WSEAS CONFERENCES. WSEAS, Unifying the Science

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 Volume 8,  2009
ISSN: 1109-2769
E-ISSN: 2224-2880








Issue 1, Volume 8, January 2009

Title of the Paper: Ionospheric Effects on GPS Range Finding Using 3D Ray-Tracing and Nelder-Mead Optimisation Algorithm


Authors: Siti Sarah Nik Zulkifli, Mardina Abdullah, Azami Zaharim, Mahamod Ismail

Abstract: The Earth’s ionosphere plays a crucial role in Global Positioning System (GPS) accuracy because this layer represents the largest source of positioning error for the users of the GPS after the turn-off of Selective Availability (SA). This paper studies the ionospheric effect on transionospheric signal propagation for the Earth-satellite path using 3D Jones Ray-Tracing utilizing Nelder-Mead optimisation algorithm. The ionospheric delay or advance is obtained from the difference between the distance of the ray path from the satellite to the receiver determined from the ray-tracing and the distance for propagation over the line of sight (LOS) at the velocity of light in vacuum. The difference between the standard dual-frequency models corrected range and LOS, known as Residual Range Error (RRE) is calculated. Results show that the RRE of group delay value is different from RRE of phase advance. On the other hand, the group and phase path is longer when considering the geomagnetic field effect on both GPS frequencies L1 and L2. The higher order term in total electron content (TEC) calculation that relates to the refractive index is normally neglected due to its small value, but it is clearly shown that it does have some effects in ray-tracing. This analysis needs to be considered for more accurate GPS range finding.

Keywords: GPS, Ionosphere, ray-tracing, Nelder-Mead optimization, RRE

Title of the Paper: Effects of a Supplementary Quadrature in the Collocation Method for Solving the Hartree Fock Equations in Ab-Initio Calculations


Authors: Sever Spanulescu, Mircea Moldovan

Abstract: The collocation method for solving the Hartree-Fock equations of the self-consistent field in large atomic and molecular systems is analyzed and a method for improving its performances by supplementary analytical and numerical quadrature is proposed. We used monomial and Chbyshev type trial functions and the collocation points were equidistant or Chebyshev polynomial roots. The singularities have been avoided by a function change and analytical expressions have been obtained for the most part of the integrated terms in the matrix elements, except the Hartree-Fock potential which is treated separately in a similar way. This a-priori analytical treatment ensures a greater speed and a lower condition number of the matrix necessary for the expansion’s coefficient calculus, with an important effect on the overall precision and speed. Some numerical results are presented and compared with well-known types of orbitals, demonstrating the performance increasing in terms of precision and computing effort.

Keywords: Ab–initio methods, self consistent field, Hartree-Fock equations, Collocation, Evanescence

Title of the Paper: Analytical Properties and Numerical Calculations of High Transcendental Functions Involved in the Relativistic Amplitudes of two Photon Atomic Processes


Authors: Adrian Costescu, Sever Spanulescu, Cristian Stoica

Abstract: The high transcendental functions that occur in the relativistic expressions of the amplitudes of the two photon atomic processes are analytically treated taking advantage of their specific parameters values. We present some identities and recurrence relationships that allow reducing the number of needed Appell functions and transform their imaginary part in terms of Gauss hypergeometric functions. If the physical model takes into account only the terms up till the fourth power in Zαin the real part and the seventh power in the imaginary part, some transcendental functions may be reduced to elementary functions. The numerical results obtained using the presented methods were compared with other’s authors results, displaying a very good agreement.

Keywords: Appell functions, Gauss hypergeometric functions, relativistic atomic processes

Issue 2, Volume 8, February 2009

Title of the Paper: A New Boundary Element Approach for the 3D Compressible Fluid Flow Around Obstacles


Authors: Luminita Grecu

Abstract: The paper presents a boundary element approach for the problem of the finite span airfoil in a subsonic compressible fluid flow. The singular boundary integral equation equivalent with the mathematical model characterized by partial differential equation is solved in this paper by the use of constant and linear isoparametric boundary elements of Lagrangean type. A special attention is given to the treatment of the singular integrals because their evaluation major influences the numerical solutions accuracy. Some aspects about how to treat the integrals of singular kernels in case of solving 3D problems are presented. An efficient method that is applied consists in using suitable geometrical transformations of coordinates to eliminate the singularities. A computer code based on this method is made and numerical results are obtained. The computer code is tested by making an analytical checking and the results show the efficiency of the method.

Keywords: Boundary element method, linear boundary element, singular integral, compressible fluid flow

Title of the Paper: More on the Green Solow Model with Logistic Population Change


Authors: Massimiliano Ferrara, Luca Guerrini

Abstract: This paper generalizes the model introduced by Ferrara and Guerrini [13], where two different research lines have been joined together: the one studying the effects of incorporating technological progress in pollution abatement in the Solow-Swan model (Brock and Taylor [6]), and that analyzing the role of a logistic population growth rate within the Solow-Swan model (Ferrara and Guerrini [13]). In this framework, the economy is described by a three dimensional dynamical system, whose solution can be explicitly determined. We note that physical capital can be expressed in closed-form via Hypergeometric functions. As well, we prove the model’s solution to be convergent in the log-run. We characterize the economy balanced growth path equilibrium, and find that sustainable growth occurs if technological progress in abatement is faster than technological progress in production. An environmental Kuznets curve may result along the transition to the balanced growth path. If there is no technological progress in abatement, then there is no EKC. Furthermore, the economy has a unique equilibrium (a node), which is locally asymptotically stable.

Keywords: Green Solow, Logistic population, Pollution, Sustainable growth, Environmental Kuznets curve

Title of the Paper: The Study of some Discrete IS-LM Models with Tax Revenues and Time Delay


Authors: Mihaela Neamtu, Gabriela Mircea, Dumitru Opris

Abstract: In this paper, we study some discrete IS-LM models with tax revenues and time delay. Considering its parameters as variables, we analyze the existence of the Neimark-Sacker bifurcation. We find the normal form and its Lyapunov coefficient. For each considered model, using programs in Maple 11 we make some numerical simulations that verify the theoretical results.

Keywords: IS-LM model, tax revenues, Neimark-Sacker bifurcation

Title of the Paper: Neimark-Sacker and Flip Bifurcations in a Discrete-Time Dynamic System for Internet Congestion


Authors: Gabriela Mircea, Dumitru Opris

Abstract: The aim of this paper is to study the Neimark-Sacker and flip bifurcations for the discrete-time dynamic system, which describes the Internet congestion, with a single link and two sources. We describe the algorithm in order to determine the Neimark-Sacker bifurcation and the normal form. We establish the existence of a flip bifurcation for the case when the model’s two parameters depend on the real parameter a, which influences the existence of the bifurcation. The numerical simulations verify the theoretical results.

Keywords: Internet model, Neimark-Sacker bifurcation, flip bifurcation, feedback delay, numerical simulations

Title of the Paper: About Solutions of Renewal Equations and Determinations of Failure Moments of a System as Equilibrium Points


Authors: Ilie Mitran

Abstract: The results presented in this paper lead to solving main problems of the reliability theory: specifying the failure moments of a failure and determining the solutions of renewal equations. We analyze the following situations: 1. the system structure is not taken into consideration; 2. the system structure is known. In the first case we presume that the adopted efficiency function is the average operation time and, by using specific methods of the theory of games, we can prove that there is no equilibrium type solution, so the failure moment of the system cannot be precisely determined. By solving some specific problems, type maximum or minimax, we can only get the interval where the failure point of the system is found. The optimal problem type maximum is solved by specific methods from the theory of games while the optimal problem type minimax is solved by using the maximum principle of Pontriaghin. In the second case we start from the graph structure associated to a system with renewal operations and we build immediately the equation system with finite differences and the system of differential equations associated to this graph. Applying the Laplace transformation it is determined the system availabilities and unavailabilities caused by its subsystems. The failure moments of the system are determined as equilibrium points but the difficulties in calculations lead to obtaining only an approximate solution. Knowing the failure moments of the analyzed system lead to the reconsideration of the renewal policies of the system. Practically, there are determined the approximate solutions of the renewal equations and their separation curve. Having these elements we can completely analyze the renewal process; this analysis being based both on the failure moments of the system and on the renewal costs of the analyzed system.

