14 International Congress on Computational and Applied

September 17, 2009 17:52 WSPC - Proceedings Trim Size: 9.75in x 6.5in iccam2009˙proc

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14th International Congress on Computational and AppliedMathematics(ICCAM2009)

29 September - 2 October 2009Antalya - TURKEY


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ICCAM2009Programme

andSubmitted Abstracts Book


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SCIENTIFIC COMMITTEE

Marc Goovaerts (Chair) – Katholieke Universiteit LeuvenOmer L. Gebizlioglu (Vice Chair) – Ankara UniversityZhong-zhi Bai – Chinese Academy of SciencesIsmihan Bayramoglu – Izmir University of EconomicsJan Dhaene – Katholieke Universiteit LeuvenKen Hayami – National Institute of Informatics/JapanAbdul Q.M. Khaliq – Middle Tennessee State UniversityMihael Perman – Institute for Mathematics, Physics and Mechanics/SloveniaG. Wilhelm Weber – Middle East Technical UniversityLuc Wuytack – University of Antwerp

ORGANIZING COMMITTEE

Omer L. Gebizlioglu (Chair) – Ankara UniversitySerkan Eryilmaz (Vice Chair) – Izmir University of EconomicsDevin Sezer (Vice Chair) – Middle East Technical UniversityFatih Tank (Vice Chair) – Kirikkale UniversityErsan Akyildiz – Middle East Technical UniversityBulent Karasozen – Middle East Technical UniversityDolun Oksoy – Ankara UniversitySevgi Y. Oncel – Kirikkale UniversityCihan Orhon – Ankara UniversityBirdal Senoglu – Ankara University

14th International Congress on

Computational and Applied Mathematics (ICCAM2009)

29 September‐2 October, 2009 Antalya, Turkey

Congress Programme

29 September 2009, Tuesday

12:00‐18:00 Registration 16:00‐18:00 Tutorial Session

Place: Hall 1 • “Global Optimization In Practice”

Janos D. Pinter 18:30‐20:00 Welcome Cocktail

Place: Cocktail Hall

30 September 2009, Wednesday

08:30‐09:00 Registration 09:00‐09:30 Opening Session

Place: Hall 1 Welcome and Opening Talks

09:30‐10:30 Invited Talk Session Place: Hall 1 Chair: Marc Goovaerts

• “Dependence Modelling With Copulas” Roger B. Nelsen

10:30‐11:00 Tea‐Coffee Break

11:00‐12:30 Parallel Sessions 1 Session1.1: Applied Probability and Stochastic Processes I Place: Hall 1 Chair: Refail Kasımbeyli

• Andrei Bourchtein, L. Bourchtein Dependence of the PageRank vector on the artificial links

• Serkan Eryilmaz, Funda Iscioglu Multi‐state system reliability under stress‐strength setup

• Agah Kozan, H. Tanil On distributions of bottom m scores after ℓth change

• Guvenc Arslan A Variant of the Choquet‐Deny Theorem with Application to Characterizaiton

Session1.2: Computational Methods in Physical and Social Sciences I Place: Hall 2 Chair: Masai Watanabe

• Canan Bozkaya, Tulay Kocabıyık Streamwise oscillations of a cylinder beneath a free surface: Part 1. Free surface effects on vortex formation modes

• Canan Bozkaya, Tulay Kocabıyık Streamwise oscillations of a cylinder beneath a free surface: Part 2. Free surface effects on fluid forces

• Nail Akhmediev, J. M. Soto‐Crespo, A. Ankiewicz Rogue waves: power of mathematics in understanding the phenomenon

• Ali Reza Ashrafi , M. Saheli The Eccentric Connectivity Index of Nanotubes and Nanotori

Session1.3: Differential Equations I Place: Hall 3 Chair: Bulent Karasozen

• Mesliza Mohamed, H.B. Thompson, M. Jusoh First‐Order Three‐Point Boundary Value Problems at Resonance

• Pavel Krutitskii Boundary value problems for the Helmholtz equation in domains bounded by closed curves and open arcs

• Adem Kilicman, Hassan Eltayep, Fudziah Ismail On the Partial Differential Equations with Non‐Constant Cefficients and Convolution Method

• Gulnur Celik Kizilkan, Kemal Aydin Step size strategies on the numerical integration of the systems of differential equations

Session1.4: Mathematical Programming I Place: Hall 4 Chair: M.Fernanda P.Costa

• Eren Ozceylan, T. Paksoy Modeling Facility Location and Supplier Selection with Supplier’s Product Quality and Contract Fee for Strategic Supply Chain Design

• Sureyya Ozogur Akyuz, G. Ustunkar, G. W. Weber On Numerical Optimization Methods for Infinite Kernel Learning

• Alireza Davoodi A DEA based approach for solving the multiple objective shortest path problem

• Fatma Yerlikaya Ozkurt, G.W. Weber, A. Ozmen Robustification of CMARS

Session1.5: Numerical Analysis and Software I Place: Hall 5 Chair: Kuniyoshi Abe

• Suzan Cival Buranay, A.A. Dosiyev A high accurate difference‐analytical method for solving Laplace's equation on polygons with nonanalytic boundary conditions

• Kamile Sanli Kula, Fatih Tank, Turkan Erbay Dalkilic An Application of a New Fuzzy Robust Regression Algorithm to Actuarial Science

• Fudziah Ismail, A. Karimi, N. Md Ariffin, M. Abu Hassan Comparison of Exponentially fitted Explicit Runge‐Kutta methods for Solving ODEs

• Fereidoon Khadem, M. A. Fariborzi Araghi Numerical Integration of a Fuzzy Riemann Double Integral

12:30‐13:30 Lunch Break

13:30‐15:45 Parallel Sessions 2 Session2.1: Approximation and Interpolation I Place: Hall 1 Chair: Gulen B. Tunca

• Halil Gezer, H. Aktuglu Statistical Convergence for Set‐Valued Functions

• Elias Berriochoa, A. Cachafeiro Hermite‐Birkhoff interpolation problems on the roots of the unity

• Liping Yang, X. Xie Weak and strong convergence theorems for a finite family of $I‐$asymptotically nonexpansive mapping

• Serife Bekar, H. Aktuglu q‐Statistical Convergence

• Anvarjon Ahmedov, Norashikin Abdul Approximation of the functions from $LLog^2(S^N)$ by Fourier‐Laplace series

• Yunus Hassen, Barry Koren A novel 2D finite‐volume method for advection problems with embedded moving‐boundaries

Session2.2: Numerical Linear Algebra I Place: Hall 2 Chair: Marc Goovaerts

• Venancio Tomeo, Jesus Abderraman Explicit Representation of Hessenbergians: Application to General Orthogonal Polynomials

• Fatih Yilmaz, Humeyra Kıyak, Irem Gurses, Mehmet Akbulak, Durmus Bozkurt The Powers of Anti(2k+1)‐Diagonal Matrices and Fibonacci Numbers

• Fatih Yilmaz, Humeyra Kıyak, Irem Gurses, Mehmet Akbulak, Durmus Bozkurt On computing powers for one type of matrice by Pell and Jacobsthal Numbers

• Hasan Huseyin Gulec, N. Taskara, K. Uslu On the properties of generalized Fibonacci and Lucas numbers with binomial coefficients

• Seiji Fujino, Y. Kusakabe, M. Harumatsu IDR‐based relaxation methods for solving linear systems

• Kensuke Aishima, T. Matsuo, K. Murota, M. Sugihara A Shift Strategy for Superquadratic Convergence in the dqds Algorithm for Singular Values

Session2.3: Optimization I Place: Hall 3 Chair: Ana Maria A.C.Rocha

• Lino Costa, Isabel Espírito Santo, Edite M.G.P. Fernandes A Hybrid Genetic Pattern Search Augmented Lagrangian Method for Constrained Global Optimization

• Herman Mawengkang Production Planning under Stochastic Demand for Fish Processed Product at North Sumatera Province, Indonesia

• Mahnaz Mirbolouki, F. Hosseinzadeh Lotfia, N.Nematollahi, M.H. Behzadi, M.R. Mozaffari Centralized Resource Allocation with Stochastic Data

• Ana Maria A. C. Rocha, Tiago F. M. C. Martins, Edite M. G. P. Fernandes On the augmented Lagrangian methodology in a population based global optimization algorithm

• Eman Hamad Al‐Shemas, A. Hamdi A Regularized Modified Lagrangian Method for Nonlinearly Constrained Monotone Variational Inequalities

• Miguel Gabriel Villarreal‐Cervantes, Carlos Alberto Cruz‐Villar, Jaime Alvarez‐Gallegos A new multiobjective differential evolution strategy for scattering uniformly the Pareto solution set for designing mechatronic systems

Session2.4: Special Functions Place: Hall 4 Chair: Patricia J.Y.Wong

• Lidia Fernandez, T. E. Perez, M. A. Pinar On Koornwinder classical orthogonal polynomials

• Rabia Aktas, A.Altın, F. Taşdelen Yeşildal A note on a family of two variable polynomials

• Cem Kaanoglu, Mehmet Ali Ozarslan Some generalizations of multiple Hermite polynomials via Rodrigues formula

• Emine Ozergin, M.A. Ozarslan, A. Altin Extension of Gamma, Beta and Hypergeometric Functions

• Onur Karaoglu, Ayse Betul Koc, Haldun Alpaslan Peker, Yildiray Keskin, Yucel Cenesiz, Galip Oturanc, Sema Servi Application of Padé approximation of differential transform method to the solution of prey and predator problem

• Pablo Sanchez‐Moreno, A. Zarzo, J.S. Dehesa Jensen divergence based on Fisher's information

Session2.5: Statistics and Data Analysis I Place: Hall 5 Chair: Ismihan Bayramoglu

• Mustafa Cagatay Korkmaz, Coskun Kus, Asir Genc Weibull‐Negative Binomial Distribution

• Yeliz Mert Kantar, Birdal Senoglu, Omer L. Gebizlioglu Comparison of a New Robust Test and Non‐parametric Kruskal‐Wallis Test in One‐way Analysis Of Variance Model

• Neslihan Iyit, A. Genc

General Linear Model (GLM) Approach to Repeated Measurements Data Involving Univariate Analysis of Variance (ANOVA) and Multivariate Analysis of Variance (MANOVA) Techniques

• Alper Sinan, A. Genc Comparing Estimation Results in Nonparametric and Semiparametric Models

• Noor Akma Ibrahim, N. Poh Bee Confidence Intervals for Mean Time to Failure in Two‐Parameter Weibull with Censored Data

• Tutut Herawan, Mustafa Mat Deris Rough Set‐based Functional Dependency Approach for Clustering Categorical Data


16:15‐18:30

Parallel Sessions 3 Session 3.1: Mathematical Modeling, Analysis, Applications I Place: Hall 1 Chair: Alejandro Zarzo

• Turkan Erbay Dalkilic, Aysen Apaydin Parameter Estimation by ANFIS in Cases Where Outputs are Non‐Symmetric Fuzzy Number

• Fatemesadat Salehi S.M.H. Karimian, H. Alisadeghi A Multizone Overset Algorithm for the Solution of Flow around Moving Bodies

• Nihal Yokus, E. Bairamov Spectral Singularities of Sturm‐Liouville Problems with Eigenvalue Dependent Boundary Conditions

• Zeynep Eken, S.Sezer Vague DeMorgan Complemented Lattices

• Zainidin Karimovich Eshkuvatov Approximating the singular integrals of Cauchy type with weight function on the interval

• Bulent Karasozen, Ayhan Aydin Lobatto IIIA‐IIIB Discretization for the Strongly Coupled Nonlinear Schr\"odinger Equation

Session 3.2: Approximations and Interpolation II Place: Hall 2 Chair: Miguel Angel Fortes

• Hussain Mohammed Al‐Qassem , L. Cheng, Y. Pan Rough oscillatory singular integrals on Rⁿ

• Raffaele D'Ambrosio, E. Esposito, B. Paternoster Exponentially fitted two‐‐step hybrid methods for y''=f(x,y)

• Nazri Mohd Nawi, Rozaida Ghazali, Mohd Najib Mohd Salleh Improving the Gradient based search Direction to Enhance Training Efficiency of Back Propagation based Neural Network algorithms

• F. Tasdelen Yesildal, Gurhan Icoz On Linear positive operators including q‐Konhauser Polynomials

• Veronica Biga, Daniel Coca, Visakan Kadirkamanathan, Stephen A. Billings An Alternative Region‐Based Active Contour Model Using Cauchy‐Schwartz Divergence

• Gulen Bascanbaz Tunca, Yalcin Tuncer On Chlodovsky variant of multivariate beta operator

Session 3.3: Nonlinear Equations and Mathematical Modeling Place: Hall 3 Chair: Ersan Akyıldız

• Enes Yilmaz, M. U. Akhmet, D. Arugaslan Stability analysis of recurrent neural networks with deviated argument of mixed type

• Turgut Tollu, N. Taskara, K. Uslu The Periodicity of Solutions of a Rational Difference Equations x(n+1)=[ p(n).x(n‐k)+x(n‐(k+1))]/[ q(n)+x(n‐(k+1))] with (k+1)th Periodic Coefficients

• Emine Hekimoglu, N. Taskara, K. Uslu On the behavior of solutions of a rational system x(n+1)=1/[y(n‐1)] , y(n+1)=x(n‐1)/[x(n).y(n‐2)]

• Behzad Ghanbary, Jafar Biazar A modification on some improved Newton's method without direct function evaluations

• Patricia J. Y. Wong, Fengmin Chen Error Inequalities for Discrete Hermite Interpolation

• Josep Arnal Parallel Newton‐like methods for solving systems of nonlinear equations

Session 3.4: Computational Methods in Physical and Social Sciences II Place: Hall 4 Chair: Jose M.Matias

• Demet Ersoy, V. Yakhno Deriving Elastic Fields in an Anisotropic Bi‐material

• Sengul Kecelli, V. Yakhno A Boundary Value Problem of the Frequency‐Dependent Maxwell's System for Layered Materials

• Sevgi Yurt Oncel, Omer L. Gebizlioglu, Fazil Aliyev Multiple Logistic Regression A Study on the Multiple Logistic Regression Analysis To Determine Risk Factors For The Smoking Behavior

• Yoji Otani, M. Watanabe, L. Ying, K. Yamamoto, Hashentuya Numerical simulation of tsunami generated in North Pacific Ocean near Japan

• Ata Olah Abbasi, B. Vosoughi Vahdat A new numerical method for solving 2D Electrical Impedance Tomography Inverse Problem

• Tertia Delia Nova, H. Mawengkang, M. Watanabe Control strategy of avian influenza based on modeling and simulation

Session 3.5: Mathematical Programming II Place: Hall 5 Chair: Venancio Tomeo

• Eren Ozceylan, T. Paksoy, N.Y. Pehlivan Fuzzy Optimization of A Multi Stage Multi Item Closed‐Loop Flexible Supply Chain Network Under Fuzzy Material Requirement Constraints

• Gerhard‐Wilhelm Weber, E. Kropat, C.S. Pedamallu Identification, Optimization and Dynamics of Regulatory Networks under Uncertainty

• Erkki Laitinen , I. Konnov, O. Kashina Multi‐Criteria Optimization for Distribution of Spatial Resources

• Mahnaz Mirbolouki, F.Hosseinzadeh Lotfi, G.R. Jahanshahloo, M.H. Behzadi Finding Efficient and Inefficient Outlier Layers by Using Skewness Coefficient

• Hendaru Sadyadharma, Z. Nasution, H. Mawengkang Multi‐Objective Optimization Model for Solving Risk‐Based Environmental Production Planning Problem in Crude Palm Oil Industry

• Sacha Varone, David Schindl Staff scheduling with priority constraints

1 October 2009, Thursday

09:00‐10:00 Invited Talk Session Place: Hall 1 Chair: Gerhard Wilhelm Weber

• “NULISS:Non‐Uniform Local Interpolatory Subdivision Surfaces” Lucia Romani


10:30‐12: 45

Parallel Sessions 4 Session 4.1: Mathematical Modeling, Analysis, Applications II Place: Hall 1 Chair: Alireza Ashrafi

• Fatma Tasdelen Yesildal, Burak Sekeroglu, H.M. Srivastava Some Properties of Q‐Biorthogonal Polynomials

• İsmail Yaslan Positive solutions for nonlinear first‐order m‐point boundary value problem on time scale

• Fengmin Chen, Patricia J. Y. Wong Error Estimates for Discrete Spline Interpolation

• Masaji Watanabe, F. Kawai Computational analysis for microbial depolymerization processes of xenobiotic polymers based on mathematical models and experimental results

• Tahir Khaniyev, I. Unver, Z. Mammadova Asymptotic Results for a Semi‐Markovian Random Walk with a Normal Distributed Interference of Chance

• Mustafa Kahraman, Nurgul Gokgoz, Hakan Oktem A Model of Vascular Tumor Growth by Hybrid Systems

Session 4.2: Applied Probability and Stochastic Processes II Place: Hall 2 Chair: Roger B. Nelsen

• M.R. Akramin M. Mazwan Mahat, A. Juliawati, A.H. Ahmad, A.R.M. Rosdzimin Probability Failure Analysis for Cracked Structure

• Burak Uyar, H. Tanil On exceedances based on the list of top m scores after ℓth change

• Jose M. Matias, T. Rivas, C. Ordonez, J. Taboada Functional Approach Using New $L^{\ast }a^{\ast }b^{\ast }$ color functions to evaluate colour changes in granites after desalination using different methods

• Ceren Eda Can, M. Rainer On LIBOR and swap market models: calibration to caps and swaption markets

• Zhaoning Shang, Marc Goovaerts Analytical Recursive Algorithm for Path‐dependent Option Pricing with Stochastic Time

• Rovshan Aliyev, T.Kesemen , T.Khaniyev On the Semi‐Markovian Random Walk with Delay and Weibull Distributed Interference of Chance

Session 4.3: Computational Methods in Physical and Social Sciences III Place: Hall 3 Chair: Hassan Yousefi‐Azari

• Jisheng Kou, Xiuhua Wang, Yitian Li A nonlinear preconditioner for Jacobian‐free Newton‐Krylov methods

• Ludmila Bourchtein, Andrei Bourchtein A splitting semi‐implicit scheme for large‐scale atmospheric dynamics model

• Dogan Yildiz, Atif Evren Multilevel Factor Modeling as an Alternative in Evaluating the Performance of Statistics Education in Turkey

• Selcuk Han Aydin, M. Tezer Sezgin Stabilized FEM Solution of Steady Natural Convection Flow in a Square Cavity

• Hanieh Khalili Param , F. Bazdidi Investigation of Large Eddy Simulation and Eddy‐Viscosity Turbulence Models Applicable to Film Cooling Technique

• Eun Heui Kim, C. Lee, B. Englert Transonic problems in multi‐dimensional conservation laws

Session 4.4: Mathematical Programming III Place: Hall 4 Chair: Herman Mawengkang

• Masoud Allame, B. Vatankhahan, S. Abbasbandy Modified iteration methods to solve system Ax=b

• Eren Ozceylan, T. Paksoy A Multi‐Objective Mixed Integer Programming Model for Multi Echelon Supply Chain Network Design and Optimization

• Ali Osman Cibikdiken, Kemal Aydin Effect of Floating Point Aritmetic on Monodromy Matrix Computation of Periodic Linear Difference Equation System

• Mohammad Hassan Behzadi, F. Hosseinzadeh Lotfi, N. Nematollahi, M. Mirbolouki Ranking Decision Making Units with Stochastic Data by Using Coefficient of Variation

• Gurkan Ustunkar, S. Özöğür‐Akyüz, U. Sezerman, G. W. Weber, N. Baykal Application of Advanced Machine Learning Methods For SNP Discovery in Complex Disease Association Studies

• Ulas Ozen, S. A. Tarim, M. K. Dogru, R. Rossi An Efficient Computational Method for Non‐Stationary (R,S) Inventory Policy with Service Level Constraints

Session 4.5: Statistics and Data Analysis II Place: Hall 5 Chair: Fatih Tank

• Senol Erdogmus, E. Koc, S. Ayhan A Comprehensive Kansei Engineering Algorithm: An application of the university web page design

• Guvenc Arslan, I. Ozmen, B.O. Turkoglu A JAVA Program for the Multivariate Zp and Cp Tests and Its Application

• Ovgu Cidar, Y. Tandogdu Smoothing the Covariance Based on Functional Principal Component Analysis

• Yucel Tandogdu Functional Predictor and Response Variables Under Non‐Gaussian Conditions

• Mustafa Cagatay Korkmaz, Coskun Kus, Asir Genc Exponential‐Negative Binomial Distribution

• Tutut Herawan, Mustafa Mat Deris Soft Set Theory for Maximal Association Rules Mining


13:45‐14:45

Invited Talk Session Place: Hall 1 Chair: Omer L. Gebizlioglu

• “Ordered Random Variables‐Recent Developments” Ismihan Bayramoglu

15:30‐19:00 Tour to the old town fortress/marina and museum visit

20:00 Congress Dinner

2 October 2009, Friday

09:00‐10:30 Parallel Sessions 5 Session 5.1: Mathematical and Computational Finance Place: Hall 1 Chair: Jan Dhaene

• Koen Van Weert, Jan Dhaene, Marc Goovaerts Approximations for Optimal Portfolio Selection Problems

• Gerhard‐Wilhelm Weber, Kasirga Yildirak, Efsun Kurum A Classification Problem of Credit Risk Rating Investigated and Solved by Optimization of the ROC Curve

• Muhammed‐Shahid Ebrahim, Ike Mathur Structuring Pension Funds Optimally

• Refail Kasimbeyli, G. Ozturk, O. Ustun Multi‐class classification algorithms based on polyhedral conic functions and application to companies listed on the Istanbul Stock Exchange

Session 5.2: Cryptography Place: Hall 2 Chair: Ersan Akyıldız

• Ferruh Ozbudak, M. Cenk Efficient Multiplications in

• Baris Bulent Kirlar On the elliptic curves y2=x3‐c with embedding degree one

• Mohammed Mahmoud Jaradat On the basis number of the lexicographic product of two graphs and some related problems

• Frank J. Kampas, Janos D.Pinter Nonlinear Optimization in Mathematica with MathOptimizer

Session 5.3: Differential equations II Place: Hall 3 Chair: Josep Arnal

• Muhammad Asif Gondal, A. Ostermann Exponential Runge‐‐Kutta methods for option pricing in jump‐diffusion models

• Mesliza Mohamed, M. Jusoh Discrete First‐Order Four‐Point Boundary Value Problem

• Yucel Cenesiz, Y. Keskin, A. Kurnaz The Solution of the Bagley‐Torvik Equation with the Generalized Taylor Collocation Method

• Ahmet Duman, Kemal Aydin Sensitivity of Schur Stable Linear Systems with Periodic Coefficients

Session 5.4: Numerical Linear Algebra II Place: Hall 4 Chair: Serkan Eryilmaz

• Maxim Naumov, A. Bourchtein On the Modification of an Eigenvalue Problem that Preserves an Eigenspace

• Kuniyoshi Abe, G. L. G. Sleijpen A Variational Algorithm of the GPBi‐CG Method for Solving Linear Systems

• Soheil Salahshour, Tofigh Allahviranloo Fully fuzzy linear system: New point of view

• Tofigh Allahviranloo, Soheil Salahshour Fuzzy Linear System: Satisfactory Level of Solution

Session 5.5: Approximation and Interpolation III Place: Hall 5 Chair: Dmitri V. Alexandrov

• Havva Kaffaoglu, N. Mahmudov On q‐Szász‐‐Durrmeyer Operators

• M. Cetin Kocak Ostrowski’s Fourth‐order Iterative Method Solves Cubic Equations of State

• Hatice Gul Ince, G. Bascanbaz Tunca, A. Erencin On Bivariate Bernstein‐Chlodovsky Operator

• Yoseph Hashemi, A. Jahangirian Implicit Fully Mesh‐Less Method for Compressible Viscous Flow Calculations


11:00‐12:30

Paralel Sessions 6 Session6.1: Applied Probability and Stochastic Processes III Place: Hall 1 Chair: Kasirga Yildirak

• Mustafa Kemal Dogru, G.J. van Houtum, A.G. de Kok Newsvendor Characterizations for One‐Warehouse Multi‐Retailer Inventory Systems with Discrete Demand under the Balance Assumption

• Ismail Kinaci, B. Saracoglu Modified Maximum Likelihood Estimators for Logistic Distribution under Type‐II Progressively

• Azizah Hanim Nasution , A. Syahrin, H. Mawengkang Modeling Coordination Relationships of School Communities to Achieve Environmental Behavior Using Influence Diagram

• Vilda Purutcuoglu, M. L. Tiku Testing unit root and comparison of estimates

Session6.2: Computational Methods in Physical and Social Sciences IV Place: Hall 2 Chair: Lucia Romani

• Dmitri V. Alexandrov, A.P.Malygin, I.V.Alexandrova Nonlinear Dynamics of Leads

• Reza Zolfaghari An Inverse Problem of Finding Control Parameter in a Parabolic Equation

• Mohammad Moalemi, F. Bazdidi Analysis of Laminar Film Boiling on a Vertical Surface Using a Coupled Level‐Set and Volume‐of‐Fluid Technique

• Hassan Yousefi‐Azari, A.R. Ashrafi, M.H. Khalifeh Topological Indices of Graph Operations

Session6.3: Quadrature and Integral Equations Place: Hall 3 Chair: Tahir Khaniyev

• Nik Mohd Asri Nik Long, M. Yaghobifar, Z. K. Eshkuvatov New approach for the construction of the solutions of Cauchy integral equation of the first kind

• Mohammad Ali Fariborzi Araghi, Sh. Sadigh Behzadi

The Use of variational iteration method to Solve a nonlinear Volterra‐Fredholm integro‐differential equations

• Tomoaki Okayama, T. Matsuo, M. Sugihara Modified Sinc‐collocation methods for Volterra integral equations of the second kind and their theoretical analysis

• Nagehan Akgun, M. Tezer Sezgin Differential Quadrature Solution of 2D Natural Convection in a Cavity Under a Magnetic Field

Session6.4: Mathematical Modeling, Analysis, Applications III Place: Hall 4 Chair: Seiji Fujino

• Abdelouahed Kouibia , M. Pasadas Approximation by div‐rot variational splines

• Bulent Karasozen, Fikriye Yilmaz Solving Distributed Optimal Control Problems for the Unsteady Burgers Equation in COMSOL Multiphysics

• Farnaz Derakhshan Formalizing Dynamic Assignment of Rights and Responsibilities to Agents

• Ali Deliceoglu, F. Gurcan Topology of two separation bubbles with opposite rotations in a double‐lid‐driven rectangular cavity

Session6.5: Numerical Analysis and Optimization Place: Hall 5 Chair: Janos D. Pinter

• Adigozal Dosiyev The Block‐Grid Method for Solving Laplace's Boundary Value Problem with Singularities

• Johan Hendrik DeKlerk Analytical and numerical evaluation of finite‐part integrals

• Nematollah Fouladi, M. Darbandi Automatic Zone Decomposition in Iterative Solution of Differential Equations over Unstructured Grids

• Alireza Naderi, M. Darbandi An Extended Implicit Pis Scheme to Efficent Simulation of Turbulent Flow with Moving Boundaries


13:30‐16:10

Paralel Sessions 7 Session 7.1: Optimization II Place: Hall 1 Chair: Gerhard W. Weber

• Jorge A. Ruiz‐Vanoye, Joaquín Pérez‐Ortega, Rodolfo A. Pazos R., Ocotlán Díaz‐Parra Survey of Polynomials Transformations between NP‐Complete problems

• Jorge A. Ruiz‐Vanoye, Joaquín Pérez‐Ortega, Rodolfo A. Pazos R., Ocotlán Díaz‐Parra Application of Formal Languages in the Polynomial Transformations of Instances Between Np‐Complete Problems

• Serap Kemali, Gabil R. Adilov Some Inequalities for Increasing Positively Homogeneous Functions

• Aydin Karakoca, A. Genc A Comparative Study on Parameter Estimations in Multivariate Nonlinear Model

• M. Fernanda P. Costa, Edite M.G.P. Fernandes, A. Ismael F. Vaz Interior point filter line search strategies for large scale optimization: practical behavior

• Farhad Hosseinzadeh Lotfi, H. Nikoomaram,A. Toloie Eshlaghy,M.A.Afshar Kazemi,R. Sharifi,M. Ahadzadeh Namin Interval Malmquist productivity in DEA analysis and its application in determining the regress and progress of Islamic Azad university's departments

• Radek Matousek, Martin Kuba HC12‐Highly Scalable Optimization Algorithm

Session 7.2: Mathematical Modeling, Analysis, Applications IV Place: Hall 2 Chair: Andrei Bourchtein

• Atif Evren, Dogan Yildiz Parameter Interval Estimations through Chebyshev‐ type inequalities for Nonlinear Regression Models

• Alejandro Zarzo, L. Fernandez, P. Martinez‐Gonzalez, B. Soler Special functions, non‐linearity and algebraic and differential properties: Computational aspects.

• Zubeyde Ulukok, Ramazan Turkmen Trace Inequalities for Matrices

• Mine Menekse Yilmaz, Sevilay Kirci Serenbay The Convergence of Family of Integral Operators with Positive Kernel

• Miguel Angel Fortes, P. Gonzalez, M. Pasadas Approximation of patches by C r ‐finite elements of Powell‐Sabin type

• Alejandro Fuentes‐Penna , Jorge A. Ruiz‐Vanoye, Ocotlán Díaz‐Parra Application of Formal Languages in the Polynomial Transformations of Instances Between Np‐Complete Problems

• Farhad Hosseinzadeh Lotfi, A.Toloie Eshlagy, M.R. Mozaffari, Z. Ghalej Beigi, K.Gholami Large Sensitivity of Ranking

Session 7.3: Probability Modeling and Computing Place: Hall 3 Chair: Birdal Senoglu

• Mohammad Khodabakhshi Super efficiency in stochastic data envelopment analysis: An input relaxation approach

• Sukru Acitas, Birdal Senoglu Two Level Fractional Factorials with Long‐Tailed Symmetric Error Distributions

• Alvaro Rodolfo De Pierro, E.X. Miqueles X‐ray Fluorescence Computed Tomography: Inversion Methods

• Anders Andersson , B. Nilsson Using Dirichlet‐to‐Neumann operators and Conformal Mappings with Approximate Curve Factors in Waveguide Problems

• Mila Milan Stojakovic Imprecise probability and application in finance

• Mehdi Zamani An Efficient 2‐D Model for Analysis of Nonuniform Rock Masses

Session 7.4: Mathematical Modeling and Data Analysis Place: Hall 4 Chair: Pablo Sanchez‐Moreno

• Tugba Sarac A new hybrid algorithm for quadratic knapsack problem

• Ahmet Pekgör, A. Genc Criteria Function Efficiency Against Outliers in Nonlinear Regression

• Nergiz Kasımbeyli, Tugba Sarac A two‐objective integer programming mathematical model for a one‐dimensional assortment problem

• A. Asgharzadeh, R. Valiollahi Estimation of reliability P(Y < X) for the proportional reversed hazard models using lower record data

• Ceren Eda Can, N. Erbil, G. W. Weber Libor Market Model as a Special Case of Parameter Estimation in Nonlinear Stochastic Differential Equations (SDEs)

• Koray Kalafatcilar, Yılmaz Akdi, Kıvılcım Metin‐Özcan Alternative Long‐run analysis of Services and Goods SectorsInflation in Turkey by Fractional and Asymmetric Cointegration Methods

• Seyhmus Yardımcı Some Relations Between Functionals On Bounded Real Sequences

Session 7.5: Mathematical Modeling and Computing Place: Hall 5 Chair: Guvenc Arslan

• Shamsul Qamar, S. Mukhtar, S. Noor, A. Seidel‐Morgenstern Efficient numerical techniques for solving batch crystallization models

• Handan Cerdik Yaslan, Valery G. Yakhno Equations of anisotropic elastodynamics as a symmetric hyperbolic system:deriving the time‐dependent Green's function

• Abbas Toloie Eshlaghy, Mohammadali Afshar Kazemi,Ebrahim Nazari Farokhi,Bahareh Sagheb Measuring the importance and the weight of decision makers

• Abbas Toloie Eshlaghy, Nasim Rastkhiz Paydar,Khadijeh Joda,Neda Rastkhiz Paydar Sensivity analysis for criteria values in decision making matrix of SAW method

• Modjtaba Ghorbani , A.R. Ashrafi, M. Saheli Rational Eigenvalues of Fullerenes

• G.H. Fath‐Tabar, A.R. Ashrafi Bounds on Estrada Index of Fullerenes

• Sinem Sezer, Ilham A.aliev A Characterization of the Riesz Potentials Space With the Aid of a Composite Wavelet Transform

16:10‐16:30 Tea‐Coffe Break

16:30‐17:00 Closing Session Place: Hall 1 Information and Closing Talks


vii

CONTENTS

Committees v

Invited Paper 1 - Dependence Modeling with Copulas 1Roger B. Nelsen

Invited Paper 2 - NULISS: Non-Uniform Local Interpolatory Sub-division Surfaces 2

Lucia Romani

Invited Paper 3 - Ordered Random Variables - Recent Developments 3Ismihan Bayramoglu

Tutorial - Global Optimization In Practice 4Janos D. Pinter

Parallel Sessions 1 5

Dependence of the PageRank vector on the artificial links 8Andrei Bourchtein

Multi-state system reliability under stress-strength setup 9Serkan Eryilmaz

On distributions of bottom m scores after l-th change 10Agah Kozan

A Variant of the Choquet-Deny Theorem with Application to Characterizaiton 11Guvenc Arslan

Streamwise oscillations of a cylinder beneath a free surface: Part 1.Free surface effects on vortex formation modes 13

Canan Bozkaya


viii

Streamwise oscillations of a cylinder beneath a free surface: Part 2.Free surface effects on fluid forces 14

Canan Bozkaya

Rogue waves: power of mathematics in understanding the phenomenon 15Nail Akhmediev

The Eccentric Connectivity Index of Nanotubes and Nanotori 16Ali Reza Ashrafi

First-Order Three-Point Boundary Value Problems at Resonance 18Mesliza Mohamed

Boundary value problems for the Helmholtz equation in domainsbounded by closed curves and open arcs 19

Pavel Krutitskii

On the Partial Differential Equations with Non-Constant Coefficientsand Convolution Method 20

Adem Kilicman

Step size strategies on the numerical integration of the systems ofdifferential equations 21

Gulnur Celik Kizilkan

Modeling Facility Location and Supplier Selection with SuppliersProduct Quality and Contract Fee for Strategic Supply Chain De-sign 23

Eren Ozceylan

On Numerical Optimization Methods for Infinite Kernel Learning 24Sureyya Ozogur Akyuz

A DEA based approach for solving the multiple objective shortestpath problem 25

Alireza Davoodi

Robustification of CMARS 26Fatma Yerlikaya Ozkurt

A high accurate difference-analytical method for solving Laplace’sequation on polygons with nonanalytic boundary conditions 28

Suzan Cival Buranay


ix

An Application of a New Fuzzy Robust Regression Algorithm to Ac-tuarial Science 29

Kamile Sanli Kula

Comparison of Exponentially fitted Explicit Runge-Kutta methodsfor Solving ODEs 40

Fudziah Ismail

Numerical Integration of a Fuzzy Riemann Double Integral 31Fereidoon Khadem


Statistical Convergence for Set-Valued Functions 36Halil Gezer

Hermite-Birkhoff interpolation problems on the roots of the unity 37Elias Berriochoa

