WSEAS CONFERENCES. WSEAS, Unifying the Science

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 Volume 10, 2011
Print ISSN: 1109-2769
E-ISSN: 2224-2880








Issue 1, Volume 10, January 2011

Title of the Paper: New Generalized Delay Integral Inequalities on Time Scales


Authors: Bin Zheng

Abstract: In this paper, some new delay integral inequalities with two independent variables on time scales are established, which can be used as a hand tool in the investigation of qualitative properties of solutions of delay dynamic equations on time scales. Some applications for the established inequalities are also presented, and new explicit bounds on unknown functions of delay dynamic equations are obtained. Our results generalize some of the results in [16, 17].

Keywords: Delay integral inequality; Time scale; Integral equation; Differential equation; Dynamic equation; Bounded

Title of the Paper: A Generalized Volterra-Fredholm Type Integral Inequality for Discontinuous Functions


Authors: Bin Zheng

Abstract: In this paper, a new generalized Volterra-Fredholm type nonlinear integral inequality for discontinuous functions is established, which can be used in analysis for the boundedness of solutions of certain Volterra-Fredholm type integral equations. Our results generalize the main results in [18, 19].

Keywords: Integral inequality discontinuous function Integral equation Differential equation Bounded

Title of the Paper: Shape of a Drum, a Constructive Approach


Authors: P. N. Shivakumar, Yan Wu, Yang Zhang

Abstract: For the classical question, “Can you hear the shape of the drum?”, the answer is known to be “yes” for certain convex planar regions with analytic boundaries. The answer is also known to be “no” for some polygons with reentrant corners. A large number of mathematicians over four decades have contributed to the topic from various approaches, theoretical and numerical. In this article, we develop a constructive analytic approach to indicate how a preknowledge of the eigenvalues lead to the determination of the parameters of the boundary. This approach is applied to a general boundary and in particular to a circle, an ellipse, and a square. In the case of a square, we obtain an insight into why the analytical procedure does not, as expected, yield an answer. For the Mathieu equation with a parameter, we demonstrate the determination of the parameter when the eigenvalues are known.

Keywords: Helmholtz equation; Eigenvalues; Mathieu equation

Title of the Paper: Linear Models in Regional and Interregional Modeling


Authors: Bohuslav Sekerka, Robert Bata

Abstract: Models, included in this paper, in contrast to the common model of inter-sector relations, focuses on products and services, but also activities with inputs in form of products and services as well. Proposed models also include regional aspect. There is described solution for the case that number of elements of products and services and number of activities are not equal, because there is a problem with finding solution.

Keywords: Decision-making, Models, Uncertainty, Risk, Regions

Issue 2, Volume 10, February 2011

Title of the Paper: Transient Temperature Solutions of a Cylindrical Fin


Authors: G.-C. Kuo, Y.-H. Hu, W.-L. Liaw, K.-J Wang, K.-Y. Kung

Abstract: Analytical temperature solutions to the transient heat conduction for a two dimensional cylindrical fin with arbitrary convective effects on lateral surface is obtained by the method of superposition and separation variables. The temperature distributions are generalized for a linear combination of the product of Bessel function, Fourier series and exponential type for nine different cases. Relevant connections with some other closely-related recent works are also indicated.

Keywords: Bessel function, Fourier series, Heat conduction, Temperature distribution, Separation variables, superposition

Title of the Paper: A Further Improved (G'/G )- Expansion Method and the Extended Tanh- Method for Finding Exact Solutions of Nonlinear PDEs


Authors: Elsayed M. E. Zayed

Abstract: In the present article, we construct the exact traveling wave solutions of nonlinear PDEs in mathematical physics via the (1 + 1) dimensional modified Kawahara equation by using the following two methods: (i) A further improved (G'/G )- expansion method, where G = G(ξ) satisfies the auxiliary ordinary differential equation [G''(ξ)]^2 = aG^2(ξ) + bG^4(ξ) + cG^6(ξ), where ξ = x - Vt while a, b, c and V are constants. (ii) The well known extended tanh- function method. We show that the exact solutions obtained by these two methods are equivalent. Note that the first method (i) has not been used by anyone before.

Keywords: (G'/G )- expansion method, auxiliary equation, extended tanh- function method, traveling wave solutions, modified Kawahara equation

Title of the Paper: β0-Excellent Graphs


Authors: A. P. Pushpalatha, G. Jothilakshmi, S. Suganthi, V. Swaminathan

Abstract: Claude Berge [1] in 1980, introduced B graphs. These are graphs in which every vertex in the graph is contained in a maximum independent set of the graph. Fircke et al [3] in 2002 made a beginning of the study of graphs which are excellent with respect to various graph parameters. For example, a graph is domination excellent if every vertex is contained in a minimum dominating set. The B-graph of Berge was called β0 excellent graph. β0 excellent trees were characterized [3]. A graph is just β0 excellent if every vertex belongs to exactly one maximum independent set of the graph.This paper is devoted to the study of β0 excellent graphs and just β0 excellent graphs.

