on a global existence theorem of small amplitude solutions for nonlinear wave equations in an exterior domain soit un domaine non borne dans un espace euclidien a n dimensions r n a frontiere compacte et c on considere le probleme mixte u u f t x d 1 d 1 u f t x dans 0 u 0 sur 0 u 0 x u 0 x t u 0 x u 1 x dans f est une fonction non lineaire a valeur reelle et d 1 d 1 u t j x u 1 j 2

convergence rates for markov chains this is an expository paper that presents various ideas related to nonasymptotic rates of convergence for markov chains such rates are of great importance for stochastic algorithms that are widely used in statistics and in computer science they also have applications to analysis of card shuffling and other areas in this paper we attempt to describe various mathematical techniques that have been used to bound such rates of convergence in particular we describe eigenvalue analysis random walks on groups coupling and minorization conditions connections are made to modern areas of research wherever possible elements of linear algebra probability theory group theory and measure theory are used but efforts are made to keep the presentation elementary and accessible

a markov chain analysis of genetic algorithms with power of 2 cardinality alphabets abstract in this paper we model the run time behavior of gas using higher cardinality representations as markov chains define the states of the markov chain and derive the transition probabilities of the corresponding transition matrix we analyze the behavior of this chain and obtain bounds on its convergence rate and bounds on the runtime complexity of the ga we further investigate the effects of using binary versus higher cardinality representation of a search space

degree of population diversity a perspective on premature convergence in genetic algorithms and its markov chain analysis in this paper a concept of degree of population diversity is introduced to quantitatively characterize and theoretically analyze the problem of premature convergence in genetic algorithms gas within the framework of markov chain under the assumption that the mutation probability is zero the search ability of ga is discussed it is proved that the degree of population diversity converges to zero with probability one so that the search ability of a ga decreases and premature convergence occurs moreover an explicit formula for the conditional probability of allele loss at a certain bit position is established to show the relationships between premature convergence and the ga parameters such as population size mutation probability and some population statistics the formula also partly answers the questions of to where a ga most likely converges the theoretical results are all supported by the simulation experiments

l p estimates for the linear wave equation and global existence for semilinear wave equations in exterior domains we consider the initial boundary value problem for the semilinear wave equation u tt delta u a x u t f u mbox in omega times 0 infty u x 0 u 0 x u t x 0 u 1 x mbox and u partial omega 0 where omega is an exterior domain in r n a x u t is a dissipative term which is effective only near the critical part of the boundary we first give some l p estimates for the linear equation by combining the results of the local energy decay and l p estimates for the cauchy problem in the whole space next on the basis of these estimates we prove global existence of small amplitude solutions for semilinear equations when omega is odd dimensional domain when n 3 mbox and f u alpha u our result is applied if alpha 2 sqrt 3 1 we note that no geometrical condition on the boundary partial omega is imposed

certain results for the 2 variable apostol type and related polynomials in this article the 2 variable general polynomials are taken as base with apostol type polynomials to introduce a family of 2 variable apostol type polynomials these polynomials are framed within the context of monomiality principle and their properties are established certain summation formulae for these polynomials are also derived examples of some members belonging to this family are considered and numbers related to some mixed special polynomials are also explored

fourier expansions and integral representations for the apostol bernoulli and apostol euler polynomials we investigate fourier expansions for the apostol bernoulli and apostol euler polynomials using the lipschitz summation formula and obtain their integral representations we give some explicit formulas at rational arguments for these polynomials in terms of the hurwitz zeta function we also derive the integral representations for the classical bernoulli and euler polynomials and related known results

a general steady state distribution based stopping criteria for finite length genetic algorithms we propose two general stopping criteria for finite length simple genetic algorithms based on steady state distributions and empirically investigate the impact of mutation rate string length crossover rate and population size on their convergence our first stopping criterion is based on the second largest eigenvalue of the genetic algorithm transition matrix and the second stopping criterion is based on minorization conditions

algebraic properties and fourier expansions of two dimensional apostol bernoulli and apostol euler polynomials we define the two dimensional 2d apostol bernoulli and the 2d apostol euler polynomials respectively via the generating functions t e x t y t m e t 1 n 0 b n x y t n n 2 e x t y t m e t 1 n 0 e n x y t n n as parametrized polynomial families they are essentially the same we study their basic algebraic properties generalizing some well known formulas and relations for apostol bernoulli and bernoulli polynomials we determine the fourier series of x x b n x y y x b n x y and x y x b n x y for x y 0 1 0 1 these contain as a special case the fourier series of the one dimensional apostol bernoulli and apostol euler polynomials