Weak and strong convergence theorems for a finite family ofI−asymptotically nonexpansive mapping 38

Liping Yang

q-Statistical Convergence 39Serife Bekar

Comparison of Exponentially fitted Explicit Runge-Kutta methodsfor Solving ODEs 40

Fudziah Ismail

A novel 2D finite-volume method for advection problems with embed-ded moving-boundaries 41

Yunus Hassen

Explicit Representation of Hessenbergians: Application to General Or-thogonal Polynomials 44

Venancio Tomeo

The Powers of Anti(2k+1)-Diagonal Matrices and Fibonacci Numbers 45Fatih Yilmaz

On computing powers for one type of matrice by Pell and Jacobsthal Numbers 46


x

Fatih Yilmaz

On the properties of generalized Fibonacci and Lucas numbers withbinomial coefficients 47

Hasan Huseyin Gulec

IDR-based relaxation methods for solving linear systems 48Seiji Fujino

A Shift Strategy for Superquadratic Convergence in the dqds Algo-rithm for Singular Values 49

Kensuke Aishima

A Hybrid Genetic Pattern Search Augmented Lagrangian Method forConstrained Global Optimization 51

Lino Costa

Production Planning under Stochastic Demand for Fish ProcessedProduct at North Sumatera Province, Indonesia 52

Herman Mawengkang

Centralized Resource Allocation with Stochastic Data 53Mahnaz Mirbolouki

Special functions, non-linearity and algebraic and differential proper-ties: Computational aspects 54

Ana Maria A. C. Rocha

A Regularized Lagrangian Method for Nonlinearly Constrained Mono-tone Variational Inequalities 55

Eman Hamad Al-Shemas

A new multiobjective differential evolution strategy for scattering uni-formly the Pareto solution set for designing mechatronic systems 56

Miguel Gabriel Villarreal-Cervantes

On Koornwinder classical orthogonal polynomials 59Lidia Fernandez

A note on a family of two variable polynomials 60Rabia Aktas

Some generalizations of multiple Hermite polynomials via Rodrigues formula 61


xi

Cem Kaanoglu

Extension of Gamma, Beta and Hypergeometric Functions 62Emine Ozergin

Application of Pade approximation of differential transform methodto the solution of prey and predator problem 63

Onur Karaoglu

Jensen divergence based on Fisher’s information 168Pablo Sanchez-Moreno

Weibull-Negative Binomial Distribution 66Mustafa Cagatay Korkmaz

Comparison of a New Robust Test and Non-parametric Kruskal-WallisTest in One-way Analysis Of Variance Model 67

Yeliz Mert Kantar

General Linear Model (GLM) Approach to Repeated MeasurementsData Involving Univariate Analysis of Variance (ANOVA) and Mul-tivariate Analysis of Variance (MANOVA) Techniques 68

Neslihan Iyit

Comparing Estimation Results in Nonparametric and Semiparametric 69Alper Sinan

Confidence Intervals for Mean Time to Failure in Two-ParameterWeibull with Censored Data 70

Noor Akma Ibrahim

Rough Set-based Functional Dependency Approach for ClusteringCategorical Data 71

Tutut Herawan


Parameter Estimation by ANFIS in Cases Where Outputs are Non-Symmetric Fuzzy Number 76

Turkan Erbay Dalkilic

A Multizone Overset Algorithm for the Solution of Flow around Mov-


xii

ing Bodies 77Fatemesadat Salehi

Spectral Singularities of Sturm-Liouville Problems with EigenvalueDependent Boundary Conditions 78

Nihal Yokus

Vague DeMorgan Complemented Lattices 79Zeynep Eken

Approximating the singular integrals of Cauchy type with weight func-tion on the interval 80

Zainidin Karimovich Eshkuvatov

Lobatto IIIA-IIIB Discretization for the Strongly Coupled NonlinearSchrodinger Equation 81

Bulent Karasozen

Rough Oscillatory Singular Integrals on Rn 83Hussain Mohammed Al-Qassem

Exponentially fitted two–step hybrid methods for y′′ = f(x, y) 84Raffaele D’Ambrosio

Improving the Gradient based search Direction to Enhance TrainingEfficiency of Back Propagation based Neural Network algorithms 85

Nazri Mohd Nawi

Approximation Properties of Q-Konhauser Polynomials 86Gurhan Icoz

Modeling An Alternative Region-Based Active Contour Model UsingCauchy-Schwartz Divergence 87

Veronica Biga

On Chlodovsky variant of multivariate beta operator 88Gulen Bascanbaz Tunca

Stability analysis of recurrent neural networks with deviated argumentof mixed type 90

Enes Yilmaz

The Periodicity of Solutions of the Rational Difference Equation


xiii

xn+1 = pnxn−k+xn−(k+1)

qn+xn−(k+1)91

D. Turgut Tollu

On the behavior of solutions of a rational system x(n+1) = 1/[y(n−1)], y(n + 1) = x(n− 1)/[x(n).y(n− 2)] 92

Emine Hekimoglu

A modification on some improved Newton’s method without directfunction evaluations 93

Behzad Ghanbary

Error Inequalities for Discrete Hermite Interpolation 94Patricia J. Y. Wong

Parallel Newton-like methods for solving systems of nonlinear equations 95Josep Arnal

Deriving Elastic Fields in an Anisotropic Bi-material 97Demet Ersoy

A Boundary Value Problem of the Frequency-Dependent Maxwell’sSystem for Layered Materials 99

Sengul Kecelli

A Study on the Multiple Logistic Regression Analysis to DetermineRisk Factors for the Smoking Behavior 101

Sevgi Yurt Oncel

Numerical simulation of tsunami generated in North Pacific Oceannear Japan 102

Yoji Otani

A new numerical method for solving 2D Electrical Impedance Tomog-raphy Inverse Problem 103

Ata Olah Abbasi

Control strategy of avian influenza based on modeling and simulation 104Tertia Delia Nova

Fuzzy Optimization of A Multi Stage Multi Item Closed-Loop FlexibleSupply Chain Network Under Fuzzy Material Requirement Constraints 106

Eren Ozceylan


xiv

Identification, Optimization and Dynamics of Regulatory Networksunder Uncertainty 107

Gerhard-Wilhelm Weber

Using Dirichlet-to-Neumann operators and Conformal Mappings withApproximate Curve Factors in Waveguide Problems 108

Erkki Laitinen

Finding Efficient and Inefficient Outlier Layers by Using Skewness Coefficient 109Mahnaz Mirbolouki

Multi-Objective Optimization Model for Solving Risk-Based Environ-mental Production Planning Problem in Crude Palm Oil Industry 110

Hendaru Sadyadharma

Staff scheduling with priority constraints 111Sacha Varone


Some Properties of Q-Biorthogonal Polynomials 116Fatma Tasdelen Yesildal

Positive solutions for nonlinear first-order m-point boundary valueproblem on time scale 117

Ismail Yaslan

Error Estimates for Discrete Spline Interpolation 118Fengmin Chen

Computational analysis for microbial depolymerization processes ofxenobiotic polymers based on mathematical models and experimental results 119

Masaji Watanabe

Asymptotic Results for a Semi-Markovian Random Walk with a Nor-mal Distributed Interference of Chance 120

Tahir Khaniyev

A Model of Vascular Tumor Growth by Hybrid Systems 121Mustafa Kahraman

Probability Failure Analysis for Cracked Structure 123


xv

M.R. Akramin

On exceedances based on the list of top m scores after l-th change 124Burak Uyar

Functional Approach Using New L∗a∗b∗ color functions to evaluatecolour changes in granites after desalination using different methods 125

Jose M. Matias

On LIBOR and swap market models: calibration to caps and swaption markets126Ceren Eda Can

Analytical Recursive Algorithm for Path-dependent Option Pricingwith Stochastic Time 127

Zhaoning Shang

On the Semi-Markovian Random Walk with Delay and Weibull Dis-tributed Interference of Chance 128

Rovshan Aliyev

A nonlinear preconditioner for Jacobian-free Newton-Krylov methods 130Jisheng Kou

A splitting semi-implicit scheme for large-scale atmospheric dynamics model 131Ludmila Bourchtein

Multilevel Factor Modeling as an Alternative in Evaluating the Per-formance of Statistics Education in Turkey 132

Dogan Yildiz

Stabilized FEM Solution of Steady Natural Convection Flow in aSquare Cavity 133

Selcuk Han Aydin

Investigation of Large Eddy Simulation and Eddy-Viscosity Turbu-lence Models Applicable to Film Cooling Technique 134

Hanieh Khalili Param

Transonic problems in multi-dimensional conservation laws 135Eun Heui Kim

Modified iteration methods to solve system Ax = b 137Masoud Allame


xvi

A Multi-Objective Mixed Integer Programming Model for Multi Ech-elon Supply Chain Network Design and Optimization 138

Eren Ozceylan

Effect of Floating Point Aritmetic on Monodromy Matrix Computa-tion of Periodic Linear Difference Equation System 139

Ali Osman Cibikdiken

Ranking Decision Making Units with Stochastic Data by Using Coef-ficient of Variation 140

Mohammad Hassan Behzadi

Application of Advanced Machine Learning Methods For SNP Dis-covery in Complex Disease Association Studies 141

Gurkan Ustunkar

An Efficient Computational Method for Non-Stationary (R,S) Inven-tory Policy with Service Level Constraints 142

Ulas Ozen

A Comprehensive Kansei Engineering Algorithm: An application ofthe university web page design 144

Senol Erdogmus

A JAVA Program for the Multivariate Zp and Cp Tests and Its Application 145Guvenc Arslan

Smoothing the Covariance Based on Functional Principal Component Analysis146Ovgu Cidar

Functional Predictor and Response Variables Under Non-Gaussian Conditions 147Ovgu Cidar

Exponential-Negative Binomial Distribution 148Mustafa Cagatay Korkmaz

Soft Set Theory for Maximal Association Rules Mining 149Tutut Herawan


Approximations for Optimal Portfolio Selection Problems 154


xvii

Koen Van Weert

A Classification Problem of Credit Risk Rating Investigated andSolved by Optimization of the ROC Curve 155


Structuring Pension Funds Optimally 156Muhammed-Shahid Ebrahim

Multi-class classification algorithms based on polyhedral conic func-tions and application to companies listed on the Istanbul Stock Exchange 157

Refail Kasimbeyli

Efficient Multiplications in F55n and F77n 159Ferruh Ozbudak

On the elliptic curves y2 = x3 − c with embedding degree one 161Baris Bulent Kirlar

On the basis number of the lexicographic product of two graphs andsome related problems 162

Mohammed Mahmoud Jaradat

Global Optimization In Practice 163Janos D. Pinter

Exponential Runge–Kutta methods for option pricing in jump-diffusion models 165

Muhammad Asif Gondal

Discrete First-Order Four-Point Boundary Value Problem 166Mesliza Mohamed

The Solution of the Bagley-Torvik Equation with the Generalized Tay-lor Collocation Method 167

Yucel Cenesiz

Jensen divergence based on Fisher’s information 168Pablo Sanchez-Moreno

On the Modification of an Eigenvalue Problem that Preserves an Eigenspace 170Maxim Naumov


xviii

A Variational Algorithm of the GPBi-CG Method for Solving Linear Systems 171Kuniyoshi Abe

Fully fuzzy linear system: New point of view 172Soheil Salahshour

Fuzzy Linear System: Satisfactory Level of Solution 173Tofigh Allahviranloo

On q-Szasz–Durrmeyer Operators 175Havva Kaffaoglu

Ostrowskis Fourth-order Iterative Method Solves Cubic Equations of State 176M. Cetin Kocak

On Bivariate Bernstein-Chlodovsky Operator 177Hatice Gul Ince

Implicit Fully Mesh-Less Method for Compressible Viscous Flow Calculations 178Yoseph Hashemi


Newsvendor Characterizations for One-Warehouse Multi-Retailer In-ventory Systems with Discrete Demand under the Balance Assumption 182

Mustafa Kemal Dogru

Modified Maximum Likelihood Estimators for Logistic Distributionunder Type-II Progressively Hybrid Censored Data 183

Ismail Kinaci

Modeling Coordination Relationships of School Communities toAchieve Environmental Behavior Using Influence Diagram 184

Azizah Hanim Nasution

Testing unit root and comparison of estimates 185Vilda Purutcuoglu

Nonlinear Dynamics of Leads 187Dmitri V. Alexandrov

An Inverse Problem of Finding Control Parameter in a Parabolic Equation 188


xix

Reza Zolfaghari

Analysis of Laminar Film Boiling on a Vertical Surface Using a Cou-pled Level-Set and Volume-of-Fluid Technique 189

Mohammad Moalemi

Topological Indices of Graph Operations 190Hassan Yousefi-Azari

New approach for the construction of the solutions of Cauchy integralequation of the first kind 192

Nik Mohd Asri Nik Long

The Use of variational iteration method to Solve a nonlinear Volterra-Fredholm integro-differential equations 193

Mohammad Ali Fariborzi Araghi

Modified Sinc-collocation methods for Volterra integral equations ofthe second kind and their theoretical analysis 194

Tomoaki Okayama

Differential Quadrature Solution of 2D Natural Convection in a CavityUnder a Magnetic Field 195

Nagehan Akgun

Approximation by div-rot variational splines 197Abdelouahed Kouibia

Solving Distributed Optimal Control Problems for the UnsteadyBurgers Equation in COMSOL Multiphysics 198

Bulent Karasozen

Formalizing Dynamic Assignment of Rights and Responsibilities to Agents 199Farnaz Derakhshan

Topology of two separation bubbles with opposite rotations in adouble-lid-driven rectangular cavity 200

Ali Deliceoglu

The Block-Grid Method for Solving Laplace’s Boundary Value Prob-lem with Singularities 202

Adigozal Dosiyev


xx

Analytical and numerical evaluation of finite-part integrals 203Johan Hendrik DeKlerk

Automatic Zone Decomposition in Iterative Solution of DifferentialEquations over Unstructured Grids 204

Nematollah Fouladi

An Extended Implicit Pis Scheme to Efficent Simulation of TurbulentFlow with Moving Boundaries 205

Alireza Naderi


Survey of Polynomials Transformations between NP-Complete problems 210Jorge A. Ruiz-Vanoye

Application of Formal Languages in the Polynomial Transformationsof Instances Between Np-Complete Problems 211

Jorge A. Ruiz-Vanoye

Some Inequalities for Increasing Positively Homogeneous Functions 212Serap Kemali

A Comparative Study on Parameter Estimations in Multivariate Non-linear Model 213

Aydin Karakoca

Interior point filter line search strategies for large scale optimization:practical behavior 214

M. Fernanda P. Costa

Interval Malmquist productivity in DEA analysis and its applicationin determining the regress and progress of Islamic Azad university’sdepartments 223

Farhad Hosseinzadeh Lotfi

Parameter Interval Estimations through Chebyshev-Type Inequalitiesfor Nonlinear Regression Models 217

Atif Evren

Special functions, non-linearity and algebraic and differential proper-ties: Computational aspects 218


xxi

Alejandro Zarzo

Trace Inequalities for Matrices 219Ramazan Turkmen

The Convergence of Family of Integral Operators with Positive Kernel 220Mine Menekse Yilmaz

Approximation of patches by Cr-finite elements of Powell-Sabin type 221Miguel Angel Fortes

Project Scheduling Problem 222Alejandro Fuentes-Penna

Interval Malmquist productivity in DEA analysis and its applicationin determining the regress and progress of Islamic Azad university’sdepartments 223


Super efficiency in stochastic data envelopment analysis: An inputrelaxation approach 225

Mohammad Khodabakhshi

Two Level Fractional Factorials with Long-Tailed Symmetric ErrorDistributions 226

Sukru Acitas

X-ray Fluorescence Computed Tomography: Inversion Methods 227Alvaro Rodolfo De Pierro

Using Dirichlet-to-Neumann operators and Conformal Mappings withApproximate Curve Factors in Waveguide Problems 228

Anders Andersson

Imprecise probability and application in finance 229Mila Milan Stojakovic

A new hybrid algorithm for quadratic knapsack problem 232Tugba Sarac

Criteria Function Efficiency Against Outliers in Nonlinear Regression 233Ahmet Pekgor


xxii

A two-objective integer programming mathematical model for a one-dimensional assortment problem 234

Nergiz Kasimbeyli

Estimation of reliability P (Y < X) for the proportional reversed haz-ard models using lower record data 235

A. Asgharzadeh

Libor Market Model as a Special Case of Parameter Estimation inNonlinear Stochastic Differential Equations (SDEs) 236

Ceren Eda Can

Alternative Long-Run Analysis of Services and Goods Sectors Infla-tion in Turkey by Fractional and Asymmetric Cointegration Methods 237

Koray Kalafatcilar

Some Relations Between Functionals On Bounded Real Sequences 238Seyhmus Yardimci

Efficient numerical techniques for solving batch crystallization models 240Shamsul Qamar

Equations of anisotropic elastodynamics as a symmetric hyperbolicsystem:deriving the time-dependent Green’s function 241

Handan Cerdik Yaslan

Measuring the importance and the weight of decision makers 244Abbas Toloie Eshlaghy

Sensitivity analysis for criteria values in decision making matrix ofSAW method 245

Abbas Toloie Eshlaghy

Rational Eigenvalues of Fullerenes 246Modjtaba Ghorbani

Bounds on Estrada Index of Fullerenes 247G.H. Fath-Tabar

A characterization of the Riesz potentials space with the aid of acomposite wavelet transform 248

Sinem Sezer


xxiii

Author Index 249


1

Dependence Modeling with Copulas

Roger B. Nelsen

Department of Mathematical SciencesLewis & Clark College, Portland

Oregon 97219USA

Abstract: Copulas have proven to be remarkably useful for modeling dependence ina variety of settings. In this talk we will survey important aspects of the theory ofcopulas that make them well suited for dependence modeling. We will discuss meth-ods for constructing one and two parameter families, dependence properties (e.g., taildependence), applications (e.g., extreme value theory, Schur-constant survival models),simulation techniques, etc. We will also discuss cautions about and limitations to the useof these copulas. We conclude with several open problems.


2

NULISS: Non-Uniform Local Interpolatory SubdivisionSurfaces

Lucia Romani

email: [email protected]

University of Milano-Bicocca, ItalyVia R. Cozzi 53, 20125 Milano - Italy

(Joint work with: C. Beccari and G. Casciola)

Abstract: A greater and greater interest for numerical algorithms providing high-qualitysurfaces passing through the vertices of a given control mesh has grown with the burst-ing diffusion and the increasing request of graphical tools in several fields like computergraphics, scientific visualization and industrial, medical, biological, topographic, geolog-ical applications. In all these contexts, it is essential to provide a shape that faithfullymimics the behavior of the underlying control net and at the same time reproduces itssalient features, when present. In this work we address these issues by the definitionof a non-uniform interpolatory surface subdivision scheme where the insertion rules de-pend on a proper local parameterization of the control net at each refinement level. Beforestarting the subdivision process, a parameter value is attached to each edge of the originalmesh, depending on the geometrical configuration of its neighboring edges. The proposednon-uniform refinement algorithm, although non-stationary, is linear and efficient sincethe local parameterization is automatically computed only once before starting the sub-division process, and recursively updated at each refinement step. The computed set ofparameters, chosen accordingly to the local geometry of the mesh, allows us to generate alimit surface that closely resembles the initial control net, independently of the valencesof vertices and faces. Moreover, special features like circular sections, sharp edges andcorners are consistently supported by opportunely setting the local edge parameters.


3

Ordered Random Variables - Recent Developments

Ismihan Bayramoglu


Department of Mathematics, Izmir University of EconomicsBalcova, Izmir

Turkey

Abstract: Order statistics have wide applications in many areas where the use of thearranged sample is important. For example, in statistical models of many experiments ofreliability analysis, life time studies, in testing of strength of materials, etc., the realiza-tions arise in nondecreasing order, therefore the use of order statistics is necessary. Orderstatistics are extensively used in statistical inferences, in the estimation theory and hy-pothesis testing. Order statistics and their properties have been studied extensively sincethe early part of the last century, and recent years have seen a particularly rapid growth.Nowadays, the theory of general models of ordered random variables arouses interest ofmany researchers. The distributions of ordered random variables for independent andidentically distributed random variables are well studied in both discrete and continuouscases.We will discuss some general models of ordered random variables, basic distribution the-ory and applications. Some new results on distribution of order statistics in the caseof exchangeable random variables will be presented. These results allows wide spreadapplications in modelling of various lifetime data, biomedical sciences, reliability andsurvival analysis, actuarial sciences etc., where the assumption of independence of datacan not be accepted and the exchange- ability is more realistic assumption.


4

Global Optimization In Practice

Janos D. Pinter


Department of Industrial EngineeringOzyegin UniversityIstanbul - Turkey

Abstract: The objective of global optimization (GO) is to find the best possible solutionof nonlinear models, in the presence of multiple local optima. As of today (2009), GOimplementations are available for compiler platforms, optimization modeling languages,and integrated scientific-technical computing systems. These tools can effectively assistengineers and scientists to develop and solve their advanced optimization models.In this presentation we discuss the state-of-art in GO software development, and presenta number of interesting applications, including numerical challenges and real-world casestudies.


PARALLEL SESSIONS 1

30 September 2009, 11:00-12:30



7

Session 1.1: Applied Probability and Stochastic Processes I

Chair: Refail KasimbeyliPlace: Hall 1


8

Dependence of the PageRank vector on the artificial links

Andrei Bourchtein


Rua Anchieta 4715, bloco K, ap.304 Pelotas 96015-420Brazil

(Joint work with: L. Bourchtein)

Abstract: In this study we present an analysis of the influence of artificial links (dan-gling vector) attributed to the dangling nodes of the web link matrix on the principaleigenvectors of that matrix, which is a part of the algorithm used by Google to rank webpages. We clarify when the choice of the dangling vector does not change the originaleigenvectors and give an evaluation for perturbations of the principal eigenvectors whenthey are subject to modification.


9

Multi-state system reliability under stress-strength setup

Serkan Eryilmaz


Department of Mathematics, Izmir University of EconomicsBalcova, Izmir

Turkey

(Joint work with: Funda Iscioglu)

Abstract: Multi-state reliability models have been found to be more flexible for model-ing engineering systems. In this study, multi-state k-out-of-n and multi-state consecutivek-out-of-n systems are considered in a stress-strength setup. The states of the system areassigned considering the number of components whose strengths are above (below) themultiple stresses avaliable in an environment. The exact state probabilities of the corre-sponding systems are computed and the results are illustrated for various stress-strengthdistributions. Properties of large systems are also investigated.

Keywords. Consecutive k-out-of-n systems; Multi-state systems; Stress-strengthreliability.


10

On distributions of bottom m scores after l-th change

Agah Kozan


Department of Statistics, Faculty of Science, Ege University35100 Bornova, Izmir

Turkey

(Joint work with: H. Tanil)

Abstract: Consider an infinite sequence which contains independent and identicallydistributed (iid) continuous random variables with distribution function (df) F. Tanil(2009) derived the joint and marginal probability density functions of top m scores afterl-th change. In this study, using the concept of ordered random variables, we obtain thejoint and marginal probability density functions of bottom m scores after l-th change.In addition, we give a structure function to construct the distribution functions, themoments, and the characteristic functions of the bottom m scores.


11

A Variant of the Choquet-Deny Theorem with Applicationto Characterizaiton

Guvenc Arslan


Baskent University,Balca Campus, Department of Statistics and Computer Sciences

06810 Ankara - Turkey

Abstract: In this paper a variant of the Choquet-Deny theorem is obtained and used toprove two recent characterization results of the uniform distribution based on spacingsof order statistics and records. These two results are combined in one relation using thisvariant of the Choquet-Deny theorem.


12

Session 1.2: Computational Methods in Physical and SocialSciences I

Chair: Masai WatanabePlace: Hall 2


13

Streamwise oscillations of a cylinder beneath a free surface:Part 1. Free surface effects on vortex formation modes

Canan Bozkaya


Department of Mathematics and StatisticsMemorial University of Newfoundland

A1C 5S7, St. John’ sCanada

(Joint work with: Serpil Kocabiyik)

Abstract: A computational study of two-phase flow problem based on a viscous in-compressible two-fluid model with an oscillating cylinder is performed. Specifically, two-dimensional flow past a circular cylinder subject to forced streamwise oscillations be-neath a free surface is considered. The numerical simulations are carried out using thecomputational fluid dynamics code developed by Dr. S. Kocabiyik’s research group atMemorial University of Newfoundland. This computational code is based on the finitevolume method for solving the two-dimensional continuity and unsteady Navier-Stokesequations in their pressure-velocity formulation and has been successfully applied to theproblem of uniform flow past cylinders including oscillating cylinders using both singleand two-phase flow models. The numerical simulations are carried out at the Reynoldsnumber of R = 200 for fixed displacement amplitude A = 0.13 for the Froude num-bers Fr ≈ 0.0; Fr = 0.2, 0.4, and the cylinder submergence depths, h = 0.25, 0.5, 0.75when the forcing cylinder oscillation frequency-to-natural vortex shedding frequency ra-tio, f/f0=1.5, 2.5, 3.5. The main objective of this study is to address the alterations ofthe near-wake region, in particular, the flow regimes and the locked-on vortex formationmodes, due to the presence of the free surface. The equivorticity patterns, streamlinesand pressure distribution contours are used for the numerical flow visualization. Thiscomputational investigation has shown that both the near wake structure and the freesurface deformations are very sensitive to the Froude number Fr, and to the cylindersubmergence depth, h. For small Froude numbers the surface deformations are minimaland they become substantial as Fr increases. As Fr increases to 0.4 and h decreases to0.25, the localized interface sharpening and wave breaking occur. This introduces a sub-stantial quantity of opposite signed vorticity from the free surface which interacts withthe upper vorticity shedding layer through diffusion and thereby, substantially changesthe wake evolution. These findings are in accord with that of previous studies for thecases of uniform flow past stationary and oscillating cylinders in the presence of a freesurface.


14

Streamwise oscillations of a cylinder beneath a free surface:Part 2. Free surface effects on fluid forces

Canan Bozkaya


Department of Mathematics and StatisticsMemorial University of Newfoundland

A1C 5S7, St. John’ sCanada

(Joint work with: Serpil Kocabiyik)

Abstract: This study presents the results of a two-dimensional computational study ofthe free surface flow past a circular cylinder forced to perform streamwise oscillations inthe presence of an oncoming uniform flow. In Part 1, we have examined the effects of theinclusion of the free surface on the vortex-shedding modes in the near wake region forthe same problem at the Reynolds number of R = 200 for fixed displacement amplitudeA = 0.13 when the forcing frequency-to-natural shedding frequency ratio, f/f0, ranges1.5-3.5. The numerical simulations are carried out using basically the same two-phaseflow model and finite volume code as that used in Part 1 for numerical simulation of theunsteady Navier-Stokes equations in their primitive variable formulation. The objectiveof this study is to examine the effect of the cylinder submergence depths, h = 0.25, 0.5,0.75 and the frequency ratios, f/f0 =1.5, 2.5, 3.5 on fluid forces as well as the totalmechanical energy transfer at two values of the Froude numbers Fr = 0.2, 0.4. The timehistories of the in-line (drag) and transverse (lift) force coefficients are plotted as well astheir power spectrum densities and Lissajous trajectories. The mean and the root-mean-square lift and drag force coefficients, are also predicted to determine the free surfaceeffects on the fluid forces. It is interesting to note that irrespective of the values of hand f/f0, the total mechanical energy transfer is negative, indicating the energy transferfrom the cylinder to the fluid unlike transverse oscillation case. However, the changesin the absolute values of the energy transfer is observed depending on the values of hand f/f0, resulting in variations in the amount of the mechanical energy transfer fromcylinder to fluid at each Fr.


15

Rogue waves: power of mathematics in understanding thephenomenon

Nail Akhmediev


Optical Sciences Group, Research School of Physics and EngineeringInstitute of Advanced StudiesAustralian National University

Canberra, ACT 0200Australia

(Joint work with: J.M. Soto-Crespo, A. Ankiewicz)

Abstract: ”Rogue waves”, ”freak waves”, ”killer waves” and similar names have beenthe topic of several recent publications related to giant single waves appearing in theocean ”from nowhere”. Hitherto, we do not have a complete understanding of this phe-nomenon due to the difficult and risky observational conditions. Those who experiencethese phenomena while being on a ship would be busy saving their lives rather thanmaking measurements. It is difficult to explain the high amplitudes that can occur in theopen ocean using linear theories based on the superposition principles. Nonlinear theo-ries of ocean waves are more likely to explain why the waves can ”appear from nowhere”than linear theories. The reason for the phenomenon can lie in the instability of a certainclass of initial conditions that tend to grow exponentially and hence have the possibilityof increasing up to very high amplitudes. Rogue waves can be described as ”waves thatappear from nowhere and disappear without a trace”. This expression can be appliedboth to rogue waves in the ocean and rational solutions of the nonlinear Schroedingerequation (NLSE). There is a hierarchy of rational solutions of ’focussing’ NLSE withincreasing order and with progressively increasing amplitude. The solutions can describe”rogue waves” with virtually infinite amplitude. They can appear from smooth initialconditions that are only slightly perturbed in a special way, and are given by our exactsolutions. Thus, a slight perturbation on the ocean surface can dramatically increasethe amplitude of the singular wave event that appears as a result. We also numericallycalculated chaotic waves of the focusing NLSE, starting with a plane wave modulatedby relatively weak random waves. We show that the peaks with highest amplitude of theresulting wave composition (rogue waves) can be described in terms of exact solutionsof the NLSE in the form of the collision of Akhmediev breathers.


16

The Eccentric Connectivity Index of Nanotubes andNanotori

Ali Reza Ashrafi


Department of MathematicsUniversity of Kashan

Kashan - Iran

(Joint work with: M. Saheli)

Abstract: Let G be a molecular graph. The eccentric connectivity index ξ(G) of G isdefined as ξ(G) =

∑u∈V (G) degG(u)εG(u), where degG(u) denotes the degree of vertex

u and εG(u) is the largest distance between u and any other vertex v of G. In thispaper an exact formula for the eccentric connectivity index of TUC4C8(S) nanotubesand nanotori are given.


17

Session 1.3: Differential Equations I

Chair: Bulent KarasozenPlace: Hall 3


18

First-Order Three-Point Boundary Value Problems atResonance

Mesliza Mohamed


Jabatan Matematik, Universiti Teknologi MARA, Kampus Arau 02600 Arau, PerlisMalaysia

(Joint work with: H.B. Thompson, M. Jusoh)

Abstract: We consider three-point boundary value problems for a system of first-orderequations in perturbed systems of ordinary differential equations at resonance. We obtainnew results for the above boundary value problems with nonlinear boundary conditions.In particular, we consider a system of first-order equations which is arising from scalarsecond-order equation. The existence of solutions is established by applying a version ofBrouwer’s Fixed Point Theorem which is due to Miranda.


19

Boundary value problems for the Helmholtz equation indomains bounded by closed curves and open arcs

Pavel Krutitskii


KIAM, Department 4, Miusskaya Sq. 4, Moscow 125047Russia

Abstract: Boundary value problems for the Helmholtz equation are studied in planardomains bounded by closed curves and open arcs. Either Dirichlet or Neumann bondarycondition is specified on the whole boundary (i.e. on both closed curves and open arcs).Theorems on existence and uniqueness of a classical solution are proved. The integralrepresentation for a solution in the form of potentials is obtained. Each boundary valueproblem is reduced to the uniquely solvable Fredholm equation of the 2-nd kind and indexzero for the density in potentials. Dirichlet and Neumann problems for the propagativeHelmholtz equation are studied for exterior domain [5-8], while problems for dissipativeHelmholtz equation [1-4] are studied in both interior and exterior domains. Problems indomains bounded by closed curves and problems in the exterior of open arcs in a planeare particular cases of our problems.

References:1. Krutitskii P.A. // Hiroshima Math.J., 1998, v.28, 149-168.

2. Krutitskii P.A. // ZAMM, 1997, v.77, No.12, p.883-890.

3. Krutitskii P.A. // Zeitschr. Analys. Anwend., 1997, v.16, No.2, p.349-362.

4. Krutitskii P.A. // Int.J.Maths.Math.Sci., 1998, v.21, 209-216.

5. Krutitskii P.A. // Nonlin. Anal., TMA, 1998, v.32, 135-144.

6. Krutitskii P.A. // J. Math. Kyoto Univ., 1998, v.38, No.3, p.439-452.

7. Krutitskii P.A. // Math. Comp. Simul., 2000, v.52, 345-360.

8. Krutitskii P.A. // ZAMM, 2000, v.80, No.8, p.535-546.


20

On the Partial Differential Equations with Non-ConstantCoefficients and Convolution Method

Adem Kilicman


Department of MathematicsUniversity Putra Malaysia

43400 UPM, SerdangSelangor - Malaysia

(Joint work with: Hassan Eltayeb)

Abstract: The purpose of this study is to compute solutions of some explicit initial-boundary value problems for the one-dimensional wave equation with non constant co-efficients by means of the Laplace transform which in general has no solution.


21

Step size strategies on the numerical integration of thesystems of differential equations

Gulnur Celik Kizilkan


Selcuk University, Science Faculty, Math Department, Kampus/Konya - TURKEY

(Joint work with: K. Aydin)

Abstract:In this study, the step size strategies have been obtained such that the localerror is smaller than desired error level in the numerical integration of

X′(t) = AX(t)

andX′(t) = AX(t) + ϕ(t, X)

equation systems in interval [t0, T ]. The algorithms have been given that calculate stepsizes and numerical solutions according to these strategies and numerical solutions. Thealgorithms have been supported by the numerical examples.


22

Session 1.4: Mathematical Programming I

Chair: M Fernanda P. CostaPlace: Hall 4


23

Modeling Facility Location and Supplier Selection withSuppliers Product Quality and Contract Fee for Strategic

Supply Chain Design

Eren Ozceylan


Selcuk University, Industrial Engineering Department, Campus 42100, KonyaTurkey

(Joint work with: T. Paksoy)

Abstract: This paper proposes a novel mixed integer linear programming model forsolving supply chain network design problems including deterministic parameters, choiceof multi-quality products of suppliers, supplier engagement contracts, and single-periodcontexts with total profit maximizing. The strategic level of supply chain planning andtactical level planning of supply chain are aggregated to propose an integrated model.The model integrates location and capacity choices for suppliers, plants, distributioncenters and retailers selection, product range assignment and production flows accordingto suppliers product quality choices. There is a trade-off between product quality whichis transported from suppliers and its production costs in manufacturers. There are threequality levels for a product according to its procurement: First Quality, Second Qualityand Third Quality. Decision maker has to choose the supplier which he/she will work withevaluating its engagement fee and its quality. Engagement decisions whether will be ornot, for the suppliers are binary decision variables and the production and transportationflow decisions have continuous decision variables. An integrated supply chain networksystem consists of multiple suppliers, manufacturers, distribution centers, retailers areconsidered. Finally, the proposed model is discussed with a numerical example.


