Publication Date: 2006
Journal of Optimization Theory and Applications (00223239)130(2)pp. 359-365
In this paper, we consider a generalization of convexity for nonsmooth multiobjective programming problems. We obtain sufficient optimality conditions under generalized (F, ρ)-convexity. © 2006 Springer Science+Business Media, Inc.
Publication Date: 2007
Numerical Functional Analysis and Optimization (15322467)28(11-12)pp. 1355-1367
A class of nonsmooth multiobjective fractional programming is formulated. We establish the necessary and sufficient optimality conditions without the need of a constraint qualification. Then a mixed dual is introduced for a class of nonsmooth fractional programming problems, and various duality theorems are established without a constraint qualification.
Security quantification is a topic that has gained a lot of interest in the research community during the recent years. In this paper, a new method is proposed for modeling and quantifying attack effects on a computer system. In this work, intrusion process is considered as atomic sequential steps. Each atomic step changes the current system state. On the other hand, system tries to prevent and detect the attacker activity and therefore can transfer the current system state to a secure state. Intrusion process modeling is done by a semi-Markov chain (SMC). Distribution functions assigned to SMC transitions are uniform distributions. Uniform distributions represent the sojourn time of the attacker or the system in the transient states. Then the SMC is converted into a discrete-time Markov chain (DTMC). The DTMC is analyzed and then the probability of attacker success is computed based on mathematical theorems. The SMC has two absorbing for representing success and failure states of intrusion process.©2008 IEEE.
Publication Date: 2008
Journal of Optimization Theory and Applications (00223239)136(1)pp. 77-85
We consider a nonsmooth vector optimization continuous-time problem. We establish weak and strong duality theorems under generalized convexity assumptions. © 2007 Springer Science+Business Media, LLC.
Publication Date: 2008
Journal of Optimization Theory and Applications (00223239)136(1)pp. 61-68
A mixed-type dual for a nonsmooth multiobjective optimization problem with inequality and equality constraints is formulated. We obtain weak and strong duality theorems for a mixed-type dual without requiring the regularity assumptions and the nonnegativeness of the Lagrange multipliers associated to the equality constraints. We apply also a nonsmooth constraint qualification for multiobjective programming to establish strong duality results. In this case, our constraint qualification assures the existence of positive Lagrange multipliers associated with the vector-valued objective function. © 2007 Springer Science+Business Media, LLC.
Publication Date: 2008
International Journal for Numerical Methods in Engineering (00295981)76(4)pp. 501-520
A meshless local boundary integral equation (LBIE) method is proposed to solve the unsteady two- dimensional Schrödinger equation. The method is based on the LBIE with moving least-squares (MLS) approximation. For the MLS approximation, nodal points spread over the analyzed domain are utilized to approximate the interior and boundary variables. A time-stepping method is employed to deal with the time derivative. An efficient method for dealing with singular domain integrations that appear in the discretized equations is presented. Finally, numerical results are considered for some examples to demonstrate the accuracy, efficiency and high rate of convergence of this method. Copyright © 2008 John Wiley & Sons, Ltd.
Publication Date: 2008
Journal of Global Optimization (09255001)41(1)pp. 103-115
We consider nonsmooth multiobjective fractional programming problems with inequality and equality constraints. We establish the necessary and sufficient optimality conditions under various generalized invexity assumptions. In addition, we formulate a mixed dual problem corresponding to primal problem, and discuss weak, strong and strict converse duality theorems. © 2007 Springer Science+Business Media LLC.
Publication Date: 2008
Journal of Optimization Theory and Applications (00223239)136(1)pp. 69-76
A nonsmooth multiobjective continuous-time problem is introduced. We establish the necessary and sufficient optimality conditions under generalized convexity assumptions on the functions involved. © 2007 Springer Science+Business Media, LLC.
Publication Date: 2008
Journal of Pure and Applied Algebra (00224049)212(4)pp. 727-734
In this paper we study the probability that the commutator of two randomly chosen elements in a finite group is equal to a given element of that group. Explicit computations are obtained for groups G which | G′ | is prime and G′ ≤ Z (G) as well as for groups G which | G′ | is prime and G′ ∩ Z (G) = 1. This paper extends results of Rusin [see D.J. Rusin, What is the probability that two elements of a finite group commute? Pacific J. Math. 82 (1) (1979) 237-247]. © 2007 Elsevier Ltd. All rights reserved.