Keywords: β0-excellent and just β0 excellent, Harary graphs, Generalized Petersen graph

Title of the Paper: Analysis of a Deteriorating Cold Standby System with Priority


Authors: Lixia Ma, Genqi Xu, Nikos E. Mastorakis

Abstract: A deteriorating cold standby repairable system consisting of two dissimilar components and one repairman is studied in this paper. Suppose that the life of each component satisfies the exponentially distribution and repair time of the component satisfies the general distribution, the component 1 has priority in use and repair. Firstly, a mathematical model is built via the differential and partial differential equations. And then using the C0-semigroup theory of bounded linear operators, the existence and uniqueness of the solution, the non-negative steady-state solution and the exponential stability of the system are derived. Based on the stability result, some reliability indices of the system and an optimization problem are presented at the end of the paper.

Keywords: C0 Semigroup, Well-Posedness, Asymptotic Stability, Exponential Stability, Availability

Issue 3, Volume 10, March 2011

Title of the Paper: A Heuristic for the Multi-knapsack Problem


Authors: Jose Grandon, Ivan Derpich

Abstract: In this work a heuristic for the problem multi-knapsack , based on directions of ascent is presented. These directions are generated from a center of the polyhedron and they conduct to good approximations of the integer solutions. For it a center of the polyhedron of the relaxed problem is obtained. Then an interior ellipse is constructed in this polyhedron and those eigenvectors of the ellipse that present the best objective ascent of the function are selected as ascent direction. For determine how many eigenvectors to use, an angle that relate the eigenvector with the objective function, was used. The heuristic algorithm has been proved with problems from the OR-library. Four groups of problems were proved with 30 instances every one, combining 100 and 250 variables with 5 and 10 constraints. The results show process time that are from a little seconds for little problems, to 400 seconds for bigger problems. The Cpu time average is 190 seconds. The errors of the best solution found measured using the integrality gap are in order to 3% in the worst case.

Keywords: Heuristics, Integer Programming, Multi-knapsack

Title of the Paper: Introduction to the Rectangular Trigonometry in Euclidian 2D-Space


Authors: Claude Bayeh

Abstract: Trigonometry is a branch of mathematics that deals with relations between sides and angles of triangles. It has some relationship to geometry, though there is disagreement on exactly what that relationship is. For some, trigonometry is just a subtopic of geometry. The trigonometric functions are very important in technical subjects like Astronomy, Relativity, science, engineering, architecture, and even medicine. In this paper, the rectangular trigonometry is introduced in order to be in the future a part of the General trigonometry topic. Thus, the definition of this original part is presented. The rectangular trigonometric functions are also defined. The importance of these functions is by producing multi signal forms by varying some parameters of a single function. Different signals and forms are analyzed and discussed. The concept of the rectangular Trigonometry is completely different from the traditional trigonometry in which the study of angles is not the relation between sides of a right triangle that describes a circle as the previous one, but the idea here is to use the relation between angles and sides of a rectangular form with the internal and external circles formed by the intersection of the rectangular form and the positive parts of x’ox and y’oy axis in the Euclidian 2D space and their projections. This new concept of relations will open a huge gate in the mathematical domain and it can resolve many complicated problems that are difficult or almost impossible to solve with the traditional trigonometry, and it can describe a huge number of multi form periodic signals.

Keywords: Mathematics, geometry, trigonometry, angular function, multi form signal, power electronics

Title of the Paper: Exact Traveling Wave Solutions of Nonlinear Variable Coefficients Evolution Equations with Forced Terms using the Generalized (G'/G) Expansion Method


Authors: Elsayed Zayed, Mahmoud Abdelaziz

Abstract: The exact traveling wave solutions of the nonlinear variable coefficients Burgers-Fisher equation and the generalized Gardner equation with forced terms can be found in this article using the generalized (G'/G)-expansion method. As a result, hyperbolic, trigonometric and rational function solutions with parameters are obtained. When these parameters are taken special values, the solitary wave solutions are derived from the hyperbolic function solutions. It is shown that the proposed method is direct, effective and can be applied to many other nonlinear evolution equations in the mathematical physics.