bounds for eigenvalues of certain stochastic matrices abstract we consider the class of stochastic matrices m generated in the following way from graphs if g is an undirected connected graph on n vertices with adjacency matrix a we form m from a by dividing the entries in each row of a by their row sum being stochastic m has the eigenvalue 1 and possibly also an eigenvalue 1 we prove that the remaining eigenvalues of m lie in the disk 1 n 3 and show by examples that the order of magnitude of this estimate is best possible in these examples g has a bar bell structure in which n 3 of the vertices are arranged along a line with n 3 vertices fully interconnected at each end we also obtain better bounds when either the diameter of g or the maximal degree of a vertex is restricted

new stopping criterion for genetic algorithms abstract genetic algorithms have been successfully applied in a wide variety of problems although widely used there are few theoretical guidelines for determining when to terminate the search one result by aytug and koehler provides a loose bound on the number of ga generations needed to see all populations and hence an optimal solution with a specified probability in this paper we derive a tighter bound this new bound is on the number of iterations required to achieve a level of confidence to guarantee that a genetic algorithm has seen all strings and hence an optimal solution

convergence criteria for genetic algorithms in this paper we discuss convergence properties for genetic algorithms by looking at the effect of mutation on convergence we show that by running the genetic algorithm for a sufficiently long time we can guarantee convergence to a global optimum with any specified level of confidence we obtain an upper bound for the number of iterations necessary to ensure this which improves previous results our upper bound decreases as the population size increases we produce examples to show that in some cases this upper bound is asymptotically optimal for large population sizes the final section discusses implications of these results for optimal coding of genetic algorithms

a class of multi objective supply chain networks optimal model under random fuzzy environment and its application to the industry of chinese liquor an important issue when shipping cost and customers demand are random fuzzy variables in supply chain network scn design problem is to find the network strategy that can simultaneously achieve the objectives of minimization total cost comprised of fixed costs of plants and distribution centers dcs inbound and outbound distribution costs and maximization customer services that can be rendered to customers in terms of acceptable delivery time in this paper we propose a random fuzzy multi objective mixed integer non linear programming model for the scn design problem of luzhou co ltd which is representative in the industry of chinese liquor by the expected value operator and chance constraint operator the model has been transformed into a deterministic multi objective mixed integer non linear programming model then we use spanning tree based genetic algorithms st ga by the prufer number representation to find the scn to satisfy the demand imposed by customers with minimum total cost and maximum customer services for multi objective scn design problem of this company under condition of random fuzzy customers demand and transportation cost between facilities furthermore the efficacy and the efficiency of this method are demonstrated by the comparison between its numerical experiment results and those of tradition matrix based genetic algorithm

scattering for semilinear wave equations with small data in three space dimensions on considere la theorie de la diffusion pour des equations d onde semilineaires du type u tt u f u a 3 dimensions d espace ou f u u p 1 u ou f u u p r p 1

a non dominance based online stopping criterion for multi objective evolutionary algorithms a non dominance criterion based metric that tracks the growth of an archive of non dominated solutions over a few generations is proposed to generate a convergence curve for multi objective evolutionary algorithms moeas it was observed that similar to single objective optimization problems there were significant advances toward the pareto optimal front in the early phase of evolution while relatively smaller improvements were obtained as the population matured this convergence curve was used to terminate the moea search to obtain a good trade off between the computational cost and the quality of the solutions two analytical and two crashworthiness optimization problems were used to demonstrate the practical utility of the proposed metric

stabilization of local energy in an exterior domain for the wave equation with a localized dissipation abstract we derive an algebraic decay rate for the local energyeloc t of the solutions to the initial boundary value problem of the wave equation with a localized dissipation in an exterior domain the dissipative terma x utis assumed to be effective only on a neighbourhood of a part of the boundary x0 x x x0 x 0 for somex0 where x is unit outward normal atxwith respect to it should be noted that we make no geometrical condition on the boundary ifv rn 0 is star shaped with respect tox0 x0 is empty and hence we may assumea x 0 thus our result is a natural extension of the well known most classical result

convergence analysis of canonical genetic algorithms this paper analyzes the convergence properties of the canonical genetic algorithm cga with mutation crossover and proportional reproduction applied to static optimization problems it is proved by means of homogeneous finite markov chain analysis that a cga will never converge to the global optimum regardless of the initialization crossover operator and objective function but variants of cga s that always maintain the best solution in the population either before or after selection are shown to converge to the global optimum due to the irreducibility property of the underlying original nonconvergent cga these results are discussed with respect to the schema theorem