24

On Numerical Optimization Methods for Infinite KernelLearning

Sureyya Ozogur Akyuz


Faculty of Engineering and Natural Sciences, Vision and Pattern Recognition Lab.Sabanci University, Orhanli Tuzla, 34956, Istanbul - Turkey

(Joint work with: G. Ustunkar, G. W. Weber)

Abstract: A subfield of artificial intelligence, machine learning (ML), is concerned withthe development of algorithms that allow computers to “learn”. ML is the process oftraining a system with large number of examples, extracting rules and finding patternsin order to make predictions on new data points (examples). The most common ma-chine learning schemes are supervised, semi-supervised, unsupervised and reinforcementlearning. These schemes apply to natural language processing, search engines, medicaldiagnosis, bioinformatics, detecting credit fraud, stock market analysis, classification ofDNA sequences, speech and hand writing recognition in computer vision, to encounterjust a few. In this study, we focus on optimization methods for developing Support VectorMachines (SVMs) which is one of the most powerful methods currently in machine learn-ing. In ML algorithms, one of the crucial issues is the representation of the data. Discretegeometric structures and, especially, linear separability of the data play an important rolein ML. If the data is not linearly separable, a kernel function transforms the nonlineardata into a higher-dimensional space in which the nonlinear data are linearly separa-ble. As the data become heterogeneous and large-scale, single kernel methods becomeinsufficient to classify nonlinear data. Convex combinations of kernels were developed toclassify this kind of data in Bach et. al. 2004. Nevertheless, selection of the finite combi-nations of kernels is limited up to a finite choice. In order to overcome this discrepancy,a novel method of “infinite” kernel combinations for learning problems which is namedby Infinite Kernel Learning (IKL) has recently been proposed by Ozogur-Akyuz et.al.2008, with the help of infinite and semi-infinite programming regarding all elements inkernel space. This will provide to study variations of combinations of kernels when con-sidering heterogeneous data in real-world applications. Looking at all infinitesimally fineconvex combinations of the kernels from the infinite kernel set, the margin is maximizedsubject to an infinite number of constraints with a compact index set and an additional(Riemann-Stieltjes) integral constraint due to the combinations. After a parametrizationin the space of probability measures, it becomes semi-infinite. In this study, we built IKLmodel with well known numerical methods of semi-infinite programming and comparedthe numerical results. We improved the discretization method for our specific model andproposed two new algorithms. The simulation of the IKL is performed on different datasets from UCI machine learning repository. Finally, we proved the convergence of the nu-merical methods and we analyzed the conditions and assumptions of these convergencetheorems such as optimality and convergence.


25

A DEA based approach for solving the multiple objectiveshortest path problem

Alireza Davoodi


Department of Mathematics, Islamic Azad University, Neyshabur Branch, Neyshabur, Iran

Abstract: Finding the shortest (least costly) path in a network is one of the importantand interesting subjects in network flow problems. When each arc has just one type ofcost, there exist some simple methods to find the shortest path. But if there are more thanone type of cost (vector of cost), the non-dominated path plays the role of the best path.In this case a Multiple Objective problem is created to find the non-dominated path.In this paper a DEA based approach is introduced to find the non-dominated path(s)in a multiple cost network. This method can determine all non-dominated paths andthe best one. Finally, when the priority and importance of these costs are different fromeach other, a modified model is introduced to solve them which is capable of identifyingnon-dominated paths based on the incorporating of Weight Restrictions in DEA models.


26

Robustification of CMARS

Fatma Yerlikaya Ozkurt


Middle East Technical University Department of Mathematics and Institute of AppliedMathematics Inonu Bulvari 06531 Ankara - Turkey

(Joint work with: G.W. Weber, A. Ozmen)

Abstract: CMARS developed at IAM, METU, as an alternative approach to a well-known regression tool MARS from data mining and estimation theory, is based on apenalized residual sum of squares (PRSS) for MARS as a Tikhonov regularization (T.R.)problem. CMARS treated this problem by a continuous optimization technique calledConic Quadratic Programming (CQP) which is permitting to use interior point meth-ods. CMARS is particularly powerful in handling complex and heterogeneous data. Inthis presentation, we include the existence of uncertainty in the future scenarios intoCMARS. In fact, generally, those data include noise in both input and output variable:the data of the regression problem is not exactly known or cannot be exactly measured,or the exact solution of the problem cannot be implemented due to inherent inaccuracyof the devices. Furthermore, the data can undergo small changes by variations in theoptimal experimental design. This altogether leads to uncertainty in constraints and ob-jective function. To overcome this difficulty, we refine to use our CMARS algorithm byimportant robust optimization which purposes to find an optimal or near optimal solu-tion that is feasible for every possible realization of the uncertain scenario. We analyzehow uncertainty enters the CMARS model, firstly, with complexity terms in the form ofintegrals of squared first and second order derivatives of the model functions and, then,the discretized TR and, finally, the CQP form of the problem. Then, we employ robustoptimization as developed by Aharon Ben-Tal, Laurent El Ghaoui et al.. In this study,we present the new Robust CMARS (RCMARS) in theory, method and applied to reallife problems, we discuss structural frontiers and give and outlook to future research.


27

Session 1.5: Numerical Analysis and Software I

Chair: Kuniyoshi AbePlace: Hall 5


28

A high accurate difference-analytical method for solvingLaplace’s equation on polygons with nonanalytic boundary

conditions

Suzan Cival Buranay


Department of Mathematics, Eastern Mediterranean UniversityGazimagusa, Cyprus, Mersin 10

Turkey

(Joint work with: A. Dosiyev)

Abstract: In most of existing high accurate methods (see [1], [2]) for solving Laplace’sboundary value problems with singularities, boundary functions on the sides that causethe singularity are given as analytic functions of the arclength measured along the bound-ary of the polygon. The boundary functions being nonanalytic on the mentioned sidesarise difficulties on the methods based on series expansion of the exact solution aroundthe singular points. In this presentation, we develop the high accurate Block Grid Method[2] for the solution of the Dirichlet problem on polygons by combining finite differenceapproximation of Laplace’s equation with the approximation of the special integral rep-resentation of the exact solution for nonanalytic boundary functions around the singularpoints.

References

[1] Z.C. Li, Combined Methods for Elliptic Problems with Singularities, Interfaces andInfinities. Kluwer Academic Publishers, Dordrech, Boston and London, 1998.[2] A.A. Dosiyev, The high accurate block-grid method for solving Laplace’s boundaryvalue problem with singularities, SIAM J. Numer. Anal.,42,1, 153-178, 2004.


29

An Application of a New Fuzzy Robust RegressionAlgorithm to Actuarial Science

Kamile Sanli Kula


Ahi Evran UniversityFaculty of Arts and SciencesDepartment of Mathematics

40200 Kirsehir - Turkey

(Joint work with: Fatih Tank, Turkan Erbay Dalkilic)

Abstract: In this study, a fuzzy robust regression method is proposed to constructa model that describes the relation between dependent and independent variables ininsurance. Our approach is an alternative to ordinary least squares and classical robustregression methods in insurance. Furthermore, a new model which contains data onmonth of and number of payments, is proposed. This new approach allows to determinetotal claim amounts in the related month as an alternative to the model suggested byRousseeuw et. al.


30

Comparison of Exponentially fitted Explicit Runge-Kuttamethods for Solving ODEs

Fudziah Ismail

email: fudziah [email protected]

Department of Mathematics, Universiti Putra Malaysia43400, Serdang, Selangor

Malaysia

(Joint work with: A. Karimi, N. Md Ariffin, M. Abu Hassan)

Abstract: Based on the near-optimal RK44M method derived by Dormand (1996) weconstructed the exponentially fitted Runge-Kutta method using the technique introducedby Simos (1998) and also the technique suggested by Berghe et. al (1999) resulting intwo types of exponentially fitted Runge-Kutta methods. Numerical experiments basedon the two techniques as well as the original RK44M are tabulated and compared interms of accuracy, which clearly shown the advantage of the technique used by Berghe.


31

Numerical Integration of a Fuzzy Riemann Double Integral

Fereidoon Khadem

email: khadem [email protected]

Department of Mathematics, Zanjan BranchIslamic Azad University

Zanjan - Iran

(Joint work with: M.A. Fariborzi Araghi)

Abstract: In this paper, the double fuzzy Riemann integrals and their numerical in-tegration are proposed. At first, we introduce a double fuzzy Riemann integral whoseintegrand is a fuzzy-valued function and limits of integration are crisp real numbers. Forthis purpose, we prove a theorem to show the a-level set of the double fuzzy integralwhich is a closed interval where end points are double crisp Riemann integrals.In thiscase, we apply the double Simpson’s rule in order to approximate these double integrals.Also we present an algorithm to approximate the value of the membership function of thedouble fuzzy integral in a given point like r in 0-level. Finally, two numerical examplesare solved to illustrate the efficiency of the proposed method.


32


PARALLEL SESSIONS 2

30 September 2009, 13:30-15:45



35

Session 2.1: Approximation and Interpolation I

Chair: Gulen B. TuncaPlace: Hall 1


36

Statistical Convergence for Set-Valued Functions

Halil Gezer


Department of Mathematics, Eastern Mediterranean University,Gazimagosa, Cyprus, Mersin 10, Turkey

(Joint work with: H. Aktuglu)

Abstract: In this paper we consider statistical convergence for set-valued functions. Wealso prove a Korovkin Type Approximation Theorem for set valued functions in the senseof statistical convergence.


37

Hermite-Birkhoff interpolation problems on the roots of theunity

Elias Berriochoa


Universidad de Vigo, Facultad de Ciencias Campus as Lagoas s/n 32004 Ourense, Spain

(Joint work with: A. Cachafeiro)

Abstract: We consider a general Hermite-Birkhoff interpolation problem on the n-rootsof the unity, {z1, · · · , zn}, that is, given p nonnegative different integers ν1, · · · , , νp andp n-dimensional vectors (u1,ν1 · · ·un,ν1 ) · · · (u1,νp · · ·un,νp ), the problem is to find apolynomial p(z) of lower degree satisfying the conditions:

p(j)(zi) = ui,νj for i = 1, · · · , n j = ν1, · · · , νp.

An important topic in the Hermite-Birkhoff problem is the existence and uniqueness ofthe solution. If in the previous problem we say that it uses p derivatives ν1, · · · , νp, inour contribution we deal with ν1 = 0 and we study:

(1) Existence and uniqueness for the problem with 2 derivatives.

(2) Existence and uniqueness for the problem with 3 derivatives.

(3) We give an algorithm to decide when the problem with p derivatives has unique solution.

Taking into account the previous results we obtain analogous Hermite-Birkhoff inter-polation problems for four privileged nodal systems on the bounded interval. Finallywe present algorithms to obtain explicit solutions of the Hermite-Birkhoff interpolationproblems with a low cost on the unit circle as well as on the bounded interval, (see [1]).

References

1. E. Berriochoa, A. Cachafeiro, Algorithms for solving Hermite Interpolation problemsusing the Fast Fourier Transform, J. Comput. Appl. Math. accepted.

2. I.J. Schoenberg, On Hermite-Birkhoff interpolation, J. Math. Anal. Appl. 16 (1966),538-543.


38

Weak and strong convergence theorems for a finite family ofI−asymptotically nonexpansive mapping

Liping Yang


University of Minho, Department of Mathematics for Sciencie and Technology - Portugal

(Joint work with: X. Xie)

Abstract: The purpose in this paper first introduce the class of I−asymptotically nonex-pansive nonself-maps. Then, an iteration scheme for approximating common fixed pointsof a finite family of Ii−asymptotically nonexpansive nonself-mappings belonging to thisclass (when such common fixed points exist) is constructed,and strong and weak con-vergence theorems are proved. Our theorems improve and generalize important relatedresults of the previously known results in this area.


39

q-Statistical Convergence

Serife Bekar



(Joint work with: H. Aktuglu)

Abstract: In the present work we introduced a q-analogue of the Cesaro Matrix of orderone and we define a new type of convergence, called q-Statistical convergence.


40

Comparison of Exponentially fitted Explicit Runge-Kuttamethods for Solving ODEs

Fudziah Ismail

email: fudziah [email protected]

Department of Mathematics, Universiti Putra Malaysia43400, Serdang, Selangor

Malaysia

(Joint work with: A. Karimi, N. Md Ariffin, M. Abu Hassan)

Abstract: Based on the near-optimal RK44M method derived by Dormand (1996) weconstructed the exponentially fitted Runge-Kutta method using the technique introducedby Simos (1998) and also the technique suggested by Berghe et. al (1999) resulting intwo types of exponentially fitted Runge-Kutta methods. Numerical experiments basedon the two techniques as well as the original RK44M are tabulated and compared interms of accuracy, which clearly shown the advantage of the technique used by Berghe.


41

A novel 2D finite-volume method for advection problemswith embedded moving-boundaries

Yunus Hassen


CWI & Fac. Aeros. Eng, TU DelftMAS2: Modeling, Simulation & Analysis (CWI) Science Park 123

1098 XG AmsterdamNetherlands

(Joint work with: Barry Koren)

Abstract: In this work, we present an accurate method, using a novel immersed-boundary approach, for solving advection problems numerically. As is standard in theimmersed-boundary methods, moving bodies are embedded in a fixed, two-dimensional,Cartesian grid. We employ the method of lines — a higher-order cell-averaged fixed-grid finite-volume method for the spatial discretization and the explicit Euler’s schemefor the time integration. The essence of the present method is that specific fluxes inthe vicinity of a moving body are computed in such a way that they accurately andmonotonously accommodate the boundary conditions valid on the moving body. Theimmersed-boundary method, in general, is a method in which boundary conditions areindirectly incorporated into the governing equations. It is very suitable for simulatingflows around flexible, moving and/or complex bodies (see4 for a comprehensive review).Basically, the bodies of interest are just embedded in non-deforming Cartesian grids thatdo not conform to the shape of the body. The governing equations are modified to includethe effect of the embedded bodies (EBs). Doing so, mesh (re)generation difficulties asso-ciated with body-fitted grids are obviated; and, the underlying regular fixed grid allowsto use a simple data structure as well as simpler numerical schemes over a majority ofthe domain. Here, considering we have a solid-body immersed inside a fluid domain, weobtain the discrete EBs associated with individual control volumes, at any given time.The body is immersed into the fixed, Cartesian, finite-volume grid and the points of in-tersections of the boundaries of the immersed body with the walls of each computationalcell are detected. Then, these discrete EBs are accurately aligned with the grid linesand the fluxes that are affected by the EBs are especially modified. As a result, thesefixed-grid fluxes (indirectly) incorporate the embedded-boundary conditions associatedwith the respective moving EBs (see1 for details). To suppress wiggles, tailor-made lim-iters are introduced for the special fluxes. Over the majority of the domain, where wedo not have influence of EBs, we use standard methods, i.e. van Leer’s κ-scheme3 andKoren’s κ= 1

3-limiter,2 on the underlying regular fixed-grid. Moreover, for the temporal

discretization, we employ a special technique — the time integration is locally adaptive.Depending on the crossing of finite-volume walls by an EB, time steps are split in thevicinity of each EB, to avoid an abrupt flux-reversal. As a result, we achieve a gradualtransition of the fluxes, in time, at those walls. To validate our method, we consider aunit hypothetical ‘cylinder’ of arbitrary radius, as an initial solution for the quantity tobe advected. The sharp discontinuities of the initial solution are assumed to be infinitely


42

thin EBs (‘wall of the cylinder’) going with the flow. The ‘cylinder’ is then placed atan arbitrary initial location and advected with the Molenkamp velocity field.5 An exactsolution for this problem is computed with the method of characteristics. The numeri-cal results obtained for linear scalar advection problems are remarkably very accurate,without requiring much computational overhead. They show a significant improvementin resolution over those computed using the standard methods. It is anticipated that themethod can be easily extended to real fluid-flow equations.

References

1. Y. Hassen & B. Koren: Finite-volume discretizations and immersed boundaries, in:B. Koren, C. Vuik (Eds.), Lect. Notes Comput. Sci. Eng. 71 (2009), Springer-Verlag,Berlin (in press).

2. B. Koren: A robust upwind finite-volume method for advection, diffusion and sourceterms, in: C.B. Vreugdenhil, B. Koren (Eds.), Notes Numer. Fluid Mech. 45 (1993),Vieweg, Braunschweig, pp.117–138.

3. B. van Leer: Upwind-difference methods for aerodynamic problems governed by theEuler equations, in: B.E. Engquist, S. Osher, R.C.J. Somerville (Eds.), Lect. Appl.Math. 22(2) (1985), Amer. Math. Soc., Providence, RI, pp.327-336.

4. R. Mittal & G. Iaccarino: Immersed boundary methods, Annu. Rev. Fluid Mech. 37(2005), 239–261.

5. C.R. Molenkamp: Accuracy of finite-difference methods applied to the advection equa-tion, J. Appl. Meteor. 7 (1968), 160–167.


43

Session 2.2: Numerical Linear Algebra I

Chair: Marc GoovaertsPlace: Hall 2


44

Explicit Representation of Hessenbergians: Application toGeneral Orthogonal Polynomials

Venancio Tomeo


University Complutense of Madrid, Statistic SchoolAvda Puerta de Hierro s/n. 28040 - Madrid

Spain

(Joint work with: Jesus Abderraman)

Abstract: An explicit representation for the determinant of any upper Hessenbergmatrix in Cn×n, with non nulls subdiagonal terms, is achieved by means of a quasi-triangular matrix with the same determinant value. It gives rise to a representationwith nested functions on matrix elements hi,j from the original Hessenberg matrix. Likean interesting application, this representation is introduced on polynomials belongingto general orthogonal sequences on the complex plane {Pn(z)}∞n=0, whose terms are

Pn(z) = |Inz − Dn|, with Dn a upper Hessenberg matrix. Here the polynomials aremonic without loss of generality. The compact representation is valid for any known, orunknown, class of general orthogonal polynomials. Comparison with recognized repre-sentations of some orthogonal polynomials illustrates its generality.


45

The Powers of Anti(2k+1)-Diagonal Matrices and FibonacciNumbers

Fatih Yilmaz


Selcuk University, Faculty of ScienceDepartment of Mathematics

42003 Selcuklu, Konya

(Joint work with: Humeyra Kiyak, Irem Gurses, Mehmet Akbulak, Durmus Bozkurt)

Abstract: At this study, we consider arbitrary integer powers of anti(2k+1)diagonaln-square matrices (n=4k, k=1,2,...). We compute integer powers of this matrix and givea formula with Fibonacci numbers and also investigate some properties of the matrix.References[1] A. P. Stakhov, Fibonacci matrices, a generalization of the Cassini Formula, and anew coding theory, Chaos, Solitons and Fractals, 30 (2006) 56-66.[2] M. Basu, B. Prasad, The generalized relations among the code elements for Fibonaccicoding theory, Chaos, Solitons and Fractals, 10.1016/j.chaos.2008.09.030.[3] T. Koshy, Fibonacci and Lucas Numbers with Applications, Wiley-Interscience Pub-lication, 2001.


46

On computing powers for one type of matrice by Pell andJacobsthal Numbers

Fatih Yilmaz


Selcuk University, Faculty of ScienceDepartment of Mathematics

42003 Selcuklu, Konya

(Joint work with: Humeyra Kiyak, Irem Gurses, Mehmet Akbulak, Durmus Bozkurt)

Abstract: We compute arbitrary positive integer powers of the following matricesA=pentadiag(-1,0,1,0,-1) related with Pell and Jacobsthal numbers. Also we investigatesome properties of this matrices.


47

On the properties of generalized Fibonacci and Lucasnumbers with binomial coefficients

Hasan Huseyin Gulec


Selcuk University, Science Faculty, Department of MathematicsKonya - Turkey

(Joint work with: N. Taskara, K. Uslu)

Abstract:In this study, new properties of generalized Fibonacci and Lucas sequencesG(n), n=1,2,... with binomial coefficients have been obtained by using properties ofFibonacci F(n) and Lucas L(n) numbers with binomial coefficients.


48

IDR-based relaxation methods for solving linear systems

Seiji Fujino


Kyushu University6-10-1 Hakozaki Higashi-ku, Fukuoka 812-8581

Japan

(Joint work with: Y. Kusakabe, M. Harumatsu)

Abstract:The classical Jacobi, GS(Gauss-Seidel) and SOR (Successive Over-Relaxation) methods are well known. Moreover the GS and SOR methods have beenused for solution of problems which stem from a variety of applications. The GS andSOR methods, however, have some issues in reality. Because the GS and SOR methodsgreatly depend on spectrum of iteration matrix. In my talk, we extend IDR (InducedDimension Reduction) Theorem proposed by Sonneveld and van Gijzen in 2008 to theresidual of the conventional iterative methods, and accelerate its convergence and stabil-ity of the conventional methods. Through numerical experiments, we reveal significanteffect of accelerated residual of the Sonneveld typed Jacobi, GS and SOR methods.


49

A Shift Strategy for Superquadratic Convergence in the dqdsAlgorithm for Singular Values

Kensuke Aishima

email: Kensuke [email protected]

University of Tokyo, 7-3-1, Hongo, Bunkyoku, Tokyo- Japan

(Joint work with: T. Matsuo, K. Murota, M. Sugihara)

Abstract: In 1994, the dqds algorithm was proposed by Fernando–Parlett [2] to computethe singular values of bidiagonal matrices to high relative accuracy. The dqds algorithmis currently implemented in LAPACK as DLASQ routine which has a complicated shiftstrategy evolved in order to achieve high efficiency. In ICCAM2008, we proved thatDLASQ enjoys a superquadratic convergence, based on a convergence theory of thedqds algorithm established in [1]. In this talk, we will present a simple and novel shiftstrategy for the superquadratic convergence in the dqds algorithm. We will also presenta numerical example to illustrate the superquadratic convergence.

References

1. K. Aishima, T. Matsuo, K. Murota and M. Sugihara: On Convergence of the dqdsAlgorithm for Singular Value Computation, SIAM J. Matrix Anal. Appl., Vol. 30(2008), pp. 522–537.

2. K. V. Fernando and B. N. Parlett: Accurate singular values and differential qd algo-rithms, Numer. Math., Vol. 67 (1994), pp. 191–230.


50

Session 2.3: Optimization I

Chair: Ana Maria A.C.RochaPlace: Hall 3


51

A Hybrid Genetic Pattern Search Augmented LagrangianMethod for Constrained Global Optimization

Lino Costa


Production and Systems DepartmentCampus de Gualtar, Braga

Portugal

(Joint work with: Isabel Espirito Santo, Edite M.G.P. Fernandes )

Abstract: Hybridization of genetic algorithms with local search approaches can enhancetheir performance in global optimization. Genetic algorithms, as most population basedalgorithms, require a considerable number of function evaluations. This may be an impor-tant drawback when the functions involved in the problem are computationally expensiveas it occurs in most real world problems. Thus, in order to reduce the total number offunction evaluations, local and global techniques may be combined. Moreover, the hy-bridization may provide a more effective tradeoff between exploitation and explorationof the search space. In this study, we propose a new hybrid genetic algorithm based ona local pattern search that relies on an augmented Lagrangian function for constraint-handling. The local search strategy is applied to a subset (the elite) of the population.Numerical results with a set of benchmark constrained problems are provided.


52

Production Planning under Stochastic Demand for FishProcessed Product at North Sumatera Province, Indonesia

Herman Mawengkang


Department of Mathematics, The University of Sumatera UtaraFMIPA USU, Medan

Indonesia

Abstract: Marine fisheries plays an important role in the economic development of In-donesia. Besides being the most affordable source of animal protein in the diet of mostpeople in the country, this industrial sector could provide employment to thousands wholives at coastal area. In this paper we consider the management of small scale tradi-tional business at North Sumatera Province which performs processing fish into severallocal seafood products. The inherent uncertainty of data (e.g. demand, fish availability),together with the sequential evolution of data over time leads the production planningproblem to a nonlinear mixed-integer stochastic programming model. We use scenariogeneration based approach for solving the model.


53

Centralized Resource Allocation with Stochastic Data

Mahnaz Mirbolouki


Department of MathematicsScience and Research Branch

Islamic Azad UniversityTehran, Iran

(Joint work with: F. Hosseinzadeh Lotfia, N.Nematollahi, M.H. Behzadi, M.R. Mozaffari)

Abstract:Data Envelopment Analysis (DEA) is a technique based on mathematical pro-gramming for evaluating the efficiency of homogeneous Decision Making Units (DMUs).In this technique inefficient DMUs are projected on to the frontier which constructedby the best performers. Centralize Resource Allocation (CRA) is a method in which allDMUs are projected on to the efficient frontier through solving just are DEA model. Theindent of this paper is to present the Stochastic Centralized Resource Allocation (SCRA)in order to allocate centralized resource where inputs and outputs are stochastic. Theconcept discussed throughout this paper is illustrated using aforementioned example.

keywords: Data envelopment analysis, Normal distribution, Quadratic program-ming, Resource allocation.


54

Special functions, non-linearity and algebraic and differentialproperties: Computational aspects

Ana Maria A. C. Rocha


University of Minho, Dept. Production and SystemsCampus de Gualtar 4710-057 Braga- Portugal

(Joint work with: Tiago F. M. C. Martins, Edite M. G. P. Fernandes)

Abstract: This paper implements the augmented Lagrangian methodology in a stochas-tic population based algorithm for solving nonlinear constrained global optimizationproblems. This class of global optimization problems is very important and frequentlyencountered in engineering applications. The method approximately solves a sequence ofsimple bound global optimization subproblems using a swarm intelligent algorithm. Thisis a stochastic population based algorithm that simulates fish swarm behaviors insidewater. Fish in the swarm attempts to swarm, chase or search, in order to avoid dangerand look for food. The best fish in the swarm corresponds to the best solution found.Based on this solution, the Lagrange multipliers as well as the penalty parameter areupdated in the outer iterations of the algorithm. Several widely used benchmark prob-lems are solved in a performance evaluation of the new algorithm when compared withother techniques.


55

A Regularized Modified Lagrangian Method for NonlinearlyConstrained Monotone Variational Inequalities

Eman Hamad Al-Shemas

email: e al [email protected]

PAAET,College of basic Education, Mathematics DepartmentMain Capus - Shamiya

Kuwait

(Joint work with: A. Hamdi)

Abstract: In this paper, we propose a new method for solving structured variationalinequality problems. The proposed scheme combines the recent decomposition algorithmintroduced by Deren Han [math. comp. modelling 37 (2003) 405-418] with the proximal -like techniques. under mild appropriate assumptions, we show that the method generatesconvergent sequences.


56

A new multiobjective differential evolution strategy forscattering uniformly the Pareto solution set for designing

mechatronic systems

Miguel Gabriel Villarreal-Cervantes


Av. Instituto Politecnico Nacional2508 Col. San Pedro Zacatenco, C.P. 07360 Mexico, D.F.

Mexico

(Joint work with: Carlos Alberto Cruz-Villar, Jaime Alvarez-Gallegos)

Abstract: Many processes and products in the area of mechanical and electrical engi-neering are showing an increasing integration of mechanical system with its embeddedcontrol system. This integration results in integrated systems called mechatronic sys-tems. The design of mechatronic system involves the finding an optimal balance betweenthe performance of the basic mechanical structure and the performance of the over-all control system, and this synergy results in innovative solutions which have a betterglobal performance. So, during the design phase of a mechatronic system, changes in themechanical structure and the controller must be evaluated simultaneously. Nevertheless,the design in complex mechatronic systems is not an easy task. Design problems withmultiple performance criteria require to formulate them as Pareto-based multi-objectiveoptimization problems where the best compromise should be found by evaluating severalincommensurable and often conflicting objectives. Multi-objective strategies based ondifferential evolution has been applied for solving multi-objective optimization problemssince they can solve nonlinear, non-differentiable and discontinuous problems. Never-theless, when the problem is dynamic as in the case of designing mechatronic systems,those strategies difficultly find a good Pareto front and they lack of a mechanism fordistributing the solutions along the Pareto front. The dynamic problem has the maincharacteristics of having performance indexes and constraints varying on time. In ad-dition, differential equations describing the dynamic behavior of the system must beincluded into the optimization problem. Hence, in this paper a new multi-objective evo-lutionary algorithm based on differential evolution for solving constrained multi-objectivedynamic optimization problems is presented. The proposed approach adopts a secondarypopulation in order to retain the non-dominated solutions found during the evolution-ary process. The non-dominated solutions are found using the constrained dominationprinciple. In addition, a self adaptive grid is considered for the secondary populationto hold and distribute the found non-dominated solutions. In order to avoid overflowof the self adaptive grid, each element of the grid has a previous maximum number ofnon-dominated solutions (Pareto solutions) and the excess of these solutions are removedbased on the crowding distance. The selection of the three individuals of the populationfor the mutation process of the differential evolution algorithm is changed to spread theexploration of non-dominated solutions in the elements of the self adaptive grid. Themodification of the selection scheme consists on randomly generate the three individ-


57

uals from the element of the self adaptive grid of the secondary population instead ofthe entire parent population. This selection scheme has the main advantage that onlynon-dominated solutions in the element of the grid can be considered for the mutationprocess, such that, the non-dominated solutions of one element of the grid can not bemutated with the non-dominated solutions of others elements of the grid. The main con-tribution of this work is to present a new algorithm that spreads the search explorationfor solving constrained multi-objective dynamic optimization problems. In addition, amechatronic design approach is formulated as a nonlinear multi-objective dynamic op-timization problem. The mechatronic design problem is used to validate the proposedalgorithm. The results are compared with respect to another multi-objective evolution-ary algorithm based on differential evolution and with respect to the approach that isrepresentative of the state of the art in the area: the NSGA-II.


58

Session 2.4: Special Functions

Chair: Patricia J.Y.WongPlace: Hall 4


59

On Koornwinder classical orthogonal polynomials

Lidia Fernandez


Dpto. Matematica Aplicada. Universidad de Granada,Campus Universitario de Cartuja. E-18071. Granada

Spain

(Joint work with: T.E. Perez, M.A. Pinar)

Abstract: In 1975, Tom Koornwinder studied examples of two variables analogues of theJacobi polynomials in two variables. Those orthogonal polynomials are eigenfunctionsof two commuting and algebraically independent partial differential operators. Some ofthese examples are well-known classical polynomials, such as orthogonal polynomials onthe unit ball, on the simplex or the tensor product of Jacobi polynomials in one variable.The definition of classical orthogonal polynomials considered in this work, provides adifferent perspective on the subject. We analyze in detail the Koornwinder polynomialsnot considered classical by other authors. We pay special attention to differential andstructural properties that they satisfy.References1. Fernndez, L., Prez, T. E., Piar, M. A., Classical orthogonal polynomials in two vari-ables: a matrix approach, Numer. Algorithms 39 no. 1 3 (2005) 131142.2. Koornwinder, T., Two variable analogues of the classical orthogonal polynomials, The-ory and application of special functions, Proceedings of Advanced Seminar, Mathemat-ics Research Center, University Wisconsin, Madison, WI, 1975, Publ. No. 35, AcademicPress, New York, 1975, 435495.3. Krall, H. L., Sheffer, I. M., Orthogonal polynomials in two variables, Ann. Mat. PuraAppl. Serie 4 76 (1967) 325376.


60

A note on a family of two variable polynomials

Rabia Aktas


Ankara UniversityFaculty of Science, Department of Mathematics

06100 Tandogan-AnkaraTurkey

(Joint work with: A.Altin and F. Tasdelen Yesildal)

Abstract: The main object of this paper is to construct a two-variable analogue of jacobipolynomials and give some properties of these polynomials. We show that these polyno-mials are orthogonal, then we obtain various differential formulas for these polynomials.Furthermore, we give some integral representations for these polynomials.


61

Some generalizations of multiple Hermite polynomials viaRodrigues formula

Cem Kaanoglu


Cyprus International University, Haspolat, North CyprusTurkey

(Joint work with: Mehmet Ali Ozarslan)

Abstract: The object of this paper is to develope some properties of multiple Hermitepolynomials.1 For this, we consider a family of polynomials which defined by a Rodriguesformula and in particular case the polynomials include the multiple Hermite polynomi-als.1 The explicit forms, certain operational formulas involving these polynomials andlinear generating function is obtained.1

References

1. D. W. Lee, Properties of multiple Hermite and multiple Laguerre polynomials by thegenerating function, Integral Transforms and Special Functions, Vol.18, No.12, Decem-ber 2007, 855-869.


62

Extension of Gamma, Beta and Hypergeometric Functions

Emine Ozergin



(Joint work with: M.A. Ozarslan, A. Altin)

Abstract: The main object of this paper is to present generalizations of gamma, betaand hypergeometric functions. Some recurrence relations, transformation formulas, op-eration formulas and integral representations are obtained for these new generalizations.Furthermore Tricomi type expansions are obtained for the generalized incomplete gammafunction which was introduced by Chaudhry and Zubair.1

References

1. M. A. Chaudhry and S. M. Zubair, Generalized incomplete gamma functions withapplications, Journal of Computational and Applied Mathematics 55 (1994) 99-124.


63

Application of Pade approximation of differential transformmethod to the solution of prey and predator problem

Onur Karaoglu


Selcuk UniversityDepartment of Mathematics, Faculty of Science

Campus, 42003, KonyaTURKEY

(Joint work with: Ayse Betul Koc, Haldun Alpaslan Peker, Yildiray Keskin, Yucel Cenesiz, Galip

Oturanc, Sema Servi)

Abstract: Mathematical model of the prey and predator problem is governed by systemof nonlinear Volterra differential equations. In this study, solutions under the changingconditions of the problem are considered by Pade approximation of the differential trans-form method (DTM). Generally, Pade approximation provides a high accuracy of con-vergence to true solution on truncated series solutions. Some examples are presented toshow alteration of the prey and predator rates in a population with respect to changingtime.


64

Jensen divergence based on Fisher’s information

Yoji Otani


Departamento de Matematica Aplicada Facultad de Ciencias Avenida de Fuentenueva, S/N18071 - Granada - SPAIN

(Joint work with: A. Zarzo, J.S. Dehesa)

Abstract: During the last years the Jensen-Shannon divergence between two or morearbitrary probability densities has been used in numerous mathematical and physicalcontexts. This relative information measure, in contrast to the Kullback-Leibler entropyor relative Shannon entropy, presents three important characteristics: symmetry underexchange of the involved densities, applicability to more than two densities, and finitenesseven in the case that the involved densities have non-common zeros. In this paper weintroduce a Jensen divergence based on the Fisher information. The Fisher information,in contrast to the Shannon entropy, is an information measure with a local character,providing a measure of the gradient and oscillatory content of the density. The newJensen-Fisher divergence enjoys the same properties as the Jensen-Shannon divergence;namely, non-negativity, additivity when applied to an arbitrary number of probabilitydensities, symmetry under exchange of these densities, vanishing if and only if all thedensities are equal, and definiteness when these densities present non-common zeros.Moreover,the Jensen-Fisher divergence can be expressed in terms of the relative Fisherinformation as the Jensen-Shannon divergence does in terms of the Kullback-Leiblerentropy. It is remarkable that the last property is only shared by these two divergences,in contrast with the recently introduced Jensen-Renyi and Jensen-Tsallis divergences.Here we present the theoretical grounds of the Jensen-Fisher divergence. We apply it toseveral families of probability densities (including the Rakhmanov densities associated tothe classical families of orthogonal polynomials). Finally, a comparison with the Jensen-Shannon divergence and the relative Fisher information is performed.


65

Session 2.5: Statistics and Data Analysis I

Chair: Ismihan BayramogluPlace: Hall 5


66

Weibull-Negative Binomial Distribution

Mustafa Cagatay Korkmaz


Artvin-Coruh University Science and Arts Faculty, Department of Statistics, Artvin - Turkey

(Joint work with: Coskun Kus, Asir Genc)

Abstract: Some probability distributions have been proposed to fit real life data withdecreasing failure rates. In this article, a three-parameter distribution with decreasingfailure rate is introduced by mixing Weibull and negative-binomial distributions. Variousproperties of the introduced distribution are discussed. An EM algorithm is used todetermine the maximum likelihood estimates when one parameter is given or known.Illustrative examples based on real data are also given.