Keywords: Nonlinear evolution equations; Generalized (G'/G)-expansion method; Variable coefficients Burgers-Fisher equation with the forced term; Variable coefficients generalized Gardner equation with the forced term, Exact solutions

Issue 4, Volume 10, April 2011

Title of the Paper: Spectral Analysis of a Two Unit Deteriorating Standby System with Repair


Authors: Wenzhi Yuan, Genqi Xu

Abstract: In this paper, we analyze the spectra and stability of a system consisting of a working unit and repair unit, in which the working unit consists of one main unit and one standby unit, while the standby unit may deteriorate in its standby mode. Firstly, we formulate the problem into a suitable Banach space. And then we carry out a detailed spectral analysis of the system operator. Based on the spectral analysis and C0-semigroup theory, we prove the existence of positive solution and finite expansion of the solution according to its eigenvectors. As a consequence we get that its dynamic solutions converges exponentially to the steady-state solution. Finally, we derive some reliability indices of the system.

Keywords: C0-semigroup theory, dynamic solution, steady-state, exponential stability, availability

Title of the Paper: Michel-Penot Subdifferential and Lagrange Multiplier Rule


Authors: Triloki Nath, S. R. Singh

Abstract: In this paper, we investigate some properties of Michel Penot subdifferentials of locally Lipschitz functions and establish Lagrange multiplier rule in terms of Michel-Penot subdifferentials for nonsmooth mathematical programming problem.

Keywords: Nonsmooth optimization; approximate subdifferentials; generalized gradient; Michel Penot subdifferential; Banach space

Title of the Paper: Inverse Model to Determine the Optimal Number of Drops of RDC Column Using Fuzzy Approach


Authors: Hafez Ibrahim, Jamalludin Talib, Normah Maan

Abstract: Inverse modeling is natural in many real world application including industrial chemical engineering problems. This paper describes the process of determines optimal input and output of number of drops in various stage of rotating disc contactor column using fuzzy model. An algorithm of the fuzzy model is developed to simulate the above process.

Keywords: Liquid-Liquid Extraction, RDC Column, Drop Distribution, Inverse Model, Fuzzy Environment, Fuzzy Algorithm

Issue 5, Volume 10, May 2011

Title of the Paper: Almost Runge-Kutta Methods of Orders up to Five


Authors: Abraham Ochoche, Peter Ndajah

Abstract: In this paper, we have sought to investigate the viability of a type of general linear methods called Almost Runge-Kutta (ARK) methods, as a means of obtaining acceptable numerical approximations of the solution of problems in continuous mathematics. We have outlined the derivation and implementation of this class of methods up to order five. Extensive numerical experiments were carried out and the results clearly show that ARK methods are indeed a viable alternative to existing traditional methods.

Keywords: Almost, Order, Alternative, Euler, Runge – Kutta, General Linear Methods

Title of the Paper: Spectrum of A Class of Delay Differential Equations and Its Solution Expansion


Authors: Yaxuan Zhang

Abstract: In this paper we study the spectrum and solution expansion of the differential equation with multiple delays. Firstly, we present explicitly the asymptotic expressions of the eigenvalues under certain conditions. Then we prove that the root vectors of the system fail to form a basis for the state Hilbert space. However, by a trick, we expand the solution of the system according to the root vectors. As an application, we explain how to apply solution expansion to the numerical simulation of this kind of delay differential equations.

Keywords: Delay differential equation, multiple delays, spectrum, root vector, expansion of solution, numerical simulation

Title of the Paper: Turing Instability and Wave Patterns for a Symmetric Discrete Competitive Lotka-Volterra System


Authors: Yu-Tao Han, Bo Han, Lu Zhang, Li Xu, Mei-Feng Li,Guang Zhang

Abstract: In this paper, Turing instability of a symmetric discrete competitive Lotka-Volterra system is considered. To this end, conditions for producing Turing instability of a general discrete system is attained and this conclusion is applied to the discrete competition Lotka-Volterra system. Then a series of numerical simulations of the discrete model are performed with different parameters. Results show that the discrete competitive Lotka-Volterra system can generate a large variety of wave patterns in the Turing instability region. Particularly, the diffusion coefficients can be equivalent, that is, there is neither ”activator” nor ”inhibitor”. Similar results can not be obtained for the corresponding continuous models. On the other hand, the number of the eigenvalues is illuminated by calculation and the unstable spaces can be clearly expressed. Thus, the Turing mechanism is also explained.

Keywords: Turing instability, Diffusion, Discrete system, Eigenvalue, Lotka-Volterra system, Wave pattern

Issue 6, Volume 10, June 2011

Title of the Paper: An Algebraic Approach to Multidimensional Minimax Location Problems with Chebyshev Distance


Authors: Nikolai Krivulin

Abstract: Minimax single facility location problems in multidimensional space with Chebyshev distance are examined within the framework of idempotent algebra. The aim of the study is twofold: first, to give a new algebraic solution to the location problems, and second, to extend the area of application of idempotent algebra. A new algebraic approach based on investigation of extremal properties of eigenvalues for irreducible matrices is developed to solve multidimensional problems that involve minimization of functionals defined on idempotent vector semimodules. Furthermore, an unconstrained location problem is considered and then represented in the idempotent algebra settings. A new algebraic solution is given that reduces the problem to evaluation of the eigenvalue and eigenvectors of an appropriate matrix. Finally, the solution is extended to solve a constrained location problem.

