spectral collocation method for solving fredholm integral equations on the half line the main purpose of this paper is to present a spectral collocation method to approximate the solution of fredholm integral equations of the second kind on the half line in this approach interpolation operator based on scaled laguerre functions is proposed also convergence theorems are established under suitable assumptions finally two numerical examples are presented and commented

substitution rules for aperiodic sequences of the cut and project type we consider one dimensional aperiodic sequences arising from a cut and project scheme with quadratic unitary pisot numbers a construction of the substitution rule is described under rather general assumptions it allows one to build a given cut and project sequence starting from its arbitrary point for a sequence with a convex acceptance window interval we prove that a substitution rule exists precisely if the boundary points of are in the corresponding quadratic field typically such a substitution has a reducible characteristic polynomial our main result is an algorithm for construction of such a substitution rule some examples are shown

a new generalized laguerre spectral approximation and its applications a new family of generalized laguerre polynomials is introduced various orthogonal projections are investigated some approximation results are established as an example of their important applications the mixed spherical harmonic generalized laguerre approximation is developed a mixed spectral scheme is proposed for a three dimensional model problem its convergence is proved numerical results demonstrate the high accuracy of this new spectral method

the role of crossover operator in the genetic optimization of magnetic models the ising model introduced almost 100 years ago by wilhelm lenz and ernst ising is the formalism still popular as a tool to describe magnetic properties of a wide class of materials among many issues which arise when using this model there exist problems related to the process of finding minimum energy of the system since these problems are np hard optimizations can either be performed for some approximated cases or be the subject of global optimization techniques in this paper we present an analysis of the effect of different crossover operators on the efficiency of genetic algorithm used to minimize energy in the ising model although it is not a benchmark tool we hope it may be interesting as a testing tool

a hybrid shuffled complex evolution approach based on differential evolution for unconstrained optimization numerous optimization methods have been proposed for the solution of the unconstrained optimization problems such as mathematical programming methods stochastic global optimization approaches and metaheuristics in this paper a metaheuristic algorithm called modified shuffled complex evolution msce is proposed where an adaptation of the downhill simplex search strategy combined with the differential evolution method is proposed the efficiency of the new method is analyzed in terms of the mean performance and computational time in comparison with the genetic algorithm using floating point representation gaf and the classical shuffled complex evolution sce ua algorithm using six benchmark optimization functions simulation results and the comparisons with sce ua and gaf indicate that the msce improves the search performance on the five benchmark functions of six tested functions

a complete orthonormal system of functions in l 2 infty infty space a new complete orthonormal system of functions in the l 2 infty infty space is introduced the system consists of two sequences composed of odd and even functions respectively unlike hermite and laguerre sets of functions which behave exponentially at infinity the new system exhibits asymptoticbehavior x 1 for the odd sequence and x 2 for the even one formulae representing products derivatives etc in series in the system are developed a nonlinear differential equation with a requirement for summability of the square of its solutions instead of boundary conditions is solved the example displays most of the features of the new method important for essentially nonlinear problems

numerical integration based on laguerre gauss interpolation abstract in this paper we propose two efficient numerical integrators for ordinary differential equations based on modified laguerre gauss interpolations the global convergence of proposed algorithms is proved numerical results demonstrate the spectral accuracy of these new schemes and agree well with the theoretical analysis

integration processes of ordinary differential equations based on laguerre radau interpolations in this paper we propose two integration processes for ordinary differential equations based on modified laguerre radau interpolations which are very efficient for long time numerical simulations of dynamical systems the global convergence of proposed algorithms are proved numerical results demonstrate the spectral accuracy of these new approaches and coincide well with theoretical analysis

on the canonical projection method for one dimensional quasicrystals and invertible substitution rules we show that if a quasiperiodic two symbol sequence obtained by the canonical projection method has an infinite number of predecessors with respect to a substitution rule then is an invertible substitution rule vice versa we show that every quasiperiodic two symbol sequence that has an infinite number of predecessors with respect to a non trivial invertible substitution rule can be obtained by the canonical projection method

