In this paper.variable operator and its product with shifting operator are studied.The product of power series of shifting operator with variable coefficient is defined andits convergence is proved under Mikusinski’s...In this paper.variable operator and its product with shifting operator are studied.The product of power series of shifting operator with variable coefficient is defined andits convergence is proved under Mikusinski’s sequence convergence.After turning ageneral variable coefficient linear difference equation of order n into a set of operatorequations.we can obtain the solutions of the general n-th order variable coefficientlinear difference equation.展开更多
In this note, we investigate the generalized modulus of convexity δ（λ） and the generalized modulus smoothness p（λ）. We obtain some estimates of these moduli for X=lp. We obtain inequalities between WCS coeffici...In this note, we investigate the generalized modulus of convexity δ（λ） and the generalized modulus smoothness p（λ）. We obtain some estimates of these moduli for X=lp. We obtain inequalities between WCS coefficient of a KSthe sequence space X and δX（λ）. We show that, for a wide class of class the sequence spaces X, if for some ε∈（0, 9/10] holds δx（e） 〉 1/3（1- √3/2）ε, then X has normal structure.展开更多
Let X be a Banach space with a weak uniform normal structure and C a non–empty convex weakly compact subset of X. Under some suitable restriction, we prove that every asymptotically regular semigroup T = {T(t) : t ∈...Let X be a Banach space with a weak uniform normal structure and C a non–empty convex weakly compact subset of X. Under some suitable restriction, we prove that every asymptotically regular semigroup T = {T(t) : t ∈? S} of selfmappings on C satisfying展开更多
Nature inspired optimization algorithms have made substantial step towards solving of various engineering and scientific real-life problems.Success achieved for those evolution-ary optimization techniques are due to s...Nature inspired optimization algorithms have made substantial step towards solving of various engineering and scientific real-life problems.Success achieved for those evolution-ary optimization techniques are due to simplicity and flexibility of algorithm structures.In this paper,optimal set of filter coefficients are searched by the evolutionary optimiza-tion technique called Opposition-based Differential Evolution(ODE)for solving infinite impulse response(IIR)system identification problem.Opposition-based numbering con-cept is embedded into the primary foundation of Differential Evolution(DE)technique metaphorically to enhance the convergence speed and the performance for finding the optimal solution.The population is generated with the evaluation of a solution and its opposite solution by fitness function for choosing potent solutions for each iteration cycle.With this competent population,faster convergence speed and better solution quality are achieved.Detailed and balanced search in multidimensional problem space is accomplished with judiciously chosen control parameters for mutation,crossover and selection adopted in the basic DE technique.When tested against standard benchmark examples,for same order and reduced order models,the simulation results establish the ODE as a competent candidate to others in terms of accuracy and convergence speed.展开更多
文摘In this paper.variable operator and its product with shifting operator are studied.The product of power series of shifting operator with variable coefficient is defined andits convergence is proved under Mikusinski’s sequence convergence.After turning ageneral variable coefficient linear difference equation of order n into a set of operatorequations.we can obtain the solutions of the general n-th order variable coefficientlinear difference equation.
基金supported by National Fund for Scientific Research of the Bulgarian Ministry of Education and Science, Contract MM-1401/04
文摘In this note, we investigate the generalized modulus of convexity δ（λ） and the generalized modulus smoothness p（λ）. We obtain some estimates of these moduli for X=lp. We obtain inequalities between WCS coefficient of a KSthe sequence space X and δX（λ）. We show that, for a wide class of class the sequence spaces X, if for some ε∈（0, 9/10] holds δx（e） 〉 1/3（1- √3/2）ε, then X has normal structure.
基金supported both by the Teaching and Research Award Fund for Outstanding Young Teachers in Higher Education Institutions of MOE,P.R.C.by the National Natural Science Foundation 19801023
文摘Let X be a Banach space with a weak uniform normal structure and C a non–empty convex weakly compact subset of X. Under some suitable restriction, we prove that every asymptotically regular semigroup T = {T(t) : t ∈? S} of selfmappings on C satisfying
文摘Nature inspired optimization algorithms have made substantial step towards solving of various engineering and scientific real-life problems.Success achieved for those evolution-ary optimization techniques are due to simplicity and flexibility of algorithm structures.In this paper,optimal set of filter coefficients are searched by the evolutionary optimiza-tion technique called Opposition-based Differential Evolution(ODE)for solving infinite impulse response(IIR)system identification problem.Opposition-based numbering con-cept is embedded into the primary foundation of Differential Evolution(DE)technique metaphorically to enhance the convergence speed and the performance for finding the optimal solution.The population is generated with the evaluation of a solution and its opposite solution by fitness function for choosing potent solutions for each iteration cycle.With this competent population,faster convergence speed and better solution quality are achieved.Detailed and balanced search in multidimensional problem space is accomplished with judiciously chosen control parameters for mutation,crossover and selection adopted in the basic DE technique.When tested against standard benchmark examples,for same order and reduced order models,the simulation results establish the ODE as a competent candidate to others in terms of accuracy and convergence speed.