Keywords: Single facility location problem, Chebyshev distance, Idempotent semifield, Eigenvalue, Eigenvector

Title of the Paper: Turing Instability for a Two Dimensional Semi-Discrete Oregonator Model


Authors: Li Xu, Guang Zhang, Jun-Feng Ren

Abstract: In this paper, a semi-discrete (time continuous but two-dimensional spatially discrete) Oregonator model has been given in the microscopic domain, and Turing instability theory analysis is discussed in detail. Turing instability conditions have been deduced by combining linearization method and inner product technique. Various patterns such as spiral wave, target wave, stripes and spotlike patterns are selectively obtained from numerical simulations in the Turing instability region. In particular, the effect of both system parameters and initial value on pattern formation is numerically proved.

Keywords: Semi-discrete Oregonator model; Turing instability; pattern formation; initial value; linearization method; inner product

Title of the Paper: Effect of Variable Viscosity on Convective Heat and Mass Transfer by Natural Convection from Horizontal Surface in Porous Medium


Authors: M. B. K. Moorthy, K. Senthilvadivu

Abstract: The aim of this paper is to investigate the effect of variable viscosity on free convective heat and mass transfer from a horizontal plate embedded in a saturated porous medium. The governing equations of continuity, momentum, energy and concentration are transformed into non linear ordinary differential equations using similarity transformations and then solved by using Runge – Kutta – Gill method along with shooting technique. Governing parameters for the problem under study are the variable viscosity (θc), the buoyancy ratio (N) and the Lewis number (Le). The velocity, temperature and concentration distributions are presented and discussed. The Nusselt and Sherwood number is also derived. The numerical values of local Nusselt and local Sherwood numbers have also been computed for a wide range of governing parameters θc, N and Le. The viscous and thermal boundary layer thicknesses are discussed.

Keywords: Free convection, Heat transfer, Mass transfer, Variable viscosity, Porous medium

Issue 7, Volume 10, July 2011

Title of the Paper: The Effects of the Change of Bond Insurance Premium and Capital Regulatory Ratio on Loan and Deposit Rates: An Option-Pricing Model


Authors: Shih-Heng Pao, Jyh-Horng Lin, Shu-Hui Chang

Abstract: We propose an option-based model that examines the relationships among municipal bonds with prepackaged insurance, capital insurance, and optimal bank interest margins. If the elasticity effect is positive (negative), then an increase in the bond insurance premium will increase the bank’s optimal loan rate (optimal deposit rate). If the elasticity effect is negative (positive), then an increase in the capital-to-deposit ratio will increase (decrease) the bank’s optimal loan rate. But an increase in the capital-to- deposit ratio increase the bank’s optimal deposit rate under the positive elasticity effect.

Keywords: Municipal bond, Capital-to-deposit ratio, Interest margins, Bond insurance, Elasticity, option

Title of the Paper: The Asymptotic Behavior of a Doubly Nonlinear Parabolic Equation with a Absorption Term Related to the Gradient


Authors: Huashui Zhan

Title of the Paper: Gronwall-Bellman Type Inequalities On Time Scales And Their Applications


Authors: Qinghua Feng, Fanwei Meng

Abstract: In this work, we investigate some new Gronwall-Bellman type dynamic inequalities on time scales in two independent variables, which provide a handy tool in deriving explicit bounds on unknown functions in certain dynamic equations on time scales. The established results generalize the main results on integral inequalities for continuous functions in [1] and their corresponding discrete analysis in [2].

Keywords: Dynamic inequality; Gronwall-Bellman inequality; Time scales; Dynamic equation; Bounded

Issue 8, Volume 10, August 2011

Title of the Paper: Traveling Wave Solutions for Some Nonlinear Evolution Equations by the First Integral Method


Authors: Bin Zheng

Abstract: In this paper, based on the known first integral method, we try to seek the traveling wave solutions of several nonlinear evolution equations. As a result, some exact travelig wave solutions and solitary solutions for Whitham-Broer-Kaup (WBK) equations, Gardner equation, Boussinesq-Burgers equations, nonlinear schrodinger equation and mKDV equation are established successfully.