67

Comparison of a New Robust Test and Non-parametricKruskal-Wallis Test in One-way Analysis Of Variance Model

Yeliz Mert Kantar


Anadolu University, Science FacultyDepartment of Statistics, Eskisehir

Turkey

(Joint work with: Birdal Senoglu, Omer L. Gebizlioglu)

Abstract: Observations in many real life situations do not often follow a normal distri-bution. Moreover, outliers may exist in observed data. In these situations, normal theorytests based on least squares (LS) estimators have a low power and are not robust againstplausible deviations from the assumed distribution. Therefore, we resort to nonparamet-ric test procedures to analyze the non-normal data. In the context of one-way analysisof variance, the well-known nonparametric Kruskal-Wallis test based on ranks is used tocompare the three or more groups of observations. In this paper, we compare the powerand the robustness properties of the Kruskal-Wallis test with a new test, namely thetest developed by enolu and Tiku (2004) when the distribution of error terms are typeII censored generalized logistic. It is shown that the test is more powerful and robustin general. An application on a real data set is presented by using the test based onmodified maximum likelihood (MML) estimators.


68

General Linear Model (GLM) Approach to RepeatedMeasurements Data Involving Univariate Analysis of

Variance (ANOVA) and Multivariate Analysis of Variance(MANOVA) Techniques

Neslihan Iyit


Selcuk University, Faculty of ScienceDepartment of Statistics42031 Campus-Konya

Turkey

(Joint work with: Asir Genc)

Abstract: A repeated measurements design is one in which at least one of the fac-tors consists of repeated measurements on the same subjects or experimental units, un-der different conditions. Such a factor is commonly called a ”within-subjects” factor. A”between-subjects” factor is one in which each level of the factor contains different exper-imental units. The statistical analysis of such a repeated measurements design includesmodels for both the expected value of the observations and for their within-subjectvariance-covariance structure. General linear model (GLM) which is a traditional ap-proach to repeated measurements data analysis for modeling the expected value of theobservations as a linear function of explanatory variables is appropriate when it is as-sumed that the observations from different subjects are statistically independent anduncorrelated and that the variance-covariance structure is the same for each subject.From the violations of these assumptions, random intercept model (RIM) from linearmixed models (LMMs) is the preferred one for modeling flexible within-subject variance-covariance structure of the response variable instead of GLM approach to the repeatedmeasurements data. In this paper, after defining the between-subjects factor as treatmentand the within-subjects factor as time, GLM approach involving adjusted univariate testsand multivariate analysis of variance (MANOVA) technique and also RIM from LMMsapproach to repeated measurements data is given in an application from a clinical trial.


69

Comparing Estimation Results in Nonparametric andSemiparametric

Alper Sinan


Selcuk University, Faculty of Science, Department of Statistics42031 Campus-Konya / Turkey


Abstract: In this study, estimation methods for nonparametric and semiparametricregression models are investigated. Nonparametric regression model is given by yi =∑q

j=1 mj (xji) + εi, i = 1, 2, . . . , n where y is dependent variable, xji, i = 1, 2, . . . , n,j = 1, 2, . . . , q are independent variables, εi, i = 1, 2, . . . , n are the disturbance andmj (·) , j = 1, 2, . . . , q are regression functions. Kernel estimators and median methodwhich is simple and commonly used method are evaluated in details. Choosing smoothingparameter h and the kernel function are also investigated. Semiparametric regressionmodel is given by

yi = β′Z +

q∑

j=1

mj (xji) + εi, i = 1, 2, . . . , n

where β is the parameters vector, Z is design matrix for parametric part of semipara-metric model. The model determining process and mostly used estimation methods insemiparametric regression model are investigated. Results obtained by simulations indifferent sample sizes are compared.

References

1. Roy, N., 1997, “Nonparametric and Semiparametrc Analysis of Panel Data Models:An Application to Calorie-Income Relation for Rural South India”, University of Cal-ifornia, Ph.D. Thesis, Riverside

2. Liu, Z., 1998, “Nonparametric and Semiparametric Estimation and Testing of Econo-metric Models”, The University of Guelph, Ph.D. Thesis

3. Pagan, A., Ullah, A., 1999, “Nonparametric Econometrics”, Cambridge UniversityPress, Cambridge, U.K.

4. Marlene, M., 2000, “Semiparametric Extensions to Generalized Linear Models”, Ph.D.Thesis Berlin.

5. Yatchew, A., 2003, “Semiparametric Regression for the Applied Econometrician”,Cambridge Uni. press, UK

6. Yapıcı Pehlivan, N., 2005, “Parametrik Olmayan Regresyonda Alternatif Tahmin Edi-ciler”, Selcuk University, Ph.D. Thesis, Institute of the Natural and Applied Sciences,Konya.


70

Confidence Intervals for Mean Time to Failure inTwo-Parameter Weibull with Censored Data

Noor Akma Ibrahim


Institute for Mathematical Research, Universiti Putra Malaysia43400, Serdang, Selangor

Malaysia

(Joint work with: N. Poh Bee)

Abstract: We consider a two-parameter Weibull distribution as the underlying distri-bution for a set of failure time data. For failure time distributions, the parameters areeasily estimated by the maximum likelihood method. These estimators can then be usedto estimate other quantity of interest such as the mean time to failure (MTTF) whichplays an important role in reliability analysis. From the asymptotical normality of themaximum likelihood estimators, confidence intervals can be obtained. However, theseresults might not be very accurate for small sample sizes and/or large proportion ofcensored observations. For this purpose a simulation study with varying sample size andpercentage of censoring was carried out to compare the accuracy of the asymptotical con-fidence intervals with confidence intervals based on bootstrap procedure. The alternativemethodology of confidence intervals for the MTTF of Weibull distribution function isillustrated by using real data from engineering field.

Key-Words: Two-parameter Weibull, failure time, MTTF, censored, maximum like-lihood, bootstrap


71

Rough Set-based Functional Dependency Approach forClustering Categorical Data

Tutut Herawan


Universiti Tun Hussein Onn MalaysiaParit Raja, Batu Pahat 86400, Johor

Malaysia

(Joint work with: Mustafa Mat Deris)

Abstract: Clustering data is an integral part of data mining and has attracted muchattention recently. However, few of these methods focus on categorical data. The mainidea of the rough clustering for categorical data is a clustering data set is mapped asa decision table. This can be done by introducing a decision attribute. In this paper, anovel algorithm called MADE (Maximal Attributes Dependencies) which finds a decisionattribute is presented. It is based on a maximal degree of attributes dependencies incategorical datasets. After selection, a divide and conquer method is used to cluster thedata. Experimental results on three benchmark UCI datasets, i.e. Soybean, Zoo andMushroom datasets show that MADE provides better performance with the baselinecategorical data clustering algorithm with respect to computational complexity up to64%, 77% and 83%, response time up to 63%, 67% and 57% and cluster purity up to9%, 17% and 16%, respectively.


72


PARALLEL SESSIONS 3

30 September 2009, 16:15-18:30



75

Session 3.1: Mathematical Modelling, Analysis, Applications I

Chair: Alejandro ZarzoPlace: Hall 1


76

Parameter Estimation by ANFIS in Cases Where Outputsare Non-Symmetric Fuzzy Number

Turkan Erbay Dalkilic


Karadeniz Technical UniversityFaculty of Arts and Sciences

Department of Statistics and Computer Sciences61080, Trabzon - Turkey

(Joint work with: Aysen Apaydin)

Abstract: Regression analysis is an area of statistics that deals with the investigationof the dependence of a variable upon one or more variables. Recently, much researchhas studied fuzzy estimation. There are some approach exist in the literature for theestimation of the fuzzy regression model. The two of them are frequently used in pa-rameter estimation, one of them is proposed by Tanaka et al. and it is known as linearprogramming approach and the other is fuzzy least square approach.The fuzzy inference system forms a useful computing framework based on the conceptsof fuzzy set theory, fuzzy reasoning, and fuzzy if-then rules. The fuzzy inference systemis a powerful function approximater. There are several different types of fuzzy inferencesystems developed for function approximation. The Adaptive-Network Based Fuzzy In-ference System (ANFIS) is a neural network architecture that can solve any functionapproximation problem. In this study we will use the ANFIS for parameter estimationand propose an algorithm in cases where outputs are non-symmetric fuzzy number. Inthis algorithm the error measure is defined as the difference between the estimated out-puts which are obtained by adaptive network and the target outputs. In order to obtainthe difference between two fuzzy numbers, some fuzzy ranking method must used to de-fine the operator -. There are many fuzzy ranking methods for measuring the differencebetween two fuzzy numbers in literature. In this work, the method of Chang and Lee,which is based on the concept of overall existence, will be used.


77

A Multizone Overset Algorithm for the Solution of Flowaround Moving Bodies

Fatemesadat Salehi


Aerospace Engineering DepartmentAmirkabir University of Technology

Hafez Street, Tehran - Iran

(Joint work with: S.M.H. Karimian, H. Alisadeghi)

Abstract: A two-dimensional moving mesh algorithm is developed to simulate the gen-eral motion of two rotating bodies with relative translational motion. The grid includes abackground grid and two sets of grids around the moving bodies. With this grid arrange-ment rotational and translational motions of two bodies are handled separately, with nocomplications. Inter-grid boundaries are determined based on their distances from twobodies. In this method, the overset concept is applied to hybrid grid, and flow variablesare interpolated using a simple stencil. To evaluate this moving mesh algorithm unsteadyEuler flow is solved for different cases using dual-time method of Jameson. Numericalresults show excellent agreement with experimental data and other numerical results.To demonstrate the capability of present algorithm for accurate solution of flow fieldsaround moving bodies, some benchmark problems have been defined in this paper.


78

Spectral Singularities of Sturm-Liouville Problems withEigenvalue Dependent Boundary Conditions

Nihal Yokus




(Joint work with: E. Bairamov)

Abstract: Let L denote the operator generated in L2(R+) by Sturm-Liouville equation

−y′′

+ q(x)y = λ2y, x ∈ R+ = [0,∞) ,

y′(0)

y(0)= α0 + α1λ + α2λ2,

where q is a complex valued function and αi ∈ C, i = 0, 1, 2 with α2 6= 0. In this articlewe investigate the eigenvalues and the spectral singularities of L and obtain analogs ofNaimark and Pavlov conditions for L.


79

Vague DeMorgan Complemented Lattices

Zeynep Eken


Akdeniz University, Faculty of Science and Literature, Department of Mathematics, Antalya,Turkey

(Joint work with: Sevda Sezer)

Abstract: Vague partially ordered sets and vague lattices have been studied on the basisof many-valued equivalence relations. Then, the concept of DeMorgan complement wasfuzzily defined on vague partially ordered sets. In this work, a new characterization ofvague lattices will be given and the concept of DeMorgan complement on vague latticeswill be defined. Furthermore, some examples on these concepts will be presented.


80

Approximating the singular integrals of Cauchy type withweight function on the interval

Zainidin Karimovich Eshkuvatov


Department of Mathematics, Faculty of Science, Universiti Putra Malaysia - Malaysia

Abstract: It is known that the solutions of characteristic singular integral equations(SIEs) are expressed in terms of singular integrals of Cauchy type with weight functionsof the form w(x) = (1 + x)ν(1 − x)µ, where ν = ± 1

2, µ = ± 1

2. In this paper a new

quadrature formulas (QFs) are presented to approximate the singular integrals (SIs)of Cauchy type for all the solutions of characteristic SIE on the interval [-1,1]. Linearspline interpolation and modification discrete vortices method are used to construct QFs.Estimate of errors are obtained in the classes of functions Hα(A, [−1, 1]) and C1([−1, 1]).Numerical results are presented to show the validity of the QFs constructed.


81

Lobatto IIIA-IIIB Discretization for the Strongly CoupledNonlinear Schrodinger Equation

Bulent Karasozen



(Joint work with: Ayhan Aydin)

Abstract: We construct second order symplectic and multi- symplectic integrators forstrongly coupled nonlinear Schrodinder equation using the Lobatto IIIA-IIIB partitionedRunge-Kutta method, which yield an semi-explicit scheme.Numerical dispersion proper-ties and the stability of both integrators are investigated. Numerical results for differentsolitary wave solutions confirm the excellent long time behavior of symplectic and multi-symplectic integrators by preserving local and global energy and momentum.


82

Session 3.2: Approximations and Interpolation II

Chair: Miguel Angel FortesPlace: Hall 2


83

Rough Oscillatory Singular Integrals on Rn

Hussain Mohammed Al-Qassem


Mathematics & Physics DepartmentQatar University P.O. Box 2713

Doha - Qatar

(Joint work with: L. Cheng, Y. Pan)

Abstract: We obtain appropriate sharp estimates for rough oscillatory integrals. Byusing these estimates and employing an extrapolation argument we obtain some newand previously known results for oscillatory integrals under various sharp size conditionson the kernel functions.


84

Exponentially fitted two–step hybrid methods for y′′ = f(x, y)

Raffaele D’Ambrosio


University of SalernoVia Ponte Don Melillo, 84084 Fisciano (SA)

Italy

(Joint work with: E. Esposito, B. Paternoster)

Abstract: It is the purpose of this talk to derive two-step hybrid methods for sec-ond order ordinary differential equations with oscillatory or periodic solutions, havingfrequency-dependent parameters. We show the constructive technique to derive expo-nentially fitted methods, together with a regularization technique useful to express thecoefficients in a suitable form to reduce the effects of numerical cancellation. We analysethe properties of the resulting methods, carrying out the linear stability analysis alsoin the case of parameters depending on two frequencies. We then perform some numer-ical experiments underlining the properties of the derived methods and confirming thetheoretical expectations.


85

Improving the Gradient based search Direction to EnhanceTraining Efficiency of Back Propagation based Neural

Network algorithms

Nazri Mohd Nawi


Universiti Tun Hussein Onn MalaysiaPO Box 101, 86400, Parit Raja, Batu Pahat, Johor

Malaysia

(Joint work with: Rozaida Ghazali, Mohd Najib Mohd Salleh)

Abstract: Most of the gradient based optimisation algorithms employed during trainingprocess of back propagation networks use negative gradient of error as a gradient basedsearch direction. A novel approach is presented in this paper for improving the trainingefficiency of back propagation neural network algorithms by adaptively modifying thisgradient based search direction. The proposed algorithm uses the value of gain parameterin the activation function to modify the gradient based search direction. It has beenshown that this modification can significantly enhance the computational efficiency oftraining process. The proposed algorithm is generic and can be implemented in almostall gradient based optimisation processes. The robustness of the proposed algorithmis shown by comparing convergence rates for gradient descent, conjugate gradient andquasi-Newton methods on many benchmark examples.


86

Approximation Properties of Q-Konhauser Polynomials

Gurhan Icoz


Gazi University, Faculty of Science and Literature, Department of Mathematics, Besevler,Ankara, Turkey

(Joint work with: F. Tasdelen Yesildal)

Abstract: In this work, we introduce q−Konhauser polynomials. The main object ofthis paper is to investigate the approximation properties of linear positive operatorsincluding q−Konhauser polynomials with the help of Korovkin’s theorem. The rates ofconvergence of these operators are computed by means of modulus of continuity, Peetre’sK − functional and the elements of Lipschitz class. Also we introduce the r−th ordergeneralization of these operators and we obtain approximation properties of them.


87

An Alternative Region-Based Active Contour Model UsingCauchy-Schwartz Divergence

Veronica Biga


The University of SheffieldDepartment of Automatic Control and Systems Engineering Mappin Street , Sheffield S1 3JD

United Kingdom

(Joint work with: Daniel Coca, Visakan Kadirkamanathan, Stephen A. Billings)

Abstract: In this paper, we explore the potential of a new geometric active contourmodel for image segmentation based on Cauchy-Schwartz divergence. In essence, themodel assumes that the image features of the target region and background region arerandom variables independently sampled from two probability distribution functions(PDFs) and can be separated by maximising the divergence measure. By using shapegradient tools we rigorously formulate the corresponding criterion to be optimised overthe evolving regions. A common problem in well established ratio-type models suchas the ones based on entropy and Kullback-Leibler distance are numerical errors in theapproximation of region-specific PDFs. Although kernel density estimation methods helpin overcoming this disadvantage, the problem of evaluating the criterion becomes criticalas the size of the feature space shrinks. In contrast, Cauchy-Schwartz divergence is aproduct-type measure and can be evaluated even in the case of only a few feature samplesavailable. By using texture descriptors to extract relevant regions, we demonstrate theapplicability of our model on a range of synthetic and real cell imaging examples andcompare the results against the alternative Kullback-Leibler distance approach. Finally,we focus the conclusions on robustness and versatility of our model in dealing withsegmentation problems in phase-contrast microscopy images.


88

On Chlodovsky variant of multivariate beta operator

Gulen Bascanbaz Tunca


Ankara University, Faculty of ScienceDepartment of Mathematics06100, Tandogan-Ankara

Turkey

(Joint work with: Yalcin Tuncer)

Abstract: In this work, we state Chlodovsky variant of multivariate beta operator, saymultivariate beta-Chlodovsky operator. We show that the multivariate beta-Chlodovskyoperator can preserve the properties of the general function of modulus of continuity andalso Lipschitz constant of a Lipschitz continuous function. Furthermore we set an Hω (∆)class by the function of modulus of continuity ω and taking its concave (convex) majorantω∗ into account, we give some general results for functions belonging to Hω (∆).


89

Session 3.3: Nonlinear Equations and Mathematical Modelling

Chair: Ersan AkyildizPlace: Hall 3


90

Stability analysis of recurrent neural networks with deviatedargument of mixed type

Enes Yilmaz


Middle East Technical UniversityDepartment of Mathematics and Institute of Applied Mathematics

Inonu Bulvari 06531 Ankara - Turkey

(Joint work with: M.U. Akhmet, D. Arugaslan)

Abstract: In this talk, we apply the method of Lyapunov functions for differentialequations with piecewise constant argument of generalized type to a model of recurrentneural networks (RNNs). The main novelty of the model is that it involves both advancedand delayed arguments. Sufficient conditions are obtained for global exponential stabilityof the equilibrium point. Examples with numerical simulations are presented to illustratethe results.


91

The Periodicity of Solutions of the Rational DifferenceEquation xn+1 = pnxn−k+xn−(k+1)

qn+xn−(k+1)

Turgut Tollu



Abstract: In this study, we investigated to generaliziation of the solutions of the differ-ence equation x(n + 1) = [p(n).x(n − k) + x(n − (k + 1))]/[q(n) + x(n − (k + 1))] with(k+1)-th periodic coefficients, where every k, x(−k), x(−k+1), ..., x(0) are real numbersand p(n) is not equal to q(n). Also, we obtained that the solutions were periodic withperiod (k + 1).


92

On the behavior of solutions of a rational systemx(n + 1) = 1/[y(n − 1)], y(n + 1) = x(n − 1)/[x(n).y(n − 2)]

Emine Hekimoglu




Abstract: In this study, we analysed to the solutions of a rational system x(n + 1) =1/[y(n−1)], y(n+1) = x(n−1)/[x(n).y(n−2)], where x(−1), x(0), y(−2), y(−1), y(0) arepositive real numbers. Also, we obtained that the solutions of this system were periodicwith period eight.


93

A modification on some improved Newton’s method withoutdirect function evaluations

Behzad Ghanbary


Guilan UniversityFaculty of Sciences, Department of Mathematics

Rasht - Iran

(Joint work with: Jafar Biazar)

Abstract: In this paper, we are concerned with the further study for system of nonlinearequations. Due to the fact that systems with inaccurate function values or problemswith high computational cost arise frequently in science and engineering, recently suchsystems have attracted researchers interest. In this work we present a new method whichis independent of function evolutions and has a quadratic convergence. This methodcan be viewed as a extension of some recent methods for solving mentioned systems ofnonlinear equations. Numerical results of applying this method to some test problemsshow the efficiently and reliability of method.


94

Error Inequalities for Discrete Hermite Interpolation

Patricia J. Y. Wong


School of Electrical and Electronic EngineeringNanyang Technological University

50 Nanyang Avenue, Singapore 639798, Singapore

(Joint work with: Fengmin Chen)

Abstract: In this paper we shall develop a class of discrete Hermite interpolates Hρffor a function f defined on the discrete interval N [a, b + 2] = {a, a + 1, · · · , b + 2}. Let

ρ : a = k1 < k2 < · · · < km = b, ki ∈ Z, 1 ≤ i ≤ m

be a uniform partition of N [a, b]. We say Hρf is the discrete Hermite interpolate of f ifHρf(t) is a quintic polynomial in each subinterval [ki, ki+1], 1 ≤ i ≤ m− 1 with

Hρf(ki) = f(ki), ∆Hρf(ki) = ∆f(ki), ∆2Hρf(ki) = ∆2f(ki), 1 ≤ i ≤ m.

Further, we shall offer explicit error bounds for the discrete Hermite interpolate, i.e.,

‖f −Hρf‖ ≤ aj maxt∈N [a,b+2−j]

|∆jf(t)|, 2 ≤ j ≤ 6

where the constants aj , 2 ≤ j ≤ 6 are explicitly given.


95

Parallel Newton-like methods for solving systems ofnonlinear equations

Josep Arnal


University of Alicante, Carretera San Vicente del Raspeigs/n - 03690 San Vicente del Raspeig - Alicante

Spain

Abstract: A class of Newton-like iterative methods for the parallel solution of systems ofnonlinear algebraic equations is investigated. The methods permit that the Jacobian besingular at some points. Theorems are obtained demonstrating convergence for the caseswhen the jacobian matrix is monotone and when the jacobian matrix is an H-matrix.Numerical experiments of these methods on a parallel computing system are discussed.Experiments show the e?ectiveness and feasibility of the new methods.


96

Session 3.4: Computational Methods in Physical and SocialSciences II

Chair: Jose M.MatiasPlace: Hall 4


97

Deriving Elastic Fields in an Anisotropic Bi-material

Demet Ersoy


Department of MathematicsIzmir University of Economics

Balcova, 35330, IzmirTurkey

(Joint work with: V. Yakhno)

Abstract: In this paper we consider a bi-material consisting of two elastic anisotropicplates with the same thickness. One layer of this bi-material is located between twoplanes

P1 = {x = (x1, x2, x3) : −∞ < x1 < ∞, −∞ < x2 < ∞, x3 = 0} ,

P2 =

{x = (x1, x2, x3) : −∞ < x1 < ∞, −∞ < x2 < ∞, x3 =

`

2

}

and characterized by elastic moduli C−jk`m and density ρ−.The second layer of bi-material is situated between two planes

P2 =

{x = (x1, x2, x3) : −∞ < x1 < ∞, −∞ < x2 < ∞, x3 =

`

2

},

P3 = {x = (x1, x2, x3) : −∞ < x1 < ∞, −∞ < x2 < ∞, x3 = `}and characterized by elastic moduli C+

jk`m and density ρ+.

A plane wave with normal vector e3 = (0, 0, 1) drops on one side of bi-material attime t = 0. We consider the vibration problem which consists of finding the displacementvector

u(x, t) = (u1(x, t), u2(x, t), u3(x, t))

for each point x of bi-material for the time t from [0, T ], where T is a given number.The mathematical model of the vibration in this bi-material is given by the following

anisotropic system of elasticity [1,2,3]:

ρ∂2uj

∂t2=

3∑

k=1

∂σjk

∂xk, (x1, x2) ∈ R2, x3 ∈ (0,

`

2) ∪ (

`

2, `), t ∈ R, (1)

with initial data

uj(x, t)|t<0 = 0, (x1, x2) ∈ R2, x3 ∈ (0,`

2) ∪ (

`

2, `), (2)

and boundary conditions

σj3|x3=0 = −δ3j · δ(t), σj3|x3=0

∣∣∣x3=`−0

= 0, t ∈ R, (3)

and matching conditions

uj(x, t)|x3= `

2−0= uj(x, t)|

x3= `2+0

, t ∈ R, (4)


98

σj3|x3= `2−0

= σj3|x3= `2+0

, t ∈ R, (5)

where j = 1, 2, 3; σjk =∑3

`,m=1 Cjk`m(x3)∂uj

∂xmfor all j, k = 1, 2, 3; Cjk`m(x3) and

ρ(x3) have the following forms:

Cjk`m(x3) =

{C−jk`m, if 0 < x3 < `

2,

C+jk`m, if `

2< x3 < `;

ρ(x3) =

{ρ−, if 0 < x3 < `

2,

ρ+, if `2

< x3 < `,

(6)

where C−jk`m, C+jk`m, ρ− > 0, ρ+ > 0 are given constants for all j, k, `, m = 1, 2, 3; T is

a given positive number; δ3j is Kronecker symbol, δ(t) is Dirac delta function dependingon t and u(x, t) = (u1(x, t), u2(x, t), u3(x, t)) is unknown vector function depending onx, t.

An explicit formula for a solution of the vibration problem (1) − (5) has been found.Using this formula the simulation of elastic fields have been obtained.

Keywords: System of anisotropic elasticity, bi-materials, elastic wave, boundary condi-tions, matching conditions, simulation.

References

1. Dieulesaint E. and D.Royer, ”Elastic Waves in Solids I” Springer-2000.2. Fedorov F.I., ”Theory of elastic waves in crystals” Plenum Press-1968.3. Ting T.C.T.,”Anisotropic elasticity: Theory and applications” Oxford University

Press-1996.


99

A Boundary Value Problem of the Frequency-DependentMaxwell’s System for Layered Materials

Sengul Kecelli


Department of MathematicsDokuz Eylul University

Tinaztepe Kampusu 35160, Buca -IzmirTurkey

(Joint work with: V. Yakhno)

Abstract: The main object of the paper is a boundary value problem of the frequency-dependent Maxwell’s system for a layered material. The frequency-dependent Maxwell’ssystem has the following form (Eom,2004)

curlxH(x, ω) = (−iω)εE(x, ω) + J(x, ω), (1)

curlxE(x, ω) = (iω)µH(x, ω), (2)

divx(εE(x, ω)) = ρ(x, ω), (3)

divx(µH(x, ω)) = 0, (4)

where x = (x1, x2, x3) ∈ R3, i2 = −1; ω is a given number (frequency).

We assume that vector functions H, E, J and the scalar function ρ are independentof x3, that is, they depend on variables x1, x2 and the frequency ω.

LetD = {x = (x1, x2) : 0 < x1 < b1, 0 < x2 < b2} ,

Dk = {x = (x1, x2) : 0 < x1 < b1, rk−1 < x2 < rk, } ,

where b1 > 0, b2 > 0, r0 = 0, rN = b2, rk k = 1, 2, . . . , N are given numbers. Let Γbe the boundary of the domain D.

We assume also that the magnetic permeability µ(x) and the electric permittivityε(x) are given in the form

ε(x) =

ε1, x ∈ D1,ε2, x ∈ D2,...

.

..εN , x ∈ DN .

; µ(x) =

µ1, x ∈ D1,µ2, x ∈ D2,...

.

..µN , x ∈ DN .

The Conservation law of charge is satisfied:

divxJ(x, ω) + (−iω)ρ(x, ω) = 0. (5)

Let J(x, ω) be a given vector function for x ∈ D, ω 6= 0 be a fixed number, ρ(x, ω)be a function satisfying (5). The main problem of this paper is to find H(x, ω), E(x, ω)


100

satisfying (1)-(4) and the following boundary and matching conditions (Eom, 2004)

(E× ~n)∣∣Γ

= 0, (H× ~n)∣∣Γ

= 0, (6)

(D · ~n)∣∣Γ

= 0, (B · ~n)∣∣Γ

= 0, (7)

(E× ~ν)∣∣Sk

= 0 ⇒ (E∣∣S+

k−E

∣∣S−

k)× ~ν = 0;

(H× ~ν)∣∣Sk

= 0 ⇒ (H∣∣S+

k−H

∣∣S−

k)× ~ν = 0;

(D · ~ν)∣∣Sk

= 0 ⇒ (µE∣∣S+

k− εE

∣∣S−

k) · ~ν = 0;

(B · ~ν)∣∣Sk

= 0 ⇒ (µH∣∣S+

k− µH

∣∣S−

k) · ~ν = 0,

(8)

where k = 1, . . . , (N − 1); ~n is an external normal vector to Γ and ~ν = (0, 1, 0);D = εE and B = µH denotes electric and magnetic flux densities, respectively. Sk

denotes the surface x2 = rk, between domains Dk and Dk+1 k = 1, 2, . . . , N − 1. Thissituation means that there is no electric and magnetic fields outside of the domain D.

We have showed that the frequency-dependent Maxwell’s system (1)-(4) is reducedto two Helmholtz equations. Using boundary conditions (6)-(7) and matching conditions(8) we set up two subproblems for these Helmholtz equations. The separation of variablesand the Fourier series expansion method are used for solving subproblems.

As a result, the explicit formula for a solution of the original problem has beenobtained for cases N = 1, 2, 3. These explicit formulae are presented in the form ofFourier series expansion.

Keywords: Maxwell equations, layered medium, exact solution, the Fourier seriesexpansion method.

References

Eom, 2004. Eom, H.J. (2004). Electromagnetic wave theory for boundary-value problems.Springer, Berlin.


101

A Study on the Multiple Logistic Regression Analysis toDetermine Risk Factors for the Smoking Behavior

Sevgi Yurt Oncel


Kirikkale UniversityDepartment of Statistics

71100 Yahsihan - KirikkaleTurkey

(Joint work with: Omer L. Gebizlioglu, Fazil Aliev)

Abstract: To determine the risk factor of smoking using a multiple binary logistic re-gression method and to assess the risk variable for smoking, which is a major and growinghealth problem in many countries. We presented a questionnaire study, consisting of 1737students (869 males and 866 females, smokers or non-smokers). The data were collectedusing a standard questionnaire that contains 34 questions. The study was carried out inthe Kirikkale University, Kirikkale, Turkey in 2008. A multiple logistic regression modelwas used to evaluate the data and to find the best model. The receiver operating charac-teristic curve was found successful to predict person with risk factor for smoking. Datawere analyzed using the SPSS/PC package 15.0.We classified 68.8 % of the participants using the logistic regression model. This studysuggests that gender, smoking status of mother, smoking status of sibling, education ofmother and income are independent predictors of the risk of smoking status in our popu-lation. In addition, the findings of the present study indicate that the use of multivariatestatistical method as a multiple logistic regression in smoking, which may be influencedby many variables, is better than univariate statistical evaluation.


102

Numerical simulation of tsunami generated in North PacificOcean near Japan

Yoji Otani


Graduate School of Environmental Science, Okayama University1-1, Naka 3-chome, Tsushima, Kita-ku, Okayama 700-8530

Japan

(Joint work with: M. Watanabe, L. Ying, K. Yamamoto, Hashentuya)

Abstract:Propagation of a tsunami wave generated in Nankai Trough area in the North Pa-

cific Ocean is simulated, and numerical techniques are described and some numericalresults are presented. The simulation is based on a system of partial differential equa-tions derived from momentum equations and a continuity equation. The Gauss-Krugerprojection method is used to convert depth data given in terms of longitude and latitudeto rectangular coordinates. Finite element approximation applied to spatial derivativesleads to a system of ordinary differential equations, which can be solved numericallyby standard ODE solvers. Numerical results show the behavior of tsunami propagatingtowards coasts of Japan and changes in tsunami wave height and propagation speed.Furthermore, numerical results will be compared with observed data. Our numericaltechniques will also be verified by testing some numerical solutions against analyticalsolutions


103

A new numerical method for solving 2D ElectricalImpedance Tomography Inverse Problem

Ata Olah Abbasi


Sharif University of TechnologyDepartment of Electrical Engineering

P.O. Box: 11365-8639Iran

(Joint work with: B. Vosoughi Vahdat)

Abstract: In this paper, we present a new numerical method for solving electricalimpedance tomography inverse problem in 2D. Electrical Impedance Tomography (EIT)is a simple and economic technique to capture images from the interior of the subject.EIT is based on measurements made from electrodes on the surface of the subject. EITinverse problem (image reconstruction algorithm) is an ill-posed and nonlinear problem.Recently, an inverse solution for EIT has been developed based on block method, howeverthis method is using nonlinear algorithm. The present article provides a direct numericalmethod solution. This new approach provides fast solver algorithm and has ability tosolve complicated problems. Numerical examples prove the reliability of our method. Wehave assumed that the subject has a 2D rectangular shape and is made of similar blocks.Also the presented algorithm demonstrates a reduction of both computation time andstorage requirements without sacrificing the numerical stability.


104

Control strategy of avian influenza based on modeling andsimulation

Tertia Delia Nova


Faculty of Animal Husbandry, Andalas University, West SumateraLimau Manis, Padang

INDONESIA

(Joint work with: H. Mawengkang, M. Watanabe)

Abstract: Since outbreaks of bird flu (avian influenza) spread widely in 2003, poultryfarms have been under constant threat by loss due to the disease characteristic of do-mestic birds. Source of the disease is the influenza virus H5N1 endogenous to wild birds.Unlike wild birds, infection of virus to domestic birds brings serious symptoms leadingto death. In a production process of a poultry farm, the entire population of domesticbirds is balanced with the capacity of the farm by supply of new healthy birds and byshipping of healthy birds to be products. Some of infected birds die of the disease whileothers stay alive. However regardless of being alive or dead, infected birds remain as asource of infection unless they are completely disposed of. These factors have been takeninto account to construct a model consisting of nonlinear ordinary differential equations.Populations of susceptible birds and infected birds are unknown variables of those differ-ential equations. Analysis of the model has led to the conclusion that the most effectivemeasure against outbreak of bird flu within poultry farm is constant removal of infectedbirds, and that removal of infected birds can solely prevent an outbreak of bird flu.The analysis has also shown that vaccination is effective in conjunction with removalof infected birds, and that vaccination cannot prevent an outbreak without removal ofinfected birds. Study of mechanism for outbreak of bird flu is continued from the previ-ous study, and a control strategy of avian influenza based on modeling and simulationis proposed. In particular, spatial effects are taken into accounts in modeling and simu-lation. In practice, so-called rapid test is conducted to detect infection of bird flu. It isa spot-check in which samples are taken randomly from the bird population of a farm.If one bird is found positive for infection, all the birds in the farm are disposed of. Theresult of previous study shows that it is necessary to dispose of infected birds only, notall the birds in the farm.1 This conclusion is examined with spatial effects taken intoconsideration in modling and simulation.

References

1. Tertia Delia Nova, Herman Mawengkang, Masaji Watanabe, Modeling and analysis ofbird flu outbreak within a poultry farm, Submitted.


105

Session 3.5: Mathematical Programming II

Chair: Venancio TomeoPlace: Hall 5


106

Fuzzy Optimization of A Multi Stage Multi ItemClosed-Loop Flexible Supply Chain Network Under Fuzzy

Material Requirement Constraints

Eren Ozceylan



(Joint work with: T. Paksoy, N.Y. Pehlivan)

Abstract: This work applies fuzzy sets to integrating the distribution problem of amulti product, multi tiered closed loop flexible supply chain network (involves suppli-ers, factories, warehouses, distribution centers, retailers, end customers and collection,recovery, recycling centers) under fuzzy material requirement constraints. The proposedfuzzy multi-objective linear programming (FMOLP) model attempts to simultaneouslyminimize total transportation costs between all echelons and total fixed costs of man-ufacturers and distribution centers. The model has been formulated as a mixed-integerlinear programming model where data are modelled by triangular fuzzy numbers. Fi-nally, a numerical example is solved by a professional package program, compiled theresults and discussed.