Publication Date: 2008
Numerical Methods for Partial Differential Equations (10982426)24(6)pp. 1405-1415
This article describes a numerical method based on the boundary integral equation and dual reciprocity method for solving the one-dimensional Sine-Gordon (SG) equation. The time derivative is approximated by the time-stepping method and a predictor-corrector scheme is employed to deal with the nonlinearity which appears in the problem. Numerical results are presented for some problems to demonstrate the use-fulness and. accuracy of this approach. In addition, the conservation of energy in SG equation is investigated. © 2008 Wiley Periodicals, Inc.
Publication Date: 2008
Computer Methods in Applied Mechanics and Engineering (00457825)197(6-8)pp. 476-486
This paper presents the dual reciprocity boundary element method (DRBEM) for solving two-dimensional sine-Gordon (SG) equation. The integral equation formulation employs the fundamental solution of the Laplace equation, and hence a domain integral arises in the boundary integral equation. Furthermore, the time derivatives are approximated by the time-stepping method, and the domain integral also appears from these approximations. The domain integral is transformed into boundary integral by using the dual reciprocity method (DRM). The linear radial basis function (RBF) is employed for DRM. The dynamics of line solitons and ring solitons of circular and elliptic shapes are studied. Numerical results are presented for some problems involving line and ring solitons to demonstrate the usefulness and accuracy of this approach. © 2007.
Publication Date: 2008
Engineering Analysis with Boundary Elements (09557997)32(9)pp. 747-756
In this paper the meshless local Petrov-Galerkin (MLPG) method is presented for the numerical solution of the two-dimensional non-linear Schrödinger equation. The method is based on the local weak form and the moving least squares (MLS) approximation. For the MLS, nodal points spread over the analyzed domain are utilized to approximate the interior and boundary variables. A time stepping method is employed for the time derivative. To deal with the non-linearity, we use a predictor-corrector method. A very simple and efficient method is presented for evaluation the local domain integrals. Finally numerical results are presented for some examples to demonstrate the accuracy, efficiency and high rate of convergence of this method. © 2007 Elsevier Ltd. All rights reserved.
Publication Date: 2009
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (03029743)5430pp. 200-214
The aim is to propose a new approach for stochastic modeling of an intrusion process and quantitative evaluation of the probability of the attacker success. In many situations of security analysis, it is necessary to obtain the probabilities of success for attackers in an intrusion process. In the proposed method, the intrusion process is considered as elementary attack phases. In each atomic phase the attacker and the system interact and this interaction can transfer the current system state to a secure or failure state. Intrusion process modeling is done by a semi-Markov chain (SMC). The distribution functions assigned to the SMC transitions are a linear combination of some uniform distributions. These mixture distributions represent the time distribution of the attacker or the system in the transient states. In order to evaluate the security measure, the SMC is converted into a discrete-time Markov chain (DTMC) and then the resulting DTMC is analyzed and the probability of the attacker success is com uted based on mathematical theorems. The desired security measure is evaluated with respect to the temporal aspects of the attacker behavior. ©Springer-Verlag Berlin Heidelberg 2009.
Publication Date: 2009
Finite Fields and their Applications (10715797)15(3)pp. 387-391
Linear cyclic codes of length pk over the Galois ring GR (p2, m), that is ideals of the ring GR (p2, m) [u] / 〈 upk - 1 〉, are studied. The form of the dual codes is analyzed and self-dual codes are identified. © 2009 Elsevier Inc. All rights reserved.
Publication Date: 2009
Engineering Analysis with Boundary Elements (09557997)33(4)pp. 522-528
This paper describes a numerical method based on the boundary integral equation and dual reciprocity methods for solving the one-dimensional Cahn-Hilliard (C-H) equation. The idea behind this approach comes from the dual reciprocity boundary element method that introduced for higher order dimensional problems. A time-stepping method and a predictor-corrector scheme are employed to deal with the time derivative and the nonlinearity respectively. Numerical results are presented for some examples to demonstrate the usefulness and accuracy of this approach. For these problems the energy functional dissipation and the mass conservation properties are investigated. © 2008 Elsevier Ltd. All rights reserved.