Keywords: First integral method; Traveling wave solution; WBK equations, Gardner equation; Boussinesq-Burgers equations; nonlinear schrodinger equation; mKDV equation; Exact solution; Solitary solution

Title of the Paper: Relatively Relaxed Proximal Point Algorithms for Generalized Maximal Monotone Mappings and Douglas-Rachford Splitting Methods


Authors: Ram Verma

Abstract: The theory of maximal set-valued monotone mappings provide a powerful framework to the study of convex programming and variational inequalities. Based on the notion of relatively maximal relaxed monotonicity, the approximation solvability of a general class of inclusion problems is discussed, while generalizing most of investigations on weak convergence using the proximal point algorithm in a real Hilbert space setting. A well-known method of multipliers of constrained convex programming is a special case of the proximal point algorithm. The obtained results can be used to generalize the Yosida approximation, which, in turn, can be applied to generalize first-order evolution equations to the case of evolution inclusions. Furthermore, we observe that the Douglas-Rachford splitting method for finding the zero of the sum of two monotone operators is a specialization of the proximal point algorithm as well. This allows a further generalization and unification of a wide range of convex programming algorithms.

Keywords: Variational inclusion problems; Relatively maximal relaxed monotone mapping; Generalized resolvent

Title of the Paper: The Modified (G'/G)- Expansion Method and its Applications to Construct Exact Solutions for Nonlinear PDEs


Authors: Elsayed M. E. Zayed, Khaled A. Gepreel

Abstract: In the present article, we construct the traveling wave solutions involving parameters of some nonlinear PDEs; namely the nonlinear Klein - Gordon equations, the nonlinear reaction- diffusion equation, the nonlinear modified Burgers equation and the nonlinear Eckhaus equation by using the modified (G'/G)- expansion method, where G satisfies a second order linear ordinary differential equation. When these parameters are taken special values, the solitary waves are derived from the traveling waves. The traveling waves solutions are expressed by hyperbolic, trigonometric and the rational functions.

Keywords: Expansion method, nonlinear PDEs, exact solution

Title of the Paper: A Stability Result for a Generalized Trigonometric-Quadratic Functional Equation with one Unbounded Function


Authors: Charinthip Hengkrawit, Vichian Laohakosol, Janyarak Tongsomporn

Abstract: A generalized trigonometric-quadratic functional equation of the form over the domain of an abelian group and the range of the complex field is considered. Its stability is established based on the assumption that the function K is unbounded. Subject to certain natural conditions, explicit shapes of the functions H and K are determined. Several existing related results are derived as direct consequences.

Keywords: Quadratic functional equation, trigonometric functional equation, stability, unboundedness, abelian group, additive function

Issue 9, Volume 10, September 2011

Title of the Paper: The Consistency Analysis of Coefficient Regularized Classification with Convex Loss


Authors: Sheng Baohuai, Xiang Daohong

Abstract: It is known that the learning rates are the quantitative description of the consistency of a learning al- gorithm. In the present paper, we provide the learning rates for the coefficient regularized classification learning algorithm with a K?functional whose explicit rates are estimated when the loss functions are least square loss and the hinge loss.

Keywords: Coefficient regularized classification, machine learning, convex loss, differentiable loss,K-functional, learning rates

Title of the Paper: In-situ Combustion Simulation for Heavy Oil Reservoirs


Authors: Rasaq O. Olayiwola, Reuben O. Ayeni

Abstract: In this paper we study the continuity, momentum and coupled nonlinear energy and species convection-diffusion equations describing the in-situ combustion process in porous media. We assume the fuel depends on the space variablex. We examine the properties of solution under certain conditions. Using large activation energy asymptotics and shooting method we provide a numerical solution of the problem and obtained temperature and concentration profiles.

Keywords: In-situ, combustion, porous media, simulation, heavy oil, reservoirs

Title of the Paper: Stability Analysis of Periodic Solutions for Stochastic Reaction-Diffusion High-Order Cohen-Grossberg-Type Bam Neural Networks with Delays


Authors: Yunquan Ke, Chunfang Miao

Abstract: In this paper, the mean square exponential stability of the periodic solution for stochastic reaction- diffusion high-order Cohen-Grossberg-Type BAM neural networks with time delays is investigated. By construct- ing suitable Lyapunov function, applying It?o formula and Poincar/e mapping, we give some sufficient conditions to guarantee the mean square exponential stability of the periodic solution. An illustrative example are also given in the end to show the effectiveness of our results.