107

Identification, Optimization and Dynamics of RegulatoryNetworks under Uncertainty




(Joint work with: E. Kropat, C.S. Pedamallu)

Abstract: The mathematical analysis of gene-environment networks is of significant im-portance in computational biology and life sciences. Time-discrete and time-continuousdynamical systems can be applied for a modeling of the complex interactions and reg-ulating effects between the genetic and environmental variables. In order to includethe effects of random noise and uncertainty, various regression models based on inter-val arithmetics but also on spline regression and stochastic differential equations havebeen developed. In this talk, we survey recent advances on gene-environment networksbased on interval arithmetics and ellipsoidal uncertainty which correspond to the de-gree of correlation between system variables and related errors. For an identificationof parameters of a gene-environment network based on interval arithmetics, Chebychevapproximation and generalized semi-infinite optimization are applied. In addition, thetime-discrete counterparts of the nonlinear equations are introduced and their para-metrical stability is investigated. In addition, we analyze the topological landscape ofthe gene-environment networks in terms of structural stability. For an analysis of gene-environment networks under ellipsoidal uncertainty, the uncertain states of clusters ofdata variables are represented in terms of ellipsoids and the interactions between thevarious clusters are defined by affine-linear coupling rules. Explicit representations ofthe uncertain multivariate states of the system are determined with ellipsoidal calculus.In addition, we introduce various regression models that allow us to determine the un-known system parameters from uncertain (ellipsoidal) measurement data by applyingsemidefinite programming and interior point methods. We analyze the structure of theoptimization problems obtained, especially, in view of their solvability, we discuss thestructural frontiers and research challenges, and we conclude with an outlook.


108

Using Dirichlet-to-Neumann operators and ConformalMappings with Approximate Curve Factors in Waveguide

Problems

Erkki Laitinen


University of Oulu, Dep. of Math. Sci. 90014 University of OuluFinland

(Joint work with: I. Konnov, O. Kashina)

Abstract: We consider a problem of optimal allocation of a homogeneous resource inspatially distributed systems such as communication networks, where both utilities ofconsumers and network expenses must be taken into account. This approach leads toa two-objective optimization problem, which involves non-differentiable functions whosevalues are computed algorithmically. We propose several approaches to define a solutionand to construct corresponding solution methods for such problems. In particular, newsubgradient methods for non-differentiable Pareto optimization problems are suggested.Their work is illustrated by computational results on test problems.


109

Finding Efficient and Inefficient Outlier Layers by UsingSkewness Coefficient

Mahnaz Mirbolouki


Department of MathematicsScience and Research Branch


(Joint work with: F.Hosseinzadeh Lotfi, G.R. Jahanshahloo, M.H. Behzadi)

Abstract:Data Envelopment Analysis (DEA) is a mathematical programming for eval-uating the efficiency of a set of Decision Making Units (DMUs). One of the significantproblems which is under consideration in the field of DEA, is distinguishing the out-lier DMUs. Such DMUs have a different behavior in contrast to the general prevailingbehavior of the population; which is caused by the incorrect way of collecting data orother unknown factors which can be social, political and etc. These DMUs can affect theefficiency of other DMUs. Thus recognizing and excluding them from the population; orreducing their effect and proportioning their status with the population can influencethe improvement of total efficiency of population. Therefore incorrect deduction aboutthe population can be prevented. In this paper, on basis of the assumption that the effi-ciency of population must have a unimodal symmetric distribution, a method based onthe skewness of efficiency and inefficiency has been presented. By utilizing this methodall the outlier DMUs; in different layers; can be recognized.

keywords: Data Envelopment Analysis, Normal distribution, Outlier, Skewness.


110

Multi-Objective Optimization Model for Solving Risk-BasedEnvironmental Production Planning Problem in Crude Palm

Oil Industry

Hendaru Sadyadharma


Doctoral Program of Natural Resources and Environment,the University of Sumatera Utara

Kampus USU, MedanIndonesia

(Joint work with: Z. Nasution, H. Mawengkang)

Abstract: The crude palm oil industry could give significant impact to the economicdevelopment of a country. Despite obvious benefits of this industrial development, itcontributes to environmental degredation from both input and output sides of its ac-tivities. On the input side, crude palm oil mill uses much water in production processand consumes high energy. On the output side, manufacturing process generates largequantity of wastewater, solid waste/by-product and air pollution. In environmental pro-duction planning and risk management decision process in crude palm oil industry, thereare several alternatives need to be analyzed in terms of multiple noncommonsurate cri-teria, and many different stakeholders with conflicting preferences are involved. In thispaper we propose a multi-objective optimization model for tackling such environmentalrisk production planning problem. In order to solve the model we develop an interactivemethod which involves analytical hierarchy process (AHP) strategy.


111

Staff scheduling with priority constraints

Sacha Varone


Haute Ecole de Gestion de GeneveRoute de Drize 7 1227 Carouge

SWITZERLAND

(Joint work with: David Schindl)

Abstract:Staff scheduling, also known as timetabling, is a task to be done in any organ-isation. In this paper we model this problem as a minimal cost at maximal flow networkproblem, therefore with a polynomial time complexity. Besides the usual availabilityand skills constraints, we consider additional constraints: targeted workload, satisfactionof employees seen as a rotation constraint, some tasks require several employees, someemployee can not be assigned to a same task. We consider cost specifications as thoseassociated to the types of employee, overtime, task delayed, profit associated with theexecution of a task. We also analyse the limits of our model, showing types of constraintsthat transform the problem into a NP-hard problem.


112


PARALLEL SESSIONS 4

1 October 2009, 10:30-12:45



115

Session 4.1: Mathematical Modelling, Analysis, Applications II

Chair: Alireza AshrafiPlace: Hall 1


116

Some Properties of Q-Biorthogonal Polynomials

Fatma Tasdelen Yesildal




Abstract: Almost four decades ago, Konhauser introduced and studied a pair ofbiorthogonal polynomials which are suggested by the classical Laguerre polynomials.The so-called Konhauser biorthogonal polynomials of the second kind were indeed con-sidered earlier by Toscano without their biorthogonality property which was emphasizedupon in Konhausers investigation. Many properties and results for each of these biorthog-onal polynomials (such as generating functions, Rodrigues formulas, recurrence relations,and so on) have since been obtained in several works by others. The main object of thispaper is to present a systematic investigation of the general family of q-biorthogonalpolynomials. Several interesting properties and results for the q-Konhauser polynomialsare also derived.


117

Positive solutions for nonlinear first-order m-point boundaryvalue problem on time scale

Ismail Yaslan


Pamukkale UniversityDepartment of Mathematics

20070, DenizliTurkey

Abstract: In this study, we investigate the existence of positive solutions for nonlin-ear first-order m-point boundary value problem on time scales by means of fixed pointtheorems.


118

Error Estimates for Discrete Spline Interpolation

Fengmin Chen


School of Electrical and Electronic EngineeringNanyang Technological University

50 Nanyang Avenue, Singapore 639798, Singapore

(Joint work with: Patricia J. Y. Wong)

Abstract: We shall develop a class of discrete spline interpolates Sρf for a function fdefined on the discrete interval N [a, b + 2] = {a, a + 1, · · · , b + 2}. Let

ρ : a = k1 < k2 < · · · < km = b, ki ∈ Z, 1 ≤ i ≤ m

be a uniform partition of N [a, b]. We say Sρf is the discrete spline interpolate of fprovided that Sρf(t) is a quintic polynomial in each subinterval [ki, ki+1], 1 ≤ i ≤ m−1with

Sρf(ki) = f(ki), 1 ≤ i ≤ m

and∆Sρf(kj) = ∆f(kj), ∆2Sρf(kj) = ∆2f(kj), j = 1, m.

We also establish explicit error estimates for the discrete spline interpolate, i.e.,

‖f − Sρf‖ ≤ dj maxt∈N [a,b+2−j]

|∆jf(t)|, 2 ≤ j ≤ 6

where the constants dj , 2 ≤ j ≤ 6 are explicitly derived.


119

Computational analysis for microbial depolymerizationprocesses of xenobiotic polymers based on mathematical

models and experimental results

Masaji Watanabe


Graduate School of Environmental Science, Okayama University1-1, Naka 3-chome, Tsushima, Kita-ku, Okayama 700-8530

Japan

(Joint work with: F. Kawai)

Abstract: Water-soluble polymers are not suitable for recycle or incineration, andbiodegradation is an essential factor of environmental protection against undesirableaccumulation of those polymers. Biodegradation is also essential for water-insoluble poly-mers, so-called plastics, because they are not completely recycled nor incinerated, andit is important to understand the mechanism of microbial depolymerization processes ofxenobiotic polymers. In general, microbial depolymerization processes are classified intotwo types: exogenous type and endogenous type. In exogenous type depolymerization pro-cesses, molecules lose their weight by separation of monomer units from their terminals.Class of polymers subject to exogenous type depolymerization includes polyethylene andpolyethylene glycol. In endogenous type depolymerization processes, molecules are sepa-rated at arbitrary parts. Class of polymers subject to endogenous type depolymerizationincludes polyvinyl alcohol and polylactic acid. Mathematical models for those micro-bial depolymerization processes have been proposed, and numerical techniques basedon the models have been developed. In particular, experimental data have been takeninto analysis to solve inverse problems numerically, and transitions of weight distributionhave been simulated. In this study, mathematical analysis of microbial depolymerizationprocesses of xenobiotic polymers is continued, and numerical results are presented.


120

Asymptotic Results for a Semi-Markovian Random Walkwith a Normal Distributed Interference of Chance

Tahir Khaniyev


TOBB University of Economics and Technology, Faculty of EngineeringDepartment of Industrial Engineering

Sogutozu Cad. 43, Sogutozu, 06560, Ankara, Turkey

(Joint work with: I. Unver, Z. Mammadova)

Abstract: In this study, a semi-Markovian random walk process with a discrete inter-ference of chance (X(t)) is constructed and investigated. In this work, it is assumed thatthe random variables ζn, n ≥ 1 which describe the discrete interference of chance havea normal distribution with parameters (a, σ2), a > 0, σ > 0, concentrated in the interval(0,∞). Under this assumption, the ergodic distribution and its characteristic functionare expressed by means of a boundary functional of the process X(t). Using E.Dynkin’sprinciple and taking into account the supplementary condition: σ/a →∞ as a →∞ , themoments of the boundary functional are expressed by the characteristics of the ladderheights of the random walk. Then, three-term asymptotic expansions for the first fourmoments of the ergodic distribution of the process X(t) are obtained. Moreover, usingthe Riemann zeta function and result on Lerch’s transcendent the explicit forms of theasymptotic expansions for the ergodic moments of the Gaussian random walk are de-rived, as an example. Finally, the weak convergence theorem for the ergodic distributionof the process Wa(t) ≡ X(t)/a is proved, when a →∞.

References

(1) Feller W., Introduction to Probability Theory and Its Applications II, J. Wiley, New York,1971.

(2) Gihman I. I., Skorohod A.V., Theory of Stochastic Processes II, Springer, Berlin, 1975.

(3) Janssen A.J.E.M., Leeuwaarden J.S.H., On Lerch’s transcendent and the Gaussian randomwalk, The Annals of Applied Probability, 17, (2007) 421-439.

(4) Khaniyev T.A., Mammadova Z., On the stationary characteristics of the extended model oftype (s,S) with Gaussian distribution of summands, Journal of Statistical Computation andSimulation, 76, 10 (2006) 861-874.

(5) Khaniyev T.A., Kesemen T., Aliyev R.T., Kokangul A., Asymptotic expansions for the mo-ments of a semi-Markovian random walk with exponential distributed interference of chance,Statistics and Probability Letters, 78, 6 (2008) 785-793.

(6) Lotov V.I., On some boundary crossing problems for Gaussian random walks, The Annals ofProbability, 24, 4 (1996) 2154-2171.


121

A Model of Vascular Tumor Growth by Hybrid Systems

Mustafa Kahraman


Atilim University, Software EngineeringKizilcasar Mahallesi, 06836 Incek Glbasi

Ankara - Turkey

(Joint work with: Nurgul Gokgoz, Hakan Oktem)

Abstract: Tumor growth is a complex process which is dominated by some major in-teractions like division, migration and death of tumor cells according to the nutrientspresented in the environment and angiogenesis. Angiogenesis is the formation of bloodvessels from pre-existing vessels. Angiogenesis is the result of tumor growth and the in-teraction of tumor body with the nearby vessels. By formed new vessels, tumor bodycan gain access to rich nutrient sources. This is a fundamental step in the transition oftumors from a dormant to a malignant state. Mathematical models of both angiogenesisand tumor growth exist in the literature. However, a combined mathematical model oftumor growth involving the angiogenesis process has some implementational difficulities.In this paper we present a hybrid system model with partial differential equations of vas-cular tumor growth. Nutrient sources are dynamically changing with new formed vessels.Tumor growth is dependent to new nutrient sources. We suggest that we can representthe nutrient source by a switching varible determined by vascularization. Thus combinethe tomor growth and angiogenesis processes within the same model by using the hybridsystem formalism. The simulated vascular tumor growth is in agreement with biologicaldata.


122

Session 4.2: Applied Probability and Stochastic Processes II

Chair: Roger B. NelsenPlace: Hall 2


123

Probability Failure Analysis for Cracked Structure

M.R. Akramin


FKM, Universiti Malaysia Pahang, Lebuhraya Tun Razak, 26300 Gambang, Kuantan, PahangMalaysia

(Joint work with: M. Mazwan Mahat, A. Juliawati, A.H. Ahmad, A.R.M. Rosdzimin)

Abstract: This research work presents a probabilistic approach for fracture mechanicsanalysis of cracked structures. The main focus is on uncertainties aspect which relatesthe nature of crack in materials. The objective of this work is to calculate the rigidityof cracked structures based on failure probability by using simulation technique. Themethodology consists of cracked structures modelling, finite element calculation, gen-eration of adaptive mesh, sampling of cracked structure including uncertainties factorsand probabilistic analysis using Monte Carlo method. Probabilistic analysis representsthe priority of proceeding either suitable to repair the structures or it can be justifiedthat the structures are still in safe condition. Therefore, the hybrid finite element andprobabilistic analysis represents the failure probability of the structures by operatingthe sampling of cracked structures process. The uncertainty in the crack size can have asignificant effect on the probability of failure, particularly for the crack size with largecoefficient of variation. The probability of failure caused by uncertainties relates to loadsand material properties of the structure are estimated using Monte Carlo simulationtechnique. Numerical example is presented to show that probabilistic analysis based onMonte Carlo simulation provides accurate estimates of failure probability. Verificationof the predicted failure probability is validated with analytical solutions and relevantnumerical results obtained from other previous works. The comparisons show that thecombination between finite element analysis and probabilistic analysis based on MonteCarlo simulation provides accurate estimation of failure probability for use in fracturemechanics.


124

On exceedances based on the list of top m scores after l-thchange

Burak Uyar


Department of Statistics, Faculty of Science, Ege University35100 Bornova, Izmir

Turkey

(Joint work with: H. Tanil)

Abstract: Consider an infinite sequence of scores which are indicated as independentand identically distributed (iid) continuous random variables. Let the first m scores ofthe sequence be the initial top m scores. The current top m scores will be able to changewith the future observed scores in the sequence. Tanil (2009) derived the probabilitydensity functions of top m scores after l-th change from the beginning. In this study,distributions of exceedance statistics based on top m scores after l-th change are obtainedfor a random threshold model.


125

Functional Approach Using New L∗a∗b∗ color functions toevaluate colour changes in granites after desalination using

different methods

Jose M. Matias


Dpt. of Statistics, Univ. of Vigo, ETSEM, Lagoas - Marcosende, 36310 Vigo, Spain

(Joint work with: T. Rivas, C. Ordonez, J. Taboada)

Abstract: We use a functional data approach to evaluate changes in color in graniteafter a desalination treatment applied using different methods. Specifically, we appliedfunctional analysis of variance (ANOVA) to the colour curves calculated from the prod-uct of source reflectance, granite reflectance and the matching of colour functions by thestandard observer. Results for this method were compared with those produced by tradi-tional ANOVA based on the colorimetric coordinates L∗a∗b∗. The RGB and XY Z colourcoordinates systems are obtained by integrating the rgb and xyz colour functions, respec-tively. The L∗a∗b∗ coordinates, however, are obtained directly by transforming the XY Zcoordinates, as no corresponding functions have been proposed to date. With a view tocomparing results for both functional and scalar ANOVA for a homogeneous colour mea-surement method, these functions, whose integral will coincide with the L∗a∗b∗ values,were deduced and are proposed for the first time. The results obtained demonstrate theusefulness of the additional information supplied by the functional approach. However,this information does not replace that produced by the ANOVA for the scalar coordi-nates, and so it is recommended to use both approaches together. The new functionsassociated with the L∗a∗b∗ coordinates are perfectly interpretable in an analogous wayto the coordinates themselves, in other words, as the degree of luminosity (L∗) andthe relative positions of green-red (a∗) and of blue-yellow (b∗), except that they areinterpreted for each infinitesimal wavelength interval.


126

On LIBOR and swap market models: calibration to caps andswaption markets

Ceren Eda Can


Hacettepe University, Faculty of Science, Department of Statistics, 06800 Beytepe / AnkaraTurkey

(Joint work with: M. Rainer)

Abstract: The rapidly growing interest rate derivative market necessitates a sophis-ticated model for sufficiently accurate and efficient pricing and hedging techniques forinterest rate derivatives which are getting more complicated day after day. The (LIBOR)Market Model is presented as a tool to price and hedge interest rate derivatives which arefunctions of market-forward rates (a generic term market rate is used here to describeforward-LIBOR rates and forward-swap rates). It was developed by Miltersen, Sand-mann & Sondermann (1997), Brace, Gatarek & Musiela (1997), Musiela & Rutkowski(1997) and Jamshidian (1997). By contrast with previous interest rate models whichwere based on the evolution of the continuously compounded short rates (Black (1976),Vasicek (1977), Cox, Ingersoll and Ross (CIR) (1985), Hull and White (1994) models)or instantaneous forward rates (Heath, Jarrow and Morton (HJM)(1992)), which are notdirectly observable in the market, the stochastic objects (forward-LIBOR rates, forward-swap rates) modelled by the Market Models are quantities which are (rather directly)observable in the market. Modelling the stochastic behavior of the unobservable financialquantities leads to difficulties in calibration process. The calibration of these models to aset of market quantities (here, cap and swaption data) requires a transformation of thedynamics of these unobservable quantities into dynamics of observable quantities. To dothis, complicated numerical procedures are needed and the results are not always sat-isfactory. So, these models are fairly cumbersome to be calibrated to market quantitiesand price the complex interest rate derivatives. Hence, the Market Models can be cali-brated more easily to the relevant (caps, swaption) markets than previous interest ratemodels. Furthermore the Market Model is consistent with the market standard approachfor pricing interest rate derivatives using the Black (1976) model. Previous to the MarketModels, there was no interest rate models compatible with Black model. Typical MarketModels are the lognormal forward-LIBOR model (LFM), or LIBOR Market Model, andthe lognormal forward-swap rate model (LSM), or Swap Market Model. LFM is based onevolving the forward-LIBOR rates and prices caps with Black’s cap formula. In a similarway, LSM is based on evolving the forward-swap rates and prices swaptions with Black’sswaption formula. In this study, Market Models theory will be presented to account forthe forward-LIBOR rates and forward-swap rates dynamics. Moreover, the calibrationof the LMM to caps prices, the calibration to swaption prices and the joint calibrationto caps and swaption prices will be focused on.


127

Analytical Recursive Algorithm for Path-dependent OptionPricing with Stochastic Time

Zhaoning Shang


Katholieke Universiteit LeuvenDepartment of Accountancy, Finance and Insurance Naamsestraat 69 3000 Leuven

Belgium

(Joint work with: M. Goovaerts)

Abstract: In this paper, we developed a recursion algorithm for calculating the momentgeneration function of certain functionals of Brownian motion when time T is indepen-dently randomly distributed, e.g. exponentially distributed. The integral of the expo-nential functionals of Brownian motion, which plays a seminal role in path-dependentderivatives pricing, can be obtained by carrying out the real Laplace inversion. We firstpresent a new method to efficiently obtain the Laplace transform of the transition densityfunction for arbitrary diffusion processes of the form

X0 = x0, dXt = µ(Xt)dt + σ(Xt)dWt.

Considering the Laplace transform of this transition density with respect to the timevariable, the problem is reduced to the solution of the determination of an ordinarydifferential equation with certain boundary conditions. Using Feynman-Kac integrationcontaining a potential and in addition a δ-function perturbation, we construct an exactrecursion scheme for the Laplace transform of the transition density and the momentgenerating function of the Brownian motion functionals. Finally, we perform the realLaplace inversion based on Gaver functionals with certain nonlinear acceleration sequencetransformations to generate approximations for the distributions of the Brownian motionfunctional with stochastic time.


128

On the Semi-Markovian Random Walk with Delay andWeibull Distributed Interference of Chance

Rovshan Aliyev


Karadeniz Technical University, Faculty of Arts and SciencesDepartment of Statistics and Computer Sciences

61080, Trabzon-Turkey

(Joint work with: Tulay Kesemen, Tahir Khaniyev)

Abstract: In this paper, the semi-Markovian random walk with delay and a discreteinterference of chance process is considered. We assume that the sequence of randomvariables which describes the discrete interference of chance forms an ergodic Markovchain with Weibull stationary distribution with parameters . Under this assumption,the ergodicity of this process is proved and the asymptotic expansions for the first fourmoments of the ergodic distribution of the process are derived, as . Moreover, the asymp-totic expansions for the skewness and kurtosis of the ergodic distribution of the processare established.


129

Session 4.3: Computational Methods in Physical and SocialSciences III

Chair: Hassan Yousefi-AzariPlace: Hall 3


130

A nonlinear preconditioner for Jacobian-free Newton-Krylovmethods

Jisheng Kou


Shanghai UniversityDepartment of Mathematics, Shanghai University, Shanghai 200444

China

(Joint work with: Xiuhua Wang, Yitian Li)

Abstract: The Jacobian-free Newton-Krylov (JFNK) methods are used popularly inmany areas for computing efficiently the solution of large sparse systems of nonlinearequations. Successful application of the JFNK methods to any given problem is depen-dent on adequate preconditioning. In this paper, we present a new nonlinear precon-ditioner for JFNK methods. In our method, we solve a new nonlinear system which isequivalent to the original system but more balanced in nonlinearities. This new precon-ditioner is fully matrix-free. We apply this new preconditioner to the nonlinear systemarising from the discretization of 2D shallow-water equations. Numerical results showthat with this new preconditioner, Newton-GMRES method can be more efficient androbust.


131

A splitting semi-implicit scheme for large-scale atmosphericdynamics model

Ludmila Bourchtein


Pelotas State UniversityRua Anchieta 4715, bloco K, ap.304 Pelotas 96015-420

Brazil

(Joint work with: A. Bourchtein)

Abstract: In this study we apply splitting techniques in the context of the semi-Lagrangian semi-implicit approach in order to construct computationally efficient andaccurate numerical scheme for large-scale atmospheric dynamics model. Description ofthe designed numerical algorithm is provided and its properties of accuracy and sta-bility are discussed. Performed numerical experiments with the actual atmospheric datashowed that the developed scheme supplies accurate forecast fields for the increased timesteps chosen in accordance with the physical requirements.


132

Multilevel Factor Modeling as an Alternative in Evaluatingthe Performance of Statistics Education in Turkey∗

Dogan Yildiz


Yildiz Technical University,Faculty of Arts and Science, Department of Statistics,Davutpasa34210, Esenler, Istanbul - Turkey

(Joint work with: Atif Evren)

Abstract: Multilevel models are especially used for the analysis of data whose natureare hierarchical or clustered . These models are employed in performance evaluationanalysis and are based on the data coming from social organizations which are con-sisting of many units from (different levels) encountered especially in economy and insocial research fields such as education and health sectors. Statistical data coming fromthe studies on educational processes in different types of schools, the studies carried onfamilies with children as well as the studies on companies with many units from differ-ent levels can be investigated by multilevel modeling techniques. Social groups and unitsconstitute a hierarchical entity and within this system data coming from the same groupsare supposed to possess similar characteristics. Thus for a hierarchical data, the neces-sary assumption for observation values to be independent from each other is violatedfor standard statistical tests . In multilevel models at each different level of hierarchy (starting from a single unit, continuing by groups formed by units and clusters formed bygroups ) different mathematical models are formulated. Thus by combining these models,a unified model is supposed to be obtained. A hierarchical model is achieved by a setof hierarchical regression equations. Educational research often depends on multivariatetechniques like confirmatory factor analysis and other covariance structure techniques tostudy dimensions of systematic variation in student data. In this study, we concentrateon the issue of assessing the factor structure of a construct at aggregate levels of analysis.We use a procedure for performing multilevel confirmatory factor analysis. This proce-dure is developed recently and described by Dyer(2005) The empirical part of this studyis based on the data obtained for TUBITAK (The Scientific and Technological ResearchCouncil of Turkey) within the context of the survey on the statistics education in Turkeyin 2007. Here, the universities, statistics departments, even some statistics courses cor-respond to different levels in multilevel modeling. Our sample contains approximately2000 students ( and their answers to the questionnaire about their appreciation on thestatistics program they follow) present in the statistics departments in Turkey. Thereare 25 statistics programs and within each program there are four classes (levels) inwhich the judgements of students might show variability. Here our data show a nestedor hierarchical structure of students within classes, within schools, in school districts.

∗This paper is dedicated to our advisors.


133

Stabilized FEM Solution of Steady Natural Convection Flowin a Square Cavity

Selcuk Han Aydin


Middle East Technical University, Institute of Applied Mathematics Inonu Bulvari 06531Ankara - Turkey

(Joint work with: M. Tezer Sezgin)

Abstract: The present numerical study deals with the stabilized finite element solutionof the steady natural convection flow in a square cavity in terms of primitive variables.Linear triangular elements are used for the velocities, pressure and temperature, andthe solutions are obtained for high values of Rayleigh number (Ra) (104 ≤ Ra ≤ 106).The finite element method of SUPG type enables to obtain stable solution and avoidsoscillations especially in the pressure.


134

Investigation of Large Eddy Simulation and Eddy-ViscosityTurbulence Models Applicable to Film Cooling Technique

Hanieh Khalili Param

email: h [email protected]

Department of Mechanical EngineeringIran University of Science and Technology

Tehran 16846-13114, Iran

(Joint work with: F. Bazdidi)

Abstract: One of the most effective means of achieving a higher thermal efficiency ingas turbine engines is to increase the turbine inlet temperature provided that the turbineblades are protected from such elevated temperatures. One of the most efficient tech-niques to achieve this goal is film cooling, where the coolant air bled from the compressoris conducted into channels in the turbine blades and injected at an angle through rowsof holes drilled on the blades. This provides a thin and cool protecting layer (film) alongthe external surface of the blade. The aim of the present work is to investigate the abil-ity and accuracy of different turbulence models for the prediction of flow field and alsoto study the effect of blowing ratio (M=0.5 and 1) on the flow field. For this purpose,the interaction between a three dimensional inclined injected jet (angle, ?=30?) and thecross-flow is simulated employing different two-equation eddy-viscosity turbulence mod-els (k-?/SST and k-?) based on time-averaging, and the large eddy simulation (LES)approach. In the latter, the governing equations include the filtered time dependentNavier-Stokes equations under the conditions of incompressible and constant properties.In the LES approach, the filtering of equations is obtained by using the convolution inte-gration with the filter function. The filter function is considered as 1/V, where V is thevolume of a computational cell. The present numerical simulation is based on the use ofthe finite volume method, applying the unsteady PISO algorithm to a multi-block andnon-uniform computational grid. The spatial discretization consists of bounded centraldifferencing scheme. The time integration is performed by a second-order fully implicitscheme. Present results show that the predictions of the LES approach are in betteragreement with the available experimental data than those of the two-equation eddy-viscosity turbulence models. Also, an increase in the blowing ratio leads to a strongerpenetration of the jet into the cross flow, resulting in a more upstream located andstronger Counter-rotating Vortex Pairs (CVP).


135

Transonic problems in multi-dimensional conservation laws

Eun Heui Kim


California State University Long BeachDepartment of Mathematics and Statistics, 1250 Bellflower Blvd, Long Beach

CA 90840-1001, USA

(Joint work with: C. Lee, B. Englert)

Abstract: Many practical problems in science and engineering, for example in aero-dynamics, multi-phase flow and hemodynamics, involve conserved quantities, and leadto partial differential equations in the form of conservation laws. Understanding themathematical structure of these equations and their solutions is essential to obtain phys-ical insight into such practical problems. There are special difficulties associated (e.g.shock formation) with these equations that are not seen elsewhere and must be dealtwith carefully. Moreover, in multidimensional conservation laws, there is little theory atpresent. One approach, the study of self-similar solutions, leads to the study of equa-tions that change their type, namely, equations that are hyperbolic far from the originand mixed near the origin. Some results have been obtained recently in this area, butthere are still many open problems. We present recent results in transonic problems inmultidimensional conservation laws.


136

Session 4.4: Mathematical Programming III

Chair: Herman MawengkangPlace: Hall 4


137

Modified iteration methods to solve system Ax = b

Masoud Allame


Department of MathematicsIslamic Azad University

Khorasgan, Isfahan - IranP.O.Box 81595-158

(Joint work with: B. Vatankhahan, S. Abbasbandy)

Abstract: A new method for solving linear systems is derived. It can be considered as amodification of the coefficient matrix,A, and then apply Jacobi or Gauss-Seidel iterationmethods or any iteration methods.


138

A Multi-Objective Mixed Integer Programming Model forMulti Echelon Supply Chain Network Design and

Optimization

Eren Ozceylan



(Joint work with: T. Paksoy)

Abstract: Minimizing total costs is a traditional objective of a supply chain managementto answer customers demand. These total costs especially consist of inbound-outboundtransportation costs, production and distribution costs, facility investments costs, inven-tory holding and backorder costs, raw material or semi product costs and etc. This paperapplies a mixed integer linear programming to designing a multi echelon supply chainnetwork (SCN) via optimizing commodity transportation and distribution of SCN. Pro-posed model attempts to aim multi objectives of SCN by considering total transportationcosts and capacities of all echelons. The model composed of three different objective func-tions. The first one is minimizing the total transportation costs between all echelons andfixed costs of potential suppliers, manufacturers, distribution centers (DCs) and retailers.Second one is maximizing DCs service level in allowable terms to meet retailers demandand the last objective function is minimizing the unnecessary and unused capacity ofplants and DCs via decreasing variance of transported amounts between echelons. Fi-nally, in order to prove the validity of the proposed model, a numerical example is solvedand conclusions are discussed.


139

Effect of Floating Point Aritmetic on Monodromy MatrixComputation of Periodic Linear Difference Equation System

Ali Osman Cibikdiken


Selcuk University, Kadinhani Faik Icil MYO, Department of Computer Technologies andProgramming Konya - Turkey

(Joint work with: Kemal Aydin)

Abstract: It is important to determine that problem is well-conditioned or ill-conditioned in scientific computing. The computations in computer are done with floatingpoint arithmetics. The errors of computations in computer are unavoidable. Therefore,the floating point arithmetics effects to determine that the problem is well-conditionedor ill-conditioned. Let A(n) be a matrix of dimension N×N with period T and considerthe difference equation system

x(n + 1) = A(n)x(n), n ∈ Z (1)

With X(T ) being the monodromy matrix of the system (1), Schur stability of the system(1) is related to the results of computation errors on computation of the monodromymatrix X(T ). In this study, the effect of floating point on computation of the monodromymatrix X(T ) is investigated. The bounds are obtained for || X(T )−Y (T ) || in whichthe matrix Y (T ) is the computed value of the monodromy matrix.


140

Ranking Decision Making Units with Stochastic Data byUsing Coefficient of Variation

Mohammad Hassan Behzadi


Department of StatisticsScience and Research Branch


(Joint work with: F. Hosseinzadeh Lotfi, N. Nematollahi, M. Mirbolouki )

Abstract:Data Envelopment Analysis (DEA) is a non-parametric technique which isbased on mathematical programming for evaluating the efficiency of a set of DecisionMaking Units (DMUs). Throughout applications, managers encounter with stochasticdata and the necessity of having a method that is able to evaluate efficiency and rankefficient units has been under consideration. In this paper considering the purport ofcoefficient of variation among efficient DMUs, two ranking methods has been proposed.Within these ranking methods, a DMU will have a higher rank if it’s coefficient ofvariation be smaller. These methods are suitable when managers are able to determineweights on coefficient of variations or on inputs and outputs. At the end we applied thesemethods on a numerical example.keywords: Coefficient of variation, Data envelopment analysis, Ranking.


141

Application of Advanced Machine Learning Methods ForSNP Discovery in Complex Disease Association Studies

Gurkan Ustunkar


Middle East Technical University, Institute of Applied MathematicsAnkara-Turkey

(Joint work with: S. Ozogur-Akyuz, U. Sezerman, G. W. Weber, N. Baykal)

Abstract: Single nucleotide polymorphisms ( SNPs) are DNA sequence variations thatoccur when a single nucleotide (A,T,C,or G) in the genome sequence is altered. SNPsand other less common sequence variants are the ultimate basis for genetic differencesamong individuals, and thus the basis for most genetic contributions to disease. To makegood use of SNPs for finding genes related to disease and studying their function, betterand cheaper technological methods are needed for discovering SNPs. There is also a needfor adequate algorithms and models for reducing biological and statistical redundancyfrom thousands of SNPs and ?nding an optimal set of SNPs associated with commoncomplex diseases. However, the efficacy of searching for an optimal set of SNPs has notbeen as successful as expected in theory. One primary cause is the high dimensionalitywith highly correlated features/SNPs that can hinder the power of the identi?cation ofsmall to moderate genetic effects in complex diseases. As in many other Bioinformaticsapplications (such as sequence analysis, microarray analysis, mass spectra analysis etc.),use of feature selection techniques is an apparent need to tackle this problem. Severalcomputational methods for Feature Selection have been proposed in the literature andstudies can be grouped into three categories: filtering, wrapper, and embedded. Thesethree methods would perform differently when applied to categorical SNP data ratherthan continuous gene expression data, so there has been a need for categorical SNPdata reduction methods. Among those methods, the most promising ones are supervisedmodels. In this study, we apply various supervised feature selection methods to SNP-disease association data and compare the results. Among those methods are decisiontree, multiple regression, subgroup discovery and a recently proposed novel method forclassification of heterogeneous data called Infinite Kernel Learning (IKL), which makesuse of infinite kernel combinations with the help of infinite and semi-infinite programmingregarding all elements in kernel space. Finally, to evaluate the performance of the learningmethods we calculated a special type of statistic called ROC AUC (Receiver OperatingCharacteristic Area Under Curve).


142

An Efficient Computational Method for Non-Stationary(R, S) Inventory Policy with Service Level Constraints

Ulas Ozen


Alcatel-Lucent, Blanchardstown Industrial Park, Dublin 15, Dublin - Ireland

(Joint work with: S. A. Tarim, M. K. Dogru, R. Rossi)

Abstract: This paper provides an efficient computational approach to solve the mixedinteger programming (MIP) model developed by Tarim and Kingsman (2004) for calcu-lating the parameters of an (R, S) policy in a finite horizon with non-stationary stochasticdemand and service level constraints. Given the replenishment periods, we characterizethe optimal order-up-to levels for the MIP model and use it to guide the developmentof a relaxed MIP model, which can be solved in polynomial time. The effectiveness ofthe proposed method hinges on three novelties: (i) the proposed relaxation is computa-tionally efficient and yields an optimal solution most of the time, (ii) if the relaxationproduces an infeasible solution, this solution can be used as a tight lower bound, and also(iii) this infeasible solution can be modified easily to obtain a feasible solution, which isan upper bound for the optimal solution. In case of infeasibility, the relaxation approachis implemented at each node of the search tree in a simple branch-and-bound procedureto efficiently search for an optimal solution. Extensive numerical tests show that ourmethod dominates the MIP solution approach and can handle real-life size problems intrivial time.