Keywords: Reliability function, Markov process, Laplace transformation of availability, replacement times

Title of the Paper: Possibilities for Increasing the Use of Machineries Using Computer Assisted Statistical Methods


Authors: Ilie Mitran, Florin Dumitru Popescu, Marin Silviu Nan, Septimiu Sorin Soba

Abstract: Reliability has recently emerged from the quality concept. If quality represents the total of a product’s qualities, which make it good for use according to the destination, the reliability represents the capacity of the product to maintain its quality during the entire usage time. Reliability is the quality of the product extended through time. Reliability, maintenance, availability and capacity related aspects have been treated distinctively up to one moment. Analytically, the reliability represents the probability that during a given period of time, a product will be flawless. The technological capability or reliability represents way in which a technological system may realize, on the entire process of fulfilling a mission, the corresponding technological performances for its objectives. A unitary approach, considering all the factors, in accordance to the operating conditions of technical systems, lays the fundaments of an interdisciplinary theory, called the Theory of safety during operation. The safety during operation, S, of a machinery or of a technological system represents the way it will fulfill its mission, being a function of availability A, reliability R, capacity C and maintenance M

Keywords: Availability, average time for good operation, maintenance, probabilistic diagrams, Duane

Issue 3, Volume 8, March 2009

Title of the Paper: The Ramsey Model with Logistic Population Growth and Benthamite Felicity Function Revisited


Authors: Massimiliano Ferrara, Luca Guerrini

Abstract: In this paper we extend the study done by Ferrara and Guerrini [12], where two different research lines within the Ramsey model were joined together: the one studying the role of a logistic population growth rate (Accinelli and Brida [2]), and the one analyzing the effects of a Benthamite formulation for the utility function. The results obtained in [12] for the special case of a constant intertemporal elasticity of substitution (CIES) utility function and a Cobb-Douglas production function are provided to be still true for a general utility function and a neoclassical production function. We have that the model is described by a three dimensional dynamical system, whose unique non-trivial steady state equilibrium is a saddle point with a two dimensional stable manifold. Consequently, the speed of convergence is determined by two stable roots, rather than only one as in the basic Ramsey model. In addition, in the special case of a CIES utility function and a Cobb-Douglas technology, an explicit solution for the model can be derived, when capital’s share is equal to the reciprocal of the intertemporal elasticity of substitution.

Keywords: Ramsey, Logistic population, Benthamite, Saddle point, Exact solution

Title of the Paper: Genetic Algorithms with Nelder-Mead Optimization in the variational methods of Boundary Value Problems


Authors: Nikos E. Mastorakis

Abstract: The p-Laplacian equation is a generalization of the PDE of Laplace Equation and in this paper, we present a way of its solution using Finite Elements. Our method of Finite Elements leads to an Optimization Problem that can be solved by an appropriate combination of Genetic Algorithms and Nelder-Mead . Our method is illustrated by a numerical example. Other methods for the solution of other equations that contain the p-Laplacian operator are also discussed.

Keywords: Boundary Value Problems, Finite Elements, Genetic Algorithms with Nelder-Mead. p-Laplacian, non-Newtonian fluid flow

Title of the Paper: Troubled Asset Relief Program, Bank Interest Margin and Default Risk in Equity Return: An Option-Pricing Model


Authors: Jyh-Jiuan Lin, Ching-Hui Chang, Jyh-Horng Lin

Abstract: Will banks be willing to sell their toxic loans with the help of the Troubled Asset Relief Program (TARP)? The answer is yes as long as bids are high enough to tempt banks to deal. With the TARP’s help, an increase in the toxic loans sold to the government increases the bank’s margin and decreases the bank’s default probability in equity return when the bank encounters greater risk. This paper concludes that setting up the TARP for the ‘bad bank’ solution may be a good move for retail banking, resulting in high margin and low default risk when its target banks are willing sellers.

Keywords: Toxic Loans, Interest Margin, Default Risk, Troubled Asset Relief Program

Title of the Paper: High Order Alternating Group Explicit Finite Difference Method for Parabolic Equations


Authors: Qinghua Feng, Bin Zheng

Abstract: Based on the concept of domain decomposition we construct a class of alternating group explicit method for fourth order parabolic equations. Furthermore, an exponential type alternating group explicit method for 2D convection-diffusion equations is derived, which is effective in convection dominant cases. Both of the two methods have the property of unconditional stability and intrinsic parallelism. Domain decomposition and group computing can be obtained in both of the two methods.

Keywords: Parabolic equations, alternating group, parallel computation, unconditionally stable, finite difference

Title of the Paper: Application of the Alternating Group Explicit Method for Convection-Diffusion Equations


Authors: Qinghua Feng, Bin Zheng

Abstract: Based on an unconditionally stable finite difference implicit scheme, we present a concept of deriving a class of effective alternating group explicit iterative method for periodic boundary value problem of convectiondiffusion equations, and then give two iterative methods. The methods are verified to be convergent, and have the property of parallelism. Furthermore we construct an alternating group explicit difference method and another iterative method. All of the methods are suitable for parallel computation. Results of numerical experiments show that the methods are of higher accuracy than the known methods in [1,2,6], and will not lead to numerical instability in convection dominant case.

Keywords: Iterative method, iterative method, parallel computing, alternating group, parabolic equations

Issue 4, Volume 8, April 2009

Title of the Paper: Finite Difference Methods with Intrinsic Parallelism for Parabolic Equations


Authors: Bin Zheng, Qinghua Feng

Abstract: Based on eight saul’yev asymmetry schemes and the concept of domain decomposition, a class of finite difference method (AGE) with intrinsic parallelism for 1D diffusion equations is constructed. Stability analysis for the method is done. We also pay attention to the implementation of the parallel algorithms for 2D convectiondiffusion equations. Based on another group of saul’yev asymmetry schemes and the Crank-Nicolson scheme we construct a class of alternating group explicit Crank-Nicolson method(AGEC-N). Both of the present methods are suitable for parallel computation. Stability analysis are also given. In order to verify the methods, we present several numerical examples at the end of the paper. Results of numerical examples show all the methods are of high accuracy.

Keywords: Parallel computing, domain decomposition, alternating group, parabolic equations, finite difference

Title of the Paper: Finite Difference Method And Iterative Method With Parallelism For Dispersive Equations


Authors: Bin Zheng, Qinghua Feng

Abstract: In this paper, based on the concept of domain decomposition and alternating group, we construct a class of Finite Difference method for fifth order dispersive equations, Stability Analysis for he method is given. Then we construct a new alternating group explicit iterative method. Both the two methods are suitable for parallel computation. Results of numerical experiments show the methods are effective in computing.

Keywords: parallel computing, dispersive equations, finite difference, iterative method, asymmetry schemes, alternating group

Title of the Paper: Solution of the Schrodinger-Maxwell equations via Finite Elements and Genetic Algorithms with Nelder-Mead


Authors: Nikos E. Mastorakis

Abstract: In this paper the Numerical Solution of the system of PDEs of Schrodinger-Maxwell equations (with a general nonlinear term) via Finite Elements and Genetic Algorithms with Nelder-Mead is proposed. The method of Finite Elements and Genetic Algorithms with Nelder-Mead that has been proposed by the author recently is also used. (Recently, the existence of a nontrivial solution to the nonlinear Schrodinger-Maxwell equations in R3, assuming on the nonlinearity the general hypotheses introduced by Berestycki & Lions has been proved).

Keywords: Schrodinger-Maxwell equations, Finite Elements, Genetic Algorithms with Nelder-Mead

Title of the Paper: Existence, Uniqueness and Finite Difference Solution for the Dirichlet problem of the Schrodinger-Maxwell Equations


Authors: Nikos E. Mastorakis

Abstract: In this paper, the existence, the Uniqueness and the Finite Difference Scheme for the Dirichlet problem of the Schrodinger-Maxwell equations is going to be presented.