application of a hybrid gentic powell algorithm and a boundary element method to electical abstract an optimization method based on a genetic algorithm ga and a boundary element method is applied to solve an electrical impedance tomography problem the scheme is applied to reconstruct highly irregular shapes and to image and count objects inside a host medium of different impedance a pareto multiobjective optimization method is applied to improve the performance of the ga comparisons between the ga and a calculus based method for selected test problems show that the calculus based method outperforms the ga in simple cases but that for more complex cases the ga reaches the correct solution whereas the calculus based method does not a hybrid scheme that we developed combining a calculus based method and the ga is shown to be the most efficient and robust even when applied to the complex cases we tested the sensitivity of the current scheme is evaluated in the presence of noise

the spectral method for high order problems with proper simulations of asymptotic behaviors at infinity in this paper we investigate new spectral and multidomain spectral methods for high order problems we introduce a family of new generalized laguerre functions which are mutually orthogonal with the weight function x a d x c d 0 a and c being arbitrary real numbers the corresponding quasi orthogonal approximation and laguerre gauss radau type interpolation are proposed the spectral and multidomain spectral schemes are provided for several model problems which not only fit the mixed inhomogeneous boundary conditions on the fixed boundary exactly but also match the asymptotic behaviors at infinity reasonably numerical results demonstrate the efficiency of suggested algorithms and confirm the analysis well

generalized laguerre pseudospectral method based laguerre interpolation abstract in this paper we develop the generalized laguerre pseudospectral method for the second order ordinary differential equation based on the modified generalized laguerre approximation which is very efficient for the long time numerical simulations of dynamical systems the numerical solution possesses the spectral accuracy the global convergence of the proposed algorithm is proved numerical results demonstrate the effectiveness of the proposed method and coincide well with theoretical analysis

quasicrystals and icosians a family of quasicrystals of dimensions 1 2 3 4 governed by the root lattice e8 is constructed the use of the icosian ring found in the quaternions with coefficients in q square root 5 allows simultaneous interpretation of the construction both in physical space and as a result of the standard cut and projection method in double dimension icosians are seen to provide a natural co ordination scheme for these quasicrystals nested sequences of quasicrystals form systems whose symmetries are all derivable from inflational and reflective symmetries directly related to the arithmetic of the icosians the use of coxeter diagrams clarifies the amazing relationship of e8 and quasicrystal symmetries and leads to the fundamental chain e8 contains implies d6 contains implies a4 contains implies a1 a1 that underlies five fold symmetry in quasicrystals decomposition of quasicrystals into concentric shells and a counting formula for the cardinalities of these shells is discussed

error estimation of hermite spectral method for nonlinear partial differential equations hermite approximation is investigated some inverse inequalities imbedding inequalities and approximation results are obtained a hermite spectral scheme is constructed for burgers equation the stability and convergence of the proposed scheme are proved strictly the techniques used in this paper are also applicable to other nonlinear problems in unbounded domains

jacobi and laguerre quasi orthogonal approximations and related interpolations in this paper we investigate jacobi quasi orthogonal approximation and generalized jacobi gauss lobatto interpolation we also propose laguerre quasi orthogonal approximation and generalized laguerre gauss radau interpolation a series of sharp results on these approximations are established which are applicable to spectral and pseudospectral methods for mixed nonhomogeneous boundary value problems of high order

quadratic approximation based hybrid genetic algorithm for function optimization abstract probably the popular form of binary genetic algorithms for function optimization use tournament selection ts or roulette wheel selection rs for function optimization also single point crossover sc and uniform crossover uc are most popular and effective crossover operators in an earlier paper we had considered all four combinations of these crossover and mutation operators along with bit wise mutation called ga1 ts sc ga2 ts uc ga3 rs sc and ga4 rs uc in this paper an attempt is made to hybridize these four gas by incorporating the quadratic approximation qa operator into them the four resultant hybrid gas called hga1 hga2 hga3 and hga4 are compared with the four simple gas on a set of 22 test problems taken from literature based on the extensive numerical and graphical analysis of results it is concluded that the hga3 outperforms all rest 7 versions further we study the depth and frequency of the qa should be applied for better performance for the particular problem suite