143

Session 4.5: Statistics and Data Analysis II

Chair: Fatih TankPlace: Hall 5


144

A Comprehensive Kansei Engineering Algorithm: Anapplication of the university web page design

Senol Erdogmus


Eskihehir Osmangazi UniversitesiFen-Edebiyat Fakltesi F1 blok Istatistik Bolumu no:110

Turkey

(Joint work with: E. Koc, S. Ayhan)

Abstract: In this study, a comprehensive Kansei engineering (KA) algorithm was pro-posed to solve the web page design problem. It reveals users’ perceptions and feelingsand analyzes them using many statistical techniques. The algorithm was implementedto the university web page. The web page’s design components and their design goalsinfluencing the quality feeling in users were analyzed with conjoint and ordinal regressionanalysis. Consequently, this study provides more customer-oriented methodology in webdesign


145

A JAVA Program for the Multivariate Zp and Cp Tests andIts Application

Guvenc Arslan


Baskent University,Balca Campus, Department of Statistics and Computer Sciences

06810 Ankara - Turkey

(Joint work with: I. Ozmen, B.O. Turkoglu)

Abstract: The multivariate normality assumption is used in many multivariate sta-tistical analyses. It is, therefore, important to assess the validity of this assumption.Unfortunately the application of multivariate normality tests is still limited in manysoftware packages. The aim of this study is to develop a JAVA program for applica-tion of the and test statistics introduced by Src (2006). In addition, application of theprogram on some real data sets is presented.


146

Smoothing the Covariance Based on Functional PrincipalComponent Analysis

Ovgu Cidar



Turkey

(Joint work with: Y. Tandogdu)

Abstract: Functional Principal Component Analysis (FPCA) is an important field in theestimation problems. Determination of dominant elements of variation around an overallmean trend function is sought. Data comes from n random trajectories or subjects.They are mainly sparse in nature, time or space dependent. In this context computationof the covariance matrix from available sample data and its smoothing forms one ofthe major corner stones of a FPCA study. Sparse functional data from many differenttrajectories are assumed to be independent realizations of a smooth random functionwith mean function µ(t) and covariance function C(s, t). The orthogonal expansion of thecovariance in L2 is C(s, t) =

∑k λkφk(s)φk(t). A trajectory can be expressed as Xi(t) =

µ(t) +∑

k ξikφk(t). Mean, covariance and eigenfunctions are required to be smooth.Functional principal component (FPC) scores ξik plays a major role in the estimationof a trajectory. They are uncorrelated random variables with a mean zero and their

variances being the eigenvalues of C(s, t). Estimator of ξik is ξik = λkφTik

∑−1

Yi(Yi −µi),

where∑

Yi= cov(Yi, Yi) and Yi is the data matrix. Number of data values on the ith

subject is Ni. Ni are assumed to be i.i.d. random variables. Observations will inherentlyinclude some measurement errors εi that are also assumed to be i.i.d. with E(εij) = 0and constant variance σ2.Different methods are suggested by various researchers forsmoothing the covariance matrix. The approach taken in this study is to check thecovariance data for normality and apply c standard deviations interval to the covariancevalues by shrinking the those outside the interval to the limit values of the interval.

References

1. F. Yao, H. G. Muller, J. L. Wang; Functional Data Analysis for Sparse LongitudinalData. J of Amarican Statistical Association. 100, pp. 577-590, 2005

2. H. G. Muller; Functional Modelling and Classification of Longitudinal Data. Scandina-vian Journa of Statistics, 32, pp.223-240, 2005

3. P. Hall, H. G. Muller, J. L. Wang, Properties of Principal Component Methods forFunctional and Longitudinal Data Analysis, The Annals of Statistics, 34, pp. 1493-1517, 2006.


147

Functional Predictor and Response Variables UnderNon-Gaussian Conditions

Yucel Tandogdu



Turkey

Abstract: Generalization of the classical linear regression model E(Y | X) = β0 + β1Xby introducing the functional linear regression concept E[Y (t) | X] = µY (t) +∫= β(s, t)Xc(s)ds enables the prediction of the response trajectory from the available

sparse data. The slope parameter β1 in the linear multivariate regression, becomes theregression function β(s, t) in the functional case. Estimation of β(s, t) involves the esti-mation of the functional principal component scores ζ and ξ belonging to the predictorX and response Y functions respectively. Prediction of the response function throughconditional expectation is obtained as

E[Y ∗(t) | X∗] = µY (t) +∞∑

k=1

∞∑

m=1

σkm

ρmζ∗mφk(t)

Estimation of the functional principal component scores ζ∗m for the predictor X∗ is cru-cial and necessitates the Gaussian assumption to be introduced. However, encounteringthe the non-Gaussian behavior in the process under study, renders the introduced the-ory inappropriate to the envisaged methodology. The study of the non-Gaussian caseis considered. For the unimodal left or right skewed distributions an appropriate trans-formation to Gaussian case will suffice to use the theory under Gaussian assumption.Following the estimation process, the estimated values should be back transformed tothe initial distribution of the predictor. It must be pointed out that the response functionY does not necessarily have to follow the same distribution as the predictor X.

References

1. S. Nadarajah, Some Truncated Distributions. Acta Appl. Math. 106, pp. 105-123, 2009.2. F. Yao, H. G. Muller, J. L. Wang, Functional Linear Regression Analysis for Longitu-

dinal Data. The Annals of Statistics, 33,6, pp 2873-2903, 2005.3. G. He, H. G. Muller, J. L. Wang, Extending Correlation and Regression from Multi-

variate to Functional Data. Asymp. in Stat & Prob. M.L. Puri Ed. pp. 1-14, 2000.


148

Exponential-Negative Binomial Distribution

Mustafa Cagatay Korkmaz


Artvin-Coruh University Science and Arts Faculty, Department of Statistics, Artvin - Turkey

(Joint work with: Coskun Kus, Asir Genc)

Abstract: Some probability distributions have been proposed to fit real life data withdecreasing failure rates. In this article, a three-parameter distribution with decreasingfailure rate is introduced by mixing exponential and negative-binomial distributions.Various properties of the introduced distribution are discussed. An EM algorithm isused to determine the maximum likelihood estimates when one parameter is given orknown. Illustrative examples based on real data are also given.


149

Soft Set Theory for Maximal Association Rules Mining

Tutut Herawan


Universiti Tun Hussein Onn MalaysiaParit Raja, Batu Pahat 86400, Johor

Malaysia

(Joint work with: Mustafa Mat Deris)

Abstract: Maximal association rule introduced by Feldman in 1997 is to inspired fromthe fact that many interesting rules in datasets cannot captured by regular rules. It isbased on frequent maximal itemsets which appear maximally in many records. In thispaper, a new approach for maximal association rules mining from a transactional datasetunder soft set theory is proposed. The proposed approach is based on representation of atransactional dataset as ”standard” soft set. Using the notion of items co-occurrence, anotion of soft maximal frequent itemsets can be defined. Furthermore, definitions of softmaximal association rules, maximal support and maximal confidence are presented. Forcomparison tests, firstly, the proposed approach is elaborated through a benchmark dataset for text categorization from Reuters-21578. The results show that the captured max-imal rules are identical with traditional and rough maximal association rules. Secondly,from a data set of air pollution in Kuala Lumpur Malaysia on July 2002, the resultsshow that soft maximal association rule approach outperformed the previous approachesin capturing rules up to 87% and 50%, respectively.


150


PARALLEL SESSIONS 5

2 October 2009, 09:00-10:30



153

Session 5.1: Mathematical and Computational Finance

Chair: Jan DhaenePlace: Hall 1


154

Approximations for Optimal Portfolio Selection Problems

Koen Van Weert


Katholieke Universiteit LeuvenDepartment of Accountancy, Finance and Insurance Naamsestraat 69 3000 Leuven

Belgium

(Joint work with: J. Dhaene, M. Goovaerts)

Abstract: In Dhaene et al. (2005), multiperiod portfolio selection problems are dis-cussed, using an analytical approach to find optimal constant mix investment strategiesin a provisioning or savings context. In this paper we extend some of these results, investi-gating some specific, real-life situations. First, we generalize portfolio selection problemsto the case where a minimal return requirement is imposed. We derive an intuitive for-mula that can be used as a constraint on the admissible investment portfolios, in order toguarantee a minimal annualized return. Determining the distribution function of a sum

of random variables, describing a series of future payments, is important when solvingseveral problems in a general insurance or finance context. In this paper we extend thesolution of Vanduffel et al. (2005) allowing for more arbitrary cash flows patterns. In thefinal section we investigate the so-called flashing light reserve. In our analytical frame-work, we derive convex bounds that can be used to estimate this additional provision,and related probability levels. We always apply our results to optimal portfolio selection.


155

A Classification Problem of Credit Risk Rating Investigatedand Solved by Optimization of the ROC Curve




(Joint work with: Kasirga Yildirak, Efsun Kurum)

Abstract: The estimation of probability of default has considerable importance in riskmanagement applications where default risk usually is referred to as credit risk. Forthis reason, Basel II (Committee on Banking Supervision) proposes a revision to theinternational capital accord that implies a more prominent role for internal credit riskassessments based on the determination of the probability of default of a borrower orgroup of borrowers. In our study, we try to classify borrower firms, which are in the creditinstitutes credit pool, into rating classes with respect to their probability of default.The task of classification of firms into rating classes necessitates the finding of cut-offvalues, which separate each rating class from the others. In other words, we actuallyaim at solving two problems. The first one is to distinguish the defaults from non-defaults, and the second problem is to put non-default firms in an order based on theircredit quality and classify them into sub-rating classes. For using a model to obtain theprobability of default of each firm, ROC (Receiver Operating Characteristics) analysisis employed to assess the distinction power of our model about the default and thenon-default population. In our research, we optimize the ROC curve and to make abalanced choice of the thresholds. We also discuss and include accuracy of the modelinto our optimization problem. Therefore, a constrained optimization problem on thearea under the curve (or its complement) is carefully modelled, discretized and turnedto a penalized sum-of-squares problem of nonlinear regression. For this purpose, thealgorithms of Gauss-Newton and Levenberg-Marquardt become presented and appliedwith a stepwise solving of a regularized linear problem in order to find the iteration steps.Here, Tikhonov regularization and Conic Quadratic Programming will be proposed, too.We shall introduce to the data use, present numerical computations and interpret them.We conclude with a discussion of the structural frontiers and an outlook.


156

Structuring Pension Funds Optimally

Muhammed-Shahid Ebrahim


Financial Economics Nottingham University Business SchoolJubilee Campus, Wollaton Road Nottingham NG8 1BB

United Kingdom

(Joint work with: Ike Mathur)

Abstract: This paper studies pension fund design in the context of investment in thedebt and equity of a firm. We employ a general equilibrium framework to demonstratethat (i) the asset location puzzle is purely a risk neutral phenomenon that disappears withthe introduction of sufficient risk aversion, (ii) the inability of policy makers to managean economy with multiple firms yields a mixed equilibrium, where bonds are observedin both taxable and tax-deferred accounts, and (iii) the pareto-efficiency of DefinedBenefit plans over Defined Contribution plans is contingent on the relative administrativeexpenses and the ability to optimally define payout policy.


157

Multi-class classification algorithms based on polyhedralconic functions and application to companies listed on the

Istanbul Stock Exchange

Refail Kasimbeyli


Department of Industrial Systems EngineeringIzmir University of Economics

Balcova - IzmirTurkey

(Joint work with: G. Ozturk, O. Ustun)

Abstract: The problems of supervised data classification arise in many areas includingfinancial sector, management sciences, medicine, chemistry and so on. The aim of super-vised data classification is to establish rules for the classification of some observationsassuming that the classes of data are known. To find these rules, known training sub-sets of the given classes are used. During the last decades, many algorithms have beenproposed and studied to solve data classification problems. These algorithms are mainlybased on mathematical programming, statistical, machine learning, and neural networkapproaches. One of the promising approaches to data classification problems is based onmathematical programming techniques. There are two main approaches to apply mathe-matical programming techniques for solving supervised data classification problems. Thefirst approach is an outer approach which is based on the separation of the given trainingsets by means of a certain function. The second approach is an inner approach. In thisapproach, the given training sets are approximated by cluster centers. The new datavectors are assigned to the closest cluster and correspondingly to the set that containsthis cluster. In this paper we use the polyhedral conic functions and develop new classifi-cation methods based on an outer approach for the problem of discriminating real-worlddatasets with several classes. Given examples of points known to come from two or moreclasses, we construct a function (or functions) to discriminate between the classes. Theseclassification techniques are used to classify companies from Istanbul Stock Exchangewith respect to their credibility ratings. The feature vectors of companies are obtainedusing information from balance-sheets such as financial ratios, asset returns and so on,for the time period between 2001 and 2007 years. All these features are collected to ageneral data set. The decision support system developed, allows users to form differentdata sets, by selecting different financial ratios from the general set and thus to obtain,solve and analyze different classification problems.


158

Session 5.2: Cryptography

Chair: Ersan AkyildizPlace: Hall 2


159

Efficient Multiplications in F55n and F77n

Ferruh Ozbudak



(Joint work with: M. Cenk)

Abstract: Finite field multiplication plays an important role in the implementation ofelliptic curve cryptography and pairing based cryptography. Recently efficient multipli-cations in F55n and F77n are used for computing the Eta paring over divisor class groupsof the hyperelliptic curves y2 = xp − x + d where p is an odd prime1 in which Karat-suba type multiplications2,3 are used. Let µq(m) denote the minimum number of Fq

multiplications in order to multiply two arbitrary elements of Fqm . Karatsuba type mul-tiplications imply only µ5n (5) ≤ 15 and µ7n (7) ≤ 24. However there are more efficientmethods improving the bounds on µq(m). For example, recently we have shown thatone can obtain an explicit formula for multiplication in F55n with µ5n (5) ≤ 11 in.4,5 Inthis paper, using the recent methods for multiplication in Fqm (see,6–10) giving the bestknown bounds on µq(m) for certain values of q and m, we obtain improved values forthe explicit formulas for multiplication in F55n and F77n . For example we get explicitformulas giving µ5n (5) ≤ 10 and µ7n (7) ≤ 15, which also improve the correspondingresult in.4,5 In particular these give much more efficient eta pairing computations thanthe ones in.1 We also give timing results of implementations of Karatsuba type formulasand proposed formulas for multiplication in F55n and F77n for comparison.

References

1. E. Lee, H. Lee, and Y. Lee. Eta pairing computation on general divisors over hyper-elliptic curves y2 = xp − x + d. Journal of Symbolic Computation, (43), 452 - 474,(2008).

2. A. Karatsuba, and Y. Ofman. Multiplication of multidigit numbers by automata. SovietPhysics-Doklady, (7). 595-596, 1963.

3. A. Weimerskirch, and C. Paar. Generalizations of the Karatsuba algorithm for polyno-mial multiplication. Avaliable: http://eprint.iacr.org/2006/224.

4. M. Cenk, and F. Ozbudak. Efficient multiplication in finite fields of characteristic 3 and5 for pairing based cryptography. 3rd Information Security and Cryptology Conference,2008, Ankara, pp. 111-114.

5. M. Cenk, C. K. Koc, and F. Ozbudak. Polynomial multiplication over finite fields usingfield extensions and interpolation. Proceedings, 19th IEEE Symposium on ComputerArithmetic, Portland, Oregon, June 8-10, 2009, to appear.

6. N. Arnaud, Evaluation Derivee, Multiplication dans les Corps finis et codes correcteurs,Ph.D. dissertation, Universite de la Mediterranee, France, 2006.


160

7. S. Ballet, On the tensor rank of the multiplication in the finite fields, Journal of NumberTheory 128 (2008), 1795-1806.

8. M. Cenk, and F. Ozbudak. Efficient multiplication in F3`m , m ≥ 1 and 5 ≤ ` ≤ 18. InAfricacrypt 2008 volume 5023 of Lecture Notes in Computer Science, 406-414, Springer- Verlag.

9. M. Cenk, and F. Ozbudak. Improved polynomial multiplication formulae over F2 us-ing Chinese Remainder Theorem. IEEE Transactions on Computers, 58(4), 572 -576,(2009).

10. M. Cenk, and F. Ozbudak. On Multiplication in Finite Fields, submitted, 2009.


161

On the elliptic curves y2 = x3 − c with embedding degree one

Baris Bulent Kirlar



Abstract: In recent years, there has been many works dealing with pairing-based cryp-tography. In particular, elliptic curves with small embedding degree and large prime-order subgroup have a great interest to implement pairing-based cryptographic systems.Although many papers have proposed families of elliptic curves with embedding degreek ≥ 2, there are few papers related to the families with embedding degree k = 1. Koblitzand Menezes give a detailed work for some family of curves of the form y2 = x3 − dxwith embedding degree k = 1.

In this paper, we give further examples of elliptic curves in the form y2 = x3−c withembedding degree k = 1. This was done by first computing the number of points Np ofthe elliptic curve y2 = x3− c over the finite field Fp. We note that it was already knownNp = p + 1 + χ2(−c)

[χ3(c)J(χ2, χ3) + χ3(c)2J(χ2, χ2

3)], where χ2, χ3 are quadratic

and cubic multiplicative characters of Fp, respectively, and J(χ2, χi3) is the Jacobi sum

for i = 1, 2. Our contribution here is to compute the right hand side of this identityto obtain an explicit formula for Np. Then, using this description we give examples ofcurves y2 = x3 − c over Fp with Np = p− 1.


162

On the basis number of the lexicographic product of twographs and some related problems

Mohammed Mahmoud Jaradat


Qatar UniversityDepartment of Mathematics, Statistics and Physics

P.O.Box 2713 Doha-Qatar

Abstract: For a given graph G, the set E of all subsets of E(G) forms an |E(G)|-dimensional vector space over Z2 with vector addition XY = (XnY )[(Y nX) and scalarmultiplication 1:X = X and 0:X = ; for all X; Y 2 E. The cycle space, C(G), of a graphG is the vector subspace of (E; ; :) spanned by the cycles of G: Traditionally there havebeen two notions of minimality among bases of C(G). First, a basis B of G is called ad-fold if each edge of G occurs in at most d cycles of the basis B. The basis number, b(G),of G is the least non-negative integer d such that C(G) has a d-fold basis; a requiredbasis of C(G) is a basis for which each edge of G belongs to at most b(G) elements ofB. Second, a basis B is called a minimum cycle basis (MCB) if its total length PB2BjBj is minimum among all bases of C(G). The lexicographic product G[H] has the vertexset V (G H) = V (G) V (H) and the edge set E(G[H]) = f(u1; v1)(u2; v2)ju1 = u2 andv1v2 2 H; or u1u2 2 Gg. In this work, we give an upper bound of the basis number forthe lexicographic product of two graphs. Moreover, in a related problem, we construct aminimum cycle bases for lexicographic product of the same.


163

Global Optimization In Practice

Janos D. Pinter


Department of Industrial EngineeringOzyegin UniversityIstanbul - Turkey

(Joint work with: Frank J. Kampas)

Abstract: Mathematica (www.wolfram.com) is a well-recognized integrated scientificand technical computing system. The MathOptimizer software package, developed bythe authors, serves to solve numerically a wide range of nonlinear optimization problems.In principle, all continuous Mathematica functions can become a model component (ob-jective or constraint) function. We discuss MathOptimizer’s key features and illustrateits use to handle simple, more advanced, and non-standard optimization problems.


164

Session 5.3: Differential equations II

Chair: Josep ArnalPlace: Hall 3


165

Exponential Runge–Kutta methods for option pricing injump-diffusion models

Muhammad Asif Gondal


University of InnsbruckDepartment of Mathematics, Technikerstr. 13/7, A-6020, Innsbruck

AUSTRIA

(Joint work with: A. Ostermann)

Abstract: In this paper, we consider exponential Runge–Kutta methods for the numer-ical pricing of options. The methods are shown to be an alternative to other existingprocedures for the numerical valuation of jump-diffusion models. We show that expo-nential Runge–Kutta methods give unconditional second order accuracy for up-and-outBarrier options under Black–Scholes geometric Brownian motion model and Merton’sjump-diffusion model with constant coefficients. Exponential integrators have good sta-bility properties. These integrators are fully explicit and do not require the numericalsolution of linear systems as in contrast to standard integrators. On the other hand,exponential integrators require the evaluation of the exponential and related functionsof the Jacobian matrix. Finally, the performance of the proposed methods is illustratedthrough some numerical experiments.


166

Discrete First-Order Four-Point Boundary Value Problem

Mesliza Mohamed


Jabatan Matematik, Universiti Teknologi MARA, Kampus Arau 02600 Arau, PerlisMalaysia

(Joint work with: M. Jusoh)

Abstract: We establish existence results for solutions to four-point boundary valueproblems for systems of first-order difference equations associated with systems of first-order ordinary differential equations.


167

The Solution of the Bagley-Torvik Equation with theGeneralized Taylor Collocation Method

Yucel Cenesiz

[email protected]

Selcuk University, Science Faculty, Math Department, Kampus/Konya - TURKEY

(Joint work with: Y. Keskin, A. Kurnaz)

Abstract:In this paper, the Bagley-Torvik equation which has an important role infractional calculus is solved by generalizing the Taylor Collocation Method. The pro-posed method has a new algorithm for solving fractional differential equations. This newmethod has many advantages over variety of numerical approximations for solving frac-tional differential equations. To assess the effectiveness and preciseness of the method,results are compared with other numerical approaches.


168

Jensen divergence based on Fisher’s information

Yoji Otani


Departamento de Matematica Aplicada Facultad de Ciencias Avenida de Fuentenueva, S/N18071 - Granada - SPAIN

(Joint work with: A. Zarzo, J.S. Dehesa)

Abstract: During the last years the Jensen-Shannon divergence between two or morearbitrary probability densities has been used in numerous mathematical and physicalcontexts. This relative information measure, in contrast to the Kullback-Leibler entropyor relative Shannon entropy, presents three important characteristics: symmetry underexchange of the involved densities, applicability to more than two densities, and finitenesseven in the case that the involved densities have non-common zeros. In this paper weintroduce a Jensen divergence based on the Fisher information. The Fisher information,in contrast to the Shannon entropy, is an information measure with a local character,providing a measure of the gradient and oscillatory content of the density. The newJensen-Fisher divergence enjoys the same properties as the Jensen-Shannon divergence;namely, non-negativity, additivity when applied to an arbitrary number of probabilitydensities, symmetry under exchange of these densities, vanishing if and only if all thedensities are equal, and definiteness when these densities present non-common zeros.Moreover,the Jensen-Fisher divergence can be expressed in terms of the relative Fisherinformation as the Jensen-Shannon divergence does in terms of the Kullback-Leiblerentropy. It is remarkable that the last property is only shared by these two divergences,in contrast with the recently introduced Jensen-Renyi and Jensen-Tsallis divergences.Here we present the theoretical grounds of the Jensen-Fisher divergence. We apply it toseveral families of probability densities (including the Rakhmanov densities associated tothe classical families of orthogonal polynomials). Finally, a comparison with the Jensen-Shannon divergence and the relative Fisher information is performed.


169

Session 5.4: Numerical Linear Algebra II

Chair: Serkan EryilmazPlace: Hall 4


170

On the Modification of an Eigenvalue Problem thatPreserves an Eigenspace

Maxim Naumov


Department of Computer Science 305 N. University Street West Lafayette, IN 47907-2107USA

(Joint work with: A. Bourchtein)

Abstract: Eigenvalue problems arise in many application areas ranging from computa-tional fluid dynamics to information retrieval. In these fields we are often interested inonly a few eigenvalues and corresponding eigenvectors of a sparse matrix. In this talk, wecomment on the modifications of the eigenvalue problem that can simplify the computa-tion of those eigenpairs. These transformations allow us to avoid difficulties associatedwith non-Hermitian eigenvalue problems, such as the lack of reliable non-Hermitian eigen-value solvers, by mapping them into generalized Hermitian eigenvalue problems. Also,they allow us to expose and explore parallelism. They require knowledge of a selectedeigenvalue and preserve its eigenspace. The positive definiteness of the Hermitian partis inherited by the matrices in the generalized Hermitian eigenvalue problem. The posi-tion of the selected eigenspace in the ordering of the eigenvalues is also preserved undercertain conditions. The effect of using approximate eigenvalues in the transformation isanalyzed and numerical experiments are presented.


171

A Variational Algorithm of the GPBi-CG Method forSolving Linear Systems

Kuniyoshi Abe


Faculty of Economics and Information, Gifu Shotoku University1-38, Nakauzura, Gifu 500-8288

JAPAN

(Joint work with: G. L. G. Sleijpen)

Abstract: We treat Krylov subspace methods for solving a large sparse linear systemAx = b, where A stand for an n-by-n matrix, and x and b are n-vectors, respectively.The Bi-Conjugate Gradient (Bi-CG) method is a well-known Krylov subspace method forsolving this problem, and several hybrid BiCG methods such as the Bi-CG STABilized(BiCGSTAB) method, the BiCGStab2 method, the Generalized Product-type methodderived from Bi-CG (GPBi-CG) and the BiCGstab(l) method have been developed toimprove the convergence. The residual polynomials of the hybrid BiCG methods areexpressed by the product of the Lanczos polynomial and another polynomial Pn of degreen with Pn(0) = 1. The polynomial Pn of GPBi-CG has been built up by a pair of coupledtwo-term recurrence formulas. According to our studies, the residual norm of GPBi-CGdoes not converge on a problem, where those of BiCGStab2 and BiCGstab(2) converge.In other words, it appears that the recurrence formulas of the original GPBi-CG may beunstable.

Therefore, we propose an alternative algorithm of GPBi-CG to improve the con-vergence of the classical GPBi-CG method. The recurrence formulas of the variant ofGPBi-CG can be redesigned by coupling those of Bi-CG and the three-term recurrenceformula which is similar to the Lanczos polynomial but has different recurrence co-efficients from one. That is, the approximate solution and the residual vector in thealternative algorithm are updated by the different recurrence formulas from those of theoriginal GPBi-CG method. Numerical experiments show that our proposed GPBi-CGvariant is more effective and less affected by rounding errors than the classical GPBi-CGmethod.


172

Fully fuzzy linear system: New point of view

Soheil Salahshour


Department of Mathematics, Science and Research BranchIslamic Azad University

Tehran, Iran

(Joint work with: Tofigh Allahviranloo)

Abstract: Several problems in various areas such as economics, finance, engineeringand physics boil down to the solution of a linear system of equations. In this paper, weproposed a new method to obtain a symmetric solution of fully fuzzy liner system, whichis called FFLS. To this end, we resolve 1-cut of FFLS, then some unknown symmetricspreads are allocated to each rows of 1-cut of FFLS. So, after some manipulations, originalFFLS is transformed to solving 2n linear equations to find symmetric spreads. However,our method always give us a fuzzy number vector solution. Moreover, we propose thefirst method to obtain solution of FFLS where the decision maker can be effected onthe solution such that decision maker could select the fuzzy symmetric solution of FFLSwhich is placed in the Tolerable Solution Set(TSS) or Controllable Solution Set(CSS) orUnited Set Solution(USS). Finally, some numerical examples are given to compare ourproposed solution of FFLS than the others.


173

Fuzzy Linear System: Satisfactory Level of Solution

Tofigh Allahviranloo


Department of Mathematics, Science and Research BranchIslamic Azad University

Tehran, Iran

(Joint work with: Soheil Salahshour)

Abstract: In this paper, we propose a simple and practical method to solve fuzzy linearsystem AX = b where, X and b are fuzzy triangular vectors with non-zero spreadsand the matrix A is nonsingular matrix with real coefficients. The aim of this paper istwofold. First, we try to obtain the crisp solution of fuzzy linear system. To this end, wesolve the 1-cut of fuzzy linear system. Second, we allocate a unknown symmetric spreadto any row of fuzzy linear system in 1-cut position. Thus, fuzzy linear system in 1-cut,will be transformed to a system of interval equations. The symmetric spread of eachelements of fuzzy vector solution is derived by solving such interval system. Moreover, toinvestigate the satisfactory level of obtained solution, we propose some new assay, suchthat by putting obtained solution in the original fuzzy linear system and compare withright hand side, satisfactory level of solution by proposed assay could be obtain


174

Session 5.5: Approximation and Interpolation III

Chair: Dmitri V. AlexandrovPlace: Hall 5


175

On q-Szasz–Durrmeyer Operators

Havva Kaffaoglu


Matematik Bolumu Dogu Akdeniz Universitesi Gazimagusa KKTCTurkey

(Joint work with: N. Mahmudov)

Abstract: In the present paper, we introduce the q-Szasz-Durrmeyer operators andprove approximation results for continuous functions in terms of modulus of continuity.Furthermore we study Voronovskaja type result for the q-Szasz-Durrmeyer operators.


176

Ostrowskis Fourth-order Iterative Method Solves CubicEquations of State

M. Cetin Kocak


Ankara University, Engineering FacultyChemical Engineering Department

Tandogan 06100 AnkaraTurkey

Abstract: Successful design and operation of chemical plant require in depth knowl-edge of the pertinent processes. Simulation with a mathematical model can contributeto understanding how the plant behaves under widely different conditions. Large dimen-sionality, non-linearity, and interaction among process variables notoriously characterisechemical plant models and necessitate the use of a computer in this activity. Numericalsolution techniques are harnessed very often because an analytical answer is either un-available or intractable. Numerical integration proceeds in a piecewise fashion unless anapproximate solution is wanted at a single point. Moreover, the majority of the accompa-nying algebraic equations are solved iteratively. Pressure-volume-temperature (P-V-T)data are required in simulating chemical plants because the latter usually involve pro-duction, separation, transportation, and storage of fluids. In the absence of actual exper-imental data, the model must rely on phase behavior prediction by so-called equationsof state (EOS). The van der Waals EOS is a cubic EOS as are all the transformationsand modifications that it has undergone since its publication in 1873. Ostrowski iterativetechnique is a partial-substitution variant of Newtons popular second-order method. Al-though simple and powerful, this two-point, fourth-order scheme has been utilized verylittle since its publication over forty years ago. This paper presents its application tosolve cubic equations of state which have an important role in chemical plant simulation.


177

On Bivariate Bernstein-Chlodovsky Operator

Hatice Gul Ince


Gazi University, Faculty of Sciences and ArtsDepartment of Mathematics , Teknikokullar

06500-Ankara -Turkey

(Joint work with: G. Bascanbaz Tunca, A. Erencin)

Abstract: This work relates to bivariate Bernstein-Chlodovsky operator which is nota tensor product construction. We show that the operator preserves some properties ofthe original function, for example; function of modulus of continuity, Lipschitz constant,and a kind of monotony.


178

Implicit Fully Mesh-Less Method for Compressible ViscousFlow Calculations

Yoseph Hashemi


Center of Excellence in Computational AerospaceAmirkabir University of Technology, 424 Hafez Avenue

Tehran, Iran

(Joint work with: A. Jahangirian)

Abstract: Difficulties in generating quality meshes, particularly for viscous flow sim-ulations has recently attracted much interest towards the so-called mesh-less methods.These methods only use clouds of nodes in the influence domain of every node. Thus,they dont require the nodes to be connected to form a mesh. The flow derivatives arecalculated using different approximation methods like least squares. The main purpose ofthis paper is; 1) to develop an efficient central difference mesh-less procedure for viscousflow calculations and 2) to enhance the computational efficiency of the method by adopt-ing accelerating techniques and implicit time discretization. Thus, a pseudo-time implicittime discretization scheme is applied for mesh-less calculation of the compressible vis-cous flow equations. The Taylor series least square method is used for approximation ofderivatives at each node which leads to a central difference spatial discretization. Severalconvergence acceleration techniques such as local time stepping and residual smoothingare adopted in this approach. The capabilities of the method are demonstrated by flowcomputations around single and multi-element airfoils at subsonic and transonic flowconditions. Results are presented which indicate good agreements with the reliable nu-merical finite volume and experimental data. The computational time is considerablyreduced when using the proposed mesh-less method compared with the similar explicitmesh-less and finite-volume schemes using same point distribution.

References

1. Jahangirian A., Hashemi Y., Hybrid Unstructured Cartesian Grid with Meshless Zonesfor Compressible Flow calculations, 11th ISGG Numerical Grid Conference, May 25-28, 2009, Montral, Canada.

2. Jahangirian A., Hadidoolabi M., Unstructured moving grids for implicit calculationof unsteady compressible viscous flows, International Journal for Numerical Methodsin Fluids, Vol. 47, pp. 11071113, 2005.


PARALLEL SESSIONS 6

2 October 2009, 11:00-12:30



181

Session 6.1: Applied Probability and Stochastic Processes III

Chair: Kasiraga YildirakPlace: Hall 1


182

Newsvendor Characterizations for One-WarehouseMulti-Retailer Inventory Systems with Discrete Demand

under the Balance Assumption

Mustafa Kemal Dogru


Alcatel-Lucent Bell Labs Blanchardstown Industrial Park Blanchardstown, Dublin 15Ireland

(Joint work with: G.J. van Houtum, A.G. de Kok)

Abstract: This paper considers a one-warehouse multi-retailer inventory system thatfaces discrete stochastic demand of the customers. Under the so-called balance assump-tion (also known as the allocation assumption), we extend the optimality of base stockpolicies known for continuous demand model to the discrete demand case. Our maincontribution is we show that the optimal base stock levels satisfy newsvendor character-izations, which are in terms of inequalities, and extend the newsvendor equalities knownfor the continuous demand model. These characterizations are appealing because they(i) are easy to explain to non-mathematical oriented people like managers and MBAstudents, (ii) contribute to the understanding of optimal control, (iii) help intuition de-velopment by providing direct relation between cost and optimal policy parameters.


183

Modified Maximum Likelihood Estimators for LogisticDistribution under Type-II Progressively Hybrid Censored

Data

Ismail Kinaci



Turkey

(Joint work with: Bugra Saracoglu)

Abstract: In this study, statistical inferences for Logistic parameters under progressivelyhybrid and adaptive progressively hybrid censoring are presented. In order to estimatethe unknown parameters, the maximum likelihood estimators and the modified maximumlikelihood estimators are developed. Finally, the performances of the point estimation ofthe parameters based on the two censoring methods are compared.


184

Modeling Coordination Relationships of School Communitiesto Achieve Environmental Behavior Using Influence Diagram

Azizah Hanim Nasution


Doctoral Program of Natural Resources and Environment,the University of Sumatera Utara

PSL - Kampus USU, MedanIndonesia

(Joint work with: A. Syahrin, H. Mawengkang)

Abstract: The most effective way to promote environmental behavior is through edu-cation. The communities involved in the educational system of a school can be regardedas agents. In this situation a multi agent-based approach can be used due to the envi-ronment of the sustainable school we are modeling is complex and dynamics. Thereforeit is necessarily to manage relationships among agents to achieve coordinated behavior.In the educational system each agent is allowed to choose its action based on them.In this paper we address an approach to represent coordination relationships assumingthat agents inhabit an uncertain condition. We use influence diagram to model the co-ordination relationships such that agents are able to both represent and infer how theiractivities affect other agents activities in a way to achieve the environmental behaviorobjective.