Keywords: Schrodinger-Maxwell equations, Finite Difference, Finite Difference Schemes

Title of the Paper: Applications of High Dimensional Model Representations to Computer Vision


Authors: Emre Demiralp

Abstract: A new and powerful method for matrix decomposition is developed in this work. It is similar to singular value decomposition and the main idea comes from the univariate approximation of a function, given on a planar grid’s nodes, by two variable high dimensional model representation. The proposed method is less iteration dependent than the singular value decomposition and the components are determined via straightforward steps containing recursions. It seems to have more capabilities than the singular value decomposition as an alternative method. An illustrative application is also given.

Keywords: Singular Value Decomposition, High Dimensional Model Representation, Matrix Decomposition

Issue 5, Volume 8, May 2009

Title of the Paper: Numerical Integration of Bivariate Functions over a Non Rectangular Area by Using Fluctuationlessness Theorem


Authors: Ercan Gurvit, N. A. Baykara, Metin Demiralp

Abstract: ”Fluctuation free matrix representation approximation Method” developed by M. Demiralp can be used in approximating the multiple remainder terms of the integral of the Multivariate Taylor expansion. This provides us with a new numerical integration method for multivariate functions. However in this paper instead of dealing with a single formula which takes care of the multiple remainder terms, a new approach is undertaken. At every step of a multivariate integration only one variable is taken care of. Thus an iterative procedure which speeds up the computation rate is obtained.

Keywords: Multivariate Functions, Fluctuationlessness Theorem, Numerical Integration, Explicit Remainder Term, Taylor Expansion

Title of the Paper: Fluctuationlessness Theorem and its Application to Boundary Value Problems of ODEs


Authors: Nejla Altay, Metin Demiralp

Abstract: A numerical method based on Fluctuationlessness Approximation, which was developed recently, is constructed for solving Boundary Value Problems of Ordinary Differential Equations on appropriately defined Hilbert Spaces. The numerical solution is written in the form of a Maclaurin series. The unknown coefficients of this series are determined by constructing an (n ? 2) unknown containing linear system of equations. The eigenvalues of the independent variable’s matrix representation are used in the construction of the matrices and the vectors of the linear system. The numerical solution obtained by Fluctuationlessness Approximation is then compared with the Maclaurin coefficients of the analytical solution to observe the quality of the convergence. Some illustrative examples are presented in order to give an idea about the efficiency of the method explained here.

Keywords: Boundary Value Problems, Eigenvalues, Fluctuationlessness Approximation, Hilbert Spaces

Title of the Paper: The Application of the Fluctuation Expansion with Extended Basis Set to Numerical Integration


Authors: Cosar Gozukirmizi, Metin Demiralp

Abstract: According to the fluctuationlessness theorem the matrix representation of a function can be approximated by the image of independent variable operator’s matrix representation under that function. The independent variable operator’s action is defined as the multiplication of the operand by the independent variable. Hence itself and therefore its matrix representation is universal, do not depend on the function. The application of this approximation to numerical integration forms a quadrature whose structure can be manipulated by changing the basis set of an n-dimensional Hilbert space. This work focuses on reflecting the effects of a complementary Hilbert space to a restricted Hilbert subspace by forming the basis set as certain linear combinations of some basis functions in order to improve the accuracy of the numerical integration based on fluctuationlessness theorem.

Keywords: Numerical Integration, Fluctuation Expansion, Fluctuationlessness Theorem, Hilbert Spaces

Title of the Paper: A Reverse Technique for Lumping High Dimensional Model Representation Method


Authors: M. Alper Tunga, Metin Demiralp

Abstract: An orthogonal hyperprismatic grid whose all nodes are accompanied by the given function values can not be generally constructed due to the random nature of the given function data. This prevents the reduction of the single multivariate interpolation to more than one univariate or bivariate interpolations even approximately. It is generally quite difficult to determine an analytical structure for the target function in these problems. Lumping HDMR method is an indexing based High Dimensional Model Representation (HDMR) algorithm used to reconstruct these types of multivariate data by imposing an indexing scheme to obtain an orthogonal geometry for the given problem. By this way, the training of the given data can be accomplished. The next problem is to determine a reverse algorithm for the testing data. This work is about a new algorithm to find the correct coordinate of the given testing data in the orthogonal geometry obtained through Lumping HDMR.

Keywords: Data Partitioning, Multivariate Analysis, High Dimensional Model Representation, Lumping HDMR

Title of the Paper: Truncation Approximations For Two Term Recursive Universal Form Of Matrix Ordinary Differential Equations


Authors: Sevda Uskuplu, Metin Demiralp

Abstract: This work focuses on the construction of an error bound formula for the series solution to Okubo Form of a set linear ordinary differential equation. Okubo Form is obtained using space extension concept which introduces new unknowns into the equation under consideration at the expense of a dimension growth. This is applied to the linear matrix ordinary differential equations in this work.

Keywords: Error estimation, Ordinary Differential Equations, Okubo form

Issue 6, Volume 8, June 2009

Title of the Paper: Fluctuation Free Matrix Representation Based Univariate Integration in Hybrid High Dimensional Model Representation (HHDMR) Over Plain and Factorized HDMR


Authors: Suha Tuna, Burcu Tunga, N. Abdulbaki Baykara, Metin Demiralp

Abstract: High Dimensional Model Representation (HDMR) which was first proposed fifteen years ago is still under development for the construction of its new varieties. It is a finite term representation of a multivariate function in terms of less variate functions. Its truncation at certain level of variance serves as an approximation to the target function and the truncation level is preferred to be kept at most bivariance for practical applications. Plain HDMR is used for the functions highly additive while the Factorized HDMR is designed for dominantly multiplicative functions. The Hybrid HDMR (HHDMR) combines these two HDMR varieties into a new version of HDMR and is expected to work more efficiently than plain HDMR and FHDMR. The construction of HHDMR basically uses the components of plain HDMR since FHDMR does the same. The definite integrals appearing in the definition of these components are efficiently approximated by using the fluctuation free matrix representation method which was recently developed by M. Demiralp.

Keywords: Multivariate Functions, High Dimensional Model Representation, Approximation, Fluctuation Free Matrix Representation

Title of the Paper: A Nonlinear Perturbative Scheme to SolveWeight Optimization Problem of High Dimensional Model Representation (HDMR)


Authors: Burcu Tunga, Metin Demiralp

Abstract: One way to increase the approximating quality of the High Dimensional Model Representation (HDMR) truncations is to increase the truncation order. However this is not generally desired for practical reasons if the order climbs to the multivariances beyond the bivariance. In these circumstances the other alternative is preferred. It is to change the structure of HDMR. This can be done either by using a different but again orthogonal geometry or by changing the structure of the weight function. Weight optimization is based on the constancy maximization and in fact gives different importances to the function values at different points of the HDMR domain. Weight function is considered as the square of a linear combination of certain basis functions and the linear combination coefficients are determined to maximize the constancy. The resulting equations are nonlinear. This work attempts to solve these equations by expanding unknowns around their certain nominal values.

Keywords: Multivariate Approximation, High Dimensional Model Representation, Perturbation Expansion

Title of the Paper: On the Solution of p-Laplacian for Non-Newtonian Fluid Flow


Authors: Nikos E. Mastorakis, Hassan Fathabadi

Abstract: The p-Laplacian, or the p-Laplace operator, is a quasilinear elliptic partial differential operator of 2nd order. In this paper, we examine several numerican schemes and we investigate their solution of non-linear problems in fluid mechanics.

Keywords: Numerical schemes, p-Laplacian, non-Newtonian fluid flow, nonlinear diffusion, nonlinear partial differential equation

Title of the Paper: On Different Types of Non-Additive Set Multifunctions


Authors: Anca Croitoru, Alina Gavrilut, Nikos E. Mastorakis, Gabriel Gavrilut

Abstract: In this paper, we study different types of non-additive set multifunctions (such as: uniformly autocontinuous, null-additive, null-null-additive), presenting relationships among them and some of their properties regarding atoms and pseudo-atoms. We also study non-atomicity and non-pseudo-atomicity of regular null-additive set multifunctions defined on the Baire (Borel respectively) ±-ring of a Hausdorff locally compact space and taking values in the family of non-empty closed subsets of a real normed space.