Publication Date: 2009
Engineering Analysis with Boundary Elements (09557997)33(1)pp. 12-24
This article studies the boundary element solution of two-dimensional sine-Gordon (SG) equation using continuous linear elements approximation. Non-linear and in-homogenous terms are converted to the boundary by the dual reciprocity method and a predictor-corrector scheme is employed to eliminate the non-linearity. The procedure developed in this paper, is applied to various problems involving line and ring solitons where considered in references [Argyris J, Haase M, Heinrich JC. Finite element approximation to two-dimensional sine-Gordon solitons. Comput Methods Appl Mech Eng 1991;86:1-26; Bratsos AG. An explicit numerical scheme for the sine-Gordon equation in 2+1 dimensions. Appl Numer Anal Comput Math 2005;2(2):189-211, Bratsos AG. A modified predictor-corrector scheme for the two-dimensional sine-Gordon equation. Numer Algorithms 2006;43:295-308; Bratsos AG. The solution of the two-dimensional sine-Gordon equation using the method of lines. J Comput Appl Math 2007;206:251-77; Bratsos AG. A third order numerical scheme for the two-dimensional sine-Gordon equation. Math Comput Simul 2007;76:271-8; Christiansen PL, Lomdahl PS. Numerical solutions of 2+1 dimensional sine-Gordon solitons. Physica D: Nonlinear Phenom 1981;2(3):482-94; Djidjeli K, Price WG, Twizell EH. Numerical solutions of a damped sine-Gordon equation in two space variables. J Eng Math 1995;29:347-69; Dehghan M, Mirzaei D. The dual reciprocity boundary element method (DRBEM) for two-dimensional sine-Gordon equation. Comput Methods Appl Mech Eng 2008;197:476-86]. Using continuous linear elements approximation produces more accurate results than constant ones. By using this approach all cases associated to SG equation, which exist in literature, are investigated. © 2008 Elsevier Ltd. All rights reserved.
Publication Date: 2009
Set-Valued and Variational Analysis (09276947)17(1)pp. 63-95
We study nonsmooth mathematical programs with equilibrium constraints. First we consider a general disjunctive program which embeds a large class of problems with equilibrium constraints. Then, we establish several constraint qualifications for these optimization problems. In particular, we generalize the Abadie and Guignard-type constraint qualifications. Subsequently, we specialize these results to mathematical program with equilibrium constraints. In our investigation, we show that a local minimum results in a so-called M-stationary point under a very weak constraint qualification. © 2009 Springer Science+Business Media B.V.
Publication Date: 2009
Discrete Applied Mathematics (0166218X)157(13)pp. 2892-2903
This paper deals with cyclic codes over the Galois ring GR (p2, m). A unique set of generators for these codes and an algorithm for finding these generators are presented. The form of dual codes is studied. The obtained results on cyclic codes are extended to the class of negacyclic codes. © 2009 Elsevier B.V. All rights reserved.
Publication Date: 2009
International Journal for Numerical Methods in Engineering (00295981)79(13)pp. 1662-1682
In this paper the meshless local boundary integral equation (LBIE) method for numerically solving the non-linear two-dimensional sine-Gordon (SG) equation is developed. The method is based on the LBIE with moving least-squares (MLS) approximation. For the MLS, nodal points spread over the analyzed domain are utilized to approximate the interior and boundary variables. The approximation functions are constructed entirely using a set of scattered nodes, and no element or connectivity of the nodes is needed for either the interpolation or the integration purposes. A time-stepping method is employed to deal with the time derivative and a simple predictor-corrector scheme is performed to eliminate the non-linearity. A brief discussion is outlined for numerical integrations in the proposed algorithm. Some examples involving line and ring solitons are demonstrated and the conservation of energy in undamped SG equation is investigated. The final numerical results confirm the ability of method to deal with the unsteady non-linear problems in large domains. © 2009 John Wiley & Sons, Ltd.