Keywords: Stochastic reaction-diffusion Cohen-Grossberg-type BAM neural networks; Ito formula; Poincare mapping; periodic solution; mean square exponential stability

Title of the Paper: Robust Portfolio Selection Problem for an Insurer with Exponential Utility Preference


Authors: Hui Zhao, Ximin Rong, Jiling Cao

Abstract: In this paper, we consider the robust portfolio selection problem for an insurer in the sense of maximiz- ing the exponential utility of his wealth. This special robust investment problem, where underwriting results and a risk-free asset are considered, differs from ordinary robust portfolio selection problems. The insurer has the option of investing in a risk-free asset and multiple risky assets whose returns are described by the factor model. The rate of underwriting return is also assumed to be correlated with returns of risky assets. When the parameters are perturbed in a joint uncertainty set, the robust investment problem for an insurer is established and this problem is reformulated and solved as a cone programming problem. Finally, some computational results are given for raw market data.

Keywords: Robust optimization, Investment for insurers, Joint uncertainty set, Underwriting result, Cone programming, Factor model

Issue 10, Volume 10, October 2011

Title of the Paper: Global Exponential Stability of High-Order BAM Neural Networks with S-type Distributed Delays and Reaction Diffusion Terms


Authors: Chengrong Ma, Fengyan Zhou

Abstract: In this paper, by constructing suitable Lyapunov functional, using differential mean value theorem and homeomorphism, we analyze the global exponential stability of high-order bi-directional associative memory (BAM) neural networks with reaction-diffusion terms and S-type distributed delays. Some sufficient theorems have been derived under different conditions to guarantee the global exponential stability of the networks. Moreover, two numerical examples are presented to illustrate the feasibility and effectiveness of the results.

Keywords: High-order BAM Neural Networks; reaction- diffusion terms; S-type distributed delays; Lyapunov functional; exponential stability

Title of the Paper: Weighted Generalized Kernel Discriminant Analysis Using Fuzzy Memberships


Authors: Jing Yang, Liya Fan

Abstract: Linear discriminant analysis (LDA) is a classical approach for dimensionality reduction. However, LDA has limitations in that one of the scatter matrices is required to be nonsingular and the nonlinearly clustered struc- ture is not easily captured. In order to overcome these problems, in this paper, we present several generalizations of kernel fuzzy discriminant analysis (KFDA) which include KFDA based on generalized singular value decomposition (KFDA/GSVD), pseudo-inverse KFDA (PIKFDA) and range space KFDA (RSKFDA). These KFDA-based algorithms adopts kernel methods to accommodate nonlinearly separable cases. In order to remedy the problem that KFDA-based algorithms fail to consider that different contribution of each pair of class to the discrimination, weighted schemes are incorporated into KFDA extensions in this paper and called them weighted generalized KF- DA algorithms. Experiments on three real-world data sets are performed to test and evaluate the effectiveness of the proposed algorithms and the effect of weights on classification accuracy. The results show that the effect of weighted schemes is very significantly.

Keywords: Kernel fuzzy discriminant analysis; fuzzy membership; undersampled problem; weighting function; classification accuracy

Title of the Paper: Kernel-based Weighted Discriminant Analysis with QR Decomposition and Its Application to Face Recognition


Authors: Jianqiang Gao, Liya Fan

Abstract: Kernel discriminant analysis (KDA) is a widely used approach in feature extraction problems. However, for high-dimensional multi-class tasks, such as faces recognition, traditional KDA algorithms have a limitation that the Fisher criterion is non-optimal with respect to classification rate. Moreover, they suffer from the small sample size problem. This paper presents two variants of KDA called based on QR decomposition weighted kernel discriminant analysis (WKDA/QR), which can effectively deal with the above two problems, and based on singular value decomposition weighted kernel discriminant analysis (WKDA/SVD). Since the QR decomposition on a small size matrix is adopted, the superiority of the proposed method is its computational efficiency and can avoid the singularity problem. In addition, we compare WKDA/QR with WKDA/SVD under the parameters of weighted function and kernel function. Experimental results on face recognition show that the WKDA/QR and WKDA/SVD are more effective than KDA, and WKDA/QR is more effective and feasible than WKDA/SVD.

Keywords: QR decomposition, Kernel discriminant analysis (KDA), Feature extraction, Face recognition, small sample size (SSS)

Title of the Paper: Research on Delayed Complexity Based on Nonlinear Price Game of Insurance Market


Authors: Junling Zhang, Junhai Ma

Abstract: Based on the study of scholars, supposing that one of the two competitors in the market makes decision only with bounded rationality without delay, and the other competitor makes the delayed decision with one period and two periods, we established the dynamic price game models respectively. In this paper we mainly analyzed the stable points and their stabilities of the dynamic system with two-period delayed decision, and made computer simulations for the system stability under different decision rules and the complexity such as the bifurcations, chaos and so on. The numerical simulation results showed that, the delayed decision can not change the system’s Nash equilibrium point, however it can improve the system’s stability; the changes of delayed period and weights of delay variables will make the system’s stability area change correspondingly; when the company make decision with delay, they should consider the introducing time. Because the proper delayed periods and weights of variables will obviously improve his competition advantages.