Keywords: Uniformly autocontinuous, null-null-additive, (pseudo)-atom, non-(pseudo)-atomic, extension, regular, Darboux property

Title of the Paper: Fluctuationlessness Theorem to Approximate Univariate Functions' Matrix Representations


Authors: Metin Demiralp

Abstract: Matrix representation of functions are required to convert an operator related problem to its algebraic counterpart over certain vectors and matrices. The problems involving operators which are purely or partially algebraic are most frequently encountered ones in applications. The algebraic operator here has a Hilbert space domain defined over square integrable univariate functions on a specified interval and its action on its argument is just multiplication by a function. We focus on univariate functions for simplicity in this very first step although the generalization to multivariance seems to be rather straightforward. The main purpose of this work is to introduce a conjecture to facilitate the numerical approximation of the matrix representation of the above algebraic operator and then to prove it to get an important theorem which seems to be capable of opening new very efficient horizons in numerical analysis and in its applications. Theorem states that the matrix representation of a univariate function is the image of the matrix representation of the independent variable under the same function for a finite Hilbert space. Illustrative numerical implementations are also given.

Keywords: Matrix Representation, Fluctuation Operator, Hilbert Spaces, Projection Operators, Algebraic Multiplication Operators

Issue 7, Volume 8, July 2009

Title of the Paper: A Cutting Plane Method for Solving Convex Optimization Problems over the Cone of Nonnegative Polynomials


Authors: Iurie Caraus, Ion Necoara

Abstract: Many practical problems can be formulated as convex optimization problems over the cone of nonnegative univariate polynomials. We use a cutting plane method for solving this type of optimization problems in primal form. Therefore, we must be able to verify whether a polynomial is nonnegative, i.e. if it does not have real roots or all real roots are multiple of even order. In this paper an efficient method is derived to determine a scalar value for which the polynomial is negative and in the case that such a value exists a feasible cut is constructed. Our method is based on Sturm theorem, which allows to determine the number of distinct roots of a polynomial on a given interval, in combination with the bisection method. For numerical stability we construct the associated Sturm sequence using Chebyshev basis, and thus we can work with high degree polynomials, up to hundreds. Numerical results show the efficiency of our new approach.

Keywords: Convex optimization problems over the cone of nonnegative polynomials, cutting plane method, Chebyshev polynomials, Sturm sequence, feasible cut

Title of the Paper: Image Enhancement Algorithm based on Retinex for Small-Bore Steel Tube Butt Weld's X-Ray Imaging


Authors: Yaoyu Cheng, Yu Wang, Yan Hu

Abstract: It is very common to use X-ray digital detection for the Small-bore steel tube butt weld. But the X-ray images have some shortcomings such as that contrast is not high, background noise is big, and the details can not be shown obviously, these shortcomings take a great inconvenience for the small-bore steel tube butt weld testing. So the detection efficiency can not be increased. Based on this, the Retinex algorithm is discussed and analyzed, such as single-scale of Retinex, multi-scale of Retinex, alterable framework of Retinex. Then it is applied to use an enhancement algorithm of improved Alterable framework on Retinex, and use this enhancement algorithm for X-ray image. This enhancement algorithm do not ask for much contrast of original image, which can effectively improve the original image contrast and image quality, the details of the image achieve the best visual effects. After the theoretical analysis and experimental results, we can see that, this enhancement algorithm can effectively enhance the image contrast, inhibit the background noise, compared with homomorphic filtering and histogram equalization algorithm. The standard of the image which is processed by this method can achieve the higher testing standard compared with homomorphic filtering and histogram equalization algorithm.

Keywords: Radiographic image, image enhancement, Retinex algorithm, single-scale Retinex algorithm, Multi-scale Retinex algorithm,alterable framework model, butt weld

Title of the Paper: Defect Detection and Characteristics Description of Auto Hub Radiographic Image Based on SUSAN Operation


Authors: Yaoyu Cheng, Yan Hu, Yu Wang

Abstract: The collected images’ target object is faint in the auto hub real-time X-ray detection, so it is easily making the miscarriage of justice in the auto hub detection. Most of the current method of detection of defects is by manual detection, so it is very difficult to improve detection efficiency and detection accuracy. Aiming at these issues and combining with the characteristics that auto hub’s image have so much noise source, it is adopted SUSAN operator for defect images’ edge detection, which is based on the image second partition, and it is achieved good results in edge detection by this method . And then it carried through defect detected for the image, such as, the number, level, center of gravity, area, and circle degree of defects. This can effectively improve the detection efficiency and the accuracy of detection. The experimental results show that the method is feasible in practical applications, and it has strong anti-interference ability, good real-time detection and high efficiency compared with traditional methods.

Keywords: Auto hub, SUSAN operation, mask, edge detection, Feature Description, Geometrical features, Shape Features

Title of the Paper: How Many Are Good Enough for the Adolescent Social Network Nomination


Authors: Hsieh-Hua Yang, Chyi-In Wu, Man Kit Lei, Hung-Jen Yang

Abstract: For social network analysis, the most common method used to generate social network data is the method of Name Generator. Nonetheless, the number of nomination has been an unsolved mystery for social networkers. Namely, for each respondents, to name how many people are good enough to generate a stable network, which is able to represent the truly association structure among these respondents, still, is an empirical research question for researchers. This study devoted to explore this question and to provide a preliminary answer. A set of social network data was collected from a sample of Taipei metropolitan junior high schools, including 44 classes. In each class the students were asked to nominate ten best friends in the intimate order. It was supposed that in each class has ten sociometric data for different nomination, and the total amount of sociometric data was 440. The software UCINET6.0 was applied to analyze the social network variables, and NEGOPY4.30 to define the network position. Comparing the betweenness, constraint, and efficiency, this study found that two names will generate more diverse network position with unstable structure, three names are the minimum to get more stable network structure, four or five names are needed to observe the links between boys and girls, but more than five names seem to be redundancy.

Keywords: Social network, Nomination number, Adolescents, Junior high school, Evaluation

Title of the Paper: Transient Temperature Analysis of a Cylindrical Heat Equation


Authors: Ko-Ta Chiang, G. C. Kuo, K.-J Wang, Y. F. Hsiao, K.-Y. Kung

Abstract: The method of superposition and separation variables is applied to gain analytical solutions to the transient heat conduction for a two dimensional cylindrical fin. The temperature distributions are generalized for a linear combination of the product of Bessel function, Fourier series and exponential type for nine different cases. The solutions presented in this study can be used to verify the two- or three-dimensional numerical conduction codes. Relevant connections with some other closely-related recent works are also indicated.q

Keywords: Fourier series, Heat conduction, Separation variables, Transcendent equation, Superposition method, Temperature distribution

Title of the Paper: Efficient Algorithms for Higher-Order Derivatives of the Continued Erlang Delay Function


Authors: Jorge Sa Esteves

Abstract: In this paper we analyze the partial derivatives of any order of the continued Erlang delay function in the number of servers. Several properties with strong analytical relations between the high-order derivatives of Erlang’s B and C functions are established. Using these relations, three algorithms are proposed for the numerical computation of the cited derivatives. For comparison purposes, it is also generalized a numerical method based on a quadrature procedure suggested by D. L. Jagerman [16]. All the computational methods are compared in terms of stability, efficiency and precision. Our study concludes that a recursive matrix relation presented in a previous work [10, 11], may be used for the establishment of a simple and reliable algorithm having the best performance considering the trade-off of the different criteria. Extensive computational results are presented and discussed. In the sequel, a conjecture about the strict convexity of the first derivative of Erlang delay function is presented and supported by numerical evidence.