The aim is to develop a suitable method for quantifying security. We use stochastic modeling techniques for this purpose. An intrusion process is considered as a series of elementary attack phases and at each phase the interactions between the attacker and the system are analyzed rigorously. It is assumed that a typical attacker needs some time to perform an elementary attack phase. On the other hand, it is assumed that the attacker may be detected by the system and thus the overall intrusion process is interrupted. The attacker skill level and the system's abilities are characterized by the uniform distribution functions assigned to the transitions of the model. The underlying stochastic model is recognized as a semi- Markov chain. For security analysis, some valid assumptions about intrusion process are considered. Also, two quantitative security measures are defined and evaluated based on the model. The proposed method is demonstrated by modeling a complicated attack process and evaluating the desired security measures © 2009 IEEE.
Publication Date: 2009
Computer Physics Communications (00104655)180(9)pp. 1458-1466
The meshless local boundary integral equation (LBIE) method is given to obtain the numerical solution of the coupled equations in velocity and magnetic field for unsteady magnetohydrodynamic (MHD) flow through a pipe of rectangular and circular sections with non-conducting walls. Computations have been carried out for different Hartmann numbers and at various time levels. The method is based on the local boundary integral equation with moving least squares (MLS) approximation. For the MLS, nodal points spread over the analyzed domain, are utilized to approximate the interior and boundary variables. A time stepping method is employed to deal with the time derivative. Finally, numerical results are presented to show the behaviour of velocity and induced magnetic field. © 2009 Elsevier B.V. All rights reserved.
Publication Date: 2009
Applied Numerical Mathematics (01689274)59(5)pp. 1043-1058
In this article a meshless local Petrov-Galerkin (MLPG) method is given to obtain the numerical solution of the coupled equations in velocity and magnetic field for unsteady magnetohydrodynamic (MHD) flow through a pipe of rectangular section having arbitrary conducting walls. Computations have been carried out for different Hartmann numbers and wall conductivity at various time levels. The method is based on the local weak form and the moving least squares (MLS) approximation. For the MLS, nodal points spread over the analyzed domain are utilized to approximate the interior and boundary variables. A time stepping method is employed to deal with the time derivative. Finally numerical results are presented showing the behaviour of velocity and induced magnetic field across the section. © 2008 IMACS.
Publication Date: 2009
Numerical Functional Analysis and Optimization (15322467)30(3-4)pp. 337-351
We study a multiobjective problem with a feasible set defined by equality and inequality constraints. Then, by using the concept of K-directional derivative, we prove general optimality conditions as well as results concerning duality theorems.
Publication Date: 2009
Journal of Convex Analysis (09446532)16(1)pp. 187-210
We consider a mathematical program with equilibrium constraints (MPBC). First we obtain a Lagrange multiplier rule based on the linear sub differential involving equality, inequality and set constraints. Then we propose new constraint qualifications for M-stationary condition to hold. Finally we establish the Fritz John and Karush-Kuhn Tucker M-stationary necessary conditions for a nonsmooth (MPBC) based on the Michel-Penot subdifferential. © Heldermann Verlag.
Publication Date: 2009
Journal of Global Optimization (09255001)43(4)pp. 593-606
A nonsmooth multiobjective continuous-time problem is considered. The definition of invexity and its generalizations for continuous-time functions are extended. Then, optimality conditions under generalized invexity assumptions are established. Subsequently, these optimality conditions are utilized as a basis for formulating dual problems. Duality results are also obtained for Wolfe as well as Mond-Weir type dual, using generalized invexity on the functions involved. © 2008 Springer Science+Business Media, LLC.
Publication Date: 2009
Journal of Mathematical Analysis and Applications (10960813)351(1)pp. 170-181
We consider a nonsmooth semi-infinite programming problem with a feasible set defined by inequality and equality constraints and a set constraint. First, we study some alternative theorems which involve linear and sublinear functions and a convex set and we propose several generalizations of them. Then, alternative theorems are applied to obtain, under different constraint qualifications, several necessary optimality conditions in the type of Fritz-John and Karush-Kuhn-Tucker. © 2008 Elsevier Inc. All rights reserved.