Keywords: Duopoly, delayed decision, bifurcation, chaotic, nonlinear price game, insurance market

Issue 11, Volume 10, November 2011

Title of the Paper: Applied Research on the Coexistence Relationship between Tianjin Port and Inland Transportation System based on Population Ecology Model


Authors: Jun Wang, Junhai Ma

Abstract: First, this article takes container throughput of Tianjin Port as an example to estimate the future port scale by using genetic algorithms. Then this article applies BP neural network to compare the advantages and disadvantages of Tianjin Port and its competitors by analyzing the data of listed port companies. Finally, this article does some research on the coexistence relationship between port and transportation. The results show that Tianjin Port’s scale is beyond the inflection point of Growth curve, its speed of development will slow down. High administration cost and the lag of inland transportation construction are two major factors which constrain Tianjin Port’s development. After coexistence relationship analysis we find that the develop speeds of port and inland transportation should reach a reasonable proportion to remain symbiotic relationships.

Keywords: Port, population ecology model, genetic algorithms, BP neural network, inherent complexities, mathmatics

Title of the Paper: Rich Dynamical Behaviors of a Predator-Prey System with State Feedback Control and a General Functional Responses


Authors: Yongzhen Pei, Haiyong Wang

Abstract: In this paper, we study dynamics of a logistical predator-prey system with state feedback control and a general functional responses. By using the Poincare map, some conditions for the existence and stability of semi-trivial solution and positive periodic solution are obtained. Numerical results are carried out to illustrate the feasibility of our main results, and it is shown that a chaotic solution is generated via a cascade of period-doubling bifurcations, which implies that the presence of pulses makes the dynamic behavior more complex.

Keywords: Prey-predator system; State feedback control; Periodic solution; Extinction; Bifurcation

Title of the Paper: Dynamic Behavior in a HIV Infection Model for the Delayed Immune Response


Authors: Yongzhao Wang, Dongwei Huang, Shuangde Zhang, Hongjie Liu

Abstract: Considering full Logistic proliferation of CD4+ T-cells and retarded immune response, we analyze a HIV model in this paper. Global asymptotic stability of the infection-free equilibrium and immune-absent equilibrium is investigated, and some conditions for Hopf bifurcation around infected equilibrium to occur are also obtained by using the time delayed as a bifurcation parameter. Numerical simulating works are presented to illustrate the main results, and we can observe the effects of the proliferation rate of CD4+ T-cells for the dynamics of system. This result can be used to explain the complexity of the immune state of AIDS.

Keywords: Global stability; Delayed immune response; Logistic proliferation

Title of the Paper: About the Weak Efficiencies in Vector Optimization


Authors: Cristina Stamate

Abstract: We present the principal properties of the weak efficient points given in the literature. We study a vector optimization problems for multifunctions, defined with infimal and supremal efficient points in locally convex spaces ordered by convex, pointed closed cones with nonempty interior. We introduce and study the solutions for these problems using the algebraic and topological results for the efficient points. Also, we’ll present the links between our problems and 2 special problems, the scalar and the approximate problems as well as some saddle points theorems and duality results using a suitable Lagrangian adapted for the INFSUP problem, a generalization of the MINMAX problem.

Keywords: Order vector spaces, convex cones, efficient points

Issue 12, Volume 10, December 2011

Title of the Paper: On the Sophie Germain Prime Conjecture


Authors: Fengsui Liu

Abstract: By extending the operations +,X on natural numbers to the operations on finite sets of natural numbers, we founded a new formal system of a second order arithmetic <P(N),N,+,X,0,1,є>. We designed a recursive sieve method on residue classes and obtained recursive formulas of a set sequence and its subset sequence of Sophie Germain primes, both the set sequences converge to the set of all Sophie Germain primes. Considering the numbers of elements of this two set sequences, one is strictly monotonically increasing and the other is monotonically increasing, the order topological limits of two cardinal sequences exist and these two limits are equal, we concluded that the counting function of Sophie Germain primes approaches infinity. The cardinal function is sequentially continuous with respect to the order topology, we proved that the cardinality of the set of all Sophie Germain primes is ℵ0 using modular arithmetical and analytic techniques on the set sequences. Further we extended this result to attack on Twin primes, Cunningham chains and so on.

Keywords: Second order arithmetic,Recursive sieve method,Order topology,Limit of set sequences,Sophie Germain primes, Twin primes, Cunningham chain, Ross-Littwood paradox

Title of the Paper: Generalized Integral Inequalities for Discontinuous Functions with One or Two Independent Variables


Authors: Qinghua Feng, Fanwei Meng

Abstract: In this paper, some new integral inequalities for discontinuous functions with one or two independent variables are established, which provide new bounds for unknown functions in certain integral equations. The established inequalities generalize the main results in [14,15,16,17].