Keywords: Performance Evaluation, Queueing Systems, Erlang’s B and C Formulas, Numerical Differentiation

Title of the Paper: Nonparametric Regression for Correlated Data


Authors: Noor Akma Ibrahim, Suliadi

Abstract: This paper considers nonparametric regression to analyze correlated data. The correlated data could be longitudinal or clustered data. Some developments of nonparametric regression have been achieved for longitudinal or clustered categorical data. For data with exponential family distribution, nonparametric regression for correlated data has been proposed using GEE-Local Polynomial Kernel (LPK). It was showed that in order to obtain an efficient estimator, one must ignore within subject correlation. This means within subject observations should be assumed independent, hence the working correlation matrix must be an identity matrix. Thus to obtained efficient estimates we should ignore correlation that exist in longitudinal data, even if correlation is the interest of study. In this paper we propose GEE-Smoothing spline to analyze correlated data and study the properties of the estimator such as the bias, consistency and efficiency. We use natural cubic spline and combine with GEE in estimation. We want to study numerically, whether the properties of GEE-Smoothing spline are better than of GEE-Local Polynomial Kernel. Several conditions have been considered. i.e. several sample sizes and several correlation structures. Using simulation we show that GEE-Smoothing Spline is better than GEE-local polynomial. The bias of pointwise estimator is decreasing with increasing sample size. The pointwise estimator is also consistent even with incorrect correlation structure, and the most efficient estimate is obtained if the true correlation structure is used. We also give example using real data, and compared the result of the proposed method with parametric method and GEE-Smoothing Spline under independent assumption.

Keywords: Nonparametric regression, Longitudinal binary data, Generalized estimating equation, Natural cubic spline, Properties of estimator

Title of the Paper: Embedding Geodesic and Balanced Cycles into Hypercubes


Authors: Pao-Lien Lai, Chang-Hsiung Tsai, Hong-Chun Hsu

Abstract: A graph G is said to be pancyclic if it contains cycles of all lengths from 4 to |V (G)| in G. For any two vertices u, v ? V (G), a cycle is called a geodesic cycle with u and v if a shortest path joining u and v lies on the cycle. Let G be a bipartite graph. For any two vertices u and v in G, a cycle C is called a balanced cycle between u and v if dC(u, v) = max{dC(x, y) | dG(x, u) and dG(y, v) are even, resp. for all x, y ? V (G) }. A bipartite graph G is geodesic bipancyclic (respectively, balanced bipancyclic) if for each pair of vertices u, v ? V (G), it contains a geodesic cycle (respectively, balanced cycle) of every even length of k satisfying max{2dG(u, v), 4} ? k ? |V (G)| between u and v. In this paper, we prove that Qn is geodesic bipancyclic and balanced bipancyclic if n ? 2.

Keywords: Hypercube, Interconnection networks, Edge-bipancyclic, Geodesic bipancyclic, Balanced bipancyclic

Title of the Paper: The Performance of Robust Weighted Least Squares in the Presence of Outliers and Heteroscedastic Errors


Authors: Habshah Midi, Md. Sohel Rana, A. H. M. Rahmatullah Imon

Abstract: The Ordinary Least Squares (OLS) method is the most popular technique in statistics and is often use to estimate the parameters of a model because of tradition and ease of computation. The OLS provides an efficient and unbiased estimates of the parameters when the underlying assumptions, especially the assumption of contant error variances (homoscedasticity), are satisfied. Nonetheless, in real situation it is difficult to retain the error variance homogeneous for many practical reasons and thus there arises the problem of heteroscedasticity. We generally apply the Weighted Least Squares (WLS) procedure to estimate the regression parameters when heteroscedasticity occurs in the data. Nevertheless, there is evidence that the WLS estimators suffer a huge set back in the presence of a few atypical observations that we often call outliers. In this situation the analysis will become more complicated. In this paper we have proposed a robust procedure for the estimation of regression parameters in the situation where heteroscedasticity comes together with the existence of outliers. Here we have employed robust techniques twice, once in estimating the group variances and again in determining weights for the least squares. We call this method Robust Weighted Least Squares (RWLS). The performance of the newly proposed method is investigated extensively by real data sets and Monte Carlo Simulations. The results suggest that the RWLS method offers substantial improvements over the existing methods.

Keywords: Heteroscedasticity, Outliers, Robust Estimation, Robust Weighted Least Squares, Monte Carlo Simulation

Title of the Paper: Estimating Regression Coefficients using Weighted Bootstrap with Probability


Authors: Norazan M. R., Habshah Midi, A. H. M. R. Imon

Abstract: In this paper we propose a new Weighted Bootstrap with Probability (WBP). The basic idea of the proposed bootstrap technique is to do re-sampling with probabilities. These probabilities become the control mechanism for getting good estimates when the original data set contain multiple outliers. Numerical examples and simulation study are carried out to evaluate the performance of the WBP estimates as compared to the Bootstrap 1 and Diagnostic-Before Bootstrap estimates. The results of the study signify that the WBP method is more efficient than the other two methods.

Keywords: Regression, outliers, weighted bootstrap with probability, weighting function

Issue 8, Volume 8, August 2009

Title of the Paper: Marangoni Convection in a Variable Viscosity Fluid Layer with Feedback Control


Authors: Norihan Md. Arifin, Nurul Hafizah Zainal Abidin

Abstract: Feedback control was applied to the steady Marangoni convection in a horizontal layer of fluid with variable viscosity and free-slip at the lower boundary heated from below and cooled from above. Prediction for the onset of convection are obtained from the analysis by numerical technique.The effects of feedback control are studied by examining the critical Marangoni numbers and wave numbers. It is shown that the onset of Marangoni convection with variable viscosity can be delayed and the critical Marangoni number can be increased through the use of feedback control.

Keywords: Linear stability theory, Marangoni convection, Variable viscosity, Feedback control, Free-slip, Deformable free surface

Title of the Paper: Complete Identification of Permissible Sampling Rates for the First-Order Sampling of Multi-Band Bandpass Signals


Authors: Yan Wu, Daniel F. Linder

Abstract: The first-order sampling of multi-band bandpass signals with arbitrary band positions is considered in this paper. Gaps between the spectral sub-bands are utilized to achieve lower sampling rates than the Nyquist. The lowest possible sampling rate along with other permissible sampling rates is identified via a unique partition of the frequency axis. With the complete identification of all the permissible sampling rates, a necessary and sufficient sampling theorem for multi-band bandpass signals is presented in terms of a series of csinc-interpolators.

Keywords: Multi-band bandpass signals, Sampling theorem, First-order sampling, Nyquist rate, Permissible sampling rates, Aliasing, csinc-interpolation

Title of the Paper: Solving Linear Ordinary Differential Equations using Singly Diagonally Implicit Runge-Kutta Fifth Order Five-Stage Method


Authors: Fudziah Ismail, Nur Izzati Che Jawias, Mohamed Suleiman, Azmi Jaafar

Abstract: We constructed a new fifth order five-stage singly diagonally implicit Runge-Kutta (DIRK) method which is specially designed for the integrations of linear ordinary differential equations (LODEs). The restriction to linear ordinary differential equations (ODEs) reduces the number of conditions which the coefficients of the Runge-Kutta method must satisfy. The best strategy for practical purposes would be to choose the coefficients of the Runge-Kutta methods such that the error norm is minimized. Thus, here the error norm obtained from the error equations of the sixth order method is minimized so that the free parameters chosen are obtained from the minimized error norm. The stability aspect of the method is also looked into and found to have substantial region of stability, thus it is stable. Then a set of test problems are used to validate the method. Numerical results show that the new method is more efficient in terms of accuracy compared to the existing method.

Keywords: Runge-Kutta, Linear ordinary differential equations, Error norm

Title of the Paper: Some New Remarks about Lotka-Volterra System


Authors: Camelia Pop, Anania Aron

Abstract: Lotka-Volterra system is a well-known system used as mathematical model in biology. It was proposed as model by Alfred Lotka (1925) and Vito Volterra (1926). We are interested to study it from the mechanical geometry point of view; more exactly we study the stability problem, the existence of periodic solutions, the Lax formulation and numerical integration via Kahan and Lie-Trotter integrators.

Keywords: Hamilton-Poisson realization, Lotka-Volterra system, nonlinear stability, Arnold method, Lie-Trotter integrator, Kahan integrator, Lax formulation

Title of the Paper: Nonlinear Growth Models in the Age Measurement of the European Rabbits in Australia in the Context of Alternative Models in Multivariate Statistics


Authors: Adnan Mazmanoglu, Ali Reha Unlu

Abstract: Examining the special model Lens = a exp{-b / (Age + g)} which belongs to Dudzinski and Mykytowycz (1961), and was used in a study made by them to find the age of Oryctolagus Caniculus, which lives in Europe and is known as the European rabbit, with live eye lens weight, we showed that similar results can be obtained with the Gompertz and Logistic nonlinear regression models. We determined that the results given by the models are showing the goodness of fit, as a result of a statistical analysis. Furthermore we showed that adding various parameters to Dudzinski and Mykytowycz model will not change the results.