185

Testing unit root and comparison of estimates

Vilda Purutcuoglu


Middle East Technical University, Department of Statistics,06531 Ankara-TURKEY

(Joint work with: Moti L. Tiku)

Abstract:The problem of the unit root is one of the main challenges in nonstationarytime series data. Therefore there are a number of testing procedures in the literature tocheck this situation. However the drawback of these tests is that as the exact distributionof the sample autocorrelation coefficient is intractable, the estimation is implemented un-der the asymptotic distribution of that value which is based on the normality of the errorterms. Tiku and Wong (Communication in Statistics, 1998, 27(1), 185-198) propose anew test statistics for controlling unit root under simple AR(1) model when the errorshave long-tailed symmetric density which covers values from cauchy to normal. In thatwork by using a simulated data the critical point for the significance is computed fromthree moment chi-square and four-moment F approximations. The results indicate thatthe power of the new test, whose parameter is estimated via the modified maximumlikelihood method, is higher than those calculated under normality. In this study weextend this situation for skewed distributed errors like gamma and generalized logistic inAR(1) model with and without intercept terms and evaluate our results in a simulateddata in terms of power and type I error. Then we compare the performance of this newtest, whose errors are originated from both long-tailed symmetric and skewed distribu-tions, with well-known unit root tests, namely, Dickey-Fuller and Phillips-Perron tests,by applying different real data sets.


186

Session 6.2: Computational Methods in Physical and SocialSciences IV

Chair: Lucia RomaniPlace: Hall 2


187

Nonlinear Dynamics of Leads

Dmitri V. Alexandrov


Department of Mathematical PhysicsUrals state University

Lenin ave., 51, Ekaterinburg, 620083Russian Federation

(Joint work with: A.P. Malygin, I.V. Alexandrova)

Abstract: We present new analytical results relating to the growth and evolution ofsea ice. It is noteworthy that thin sea ice plays a central role in the surface heat andmass balance of the Arctic Ocean. In order to describe these balances, we analyze highlyresolved temperature data taken through the air/sea/ice interface during the transitionfrom an ice-free to an ice-covered Arctic Ocean surface. Our detailed analysis of the fielddata is based on the classical model of a mushy layer, which is modified in order to obtainanalytical solutions in explicit form (so, for example, ice thickness and growth rate, tem-perature distributions, conductive and latent heat fluxes are determined). Furthermore,we find that the sea-ice growth is not simply a square-root function of time. It dependson the temperature variations in the atmosphere and lies between two square-root func-tions of time for the maximum and minimum temperatures found during observations.The theory under consideration is in good agreement with observations.


188

An Inverse Problem of Finding Control Parameter in aParabolic Equation

Reza Zolfaghari


Department of MathematicIran University of Science and Technology

Tehran - Iran

Abstract: In this article an inverse problem concering heat equation with time de-pendent unknown control parameter is considered which plays a very important rolein many branches of science and engineering. A finite difference scheme based on theclassical backward time centred space (BTCS) implicit scheme is presented and due tothe boundary condition, the system of linear equations resulting from this scheme havea coefficient matrix that is a quasi-tridiagonal matrix. Then we estimate the unknowncoefficient by using predictor-corrector method based on energy overspecified condition.


189

Analysis of Laminar Film Boiling on a Vertical Surface Usinga Coupled Level-Set and Volume-of-Fluid Technique

Mohammad Moalemi

email: m [email protected]

Department of Mechanical EngineeringIran University of Science and Technology

Tehran 16846-13114, Iran

(Joint work with: F. Bazdidi)

Abstract: For modeling and analysis of laminar film boiling on a vertical Surface, thecoupled level-set and volume-of-fluid (CLSVOF) technique is employed. This methodcombines some of the advantages of both the volume-of-fluid (VOF) method and thelevel-set (LS) method. The coupled algorithm conserves mass and captures the interfacesvery accurately. In the present two-dimensional simulation, it is assumed that the plateis plane, smooth and vertical, at a constant temperature. Also, fluid properties in bothof the two phases are constant. The governing equations are extended in cartesian coor-dinates. Flow is laminar and transient. First of all, equations ruling the thermodynamicbehavior of laminar film boiling process on a vertical film flow have been extracted bythe CLSVOF function, leading to extended conservative equations. Then, the discretiza-tion of the extended equations has been carried out by the finite volume technique. TheConsistency of velocity and pressure field has been achieved using the transient SIMPLEalgorithm. The Nusselt number and boiling heat transfer coefficient have been investi-gated. Finally, the results obtained by the present numerical method are compared withthe other existing numerical and experimental data, showing reasonably good agreement.


190

Topological Indices of Graph Operations

Hassan Yousefi-Azari


School of MathematicsStatistics and Computer Science

University of TehranIran

(Joint work with: A.R. Ashrafi, M.H. Khalifeh)

Abstract: A topological index is a numerical quantity invariant under graph isomor-phisms. Such numbers are very important for studying molecular graphs of chemicalcompounds. In this talk four graph operations Cartesian product, join, composition andsymmetric difference are considered. An exact expression for some new topological indexfor these operations are presented.


191

Session 6.3: Quadrature and Integral Equations

Chair: Tahir KhaniyevPlace: Hall 3


192

New approach for the construction of the solutions ofCauchy integral equation of the first kind

Nik Mohd Asri Nik Long


Department of Mathematics, Faculty of Science and Institute for Mathematical ResearchUniversiti Putra Malaysia43400 Serdang, Selangor

Malaysia

(Joint work with: M. Yaghobifar, Z.K. Eshkuvatov)

Abstract: In this paper, the four type of solutions of Cauchy integral equations (CIE)are obtained. The main tool is that the known function, which is of Holder class, arewritten as a combination linear of the basis 1

x+2, 1

x+3, 1

x+4, · · · , 1

x+n, · · · , which are

complete in L2[−1, 1]. It is found that for the finite expansion of the known function, theexact solutions can be archived, else the approximate solutions are obtained. Numericalresults demonstrate the efficiency and the accuracy of the present technique.


193

The Use of variational iteration method to Solve a nonlinearVolterra-Fredholm integro-differential equations

Mohammad Ali Fariborzi Araghi

email: mafa [email protected]

Islamic Azad University, Central Tehran BranchDepartment of Mathematics, Islamic Azad University, Central Tehran Branch, P.O.Box

13185.768, Tehran, IranIslamic Republic of Iran

(Joint work with: Sh. Sadigh Behzadi)

Abstract: In this paper, a nonlinear Volterra-Fredholm integro-differential equation issolved by using the He’s variational iteration method (VIM). The approximate solutionof this equation is calculated in the form of a series which its components are computedeasily. The accuracy of the proposed numerical scheme is examined by comparing withthe modified Adomian decomposition method (MADM) and Taylor polynomials method(TPM). The existance, uniqueness and convergence of the proposed method are proved.


194

Modified Sinc-collocation methods for Volterra integralequations of the second kind and their theoretical analysis

Tomoaki Okayama

email: Tomoaki [email protected]

University of Tokyo, 7-3-1, Hongo, Bunkyoku, Tokyo- Japan

(Joint work with: T. Matsuo, M. Sugihara)

Abstract: In this talk we are concerned with the Sinc-collocation method that has beendeveloped by Rashidinia–Zarebnia1 for Volterra integral equations of the second kind:

u(t)−∫ t

ak(t, s)u(s) ds = g(t), a ≤ t ≤ b,

where k and g are given functions, and u is the solution to be determined. Since naiveSinc-collocation method does not work properly when the solution u is non-zero at theendpoints (t = a and b), they have introduced auxiliary basis functions that are se-lected depending on the values of u(a) and u(b). Then they have proved that the orderof the error of their method is O(‖A−1

N ‖2 exp(−c1√

N)), where AN represents the co-efficient matrix of the resulting linear equations. Their numerical experiments showedthat ‖A−1

N ‖2 does not increase rapidly, and from which they have concluded the method

converges at an exponential rate: O(exp(−c1√

N)). One of the purposes of this work isto make their method more practical and reliable in the following two senses. First, itis not realistic to assume that the values of u(a) and u(b) can be known in prior to thecomputation. In order to remedy the difficulty, we employ modified auxiliary basis func-tions that do not depend on the values of u(a) and u(b) (the same approach has alreadybeen employed for Fredholm integral equations2). Second, the convergence rate of theirmethod is still not proved because the term ‖A−1

N ‖2 is not theoretically estimated in theirerror analysis. In this project, it is rigorously proved theoretically that the convergencerate of the modified method is O(exp(−c1

√N)). The other purpose of this work is to

improve the rate of convergence. This is done by replacing the variable transformationemployed in the methods above, the standard tanh transformation, with the so-calleddouble-exponential transformation.3 It is then shown theoretically and numerically thatthe convergence rate is improved to O(exp(−c2N/ log N)).

References

1. Rashidinia, J. and Zarebnia, M.: Solution of a Volterra integral equation by theSinc-collocation method, J. Comput. Appl. Math., 206 (2007), 801–813.

2. Okayama, T., Matsuo, T. and Sugihara, M.: Improvement of a Sinc-collocationmethod for Fredholm integral equations of the second kind, DWCAA09, Alba diCanazei, Trento, Italy (2009.

3. Mori, M. and Sugihara, M.: The double-exponential transformation in numericalanalysis, J. Comput. Appl. Math., 127 (2001), 287–296.


195

Differential Quadrature Solution of 2D Natural Convectionin a Cavity Under a Magnetic Field

Nagehan Akgun


Middle East Technical UniversityDepartment of Mathematics

Inonu Bulvari 06531 Ankara - Turkey

(Joint work with: M. Tezer Sezgin)

Abstract: This study concerns with the problem of time dependent numerical simula-tion of 2D natural convection in a square cavity under a magnetic field. The differentialquadrature method is used for solving the governing equations in terms of stream func-tion, vorticity and temprature. Relaxation parameters are used for both the vorticity andthe temprature to smooth the values between tvo consecutive time levels. This enablesus to obtain inhomogenous modified Helmholtz equations for the time level concernedkeeping all the terms at the previous time level as inhomogeneity. Thus, convergenceto steady-state is accelerated by using proper values of the parameters. The results areobtained for several values of Rayleigh (Ra) and Hartmann (Ha) numbers. DifferentialQuadrature method gives quite accurate solutions by using considerably small numberof grid points in space direction. As Ra or Ha increases one needs to take smaller timeincrements to achieve a preassigned accuracy.


196

Session 6.4: Mathematical Modeling, Analysis, Applications III

Chair: Seiji FujinoPlace: Hall 4


197

Approximation by div-rot variational splines

Abdelouahed Kouibia


University of Granada, Dept of Applied Mathematics, Faculty of SciencesC.P. 18071, Granada - Spain

(Joint work with: M. Pasadas)

Abstract: In Geology, Geophysic and other Earth Sciences, it is usual to find the con-struction problem of curves and surfaces from a Lagrange or Hermite data set. Vectorfield approximation is a problem arising in many Scientific applications, such as for ex-ample fluid mechanics, meteorology, optic flow analysis, electromagnetics. In the lastyears, different technics for the construction of a curve or surface are developed, for ex-ample the interpolation or fitting by spline functions, based on the minimization of acertain functional in a Sobolev space from some data as mentioned above. In this con-text, we present in this work an approximation problem by the new notion of div-rotvariational splines. Some authors2 have studied the div-curl approximation problem byweighted minimizing splines. The same authors have studied the splines under tensionon a bounded domain in this work,1 they have discussed error and convergence for in-terpolation by div-curl spline under tension of a vector field in the classical vectorialSobolev space. In3 the authors choose a seminorm based on the decomposition of vectorfields into a rotational and a gradient part. They used the variational spline technique bydetermining the vectorial function which minimizes such seminorm over all the functionsin a suitable semi-Hilbert space which interpolates the data. We study the existence anduniqueness of the solution of such problem. Then, we establish some convergence anderror estimations results, as soon as, we compare our method with other existing oneson the literature. We show that the theory of the mimimizing functional splines mayalso be used for the approximation or for the interpolation of a vector field controlledby the divergence and the rotation of the vector field. This means that such minimizingfunctional contains various terms which are a mixed between a semi-norms of Sobolevwith a divergence and rotational expressions. Such terms are controlled by some param-eters. We study some geometrical effects of such divergence and rotational expressionsand their influence on the minimized functional.

References

1. M. N. Benbourhim and A. Bouhamidi, Error estimates for interpolating div-curl splinesunder tension on a bounded domain, J. Approximation Theory 152 (2008), pp. 66-81.

2. M. N. Benbourhim and A. Bouhamidi, Div-curl weighted minimizing splines, Analysisand Applications 5 No. 2 (2007), pp. 95-122.

3. F. Dodu and C. Rabut, Vectorial interpolation using radial-basis-like functions, Com-puters and Mathematics with Applications 43 (2002), pp. 393-411.


198

Solving Distributed Optimal Control Problems for theUnsteady Burgers Equation in COMSOL Multiphysics

Bulent Karasozen



(Joint work with: Fikriye Yilmaz)

Abstract: We use COMSOL Multiphysics for solving optimal control of unsteadyBurger’s equation without constraints, with mixed control-state constraints. Using thefirst order optimality conditions, we apply projection and semi-smooth Newton methodsfor solving the optimality system. We present results for the standard approach by inte-grating the state equation forward in time and the adjoint equation backward in time.We also consider the optimality system in the space-time cylinder as an elliptic equationand solve it adaptively. Numerical examples show the advantages and limits of the usageCOMSOL Multiphysics.


199

Formalizing Dynamic Assignment of Rights andResponsibilities to Agents

Farnaz Derakhshan


University of Tabriz29th Bahman Avn. Tabriz

Iran

Abstract: Recently, the design and development of multiagent systems (MASs) hasbecome increasingly concerned with the recognition that they will be used in a dynamicand open environment. In such environments, it is a very difficult task to anticipate allpossible runtime situations at design time. Therefore, in order to respond to changesin this environment it is necessary to allow the system to provide dynamic solutionsat runtime. This paper is concerned with one particular aspect of such solutions. Weexplicitly address the problem of dynamic assignment of rights, responsibilities (R&Rs)and sanctions to external agents in normative MASs. We propose a novel method basedon conditional norms for dynamic assignment of R&Rs and sanctions to external agents,and propose a formalism to represent a commonsense understanding of our solution.


200

Topology of two separation bubbles with opposite rotationsin a double-lid-driven rectangular cavity

Ali Deliceoglu


Erciyes UniversityFaculty of Science and Literature

Department of Mathematics38039 Melikgazi - Kayseri

Turkey

(Joint work with: F. Gurcan)

Abstract: The flow structures close to a stationary wall are investigated using bothanalytic solutions and methods from nonlinear dynamical systems. A particular regionof S (speed ratio of the lid velocities), A (height to width) parameter space has beenconsidered to construct a bifurcation diagram for the flow structure of two separationbubbles with opposite rotations in a double-lid-driven rectangular cavity.


201

Session 6.5: Numerical Analysis and Optimization

Chair: Janos D. PinterPlace: Hall 5


202

The Block-Grid Method for Solving Laplace’s BoundaryValue Problem with Singularities

Adigozal Dosiyev



Abstract: Block grid method is one of high accurate combined methods for the solutionof Laplace’s equation on polygons proposed and justified in [1] [2]. In this method ina finite neighborhood, on the block sectors, of each singular point a special integralrepresentation of the solution is approximated. Outside of these block sectors the Laplaceequation is approximated by a finite difference scheme on a finite number of overlappingrectangles. The uniform estimate for the error of approximate solution is of order ofO(hν), when the given boundary functions on the sides that not cause the singularity,belong to the Holder classes Cν,λ, where , 0 < λ < 1, ν = 2 for 5-point, ν = 4, 6 for9-point schemes. Moreover, in the block sectors the derivatives of the exact solution oforder p, p = 1, 2, ...are defined by simple differentiation of the approximate solution, andthey converge as hν with the constants depending on the index of the derivative and thedistance from the current point to the singular vertex. In this presentation we analysethe errors when the class Cν,λ is replaced by Cν−1,1. It is proved that the error of theapproximate solution in uniform metric is O(hυ(|ln h| + 1)) and can not be improved.To remove |ln h| term in error of estimation, when ν = 2 or ν = 4, a combined “5 and9” point scheme [3] is used in overlapping rectangles of which at least one of its sides lieon the boundary of the polygon.


203

Analytical and numerical evaluation of finite-part integrals

Johan Hendrik DeKlerk


Mathematics and Applied MathematicsNorth West University (Potchefstroom Campus)

Potchefstroom 2520, South Africa

Abstract: As with a new development in any subject (in this case finite-part integrals) alarge number of articles have been written on the specific topic, resulting in, what seemsto be, a web of results. This makes it difficult to keep up with the development and usageof the new field. What is perhaps necessary is an ordering of results in the form of a goodtextbook. To my view, such a book should address at least the following: (a) a historicalpresentation of the development of hypersingular integrals, (b) a summary of differentdefinitions of hypersingular integrals, (c) a discussion of available integration techniquesfor hypersingular integrals, (d) a list of relevant tables with constants for the quadratureformulae (nodes and weights), (e) a theoretical example illustrating every method given,(f) a practical example from reality which gives more flesh to the bone than a mereillustrating example, (g) a discussion of extensions that could be made in this field, and(h) a comprehensive list of bibliographic information. As far as my knowledge goes, abook of this kind has not been published yet. In this talk attention will be paid to someof these matters, especially, integration techniques and quadrature formulae (points (c)and (d)).


204

Automatic Zone Decomposition in Iterative Solution ofDifferential Equations over Unstructured Grids

Nematollah Fouladi


Sharif University of Technology, Aerospace Dep., Azadi AvenueTehran, Iran

(Joint work with: M. Darbandi)

Abstract:This paper contributes to an adaptive computational zone approach on un-structured grids. The idea behind this method comes from automatic controlling of thecomputational zone during iterative solutions of differential equations over unstructuredgrids. This method automatically tracks the disturbances which are caused in some smallportions near the inner bodies and are diffused into the computational domain duringthe iterative solutions of differential equations. So, this method avoids unnecessary com-putations by automatically dividing the computational domain into active and inactivezones. In this regard, firstly, we modify the connectivity matrix in an ordering basedmanner without requiring the additional memory storage. In this step, the domain meshnodes and elements are successively renumbered respect to their sensitivities to the innerboundary grid points. In other hand, the elements and nodes indices are improved inconnectivity matrix to construct element and node layers inside the mesh data struc-ture. This method with confinement of searching process in the data structure of anunstructured grid facilitates the grid substructures addressing. Secondly, we use a suit-able algorithm that provides a suitable management of disturbances propagation insidethe mesh domain.


205

An Extended Implicit Pis Scheme to Efficent Simulation ofTurbulent Flow with Moving Boundaries

Alireza Naderi


Sharif University of Technology, Tehran, Iran

(Joint work with: M. Darbandi)

Abstract: We extend an implicit second-order time accurate method to simulate tur-bulent flows in domains with moving boundary. The arbitrary Lagrangian-Eulerian ALEapproach is used for grid movement purpose. To enhance the efficiency of an origi-nal finite-volume based finite-element method, we treat the convection terms using aphysical influence scheme PIS. We use standard k-epsilon, RNG kepsilon, and Spalart-Allmaras eddy viscosity turbulence models to perform the efficiency of our formulations.We show that our numerical method is very accurate and efficient in simulating domainswith nonstationary fluid flow, separated turbulent flow over bluff bodies, and deep stallphenomenon over NACA0012 airfoil


206


PARALLEL SESSIONS 7

2 October 2009, 13:30-15:45



209

Session 7.1: Optimization II

Chair: Gerhard W. WeberPlace: Hall 1


210

Survey of Polynomials Transformations betweenNP-Complete problems



Centro Nacional de Investigacion y Desarrollo TecnologicoInterior internado palmira s/n Col. Lomas de Cuernavaca. Cuernavaca, Morelos

Mexico

(Joint work with: Joaquin Perez-Ortega, Rodolfo A. Pazos R., Ocotlan Diaz-Parra)

Abstract: Exists diverse polynomial reductions/transformations between NP-completeproblems, in this paper will be to show the differences between polynomial reductions andpolynomial transformation, the methodologies of polynomial reduction/transformationof instances between NP-complete problems using: the theory of NP Completeness,the theory of graphs and the application of formal languages. It will show examplesof the polynomial reductions/transformation, the restrictions to reduce/transform be-tween NP-complete problems, the verification of the reduction/transformation, besidesto show the reduction/transformations that exist between NP-Complete problems, theway to verify the reduction/transformations, and a digraph with the historical reduc-tions/transformations between instances of NP-Complete problems.


211

Application of Formal Languages in the PolynomialTransformations of Instances Between Np-Complete

Problems



Centro Nacional de Investigacion y Desarrollo TecnologicoInterior internado palmira s/n Col. Lomas de Cuernavaca. Cuernavaca, Morelos

Mexico

(Joint work with: Joaquin Perez-Ortega, Rodolfo A. Pazos R., Ocotlin Diaz-Parra)

Abstract: In this paper, we propose to define formal languages to express instances ofNP-complete problems to be used in the polynomial transformations. The new idea pro-posed of to use formal languages theory for polynomial transformations is more practicaland fast to apply to real problems than the theoretical theory of polynomial transfor-mations (it is a mechanism to determine if a problem belongs to a class of problems,but in addition to determine if a problem is more complex than another). We proposeda methodology of transformation of instances between NP-complete problems, the dif-ferences between the Johnson methodology and with our methodology, and examples ofthe polynomial transformations.


212

Some Inequalities for Increasing Positively HomogeneousFunctions

Serap Kemali


Akdeniz University Vocational School Of Technical SciencesAntalya-Turkey

(Joint work with: Gabil R. Adilov)

Abstract:In this paper we study Hermite-Hadamard type inequalities for increasing pos-itively homogeneous functions. Some examples of such inequalities for functions definedon special domains are investigated and the concrete results are obtained.


213

A Comparative Study on Parameter Estimations inMultivariate Nonlinear Model

Aydin Karakoca



Turkey


Abstract: The univariate nonlinear model can be given by,

yt = f(xt, θ

0)

+ et, t = 1, 2, . . . , n. (1)

Here we consider the case there are M such regressions called multivariate nonlinearmodel is given by

yαt = fα(xt, θ

0α

)+ eαt, t = 1, 2, . . . , n, α = 1, 2, . . . , M (2)

that are related in one of two ways (Gallant, 1987). The first arises most naturallywhen repeated measures on same subject, the second way these models can be related isthrough shared parameters. In this study, the parameter estimates for Eq(1) and Eq(2)will be obtained by modified Gauss-Newton algorithm and Genetic Algorithm. Resultsof parameter estimates will be compared.

References

1. Bates, D.M., Watts, D.G., (1988), Nonlinear Regression Analysis and Its Applications,John Wiley & Sons, Inc.

2. Gallant, A. R., (1987), Nonlinear Statistical Models, John Wiley & Sons, Inc.3. Genc, A., (1997). Cok Degiskenli Lineer Olmayan Modeller: Parametre Tahmini ve

Hipotez Testi, Ankara Universitesi, Fen Bilimleri Enstitusu Doktora Tezi.4. Holland. J., (1975), Adaptation in Natural and Artificial Systems, The University of

Michigan Press, Ann Arbor, MI, 1975.5. Goldberg, D.E., (1989) , Genetic Algorithms in Search, Optimization and Machine

Learning, Addison Wesley, Readin, MA.6. Seber, G.A, Wild, J., (1989). Nonlinear Regression. John Wiley & Sons, New York


214

Interior point filter line search strategies for large scaleoptimization: practical behavior

M. Fernanda P. Costa


University of Minho, Department of Mathematics for Sciencie and Technology - Portugal

(Joint work with: Edite M.G.P. Fernandes, A. Ismael F. Vaz)

Abstract: We present two classes of primal-dual interior point methods that rely on afilter line search strategy for large scale nonlinear optimization. The first class approxi-mately solves a sequence of associated barrier problems and each entry in the filter hasthree components. The feasibility and the centrality measures come directly from theKKT conditions of the barrier problem and the optimality measure is represented bythe barrier objective function. The other class uses the Newtons method to solve theperturbed primal-dual system to generate iteratively the search directions. The filter inthe line search strategy uses the same previously mentioned three components. We solvea well-known set of large scale optimization problems and a comparison with the Ipoptsolver is provided. The results show that both classes of filter line search methods areeffective in reaching the solutions, and are comparable in terms of number of iterations,number of function evaluations and CPU time.


215

Interval Malmquist productivity in DEA analysis and itsapplication in determining the regress and progress of

Islamic Azad university’s departments



Poonak-Hesarak-I.A.U.Science and Research BranchIran

(Joint work with: H. Nikoomaram, A. Toloie Eshlaghy, M.A. Kazemi, R. Sharifi, M. Ahadzadeh

Namin)

Abstract: In this paper, a method is proposed for obtaining productivity usingMalmquist Productivity Index on interval data. Through using this index and also DEAmodels, the progress and regress of Decision Making Units (DMU) can be calculated.Although the data are not exact and definite, but they lie in an interval, then MalmquistProductivity Index is calculated within an interval.Keywords: Data Envelopment Analysis (DEA), Efficiency, Malmquist Productivity In-dex, Interval Data.


216

Session 7.2: Mathematical Modeling, Analysis, Applications IV

Chair: Andrei BourchteinPlace: Hall 2


217

Parameter Interval Estimations through Chebyshev-TypeInequalities for Nonlinear Regression Models∗

Atif Evren


Yildiz Technical University,Faculty of Arts and Science, Department of Statistics,Davutpasa34210, Esenler, Istanbul - Turkey

(Joint work with: Dogan Yildiz)

Abstract: In linear regression models, parameter estimators are linear functions of in-dependent variables. Therefore, under the assumption of normality, parameter intervalestimation procedures can be based on normal distribution itself or other distributionswhich are derived from normality assumption like student-t distribution, chi-square dis-tribution and Snedecor F distribution. On the other hand for nonlinear regression models,parameter estimates are not simply linear functions of variables. Therefore for nonlinearmodels , interval estimation procedures are realized by assuming asymptotic normality. This assumption is, of course, not realistic all the time. In these cases, multivariateversions of Chebyshev-type inequalities can be used since all these inequalities do not re-quire strict restrictions on the distributions of variables. Sometimes the results obtainedby using these inequalities are poor. Nevertheless, these interval estimates may be helpfulespecially for obtaining initial parameter estimates since nonlinear estimation techniquesare based on iterative procedures. In this study , we propose an algorithm through whichinitial parameter estimates can be made by using Chebyshev-type inequalities. Then wecompare all results (i.e. the results obtained by assuming normality, the bootstrap resultsand the results we have obtained through this algorithm.

∗This paper is dedicated to our advisors.


218

Special functions, non-linearity and algebraic and differentialproperties: Computational aspects

Alejandro Zarzo


Departamento de Matematica APlicada, ETS Ingenieros Industriales, Universidad Politecnicade Madrid

C/ Jose Gutierez Abascal 2, 28006 Madrid , Spain

(Joint work with: L. Fernandez, P. Martinez-Gonzalez, B. Soler)

Abstract: A method for the explicit construction of general non-linear sum rules involv-ing hypergeometric type functions and their derivatives of any order is derived which onlyrequires the knowledge of the coefficients of the differential equation that they satisfy,i.e. the simplest Lame equation also known as hypergeometric type differential equation.Special attention is paid to the quadratic case for which, as illustration of the method,some particular sum rules are explicitly constructed in terms of the differential equationcoefficients. Moreover, an extension of the method to the generalized hypergeometrictype functions and some explicit applications are given.


219

Trace Inequalities for Matrices

Ramazan Turkmen


Selcuk University, Science Faculty, Department of Mathematics, Turkey

(Joint work with: Zubeyde Ulukok)

Abstract: Matrix trace inequalities are used in many areas such that analysis, statistics.In this talk, we present some inequalities on traces of the ordinary product and sum ofpositive semidefinite matrices and any matrices.


220

The Convergence of Family of Integral Operators withPositive Kernel

Mine Menekse Yilmaz


University of Gaziantep Department of Mathematics, 27310 Gaziantep, Turkey

(Joint work with: Sevilay Kirci Serenbay)

Abstract: The aim of this study is to investigate the convergence of family of generalizedintegral operators with positive kernel in space Lp. Previously unused , A modulus ofcontinuity is defined. This modulus of continuity was proven features. Using this modulusof continuity, convergence has been investigated.


221

Approximation of patches by Cr-finite elements ofPowell-Sabin type

Miguel Angel Fortes


Universidad de GranadaEdificio Politcnico. Campus de Fuentenueva

18071-Granada - Spain

(Joint work with: P. Gonzalez, M. Pasadas)

Abstract: Let D ⊂ R2 be a polygonal domain and m ∈ N. Let us consider, for eachi = 1, . . . , m, a polygonal domain Hi ⊂ D in such a way that the H′

is are disjoint,and a real function ϕi ∈ L2(Hi). We present a method to obtain a Cr-spline surfaceapproximating the functions {ϕi}1≤i≤m and minimizing the “energy functional” definedby

J (v) =m∑

i=1

∫

Hi

(v(x)− ϕi(x))2dx +

r+1∑

j=1

τj |v|2j ,

where τi ≥ 0 for i = 1, . . . , r, τr+1 > 0, v belongs to a finite element space V constructedfrom a triangulation of D of Powell-Sabin type, and | · |j denotes the usual semi-norm onthe Sobolev space Hr+1(D) for j = 1, . . . , r +1. We prove that there exists a unique ele-ment σ ∈ V such that J (σ) ≤ J (v) for all v ∈ V . We give a variational characterizationof σ, a convergence result, and we present some numerical and graphical examples.


222

Project Scheduling Problem

Alejandro Fuentes-Penna


Universidad Popular Autonoma del Estado de PueblaOtilio Montano No. 115 B-103, Colony Altavista, Cuernavaca, Morelos. CP 62010

Mexico

(Joint work with: Jorge A. Ruiz-Vanoye and Ocotlan Dıaz-Parra)

Abstract: The project management is the application of knowledge, abilities, toolsand techniques to activities of projects so that they fulfill or exceed the needs andexpectations of a project, such as: reach, time, cost and quality, requirements identified(needs) and requirements non-identified (expectations). The application areas usually aredefined in terms of: technical elements (development of software, pharmaceutical drugsor civil engineering), elements of the administration (contracts with the governmentor development of new products), and groups of industry (automobiles, chemicals orfinancial services). In this paper, we propose a new NP-hard combinatorial problemoptimization problem called Project Scheduling Problem, which search to minimize thetotal time of software project development by means of the optimal management ofthe project resources. In addition, we described the mathematical model for the newproblem, the definition of the instances and demonstrated that problem is NP-hardby means of the instances polynomial transformation(Project Scheduling Problem toTimeTable Problem).


223

Interval Malmquist productivity in DEA analysis and itsapplication in determining the regress and progress of

Islamic Azad university’s departments



Poonak-Hesarak-I.A.U.Science and Research BranchIran

(Joint work with: H. Nikoomaram, A. Toloie Eshlaghy, M.A. Kazemi, R. Sharifi, M. Ahadzadeh

Namin)

Abstract: In this paper, a method is proposed for obtaining productivity usingMalmquist Productivity Index on interval data. Through using this index and also DEAmodels, the progress and regress of Decision Making Units (DMU) can be calculated.Although the data are not exact and definite, but they lie in an interval, then MalmquistProductivity Index is calculated within an interval.Keywords: Data Envelopment Analysis (DEA), Efficiency, Malmquist Productivity In-dex, Interval Data.


224

Session 7.3: Probability, Stochastic Processes and ComputationalMethods

Chair: Birdal SenogluPlace: Hall 3


225

Super efficiency in stochastic data envelopment analysis: Aninput relaxation approach

Mohammad Khodabakhshi


Operations Research Department of MathematicsFaculty of Science, Lorestan University, Khorram Abad

Iran

Abstract: This paper addresses super-efficiency issue based on input relaxation model,e.g. Khodabakhshi and Asgharian(2008) , in stochastic data envelopment analysis. Theproposed model is not limited to use the input amounts of evaluating DMU, and one canobtain a total ordering of units by using this method. The input relaxation super effi-ciency model is developed in stochastic data envelopment analysis, and its deterministicequivalent, also, is derived which is a nonlinear program. Moreover, it is shown that thedeterministic equivalent of the stochastic super efficiency model can be converted to aquadratic program. As an empirical example, the proposed method is applied to data oftextile industry of China to rank efficient units. Finally, when allowable limits of datavariations for evaluating DMU are permitted, sensitivity analysis of the proposed modelis discussed.Keywords: DEA; Employment; Super-efficiency; Input relaxation; Chance constraints


226

Two Level Fractional Factorials with Long-Tailed SymmetricError Distributions

Sukru Acitas


Anadolu University, Science FacultyDepartment of Statistics26470 Eskisehir - Turkey

(Joint work with: Birdal Senoglu)

Abstract: In this study, we obtain the explicit estimators for the parameters in 2k fac-torial design by using the methodology known as modified maximum likelihood (MML).We also develop a test statistic based on MML estimators for testing main effects andinteractions in the one-half fraction of the 2k design. We show that our solutions are moreefficient and robust then the classical least squares (LS) solutions. We give an example.


227

X-ray Fluorescence Computed Tomography: InversionMethods

Alvaro Rodolfo De Pierro


University of Campinas, IMECC-UNICAMPApplied Mathematics Department, CP 6065, CEP 13083-030, Campinas, SP

Brazil

(Joint work with: E.X. Miqueles)

Abstract: X-ray Fluorescence Computed Tomography (XFCT) is a novel synchrotronbased imaging modality aiming at reconstructing the distribution of an element insidethe body. In XFCT, high intensity monochromatic synchrotron X-rays, with energygreater than the K-shell binding energy of the elements of interest, stimulates fluorescenceemissions, isotropically distributed, which are detected by a detector placed parallel tothe direction of the incident beam. Mapping fluorescence emission could have manyimportant biomedical applications (iodine distributions in thyroid tissue, platinum inclusters of cancer cells treated with cisplatin, etc). A continuous mathematical model forXFCT is given by the Generalized Attenuated Radon Transform (GART). In this article,we present an analytic inversion formula for the GART as well as some approximatedones based on the inversion of the Radon Transform. A comparison between the differentinversion approaches is also shown by means of simulated and real data.


228

Using Dirichlet-to-Neumann operators and ConformalMappings with Approximate Curve Factors in Waveguide

Problems

Anders Andersson


Vaxjo UniversityMSI, SE-35195 Vaxjo Sweden

Sweden

(Joint work with: B. Nilsson)

Abstract: We consider wave scattering in waveguides with comparatively arbitrary ge-ometry and boundary conditions. The setting is acoustic, but the same techniques canbe used for electro-magnetic or quantum scattering problems. When applying the socalled Building Block Method, see,4 such problems can be solved by solving a sequenceof two-dimensional wave scattering problems in infinite waveguides where all variationsin geometry and boundary conditions are smooth. Furthermore, these waveguides arestraight and with constant width outside some bounded region. To solve these subprob-lems, we

• use a global conformal mapping to transform the geometry to a straight horizontal waveguide,

• represent the field and scattering operators by matrices based on expansions in Fourier series,

• introduce Dirichlet to Neumann operators and solve equations for their matrix representationsusing standard numerical ODE solvers, see,1–3 and can hence determine a matrix representa-tion for the wave field.

For the conformal mapping, we use a variant of the Schwarz-Christoffel mapping. Themapping is modified using so called approximate curve factors, which means that polyg-onal regions with rounded corners are produced in such a way that the mapping functionis C∞ on the boundary.

References

1. L. Fishman, A. K. Gautesen, and Z. Sun, Wave Motion 26, 127–161 (1997), ISSN0165-2125.

2. Y. Y. Lu, Math. Comput. Simulation 50, 377–391 (1999), ISSN 0378-4754, wave split-ting and inverse problems (Berlin, 1997).

