent contact with them;
• continuous training for managers regarding the assessment activity;
• the existence of a revising system for incorrect assessments, done by superiors;
• counselling and support for those with poor performances in order to offer Human resources
must be used efficiently and rationally in order to ensure the improvement of labour productivity, the improvement of quality, and the worthiness of products and services achieved.
1.2. New models of performance assessment. The second part presents one example of
individual performance assessment calculation and the problem of performance evaluation and new
models of performance assessment.
Pt = (p1 × C1 ) + (p2 × C2 ) + (p3 × C3 ) + (p4 × C4 )
where
Pt - total points
p1 , p2 , p3 , p4 - points given
C1 , C2 , C3 , C4 - the weight of assessment criteria.
Example of individual performance calculation
Evaluation criteria
1. The level of meeting the performance standards
2. Assuming responsibility
3. Adequate labour complexity
4. Initiative and creativity
TOTAL:
% EX FB B S N
35 5p
- - 25 4p - - 15 - - 25 4p - - -
General equation:
P = f (c1 , c2 , c3 ) ,
P = b0 + b1 c1 + b2 c2 + b3 c3 + b12 c1 c2 + b23 c2 c3 + b13 c1 c3 .
134
Variation level
x1 (%) x2 (%) x3 (%)
Superior level (+1)
3.5
5
4.5
Basic level (0)
2.5
3.5
3
Inferior level (-1)
1.5
2
1.5
Variation interval (∆xi )
1
1.5
1.5
Further we establish the experimental matrix
Nr. exp x0 x1 x2
1
+1 +1 +1
2
+1 -1 +1
3
+1 +1 -1
4
+1 -1 -1
5
+1 +1 +1
6
+1 -1 +1
7
+1 +1 -1
8
+1 -1 -1
EFC 23
x3 x1 x2 x2 x3 x1 x3
+1 +1
+1
+1
+1
-1
+1
-1
+1
-1
-1
+1
+1 +1
-1
-1
-1
+1
-1
-1
-1
-1
-1
+1
-1
-1
+1
-1
-1
+1
+1
+1
The matrix being orthogonal, coefficients b0 , b1 , b2 , b3 , b12 , b23 , b13 are determined with the
formulae:
N
P
bi =
N
P
x iu yu
u=1
N
P
u=1
and bij =
x2iu
u=1
N
P
xiu xju yu
(xiu xju )2
u=1
The regression equation obtained according to the proposed model is the following:
y1 = 48.25 − 1.5x1 − 1.25x2 − 5x3 − 1.25x1 x2 − 0.75x1 x3 .
1.3. Conclusion. Performance assessments are exactly what they sound like: they are an
evaluation of how employees’ are currently performing on the job and a plan for making any necessary
improvements. Performance assessments are an essential tool in the Human Resources arsenal as
they provide data for other departmental functions (compensation, position determination, employee
training, and employee development, etc).
In order to be efficient, performance assessment has to integrate into an adequate human resources
management system, in which the fundamental features of assessors should be professionalism, fairness
and reliability.
The most important performance assessment objectives to the management practice, are the
following:
• appropriate unfolding of activities in the field of human resources;
• balanced rewarding of personnel;
• providing employees with the information necessary for their own development, by offering
them trust in their own resources;
• identifying individual training and development needs of personnel, as well as evaluating the
results of the training and development programmes;
• discussing the long term plans of employees, as well as the objectives of their careers;
• integrating human resources planning within the framework of all other personnel activities;
• validating selection programmes;
• improving motivation of employees;
• improving the manager-employee relationship;
135
• improving communication and intensifying cooperation between managers or superiors and
employees;
• applying the equal opportunity principle.
The potential problems that need consideration in approaching performance assessment as a
component of the performance management system are the following:
- the necessity of creating a performance culture;
- involving managers at higher levels in the assessment process in order to satisfy both individual
and organisational needs;
- the influence of performance management upon the role of its assessment through the
appropriate functioning of feedback.
For the success of the performance assessment activity I suggest the usage of certain mathematical
models and computer programmes well conceived and easy to be implemented.
Bibliography
[1]
[2]
[3]
[4]
Cole G. A., Management. Theory and Prcatice, Editura Ştiinţa, Chişinău, 2004.
Chişu Ana Viorica, The Human Resources Specialists Manual, Casa de editură IRECSON, Bucureşti, 2002.
Pănişoară Georgeta, Pănişoară, I. Ovidiu Human Resources Management, Editura Polirom, 2004.
Pitriu H. D., Managementul resurselor umane Human Resources Management Professional Performance Assessment,
Editura All Beck, 2000.
[5] Vărzaru Mihai, Human resources in Enterprises, Editura Tribuna Economică, Bucureşti, 2002.
ICAM9

ABSTRACTS AND PRE-PROCEEDINGS Baia Mare September 25

Transcription

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