Keywords: Nonlinear regression, logistic and gompertz model, gauss-newton iteration method, SPSS

Title of the Paper: Constructing Knowledge in Graph Theory and Combinatorial Optimization


Authors: Eva Milkova

Abstract: Graph theory and combinatorial optimization are powerful tools for teachers allowing them to develop logical thinking of students, increase their imagination and make them familiar with solutions to various practical problems. The paper offers some ideas how to make the teaching of these branches of applied mathematics and computer science more understandable and attractive. A case study is described which introduces the minimum spanning tree problem, its remarkable origin, and then its relation to the other problems. The approach used for teaching and learning graph theory and combinatorial optimization can serve as an inspiration for instruction of other subjects as well.

Keywords: Graph Theory, Graph Algorithms, Minimum Spanning Tree Problem, Breadth-First-Search, Education

Title of the Paper: Measurability and Gould Integrability in Finitely Purely Atomic Multisubmeasure Spaces


Authors: Alina Gavrilut, Anca Croitoru, Nikos E. Mastorakis, Gabriel Gavrilut

Abstract: In this paper, we present some results concerning measurability, Gould integrability and Lp spaces with respect to finitely purely atomic set multifunctions.

Keywords: Finitely purely atomic, atom, pseudo-atom, multisubmeasure, measurable, Gould integral, Lp space

Title of the Paper: Dynamical Mathematical Models for Plates and Numerical Solution of Boundary Value and Cauchy Problems for Ordinary Differential Equations


Authors: Tamaz S. Vashakmadze

Abstract: In the first part there are created and justified new 2D with respect to spatial coordinates nonlinear dynamical mathematical models von Karman-Mindlin-Reissner(KMR) type systems of partial differential equations for anisotropic porous, piezo, viscous elastic prismatic shells. Truesdell-Ciarlet unsolved( even in case of isotropic elastic plates) problem about physical soundness respect to von Karman system is decided. There is find also new dynamical summand ( is Airy stress function) in the another equation of von Karman type systems too. Thus the corresponding systems in this case contains Rayleigh-Lamb wave processes not only in the vertical, but also in the horizontal direction. For comlpleteness we also lead 2D Kirchhoff-Mindlin-Reissner type models for elastic plates of variable thickness. Then if KMR type systems are 1D one respect to spatial coordinates at first part for numerical solution of corresponding initial-boundary value problems we consider the finite-element method using new class of B-type splain-functions. The exactness of such schemes depends from differential properties of unknown solutions: it has an arbitrary order of accuracy respect to a mesh width in case of sufficiently smoothness functions and Sard type best coefficients characterizing remainder proximate members on less smoothing class of admissible solutions. Corresponding dynamical systems represent evolutionary equations for which the methods of Harmonic Analyses are nonapplicable. In this connection for Cauchy problem suggests new schemes having arbitrary order of accuracy and based on Gauss-Hermite processes. This processes are new even for ordinary differential equations.

Keywords: Elasticity, Poro-viscosity, Plate, Physical soundness, Finite-difference scheme, Gauss quadrature and Hermite interpolation formula, Mesh width

Title of the Paper: On One Generalization of Boundary Value Problem for Ordinary Differential Equations on Graphs in the Three-dimensional Space


Authors: D. G. Gordeziani, H. V. Meladze, T. D. Davitashvili

Abstract: The present work is the generalization of boundary value problem for ordinary differential equations on graphs. This problem is investigated and correctness of the stated problem is proved in [1]. The special attention is given to construction and research of difference analogues. Estimation of precision is given. The formulas of double-sweep method type are suggested for finding the solution of obtained difference scheme. In this work the boundary-value problems for Poisson’s equations in the three-dimensional space on some twodimensional structures with one-dimensional common part is given and investigated. This technique of investigation can be easily applied to the more complex initial data and equations. The difference scheme for numerical solution of this problem is constructed and estimation of precision is given. Such problems have practical sense and they can be used for mathematical modeling of specific problems of physics, engineering, ecology and so on.

Keywords: Differential equations on graphs, Difference scheme

Title of the Paper: Asymptotics of Solution and Finite Difference Scheme to a Nonlinear Integro-Differential Equations Associated with the Penetration of a Magnetic Field into a Substance


Authors: Temur Jangveladze, Zurab Kiguradze

Abstract: Asymptotics of solution and finite difference approximation of the nonlinear integro-differential equations associated with the penetration of a magnetic field into a substance is studied. Asymptotic properties of solutions for the initial-boundary value problem with homogeneous as well as nonhomogeneous Dirichlet boundary conditions are considered. The corresponding finite difference scheme is studied. The convergence of this scheme is proven. Numerical experiments are carried out.

Keywords: Nonlinear integro-differential equation, asymptotic behavior, finite difference scheme

Issue 9, Volume 8, September 2009

Title of the Paper: On the Translation of an Almost Linear Topology


Authors: Gabriela Apreutesei, Nikos E. Mastorakis, Anca Croitoru, Alina Gavrilut

Abstract: We present some characterizations of T1; T2 separation and metrizability for the translation of an almost linear topology

Keywords: Almost linear space, almost linear topological space, translation of a topology

Title of the Paper: Calibration and Comparison of Schema Matchers


Authors: Peter Martinek, Balazs Villanyi, Bela Szikora

Abstract: Schemas used in various environments become more and more numerous, though they do not comply to a universal standard. That is why the task of schema matching has emerged and its main objective is to find means to map a schema into another. Several initiations have occurred and algorithms have been proposed to solve the problem. They muster highly enticing solutions, though they have several flaws. We have reviewed the available algorithms and implemented some of them. We found that the accuracy of these solutions is strongly dependent on some well definable matcher characteristics, so if we calibrate the matchers they perform a lot better. Taking into account this fact we cannot compare matchers until after the necessary calibration. We propose matcher independent procedures and mathematical formulas to perform the highly desirable pre-run configuration of candidate solutions. The necessity of calibration implies that the unbiased comparison of solutions is not possible until the configuration is performed. We also introduce the technique of multiple thresholding which promises a better view of the result list returned by the individual matchers.

Keywords: Optimization of schema matching algorithms, Determine possible accuracy maxima, Similarity measure methods

Title of the Paper: Classification Approaches in Off-Line Handwritten Signature Verification


Authors: Bence Kovari, Benedek Toth, Hassan Charaf

Abstract: The aim of off-line signature verification is to decide, whether a signature originates from a given signer based on the scanned image of the signature and a few images of the original signatures of the signer. Although the verification process can be thought to as a monolith component, it is recommended to divide it into loosely coupled phases (like preprocessing, feature extraction, feature matching, feature comparison and classification) allowing us to gain a better control over the precision of different components. This paper focuses on classification, the last phase in the process, covering some of the most important general approaches in the field. Each approach is evaluated for applicability in signature verification, identifying their strength and weaknesses. It is shown, that some of these weak points are common between the different approaches and can partially be eliminated with our proposed solutions. To demonstrate this, several local features are introduced and compared using different classification approaches. Results are evaluated on the database of the Signature Verification Competition 2004.