3. Y. Y. Lu, J. Comput. Appl. Math. 173, 247–258 (2005), ISSN 0377-0427.4. Borje Nilsson and Olle Brander. IMA J. Appl. Math., 27(3):263–289 (1981).


229

Imprecise probability and application in finance

Mila Milan Stojakovic


Faculty of Engineering, University of Novi Sad, 21000 Novi Sad SerbiaSerbia and Montenegro

Abstract: Fuzzy probability is a generic name used to represent the concept in whichthe fuzzy theory is used for analyzing and modeling highly uncertain probability sys-tems. In this paper the fuzzy probability is defined over the measurable space. It isderived from a fuzzy valued measure using restricted arithmetics. The range of fuzzyprobability is the set of real valued upper semicontinuous fuzzy sets. The expectationwith respect to fuzzy probability is defined and some properties are discussed. Since L.Zadeh published his now classic paper more then forty years ago, fuzzy set theory hasattention from researches in a wide range of scientific areas, especially in recent years.Theoretical advances and applications have been made in many directions. The theoryof fuzzy sets, as its name implies, is a theory of graded concepts, a theory in which ev-erything is a matter of degree. This theory was developed to give techniques for dealingwith models for natural phenomena which do not lend themselves to analysis by classicalmethods based on probability theory and bivalent logic. Applications of this theory canbe found in artificial intelligence, computer sciences, expert systems, logic, operationsresearch, pattern recognition, decision theory, robotics and others. In the classical settheory if A ⊆ X , then this relation can be described by indicator (or characteristic)function IA : X → {0, 1}, where IA(x) = 1 if x ∈ A and IA(x) = 0 if x ∈ X\A. Onecan interpret the function IA as the degree of membership of x in X . There are only twopossibilities: 0 or 1. In fuzzy concept the set A is identified with the membership functionuA : X → [0, 1] where the interpretation uA(x) is the degree to which “x is in A”, or x iscompatible with A. Fuzzy set A of X we identify with its membership function uA. Theset of all functions u : X → [0, 1] we denote by F(X ) and we say that F(X ) is the setof all fuzzy sets defined on X . Uncertainty regarding some experiment may essentiallyhave two origins. It may arise from randomness due to natural variability of observationor it may be caused by imprecision due to partial informations, e.g. expert opinions orsparse data sets. Highly imprecise probabilistic system could be formalized using thetheory of fuzzy random variables or using the theory of fuzzy probability. An incompletedata set delivers an imprecise assessment of the probability of an event which should beexpressed by a [0,1]-fuzzy set instead by a number. In other words, probability theoryis complemented with extra dimension of uncertainty provided by fuzzy set theory. Thisconcept has received the generic name of fuzzy probability. However, this generic termhas been interpreted and mathematically formalized in various ways. One of the mostattractive interpretations of fuzzy probability is where probability of a crisp event, dueto the imprecision of background knowledge or sparsity of data sample, is expressed interms of fuzzy numbers. In our paper, the method of restricted fuzzy arithmetics is usedto treat the probabilities which are fuzzy valued but in spite of that the sum of all theindividual probabilities is one. One can consider this concept as the extension and gener-alization of the classical model of probability theory. We introduce the fuzzy probability


230

as the function derived from a finite complete fuzzy valued measure. That kind of fuzzyprobability still has some nice properties - it is normed and *additive, where *additivityis the additivity with respect to addition in restricted arithmetics. It turns out that ourmodel is suitable to define the expectation which generalize the single and interval valuedmodel. The range of fuzzy valued measure and the derived fuzzy probability is the setof real valued upper semicontinuous fuzzy sets. Since there is no any assumption aboutconvexity, this theory can be used to model and analyse probabilistic systems where thevalues of probability are highly imprecise but discrete. This mathematical model is usedto treat some financial problem- such as stock prices process - with imprecise data.


231

Session 7.4: Mathematical Programming and Data Analysis

Chair: Pablo Sanchez-MorenoPlace: Hall 4


232

A new hybrid algorithm for quadratic knapsack problem

Tugba Sarac


Eskisehir Osmangazi University, Industrial Enginnering DepartmentMeselik, 26480 Eskisehir

Turkey

Abstract: Quadratic knapsack problem (QKP) with quadratic objective function and acapacity constraint is one of the well-known combinatorial optimization problems. Manysolution methods have been proposed for this problem in the literature. One of themis Modified Subgradient (MSG) Algorithm. The performance of the MSG algorithm onsolving the QKP was examined by Sipahioglu and Sarac in 2009. They showed that thequality of the MSG solutions depends on choosing proper values of the algorithm pa-rameters. In this study, a new hybrid solution approach that a tabu search algorithm tofind the proper MSG parameter values and the MSG algorithm run together. The per-formance of the developed algorithm is evaluated and the obtained results are comparedto the previous studies in the literature.


233

Criteria Function Efficiency Against Outliers in NonlinearRegression

Ahmet Pekgor



Turkey


Abstract: In this work, it is compared the efficiency of confirmation outliers of criteriafunctions, using S scale estimators and M location estimators different criteria functionswhich are not affected by outliers in nonlinear regression. It is used six scripts whichSerbert and friends exerted and twenty four different situations. And, based on errorsthat are came by different confusion in Richards sigmoid model, It is used Monte Carlosimulation for determining efficiency of these criteria functions in confirming outliers.

Keywords: Nonlinear Regression, Criterion Function, S-Estimator, M-Estimator,Outlier

References

1. Barrera, M.S. ve Yohai V.J. (2006), A Fast Algorithm for S-Regression Estimates,Journal of Computational and Graphical Statistics, vol. 15, no.2, pp 1-14.

2. Huber, P.J, Robust Statistics, John Willey & Sons, Inc., USA, 1981.3. Rousseeuw, P. J. and Yohai, V. J. (1984), Robust Ragression by Means of S-Estimator,

in Robust and Nonlinear Time Series Analysis, eds. J. Franke, W. Hardle and R. D.Martin, (Lecture Notes in Statistics), Springer - Verlag, New York, pp. 256-272.

4. Serbert, D.M., Montgomery, D.C. and Rollier, D. (1998), A Clustering Algorithm forIdentifying Multiple Outliers in Linear Regression, Computational Statistics & DataAnalysis, vol. 27, pp. 461-484.

5. Stromberg, A.J., Computation of High Breakdown Nonlinear Regression Parame-ters,J. Am. Stat. Assoc. 88 (1993) 237.

6. Wu, J.W. ve Lee, W.C. (2006), Computational Algorithm of Least Absolute DeviationMethod for Determining Number of Outliers Under Normality, Applied Mathematicsand Computation, vol. 175, pp. 609-617.


234

A two-objective integer programming mathematical modelfor a one-dimensional assortment problem

Nergiz Kasimbeyli


Industrial Engineering DepartmentEngineering and Architecture Faculty

Eskisehir Osmangazi UniversityMeselik, Eskisehir

Turkey

(Joint work with: Tugba Sarac)

Abstract: This paper considers the one-dimensional assortment problem which includesthe determination of the number of different sizes of standard lengths to be maintainedas inventory and to be used to fulfill a set of customer orders. One of the main difficultiesin formulating and solving this kind of problems is the use of cutting orders in the mathe-matical model. Many mathematical programming approaches for solving the assortmentproblems assume the existence of the set of cutting orders. The corresponding mathe-matical models use the cutting orders as model parameters. Because of a huge numberof cutting orders to be obtained for such kind of models, this leads to computationaldifficulties in solving these problems. The purpose of this paper is therefore to developa mathematical model without the use of cutting orders. In this paper, a two objectiveinteger programming mathematical model is developed for solving a one-dimensionalassortment problem with two or more types of stock lengths. Our model involves non-linearity in the demand satisfaction constraints. Because of this nonlinearity we suggestthe special solution method presented in this paper. The mathematical model and thesolution approach are demonstrated on test problems.


235

Estimation of reliability P (Y < X) for the proportionalreversed hazard models using lower record data

A. Asgharzadeh


Dept of Statistics, University of MazandaranBabolsar-Iran

(Joint work with: R. Valiollahi)

Abstract: This paper deals with the estimation of P [Y < X] when X and Y are twoindependent random variables from a proportional reversed hazard models. Based onlower record values, the maximum likelihood estimator, Bayes estimator and approximateBayes estimator of P [Y < X] are obtained. Different confidence intervals are proposed.Monte Carlo simulations are performed to compare the different proposed methods.Analysis of a simulated data set has also been presented for illustrative purposes.


236

Libor Market Model as a Special Case of ParameterEstimation in Nonlinear Stochastic Differential Equations

(SDEs)

Ceren Eda Can


Hacettepe University, Faculty of Science, Department of Statistics, 06800 Beytepe / AnkaraTurkey

(Joint work with: N. Erbil, G. W. Weber)

Abstract: This paper is concerned with the problem of parameter estimation in non-linear stochastic differential equations based on three statistical modelling techniques,Generalized Additive Models, Multivariate Adaptive Regression Splines (MARS), Non-linear Regression Methods. These techniques will be applied to SDEs by optimization.In this study, the general structure of optimization will be described in the context ofinterest rate derivatives. Optimization in finance finds its particular application withinthe context of calibration problems. In particular, the LIBOR Market Model, based onevolving the forward-LIBOR rates, will be studied under this topic as a special case. Cal-ibration of LIBOR Market Model to some target state determined by available relevantmarket data implies a continuous optimization of the model parameters, volatility andcorrelations of the forward- LIBOR rates, such that the deviation between the targetstate and the model state variables becomes minimal. In addition, we also include regu-larization terms in order to control the complexity of the model and the stability of thesolution with respect to noise in the data. Finally, model performance will be evaluatedusing these statistical modelling techniques and the similarities and dissimilarities willbe given among these methods. We conclude by an outlook on possible future studies.


237

Alternative Long-Run Analysis of Services and GoodsSectors Inflation in Turkey by Fractional and Asymmetric

Cointegration Methods

Koray Kalafatcilar


Monetary Policy and Research DepartmentThe Central Bank of Turkey,

06100, Ulus-AnkaraTurkey

(Joint work with: Yilmaz Akdi, Kivilcim Metin-Ozcan)

Abstract: In this study we analyze the long-run relationship between goods and servicessectors inflation rates in Turkey. Deterioration in relative prices over the last decade en-couraged us to study the inflation dynamics of the two sectors. Problems we encounteredin standard time series long - run analysis tools led us to conduct the empirical work inasymmetric and fractional cointegration methods. Estimation results of fractional cointe-gration suggest, just as conventional time-series tools, that the inflation rates of the twosectors are not cointegrated, even fractionally. Application of asymmetric cointegrationmethod sheds more light on the issue and suggests that series are not cointegrated alongdownward movements either.


238

Some Relations Between Functionals On Bounded RealSequences

Seyhmus Yardimci




Abstract: In this study, we mainly concern with the functionals L∗∗ and l∗∗, re-

spectively, defined by L∗∗ (x) = lim supk

1r

r∑

i=0

|xk+i|, l∗∗ (x) = lim infr

supk

r∑

i=0

|xk+i|. on

bounded real sequences and give some inequalities between these functionals.


239

Session 7.5: Mathematical Modeling and ComputationalApproaches

Chair: Guvenc AslanPlace: Hall 5


240

Efficient numerical techniques for solving batchcrystallization models

Shamsul Qamar


Max Planck Institute for Dynamics of Complex Technical Systems, Sandtorstr. 1, 39106Magdeburg - Germany

(Joint work with: S. Mukhtar, S. Noor, A. Seidel-Morgenstern)

Abstract: Crystallization is the process of forming a solid phase from a homogeneoussupersaturated solution and therefore is a solid-liquid separation technique. It is animportant separation and purification process used in chemical, pharmaceutical, semi-conductor, and food industries. An understanding and optimization of crystallizationprocesses are important for improving the product quality and for the minimization ofproduction costs. Achieving the desired goal can be significantly supported by modelingthe underlying processes and by developing advanced control algorithms that can beused for optimization of the resulting crystal size distribution (CSD). However, an ac-curate simulation of the CSD is challenging since the distribution can extend over manyorders of magnitude in size and time. This work focuses on the numerical investigationof one- and two-dimensional batch crystallization models with size-dependent or size-independent growth rates. On the one hand, we implement the existing high resolutionfinite volume scheme, which were originally derived for the gas dynamics, for solvingmulti-dimensional batch crystallization models. On the other hand, we derive our ownnumerical techniques which we found to more efficient and accurate for solving the batchcrystallization models. Especially, our proposed numerical method is very suitable forsolving multi-dimensional batch crystallization models. The proposed numerical methodhas two parts. In the first part, a coupled ODE system of moments and solute massis solved at the discrete points of the given computational time domain. In the secondpart this discrete data is used to construct the final CSD from an algebraic equation ob-tained either by employing the method of characteristics and Duhamel’s principle or theLaplace transformation on the given model. To overcome the closure problem of momentsystem in the case of size-dependent growth rate, a Gaussian quadrature method basedon orthogonal polynomials is used for approximating integrals appearing in the momentsystem. Moreover, we have also implemented moving mesh techniques for improving theresults of the numerical schemes further. For validation, the numerical results of the pro-posed technique are compared with those from the high resolution finite volume schemes.The numerical results demonstrate the high order accuracy, efficiency and potential ofour numerical method for solving the batch crystallization models.


241

Equations of anisotropic elastodynamics as a symmetrichyperbolic system:deriving the time-dependent Green’s

function

Handan Cerdik Yaslan

[email protected]

Dokuz Eylul Universitesi Fen Edebiyat Fak. Matematik Bolumu

(Joint work with: Valery G. Yakhno)

Abstract:Let x = (x1, x2, x3) is a space variable from R3, t is a time variable from R. Letus consider a homogeneous three-dimensional space characterized by the density ρ > 0and the four order elastic moduli tensor {cijkl}3i,j,k,l=1 which components subject to thefollowing symmetry properties cijkl = cjikl = cijlk = clkij , and the positive definitenessproperty

∑3j,k,l,m=1 cjklmξjkξlm > 0, where ξjk are components of arbitrary second

order nonzero tensor ξ satisfying ξjk = ξkj . It is convenient and customary to describethe elastic moduli in terms of a 6 × 6 matrix according to the following conventionsrelating a pair (i, j) of indices i, j = 1, 2, 3 to a single index α = 1, ..., 6 :

(1, 1) ↔ 1, (2, 2) ↔ 2, (3, 3) ↔ 3,(2, 3), (3, 2) ↔ 4, (1, 3), (3, 1) ↔ 5, (1, 2), (2, 1) ↔ 6,

Using the symmetry properties this correspondence is possible due. Moreover the matrixC = (cαβ)6×6, where α = (ij), β = (kl), is symmetric and positive definite. Themathematical model of elastic wave propagation in this homogeneous, anisotropic spaceis described by the linear system of elastodynamics (Dieulesaint and Royer (1980))

ρ∂2ui

∂t2=

3∑

j=1

∂Tij

∂xj+ fi(x, t), i = 1, 2, 3, (1)

where u = (u1, u2, u3) is the displacement vector with components ui = ui(x, t); f =(f1, f2, f3) is the vector density of the external forces with components fi(x, t); Tij =Tij(x, t) are stresses defined as

Tij =3∑

k,l=1

cijkl∂uk

∂xl, i, j = 1, 2, 3. (2)

We show that relations (1) and (2) are written in the form of a first-order symmetrichyperbolic system.

A0∂V

∂t+

3∑

j=1

Aj∂V

∂xj= F, (3)

here

A0 =

(ρI3 03×6

06×3 C−1

), Aj =

(03,3 Bj

B∗j 06×6

),


242

where C−1 is the inverse matrix to C, I3 is the identity matrix of the order 3 × 3 and0l×m is the zero matrix of the order l×m;

B1 =

−1 0 0 0 0 00 0 0 0 0 −10 0 0 0 −1 0

, B2 =

0 0 0 0 0 −10 −1 0 0 0 00 0 0 −1 0 0

,

B3 =

0 0 0 0 −1 00 0 0 −1 0 00 0 −1 0 0 0

;

V = (U1, U2, U3, T1, T2, T3, T4, T5, T6)∗ , F = (f1, f2, f3, 06×1)∗ ,

Ui = ∂ui/∂t, i = 1, 2, 3; Tα, α = 1, 2, 3, 4, 5, 6 are stresses defined by

Tα = cα1∂u1

∂x1+ cα6

∂u1

∂x2+ cα5

∂u1

∂x3+ cα6

∂u2

∂x1+ cα2

∂u2

∂x2+ cα4

∂u2

∂x3

+ cα5∂u3

∂x1+ cα4

∂u3

∂x2+ cα3

∂u3

∂x3, α = 1, 2, 3, 4, 5, 6. (4)

In the last relations we denote a pair (i, j) of indices i, j = 1, 2, 3 as a single α, α = 1, ..., 6and use the above mentioned rule of the re-numeration the relations (2). In the time do-main for the considered homogeneous anisotropic elastic three-dimensional space , theGreen’s function G(x−x0, t−t0) = (Gk

j (x−x0, t−t0))3×9 is defined as a 3×9 matrix whose

k-th column Gk(x−x0, t−t0) = (Gk1(x−x0, t−t0), Gk

2(x−x0, t−t0), ..., Gk9(x−x0, t−t0))

is a solution of the system (3) for F = Ekδ(x − x0)δ(t − t0) and vanishing fort − t0 < 0 as well as |x| → ∞ for all t. Here x = (x1, x2, x3) is 3-D space vari-able, x0 = (x0

1, x02, x0

3) is 3-D parameter, t is the time variable, t0 is the time pa-rameter; δ(x − x0) = δ(x1 − x0

1)δ(x2 − x02)δ(x3 − x0

3), δ(xj − x0j ) is the Dirac delta

function considered at xj = x0j , j = 1, 2, 3; δ(t − t0) is the Dirac delta function con-

sidered at t = t0; E1 = (1, 0, 0, 01×6), E2 = (0, 1, 0, 01×6), E3 = (0, 0, 1, 01×6). Us-ing theory of the symmetric hyperbolic systems of the first order partial differentialequations ( Mizohata (1973)), ( Courant and Hilbert (1962)) we find that there exists a gen-eralized vector function with components from C1([0, T ]; S′(R3)) satisfying (3) withF = Ekδ(x−x0)δ(t− t0). Here T is an arbitrary positive real number; C1([0, T ]; S′(R3))is the class of all continuously differentiable mappings from [0, T ] into S′(R3); S′(R3)is the space of tempered distributions (generalized functions of slow growth)(see, forexample, ( Vladimirov (1971))). Moreover the components of this solution V (x, t) havefinite supports for any fixed t from [0, T ]. Using the Paley-Wiener theorem (see, forexample,( Reed and Simon (1975)) ) the image of the Fourier transform of Vj(x, t) withrespect to x = (x1, x2, x3) ∈ R3 is entire analytic function of the Fourier parametersν = (ν1, ν2, ν3) ∈ R3, i.e. if Vj(ν, t) = Fx[Vj ](ν, t), where the Fourier operator Fx isdefined by (see, for example, ( Vladimirov (1971)) )

Fx[Vj ](ν, t) =

∫ +∞

−∞

∫ +∞

−∞

∫ +∞

−∞Vj(x, t)eiνxdx1dx2dx3, j = 1, 2, 3,

ν = (ν1, ν2, ν3) ∈ R3; xν = x1ν1 + x2ν2 + x3ν3, i2 = −1,

then Vj(ν, t) may be presented in the form of the convergent power series. The coefficientsof this power series are functions depending on t only. In our paper we find explicitformulae for the coefficients of this power series, i.e. formulae for the columns of theGreen’s matrices are derived explicitly. Using these formulae the simulation of elasticwaves (components of G(x − x0, t − t0)) has been obtained for the different anisotropiccrystals.


243

References

Courant and Hilbert (1962). R. Courant and D. Hilbert, Methods of MathematicalPhysics, Interscience, Newyork, 1962.

Dieulesaint and Royer (1980). E. Dieulesaint, D. Royer, Elastic waves in solids, John Wi-ley and Sons, Chichester, 1980.

Mizohata (1973). S. Mizohata, The theory of partial differential equations. CambridgeUniversity Press, 1973.

Reed and Simon (1975). M. Reed and B. Simon, Methods of modern mathematicalphysics. II. Fourier analysis, self-adjointness, Academic Press, New York, 1975.

Vladimirov (1971). JV. S. Viladimirov, Equations of Mathematical Physics, MarcelDekker, New York, 1971.


244

Measuring the importance and the weight of decision makers



Poonak-Hesarak-I.A.U.Science and Research BrnachFaculty of Management and Economics

Iran

(Joint work with: Mohammadali Afshar Kazemi, Ebrahim Nazari Farokhi, Bahareh Sagheb)

Abstract: Criterion weights change in decision-making process, especially in multiplecriteria decision making methods, have very large effects on decision-making results andto the rank of alternatives. Many methods for criteria weighting exists, such as LINMAP,SMART, Eigenvector. Often seen that decision makers, in all methods of group decision-making (even in voting methods), participates with a same weight of importance and inthe decision making process this has its logical drawbacks.This paper introduces a simple method to find the weight of importance of humans in theindex decision making process. In fact, this article following response to this question;what is the importance of decision makers in group decision making process? The presentarticle, introduced an idea for a degree to realize the importance of decision makers usingEigenvector method, base on pair wise comparison techniques. Considering the numberof iteration of decision making matrix, using the above method, will be determined that,if the number of iteration of decision making matrix for a decision maker to reach con-vergence is low ,then DM must be have a greater importance.

At the end, a case study for indicate the importance of decision makers, in decision-making process by 3 DM decision has been carried out for identifying the importance ofdecision makers is considered.

Keywords: Multiple criteria decision making, weighting methods, Eigenvector, Pairwise comparison, importance and weight of decision makers.


245

Sensitivity analysis for criteria values in decision makingmatrix of SAW method



Poonak-Hesarak-I.A.U.Science and Research BrnachFaculty of Management and Economics

Iran

(Joint work with: Rastkhiz Paydar, Khadijeh Joda, Neda Rastkhiz Paydar)

Abstract: All of organizations around the world try to increase competitive ability re-gards to other similar companies, therefore, decision making processes are one of themost important activities for help them.

The multiple criteria decision making methods create for help better decision makingin multidimensional environment to monitor organizational resources and, generally, forranking them.

One of the simplest and applicable methods in multiple criteria decision makingis SAW (simple additive weighting method).the general problem in MADM methods islack of complementary information for final decision making. In optimizations methods(for example linear programming) the sensitivity analysis use for produce complemen-tary information and this reason helps for popularity of this methods. Although MADMmethods don’t belong optimizations methods but in this paper tries to use sensitivityanalysis approach for produce complementary information by determination of criteriavalue domain in decision making matrix.

Key Words: Multiple criteria decision making method, Ranking Methods, SAW,sensitivity analysis.


246

Rational Eigenvalues of Fullerenes

Modjtaba Ghorbani


Department of MathematicsFaculty of Science

University of KashanKashan - Iran

(Joint work with: A.R. Ashrafi, M. Saheli)

Abstract: A fullerene graph F is a cubic 3-connected plane graph with exactly 12pentagons and other hexagons. The name is taken from the fullerene molecule. It iswell-known that the molecular graph of a fullerene molecule is a fullerene graph. In thistalk, we present our recent results on the problem of computing rational eigenvalues offullerene graphs.


247

Bounds on Estrada Index of Fullerenes

G.H. Fath-Tabar


Department of Mathematics, Faculty of Science, University of Kashan,Kashan 87317-51167, Iran

(Joint work with: A.R. Ashrafi)

Abstract: A fullerene is a molecule consisting entirely of carbon atoms. Each carbonis three-connected to other carbon atoms by one double bond and two single bonds. Afullerene graph is a cubic planar graph with all faces cycles or 6−cycles. The aim of thispaper is to bound the Estrada index of fullerenes.


248

A characterization of the Riesz potentials space with the aidof a composite wavelet transform

Sinem Sezer


Akdeniz University, Faculty of EducationDepartment of Mathematics Education

07058 Antalya - Turkey

(Joint work with: Ilham A. Aliev)

Abstract: The space Iα(Lp) of Riesz potentials is defined by

Iα(Lp) = {f : f = Iαϕ, ϕ ∈ Lp(Rn)} ,

where α > 0, 1 < p < nα

and

Iαϕ(x) =1

γn(α)

∫

Rn

ϕ(y)

|x− y|n−αdy , γn(α) =

2απn/2Γ(α/2)

Γ((n− α)/2).

Most of known characterizations of the space Iα(Lp) are given in terms of finite differ-ences, see[1-3].

In this work we give a new characterization of the space Iα(Lp) in terms of acomposite wavelet-like transform, associated with some semigroup.

For f ∈ Lp(Rn), 1 < p < ∞, denote

W (β)f(x, t) =

∞∫

0

B(β)tη f(x)dµ(η), (0 < β < ∞),

where µ is a finite Borel measure on [0,∞), µ([0,∞)) = 0 and

B(β)τ f(x) =

∫

Rn

ω(β)(y, τ)f(x− y)dy, ω(β)(y, τ) = F−1ξ 7→y

(e−τ |ξ|β

).

Using the wavelet-like transform W (β)f we define the following “truncated” integrals:

D(β)ε f(x) =

∞∫

ε

W (β)f(x, t)t−1−α/βdt, (ε > 0).

The main result of this work is as follows.

Theorem: Let 0 < α < n, 1 < p < n/α, and β > α. Then f ∈ Iα(Lp) if and

only if f ∈ Lq , q = np/(n− αq), and supε>0

∥∥∥D(β)ε f

∥∥∥p

< ∞.


249

AUTHOR INDEX

Abbasbandy, S., 137Abbasi, A.O., 103Abderraman, J., 44Abe, K., 171Abu Hassan, M., 30, 40Acitas, S., 226Adilov, G.R., 212Ahmad, A.H., 123Aishima, K., 49Akbulak, M., 45, 46Akdi, Y., 237Akgun, N., 195Akhmediev, N., 15Akhmet, M.U., 90Akramin, M.R., 123Aktas, R., 60Aktuglu, H., 36, 39Akyuz, S.O., 24, 141Al-Qassem, H.M., 83Al-Shemas, E.A., 55Alexandrov, D.V., 187Alexandrova, I.V., 187Aliev, F., 101Aliev, I.A., 248Alisadeghi, H., 77Aliyev, R., 128Allahviranloo, T., 172, 173Allame, M., 137Altin, A., 60, 62Andersson, A., 228Ankiewicz, A., 15Apaydin, A., 76Araghi, M.A.F., 31, 193Arnal, J., 95Arslan, G., 11, 145Arugaslan, D., 90Asgharzadeh, A., 235Ashrafi, A.R., 16, 190, 246, 247Asri, N.M., 192Aydin, K., 21, 139Aydin, S.H., 133

Aydin,A., 81Ayhan, S., 144

Bairamov, E., 78Baykal, N., 141Bayramoglu, I., 3Bazdidi, F., 134, 189Beccari, C., 2Behzadi, M.H., 53, 109, 140Behzadi, S.S., 193Bekar, S., 39Berriochoa, E., 37Biazar, J., 93Biga, V., 87Billings, S.A., 87Bourchtein, A., 8, 131, 170Bourchtein, L., 8, 131Bozkaya, C., 13, 14Bozkurt, D., 45, 46Buranay, S.C., 28

Cachafeiro, A., 37Can, C.E., 126, 236Casciola, G., 2Cenesiz, Y., 63, 167Cenk, M., 159Cervantes, M.G.V., 56Chen, F., 94, 118Cheng, L., 83Cibikdiken, A.O., 139Cidar, O., 146Coca, D., 87Costa, L., 51Costa, M.F.P., 214

D’Ambrosio, R., 84Dıaz-Parra, O., 210, 211, 222Dalkilic, T.E., 29, 76Darbandi, M., 204, 205Davoodi, A., 25de Kok, A.G., 182


250 Author Index

De Pierro, A.R., 227Dehesa, J.S., 64, 168DeKlerk, J.H., 203Deliceoglu, A., 200Derakhshan, F., 199Deris, M.M., 71, 149Dhaene, J., 154Dogru, M.K., 142, 182Dosiyev, A., 28, 202

Ebrahim, M.S., 156Eken, Z., 79Eltayeb, H., 20Englert, B., 135Erbil, N., 236Erdogmus, S., 144Erencin, A., 177Ersoy, D., 97Eryilmaz, S., 9Eshkuvatov, Z.K., 80, 192Eshlaghy, A.T., 215, 223, 244, 245Esposito, E., 84Evren, A., 132, 217

Farokhi, E.N., 244Fath-Tabar, G.H., 247Fernandes, E.M.G.P., 51, 54, 214Fernandez, L., 59, 218Fortes, M.A., 197, 221Fouladi, N., 204Fujino, S., 48

Gallegos, J.A., 56Gebizlioglu, O.L., 67, 101Genc, A., 66, 68, 69, 148, 213, 233Gezer, H., 36Ghanbary, B., 93Ghazali, R., 85Ghorbani, M., 246Gokgoz, N., 121Gondal, M.A., 165Gonzalez, P., 221Gonzalez, P.M., 218Goovaerts, M., 127, 154Gulec, H.H., 47Gurcan, F., 200Gurses, I., 45, 46

Hamdi, A., 55Harumatsu, M., 48

Hashemi, Y., 178Hashentuya, 102Hassen, Y., 41Hekimoglu, E., 92Herawan, T., 71, 149Hosseinzadeh, L.F., 53, 109, 140, 215,

223

Ibrahim, N.A., 70Icoz, G., 86Ince, H.G., 177Iscioglu, F., 9Ismail, F., 30, 40Iyit, N., 68

Jahangirian, A., 178Jahanshahloo, G.R., 109Jaradat, M.M., 162Joda, K., 245Juliawati, A., 123Jusoh, M., 18, 166

Kaanoglu, C., 61Kadirkamanathan, V., 87Kaffaoglu,H., 175Kahraman, M., 121Kalafatcilar, K., 237Kampas, F.J., 163Kannov, I., 108Kantar, Y.M., 67Karakoca, A., 213Karaoglu, O., 63Karasozen, K., 81, 198Kariman, S.M.H., 77Karimi, A., 30, 40Kashina, O., 108Kasimbeyli, N., 234Kasimbeyli, R., 157Kawai, F., 119Kazemi, M.A., 215, 223, 244Kecelli, S., 99Kemali, S., 212Kesemen, T., 128Keskin, Y., 63, 167Khadem, F., 31Khalifeh, M.H., 190Khaniyev, T., 120, 128Khodabakhshi, M., 225Kilicman, A., 20Kim, E.H., 135


Author Index 251

Kinaci, I., 183Kirlar, B.B., 161Kiyak, H., 45, 46Kizilkan, G.C., 21Koc, A.B., 63Koc, E., 144Kocabiyik, S., 13, 14Kocak, M.C., 176Koren, B., 41Korkmaz, M.C., 66, 148Kou, J., 130Kouibia, A., 197Kozan, A., 10Kropat, E., 107Krutitskii, P., 19Kula, K.S., 29Kurnaz, A., 167Kurum, E., 155Kus, C., 66, 148Kusakabe, Y., 48

Laitinen, E., 108Lee, C., 135Li, Y., 130

Mahat, M.M., 123Mahmudov, N., 175Malygin, A.P., 187Mammadova, Z., 120Martins, T.F.M.C., 54Mathur, I., 156Matias, J.M., 125Mawengkang, H., 104, 110, 184Mawengkang, H. , 52Md Ariffin, N., 30, 40Miqueles, E.X., 227Mirbolouki, M., 109, 140Moalemi, M., 189Mohamed, M., 18, 166Moreno, P.S., 64, 168Mozaffari, M.R., 53Mukhtar, S., 240Murota, K., 49Mutsuo, T., 49, 194

Naderi, A., 205Namin, M.A., 215, 223Nasution, A.H., 184Nasution, Z., 110Naumov, M., 170

Nawi, N.M., 85Nelsen, R.B., 1Nematollahi, N., 53, 140Nikoomaram, H., 215, 223Nilsson, B., 228Noor, S., 240Nova, T.D., 104

Okayama, T., 194Oktem, H., 121Oncel, S.Y., 101Ordonez, C., 125Ortega, J.P., 210, 211Ostermann, A., 165Otani, Y., 102Oturanc, G., 63Ozarslan, M.A., 61, 62Ozbudak, F., 159Ozcan, K.M., 237Ozceylan, E., 23, 106, 138Ozen, U., 142Ozergin, E., 62Ozkurt, F.Y., 26Ozmen, A., 26Ozmen, I., 145Ozturk, G., 157

Paksoy, T., 23, 106, 138Pan, Y., 83Param, H.K., 134Pasadas, M., 221Paternoster, B., 84Paydar, N.R., 245Paydar, R., 245Pazos, R.A.R., 210, 211Pedamallu, C.S., 107Pehlivan, N.Y., 106Peker, H.A., 63Pekgor, A., 233Penna, A.F., 222Perez, T.E., 59Pinar, M.A., 59Pinter, J.D., 4, 163Poh Bee, N., 70Purutcuoglu, V., 185

Qamar, S., 240

Rainer, M., 126Rivas, T., 125


252 Author Index

Rocha, A.M.A.C., 54Romani, L., 2Rosdzimin, A.R.M., 123Rossi, R., 142Ruiz-Vanoye, J.A., 210, 211, 222

Sadyadharma, H., 110Sagheb, B., 244Saheli, M., 16, 246Salahshour, S., 172, 173Salehi, F., 77Salleh, M.N.M., 85Santo, I.E., 51Sarac, T., 232, 234Saracoglu, B., 183Schindl, D., 111Seidel-Morgenstern, A., 240Senoglu, B., 67, 226Serenbay, S.K., 220Servi, S., 63Sezer, S., 79, 248Sezerman, U., 141Sezgin, M.T., 133, 195Shang, Z., 127Sharifi, R., 215, 223Sinan, A., 69Sleijpen, G.L.G., 171Soler, B., 218Soto-Crespo, J.M., 15Stojakovic, M.M., 229Sugihara, M., 49, 194Syahrin, A., 184

Taboada, J., 125Tandogdu, Y., 146, 147Tanil, H., 10, 124Tank, F., 29Tarim, S.A., 142Taskara, N., 47, 91, 92Thompson, H.B., 18Tiku, M.L., 185Tollu, D.T., 91Tomeo, V., 44Tunca, G.B., 88, 177Tuncer, Y., 88Turkmen, R., 219Turkoglu, B.O., 145

Ulukok, Z., 219Unver, I., 120

Uslu, K., 47, 91, 92Ustun, O., 157Ustunkar, G., 24, 141Uyar, B., 124

Vahdat, B.V., 103Valiollahi, R., 235van Houtum, G.J., 182Van Weert, K., 154Varone, S., 111Vatankhahan, B., 137Vaz, A.I.F., 214Villar, C.A.C., 56

Wang, X., 130Watanabe, M., 102, 104, 119Weber, G.W., 24, 26, 107, 141, 155, 236Wong, P.J.Y., 94, 118

Xie, X., 38

Yaghobifar, M., 192Yakhno, V., 97, 99Yakhno, V.G., 241Yamamoto, K., 102Yang, L., 38Yardimci, S., 238Yaslan, H.C., 241Yaslan, I., 117Yesildal, F.T., 60, 86, 116Yildirak, K., 155Yildiz, D., 132, 217Yilmaz, E., 90Yilmaz, F., 45, 46, 198Yilmaz, M.M., 220Ying, L., 102Yokus, N., 78Yousefi-Azari, H., 190

Zarzo, A., 64, 168, 218Zolfaghari, R., 188

Documents

14 International Congress on Computational and Applied