a self adaptive chaotic differential evolution algorithm using gamma distribution for unconstrained global optimization evolutionary algorithms eas have yielded promising results for solving nonlinear non differentiable and multi modal optimization problems due to its population based nature eas can avoid being trapped in a local optimum and consequently have the ability to find global optimal solutions as a novel evolutionary technique differential evolution de has received increasing attention and wide applications in a variety of fields de algorithm uses an efficient way of self adapting mutation using small populations for function optimization over continuous spaces the potentialities of de are its simple structure easy use convergence property quality of solution and robustness in this paper an effective self adaptive de algorithm based on gaussian probability distribution gamma distribution and chaotic sequence degc for solving continuous global optimization problems is proposed the proposed degc algorithm is tested on several benchmark functions from the usual literature numerical results comparisons with a classical de approach and a self adaptive de approach demonstrate the effectiveness and efficiency of the proposed degc algorithm

fractional spectral and pseudo spectral methods in unbounded domains theory and applications abstract this paper is intended to provide exponentially accurate galerkin petrov galerkin and pseudo spectral methods for fractional differential equations on a semi infinite interval we start our discussion by introducing two new non classical lagrange basis functions nlbfs 1 and nlbfs 2 which are based on the two new families of the associated laguerre polynomials galfs 1 and galfs 2 obtained recently by the authors in 28 with respect to the nlbfs 1 and nlbfs 2 two new non classical interpolants based on the associated laguerre gauss and laguerre gauss radau points are introduced and then fractional pseudo spectral differentiation and integration matrices are derived convergence and stability of the new interpolants are proved in detail several numerical examples are considered to demonstrate the validity and applicability of the basis functions to approximate fractional derivatives and integrals of some functions moreover the pseudo spectral galerkin and petrov galerkin methods are successfully applied to solve some physical ordinary differential equations of either fractional orders or integer ones some useful comments from the numerical point of view on galerkin and petrov galerkin methods are listed at the end

the nature of the atomic surfaces of quasiperiodic self similar structures quasiperiodic self similar chains generated by substitutions i e deterministic concatenation rules and their diffraction spectra are analysed in a systematic fashion from the viewpoint of the superspace formalism a substitution acting on n objects generates quasiperiodic chains if and only if the associated substitution matrix fulfils two arithmetic conditions pisot property and unit determinant the structures thus obtained can be alternatively built as sections of periodic patterns in an n dimensional superspace which are regular repetitions of an atomic surface the authors derive a general algorithm to construct this atomic surface it is a compact set of the n 1 dimensional internal space which is a unit cell for a lattice of translations the atomic surface is nevertheless not necessarily connected and its boundary is generically an anisotropic self similar fractal the dimension db of this boundary is shown to govern the anomalously slow fall off of the intensities of bragg diffractions and therefore to influence physical properties

mixed spectral method for three dimensional exterior problems using spherical harmonic and generalized laguerre functions in this paper we develop the mixed spectral method for three dimensional exterior problems using spherical harmonic and generalized laguerre functions some basic approximation results are established the mixed spectral schemes are proposed for two model problems their convergences are proved numerical results demonstrate the efficiency of this new approach

a novel splicing decomposable binary encoding and its operators for genetic and evolutionary algorithms abstract in this paper we introduce a new genetic representation a splicing decomposable s d binary encoding which was proposed based on some theoretical guidance and existing recommendations for designing efficient genetic representations the s d binary representation can be spliced and decomposed to describe potential solutions of the problem with different precisions by different number of uniform salient building blocks bbs according to the characteristics of the s d binary representation genetic and evolutionary algorithms geas can be applied from the high scaled to the low scaled bbs sequentially to avoid a noise from the competing bbs and improve geas performance our theoretical and empirical investigations reveal that the s d binary representation is more proper than other existing binary encodings for geas searching moreover we define a new genotypic distance on the s d binary space which is equivalent to the euclidean distance on the real valued space during geas convergence based on the new genotypic distance geas can reliably and predictably solve problems of bounded complexity and the methods depended on the euclidean distance for solving different kinds of optimization problems can be directly used on the s d binary space