Keywords: Signature verification; off-line; classification, shape descriptor, neural network

Title of the Paper: Optimal Analysis MAX MIN of the Dependency between the Energy Consumption of Electrical Actions and their Operation Safety


Authors: Ilie Mitran, Florin Dumitru Popescu

Abstract: The study sets off the relation between the reliability of an electric drive system and the specific consumption of energy through the efficiency function used as a quantizing analytical element for the medium energy consumption throughout the safe functioning period of the system. The stability moments of the system as well as the collapse moments are determined using the MIN-MAX or MAX-MIN optimizing methods and also elements belonging to the theory of probabilities and differential calculus. An essential obtained result is represented by the dependence relation between the reduction of the specific power consumption which corresponds to a certain increase in the safe operation of the system. Economically, knowing these results leads to considerable saves of materials, human resources and finances. The explanation of these economic consequences is connected primarily with the fact that the results presented are an immediate consequence of correlating fundamental elements of electrical actions, system reliability and economic analysis and calculation (based mainly on minimizing different types of costs). The purpose of this paper is to determine, mainly, the specific electrical energy consumption and the reliability function for extreme properties (minimum for the specific electrical energy consumption and maximum for the reliability function). Secondly, to determine the equilibrium point of the specific electrical energy consumption and of the reliability of the analyzed system. Thirdly, to draw conclusions that will allow the economic analysis.

Keywords: Reliability, standardized energy consumption, stability moment, efficiency function

Title of the Paper: Diagonally Stable Tridiagonal Switched Linear Systems


Authors: Isabel Bras

Abstract: A stability analysis is carried out for certain classes of switched linear systems with tridiagonal structure, under arbitrary switching signal. This analysis is made using diagonal common quadratic Lyapunov functions. Namely, necessary and sufficient conditions for the existence of such Lyapunov functions are proposed for second order switched systems and for third order switched systems with Toeplitz tridiagonal structure.

Keywords: Switched linear systems, quadratic Lyapunov stability, diagonal stability

Title of the Paper: On Modeling Ubiquitous Cloud: Estimation of Traffic


Authors: Shuji Kawasaki, Masakazu Higuchi, Hitomi Murakami

Abstract: The Ubiquitous Cloud is a concept of large-scale information service network as a social infra-structure. It is featured by real-world context information extraction, user information profiling and self-cofiguration/-control of network. The objective of the research is to evaluate the network traffic theoretically and thus give a guideline of network design. In this paper, we especially consider those traffic factors that are related to movement of mobile users and rea-time services, and thus discuss some necessary requirements for the network specification.

Keywords: Context-awareness, profiling, self-reconfiguration, spatio-temporal dynamics, long-range dependence, self-similarity, elephant-mice flow

Title of the Paper: On Existence and Uniqueness of the Cauchy Problem for Parabolic Equations with Unbounded Coefficients


Authors: Huashui Zhan

Abstract: A new kind of entropy solution to the Cauchy problem for strong degenerate parabolic equations with unbounded coefficients is quoted. Suppose that u0 2 L1(RN), E = fEig 2 (L2(QT ))N and divE 2 L2(QT ), by a modified regularization method and choosing a suitable test function, the BV estimates are got, the existence of the entropy solution is obtained. At last, by Kruzkov bi-variables method, the stability of the solutions is obtained too.

Keywords: Cauchy problem, Degenerate parabolic equation, Existence, Unbounded coefficient

Title of the Paper: Introduction to the Elliptical Trigonometry


Authors: Claude Bayeh, Mouafac Bernard, Nazih Moubayed

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 science, engineering, architecture, and even medicine. In this paper, the elliptical trigonometry is introduced in order to be in the future a part of the trigonometry topic. Thus, the definition of this original part is presented. The elliptic trigonometric functions are also defined. The importance of these functions in producing different signals and forms are analyzed and discussed.

Keywords: Mathematics, geometry, trigonometry, trigonometric functions, derivative functions, simulation

Title of the Paper: A Three-Dimension Double-Population Thermal Lattice BGK Model for Simulation of Natural Convection Heat Transfer in a Cubic Cavity


Authors: C. S. Nor Azwadi, S. Syahrullail

Abstract: In this paper, a double-population thermal lattice Boltzmann was applied to solve three dimensional, incompressible, thermal fluid flow problem. The simplest lattice BGK D3Q6 model was proposed to determine the temperature field while D3Q15 or D3Q19 for the density and velocity fields. The simulation of natural convection in a cubic cavity with Prandtl number 0.71 and Rayleigh number ranging from 103 to 105 were carried out and compared with the published results in literature. It was observed that the combination of D3Q6 and D3Q19 produces better numerical stability and accuracy compared to D3Q6 with D3Q15 for the simulation at high Rayleigh numbers.

Keywords: Double population, lattice Boltzmann, distribution function, BGK collision, natural convection

Issue 10, Volume 8, October 2009

Title of the Paper: Gravitational Capture Using a Four-Body Model


Authors: Alexandre Lacerda Machuy, Antonio Fernando Bertachini De Almeida Prado, Terezinha De Jesus Stuchi

Abstract: A spacecraft (or any particle with negligible mass) suffers a gravitational capture when its orbit changes from hyperbolic (small positive energy) around a celestial body into elliptic (small negative energy) using only gravitational forces. The force responsible for this modification in the orbit of the spacecraft is the gravitational force of the third and the fourth bodies involved in the dynamics. Those forces are equivalent of a zero cost control applied to the spacecraft, equivalent to a continuous thrust. One of the most important applications of this property is the construction of trajectories to the Moon. The concept of gravitational capture is combines with the principles of the gravity-assisted maneuver and the bi-elliptic transfer orbit, to generate a trajectory that requires a fuel consumption smaller than the one required by the Hohmann transfer. The present paper study the energy required for the ballistic gravitational capture in a dynamical model that has the presence of four bodies. Those bodies are assumed to follow the assumptions of the bi-circular model. In particular, the Earth-Moon-Sun-Spacecraft system is considered.

Keywords: Astrodynamics, Celestial Mechanics, Space Trajectories, Gravitational Capture, Space Missions

Title of the Paper: A Preprocessing Procedure for Fixing the Binary variables in the Capacitated Facility Location Problem through Pairing and Surrogate Constraint Analysis


Authors: Maria A. Osorio, Abraham Sanchez

Abstract: The Osorio and Glover (2003) use of dual surrogate analysis is exploited to fix variables in capacitated facility location problems (CFLP). The surrogate constraint is obtained by weighting the original problem constraints by their associated dual values in the LP relaxation. A known solution is used to convert the objective function in a constraint that forces the solution to be less or equal to it. The surrogate constraint is paired with the objective function to obtain a combined constraint where negative variables are replaced by complemented variables and the resulting constraint used to fix binary variables in the model.

Keywords: Capacitated Facility Location Problem, Surrogate Constraints, Duality, Constraint Pairing

Title of the Paper: A Comparative Study of Hybrid, Neural Networks and Nonparametric Regression Models in Time Series Prediction


Authors: Dursun Aydin, Mammadagha Mammadov

Abstract: This paper presents a comparative study of the hybrid models, neural networks and nonparametric regression models in time series forecasting. The components of these hybrid models are consisting of the nonparametric regression and artificial neural networks models. Smoothing spline, regression spline and additive regression models are considered as the nonparametric regression components. Furthermore, various multilayer perceptron algorithms and radial basis function network model are regarded as the artificial neural networks components. The performances of these models are compared by forecasting the series of number of produced Cars and Domestic product per capita (GDP) data occurred in Turkey. This comparisons show that hybrid models proposed in this paper have denoted much more excellent performance than the hybrid models in literature.

Keywords: Time series, Neural networks, Multilayer perceptrons, Radial basis function, Nonparametric regression, Additive regression model, Hybrid models

Title of the Paper: A Mathematical Theory of Psychological Dynamics


Authors: Alin Gilbert Sumedrea, Livia Sangeorzan

Abstract: The psychological dynamics is governed by the ”observable-unobservable” systemic ratio. The plausible existence of the dynamics of the psychological laws is justified by the presence of a complex psycho-physiological apparatus which changes the informational biofeedback into energy. The psychological insight represented by the (unobservable) psychological soft component obeys the functional models [6] which define the psychological system. The psychological Gordian knot consists in identifying the manner in which the unobservable psychological fact changes into physiology and vice versa. The psychological literature is well represented, especially by the behavior models of the physiological hard component [1], [7], [17], [18]. This paper tries to develop a mathematical theory of psychological insight. The purpose is to create an unifying theory between the functionality of the psychological soft and of the physiological hard – having, from our point of view, the capacity to solve the Gordian knot – based on the results of this paper.