Keywords: Integral inequality, Discontinuous function, Integral equation, Bounded, Qualitative analysis

Title of the Paper: Fuzzy Time Series Model Incorporating Predictor Variables and Interval Partition


Authors: Hsien-Lun Wong, Chi-Chen Wang

Abstract: Prediction is a critical component in decision-making process for business management. Fuzzy Markov model is a common approach for dealing with the prediction of time series. However, not many studies devoted their attention to the effect of the parameters on model fitting for fuzzy Markov model. In the paper, we examine the prediction ability for fuzzy Markov model, based on the data of Taiwan’s exports and foreign exchange rate. The empirical results indicate that fuzzy Markov model performs better for longer period forecasting; moreover, neither increment information nor increasing window basis would improve the performance for fuzzy Markov model. An advantage of the paper provides a beneficial knowledge when using Markov model for prediction.

Keywords: Fuzzy time series, Fuzzy Markov model, High order fuzzy relationship, Increment information, Interval partition, Taiwan exports

Title of the Paper: Population Dynamics: A Geometrical Approach of Some Epidemic Models


Authors: M. E. Kahil

Abstract: Recently, the behavior of different epidemic models and their relation both to different types of ge- ometries and to some biological models has been revisited. Path equations representing the behavior of epidemic models and their corresponding deviation vectors are examined. A comparison between paths and their deviation vectors in Riemannian and Finslerian Geometries is presented.

Keywords: Epidemic model, Path equation, Geometrical method

Title of the Paper: Ergodic Theorems with Respect to Lebesgue


Authors: Eleonora Catsigeras

Abstract: We study, from the ergodic viewpoint, the asymptotic dynamics in the future of a full Lebesgue set of initial states. The dynamical systems under research are deterministic and evolving with discrete time n ∈ N by the forward iterations of any continuous map f : M 7→ M acting on a finite-dimensional, compact and Riemannian manifold M. First, we revisit the classic definition of physical or SRB probability measures, and its generalized notion of weak physical probabilities. Then, inspired in the statistical meaning of the ergodic attractors defined by Pugh and Schub, which support ergodic physical measures, we define the more general concept of ergodic-like attractor. We prove that any such generalized attractor is the support of weak physical probabilities and conversely. Then, we revisit the proof of existence of weak physical probabilities and conclude that any continuous dynamics exhibits at least one ergodic-like attractor.

Keywords: Ergodic theory, physical measures, ergodic attractors, topological dynamics, theoretical measure dynamics

Title of the Paper: A General Iterative Algorithm for Equilibrium Problems and Strict Pseudo-Contractions in Hilbert Spaces


Authors: Ming Tian, Lei Liu

Abstract: In this paper an iterative scheme is presented for finding a common element of the set of solutions of the variational inequality, fixed points of strict pseudo-contraction and solutions of equilibrium problem in Hilbert spaces. Under suitable conditions, it is proved that implicit and explicit schemes are of strong convergence properties. Obtained results improve and extend the existed results.

Keywords: Nonexpansive mapping, Fixed point, Equilibrium problem, Strict pseudo-contraction, Variational inequality, Iterative algorithm

Title of the Paper: Exponential p−Stability of Impulsive Stochastic Fuzzy Cellular Neural Networks with Mixed Delays


Authors: Qianhong Zhang, Lihui Yang

Abstract: This paper deals with an impulsive stochastic fuzzy cellular neural networks with both time-varying and infinite distributed delays. Based on M-matrix theory and stochastic analysis technique, a sufficient condition is obtained to ensure the existence, uniqueness, and global exponential p−stability of the equilibrium point for the addressed impulsive stochastic fuzzy cellular neural network with mixed delays. Moreover a numerical example is given to illustrate the effectiveness of stability results.

Keywords: Stochastic fuzzy cellular neural networks, Brownian motion, Global exponential p−stability, Mixed delays, Impulse

Title of the Paper: Positive Solutions for Singular Third-Order Nonhomogeneous Boundary Value Problems with Nonlocal Boundary Conditions


Authors: Ping Kang

Abstract: Under various weaker conditions, we establish various results on the existence and nonexistence of positive solutions for singular third-order nonhomogeneous boundary value problems with nonlocal boundary conditions. The arguments are based upon the fixed point theorem of cone expansion and compression. Finally, we give two examples to demonstrate our results.

Keywords: Positive solutions, Fixed points, Boundary value problems, Nonhomogeneous, Ordinary differential equations

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