inflation centres of the cut and project quasicrystals a rather general form of the conventional cut and project scheme is used to define quasicrystals as point sets in real n dimensional euclidean space the inflation or equivalently the self similarity properties of such quasicrystals are studied here assuming only the convexity of the acceptance window our result is a description of inflation centres of all types in a quasicrystal and a proof that our description is complete there are no other inflation centres for any chosen quasicrystal point internal inflation centre u its inflation properties are given as a set of scaling factors it turns out that the scaling factors form a one dimensional quasicrystal with a u dependent acceptance window scaling window the intersection of the scaling windows associated with all points of a quasicrystal is the one dimensional quasicrystal of universal internal scaling symmetries its acceptance window is the interval external inflation centres of a cut and project quasicrystal are those which are not among quasicrystal points their complete description is given analogically to the description of the internal ones imposing some additional requirements on the scaling factors between any two adjacent quasicrystal points one finds a countable infinity of external inflation centres the scaling factors belonging to any such centre u form an infinite u dependent subset of points of the quasicrystal with acceptance window containing

approximation of some diffusion evolution equations in unbounded domains by hermite functions spectral and pseudospectral approximations of the heat equation are analyzed the solution is represented in a suitable basis constructed with hermite polynomials stability and convergence estimates are given and numerical tests are discussed

the laguerre spectral method for solving neumann boundary value problems in this paper we propose a laguerre spectral method for solving neumann boundary value problems this approach differs from the classical spectral method in that the homogeneous boundary condition is satisfied exactly moreover a tridiagonal matrix is employed instead of the full stiffness matrix encountered in the classical variational formulation of such problems for analyzing the numerical errors some basic results on laguerre approximations are established the convergence is proved the numerical results demonstrate the efficiency of this approach

stable and efficient spectral methods in unbounded domains using laguerre functions stable and efficient spectral methods using laguerre functions are proposed and analyzed for model elliptic equations on regular unbounded domains it is shown that spectral galerkin approximations based on laguerre functions are stable and convergent with spectral accuracy in the usual not weighted sobolev spaces efficient accurate and well conditioned algorithms using laguerre functions are developed and implemented numerical results indicating the spectral convergence rate and effectiveness of these algorithms are presented

generalized laguerre interpolation and pseudospectral method for unbounded domains in this paper error estimates for generalized laguerre gauss type interpolations are derived in nonuniformly weighted sobolev spaces weighted with omega alpha beta x x alpha e beta x alpha 1 beta 0 generalized laguerre pseudospectral methods are analyzed and implemented two model problems are considered the proposed schemes keep spectral accuracy and with suitable choice of basis functions lead to sparse and symmetric linear systems

spectral methods using rational basis functions on an infinite interval by using the map y l cot t where l is a constant differential equations on the interval y can be transformed into t 0 and solved by an ordinary fourier series in this article earlier work by grosch and orszag j comput phys 25 273 1977 cain ferziger and reynolds j comput phys 56 272 1984 and boyd j comput phys 25 43 1982 57 454 1985 siam j numer anal 1987 is extended in several ways first the series of orthogonal rational functions converge on the exterior of bipolar coordinate surfaces in the complex y plane second galerkin s method will convert differential equations with polynomial or rational coefficients into banded matrix problems third with orthogonal rational functions it is possible to obtain exponential convergence even for u y that asymptote to a constant although this behavior would wreck alternatives such as hermite or sinc expansions fourth boundary conditions are usually natural rather than essential in the sense that the singularities of the differential equation will force the numerical solution to have the correct behavior at infinity even if no constraints are imposed on the basis functions fifth mapping a finite interval to an infinite one and then applying the rational chebyshev functions gives an exponentially convergent method for functions with bounded endpoint singularities these concepts are illustrated by five numerical examples