Keywords: Amplitude of the tensional state, Extinction of the tensional state, Lie group, Metrics, Neuropsychological activation, Psychological experience, Tensional dynamics

Title of the Paper: Convergence Theorems for Totally-Measurable Functions


Authors: Anca Croitoru, Alina Gavrilut, Nikos E. Mastorakis

Abstract: We establish some convergence theorems for sequences of totally-measurable functions with respect to a submeasure of finite variation. We also present relationships among different types of convergences such as convergence in submeasure, almost uniformly convergence, convergence in Lp spaces.

Keywords: Totally-measurable, convergence, submeasure, Lp space

Issue 11, Volume 8, November 2009

Title of the Paper: Weight-Decay Regularization in Reproducing Kernel Hilbert Spaces by Variable-Basis Schemes


Authors: Giorgio Gnecco, Marcello Sanguineti

Abstract: The optimization problems associated with various regularization techniques for supervised learning from data (e.g., weight-decay and Tikhonov regularization) are described in the context of Reproducing Kernel Hilbert Spaces. Suboptimal solutions expressed by sparse kernel models with a given upper bound on the number of kernel computational units are investigated. Improvements of some estimates obtained in Comput. Manag. Sci., vol. 6, pp. 53-79, 2009 are derived. Relationships between sparseness and generalization are discussed.

Keywords: Learning from data, regularization, weight decay, suboptimal solutions, rates of approximation

Title of the Paper: Sensivity and Stability of Singular Systems under Proportional and Derivative Feedback


Authors: M. Isabel Garcia-Planas

Abstract: We consider triples of matrices (E; A;B), representing singular linear time invariant systems in the form Ex_ (t) = Ax(t) + Bu(t), with E;A 2 Mp£n(C) and B 2 Mn£m(C), un- der proportional and derivative feedback. Using geometrical techniques we obtain miniversal deformations that permit us to study sensivity and structural stability of singular systems.

Keywords: Singular linear systems, proportional and derivative feedback, canonical reduced form, structural invariants, structural stability

Title of the Paper: A Study of the In-service Hot Spot and Attendance Model of Professional Development


Authors: Lung-Hsing Kuo

Abstract: The purpose of this study was to present a way to identify the in-service hot spot and create an attendance model based upon the profile information and distance away from the hot spot. Empirical data was gathered for verifying purpose. It was argued that distance for joining professional development could be a factor affecting the attendance. The research data were collected from 9824 senior high school teachers who attended in-service advancement education activities from January to November in 2008. The teachers' profile information was collected from “Nationwide Teacher In-service Education Information Web” ( database. And then Google Earth was drawn upon to get the latitude and longitude of each teacher’s working site and the Discipline Centers’ sites in which teachers attended in-service advancement education activities to obtain the straight distance. Besides, the TWD67 system—the Route Guide System devised by Institute of Transportation, Ministry of Transportation and Communications, Taiwan, R.O.C. was applied to obtain the distance by road. The descriptive statistics, t-tests, and one-way ANOVA were used to analyze the data. The results of the study indicated that “hot spots” of in-service advancement education activities which were held by Discipline Centers and which senior high school teachers attended were mainly located in Taipei City and Kaohsiung City. A total of ten background variables of teachers were examined to compare mean group differences (gender, age, educational background, marital status, additionally administrative duty, first registered specialty, total of in-service teachers' registered specialties, school type, school size, and school location). There were differences in the straight distance and distance by road among teachers’ age, educational background, marital status, first registered specialty, total of in-service teachers' registered specialties, school type, school size, and school location.

Keywords: In-service Hot Spot, Professional Development, Attendance, High School Curriculum Guideline, Discipline Centers, In-service advancement education, straight distance, distance by road

Title of the Paper: The Coupled Method Fuzzy-AHP Applys to Solve Multi-criteria Decision Making Problems


Authors: Xinpei Jiang, Bao Zheng, Liying Wang

Abstract: The multi-criteria decision making (MCDM)problems with fuzzy preference information on alternatives are essential problems of the importance of weighting and ranking. In order to solve this problem, Analytical Hierarchy Process(AHP) and fuzzy comprehensive evaluation method are coupled to form a new approach named Fuzzy-AHP.This method is different from the traditional FAHP,which used to facilitate the pairwise comparison process and avoid the complex and unreliable process of comparing fuzzy utilities.It utilizes the advantage of AHP on computing index weight and comparing index in the same row than at ranking and the advantage of fuzzy comprehensive evaluation method on establishing quantitative indexes membership and qualitative indexes membership and classifying level.Finally, a numerical example is presented to clarify the methodology ,the model evaluation results showed that the proposed system is able to provide very. good solution both in accuracy, and speed for the top managers.

Keywords: MCDM, Fuzzy , AHP, index , weighing, membership degree, matrix

Title of the Paper: Global Diversification, Hedging Diversification, and Default Risk in Bank Equity: An Option-Pricing Model


Authors: Jyh-Horng Lin, Jyh-Jiuan Lin, Rosemary Jou

Abstract: Many banks diversify their operations, either across different national markets (global diversification), across different borrowers by offsetting credit risks (hedging diversification), or both. Can multiple diversifications provide greater safety for banks? This paper aims to answer this question by using an option-based pricing model to formulate the default risk in bank equity returns under global and hedging diversifications. In particular, we apply Vassalou and Xing’s (2004) formula, which is a nonlinear option-based function of the default probability of an individual bank’s equity return. This formula is calculated using the contingent claim methodology of Black and Scholes (1973) and Merton (1974). We find that the extent of global diversification may provide greater safety for banks, but also that the extent of hedging diversification may not.

Keywords: Default Risk, International Lending Diversification, Loan Portfolio Swap

Issue 12, Volume 8, December 2009

Title of the Paper: Numerical Simulations for Dynamic Stochastic and Hybrid Models of Internet Networks


Authors: G. Mircea, M. Neamtu, A. L. Ciurdariu, D. Opris

Abstract: In this paper, we consider Internet models, which respond to a congestion signal from the network described by a stochastic and hybrid differential equation. We consider Internet networks with one source and r access links, as well as with r sources and one access link. We analyze the conditions for the existence of a solution and the algorithms needed to determine the solution. We carry out numerical simulations for certain parameter values.

Keywords: Internet models, networks, dynamic stochastic models, stochastic delay differential equation, Euler method, numerical simulations

Title of the Paper: Optimal Control Applied to a Ramsey Model with Taxes and Exponential Utility


Authors: Olivia Bundau

Abstract: In this paper we analyze an economical growth model with taxes and exponential utility in continuous and infinite time. This economical growth model leads to an optimal control problem. The necessary and sufficient conditions for optimality are given. Using the optimality conditions we prove the existence, uniqueness and stability of the study state for a differential equations system. Also we have investigated the dependence of the steady state (k?, c?) on the growth rate of the labor force n and the effects of fiscal policy changes on welfare.

Keywords: Mathematical models applied in economies, endogenous growth, optimal policy

Title of the Paper: The Study of Micro-Fluid Boundary Layer Theory


Authors: Long Li, Huashui Zhan

Abstract: Similar to the study of Prandtl system, by the well-known Oleinik linear method, the paper gets existence, uniqueness of the solution for an initial boundary problem.

Keywords: Micro-fluid boundary layer, Uniqueness, Existence, Classical solution

Title of the Paper: An Improved Method for Successive Data Schism and Interpolation


Authors: Ahmed N. H. Alnuaimy, Mahamod Ismail, Mohd A. M. Ali, Kasmiran Jumari

Abstract: This paper presents an improved type of data schism and interpolation called Alnuaimy-Mahamod Interpolation based on the mean and variance to calculate the entire point between two known points. A new mathematical method is developed for interpolation from a given set of data points in a plane and for fitting a smooth curve to the points. This method is devised in such a way that the resultant curve will pass through the given points and will appear smooth and natural. Data schism and interpolation describes the behaviors of the calculated points which behave as bacteria reproduction. This type of interpolation based on calculation of the mean and the variance of two adjacent points and modify of these calculate values by named factors to be used to calculate the entire points. Our type of interpolation can be working as linear midpoint interpolation, linear interpolation and smooth curve fitting.

Keywords: Interpolation, midpoint interpolation, linear interpolation and smooth curve fitting

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