laguerre galerkin method for nonlinear partial differential equations on a semi infinite interval summary a laguerre galerkin method is proposed and analyzed for the burgers equation and benjamin bona mahony bbm equation on a semi infinite interval by reformulating these equations with suitable functional transforms it is shown that the laguerre galerkin approximations are convergent on a semi infinite interval with spectral accuracy an efficient and accurate algorithm based on the laguerre galerkin approximations to the transformed equations is developed and implemented numerical results indicating the high accuracy and effectiveness of this algorithm are presented

a critical review of discrete filled function methods in solving nonlinear discrete optimization problems many real life problems can be modeled as nonlinear discrete optimization problems such problems often have multiple local minima and thus require global optimization methods due to high complexity of these problems heuristic based global optimization techniques are usually required when solving large scale discrete optimization or mixed discrete optimization problems one of the more recent global optimization tools is known as the discrete filled function method nine variations of the discrete filled function method in literature are identified and a review on theoretical properties of each method is given some of the most promising filled functions are tested on various benchmark problems numerical results are given for comparison

a natural class of generalized fibonacci chains in this paper we propose a class of substitution rules that generate quasiperiodic chains sharing their typid properties with the quasiperiodic fibonacci chain for a subclass we explicitly con vct the atomic surface moreover scaling properties of the energy specmm are discussed in relation to the dynamics of trace maps

generalized hermite spectral method and its applications to problems in unbounded domains in this paper we develop a spectral method based on generalized hermite functions with weight chi x equiv1 we also establish some basic results on generalized hermite orthogonal approximations which play an important role in spectral methods as examples the generalized ginzburg landau equation in a population problem and an elliptic equation with a harmonic potential are considered related spectral schemes are proposed and their convergence is proved numerical results demonstrate the spectral accuracy of this approach

the role of different genetic operators in the optimization of magnetic models abstract in the paper we continue the analysis of the influence of genetic operators on the efficiency of global optimization of ising model for such a model the physical problem of finding the minimum energy is defined its solution enables to determine the phase state of system in the given temperature and consequently the phase transition point the process of minimum energy search is np hard we showed that for a selected set of crossover operators we can obtain similar behavior but different exact numerical characteristics here we study how the other procedures and parameters can influence the optimization process we take into account such features like selection mutation objective function or niching we try also to build a hybrid algorithm with a specific problem related local search procedure we hope that the presented results can indicate the great possibilities of magnetic models as a test problem

proving the deterministic period breaking of linear congruential generators using two tile quasicrystals we describe the design of a family of aperiodic prngs aprngs we show how a one dimensional two tile cut and project quasicrystal 2tqc used in conjunction with lcgs in an aprng generates an infinite aperiodic pseudorandom sequence in the suggested design any 2tqc corresponding to unitary quadratic pisot number combined with either one or two different lcgs can be used

enhancing pso methods for global optimization the particle swarm optimization pso method is a well established technique for global optimization during the past years several variations of the original pso have been proposed in the relevant literature because of the increasing necessity in global optimization methods in almost all fields of science there is a great demand for efficient and fast implementations of relative algorithms in this work we propose three modifications of the original pso method in order to increase the speed and its efficiency that can be applied independently in almost every pso variant these modifications are a a new stopping rule b a similarity check and c a conditional application of some local search method the proposed were tested using three popular pso variants and a variety test functions we have found that the application of these modifications resulted in significant gain in speed and efficiency

a hybrid genetic algorithm for a class of global optimization problems with box constraints in this paper a new hybrid genetic algorithm is proposed which combines the genetic algorithm with hill climbing search steps differently from some former algorithms the new algorithm can be widely applied to a class of global optimization problems for continuous functions with box constraints finally numerical examples show that this algorithm can yield the global optimum with high efficiency

canonical substitutions tilings of ammann beenker type we present a large class of parallelogram tilings that have two important features in common with the ammann beenker tiling they can be constructed by canonical projection from z4 r4 to a plane and they admit substitution rules