关于Wiener过程泛函连续模的精确收敛速度

设{W（t）,t≥0}是一标准Wiener过程,记S是Strassen重对数律的紧集类·本文中我们讨论了两个变量sup_0≤t≤1-h inf_f∈S sup_0≤x≤1 |(W(t+hx)-W(t))(2h log h^-1)^-1/2 - f(x)|及inf_0≤t≤1-h sup_0≤x≤1 |(W(t + hx) - W(t))(2hlogh^-1)^-1/2- f(x)|（对任何f∈S）趋于零的精确的收敛速度.作为一个推广,我们建立了Wiener过程的不可微模与泛函的连续模之间的一种关系.     

On Estimating Integral Moduli of Continuity of Functions of Several Variables in Terms of Fourier Coefficients

Inequalities are derived which enable one to estimate integral moduli of continuity of functions of several variables in terms of Fourier coefficients.     

Pointwise Approximation by Szàsz-Mirakjan Quasi-Interpolants

Recently some classical operator quasi-interpolants were introduced to obtain much faster convergence. A.T. Diallo investigated some approximation properties of Szàsz-Mirakjan Quasi-Interpolants, but he obtained only direct theorem with Ditzian-Totik modulus ω2rψ(f, t). In this paper, we extend Diallo's result and solve completely the characterization on the rate of approximation by the method of quasi-interpolants to functions f ∈ CB[0, ∞) by making use of the unified modulus ω2rψλ> (f, t) (0 ≤λ≤ 1).     

一种新的双模式盲均衡算法研究

针对恒模算法(CMA)收敛速度较慢、收敛后均方误差较大的缺点,提出一种新的双模式盲均衡算法.在算法初期,利用能快速收敛的归一化恒模算法(NCMA)进行冷启动,在算法收敛后切换到判决引导(DD-LMS)算法,减少误码率.计算机仿真表明,提出的新算法有较快的收敛速度和较低的误码率.     

Smoothness Properties of Modified Bernstein-Kantorovich Operators

In this article, we consider modified Bernstein-Kantorovich operators and investigate their approximation properties. We show that the order of approximation to a function by these operators is at least as good as that of ones classically used. We obtain a simultaneous approximation result for our operators. Also, we prove two direct approximation results via the usual second-order modulus of smoothness and the second-order Ditzian-Totik modulus of smoothness, respectively. Finally, some graphical illustrations are provided.     

On Approximation by Neural Networks with Optimized Activation Functions and Fixed Weights

Recently, Li [16] introduced three kinds of single-hidden layer feed-forward neural networks with optimized piecewise linear activation functions and fixed weights, and obtained the upper and lower bound estimations on the approximation accuracy of the FNNs, for continuous function defined on bounded intervals. In the present paper, we point out that there are some errors both in the definitions of the FNNs and in the proof of the upper estimations in [16]. By using new methods, we also give right approximation rate estimations of the approximation by Li’s neural networks.     

On a class of Köthe sequence spaces with normal structure

In this note, we investigate the generalized modulus of convexity δ ( λ ) and the generalized modulus smoothness ρ ( λ ) . We obtain some estimates of these moduli for X = lp . We obtain inequalities between WCS coefficient of a K¨othe sequence space X and δ ( λ ) X . We show that, for a wide class of K¨othe sequence spaces X, if for some ε∈ (0, 9 10 ] holds δ X (ε) > 1 3 1 √ 3 2 ε, then X has normal structure.     

Capacity relations in a flat quadrilateral

We consider the relationship between the p-capacity of the pairs of opposite sides of a flat quadrilateral and the resultant class of extremal mappings.     

Temperature dependence of an elastic modulus in generalized linear micropolar thermoelasticity

The model of the equations of generalized linear micropolar thermoelasticity with two relaxation times in an isotropic medium with temperature-dependent mechanical properties is established. The modulus of elasticity is taken as a linear function of reference temperature. Laplace and exponential Fourier transform techniques are used to obtain the solution by a direct approach. The integral transforms have been inverted by using a numerical technique to obtain the temperature, displacement, force and couple stress in the physical domain. The results of these quantities are given and illustrated graphically. A comparison is made with results obtained in case of temperature-independent modulus of elasticity. The problem of generalized thermoelasticity has been reduced as a special case of our problem.     

The rate of convergence of q-Durrmeyer operators for 0

Vijay Gupta  Wang Heping 《Mathematical Methods in the Applied Sciences》2008,31(16):1946-1955

Optimal Constant in Approximation by Bernstein Operators

We obtained that for any n N, C = 1 is the smallest constant for which the inequality ||B _n (f) - f|| C ₂(f, 1/n) holds on the class of continuous functions f, as well as on the class of bounded functions f, where B _n is the Bernstein operators of degree n, ₂ is the second order modulus and || || is the sup-norm.     

凸连续模的性质

本在介绍连续模概念的基础上，对凸连续模做了进一步的研究或提出新的证法。     

正交各向异性薄板弯曲问题分裂模量有限元法

讨论了建立分裂模量有限元法的必要性,推导了正交各向异性薄板弯曲问题分裂模量变分原理的泛函,以此为基础建立了该问题的分裂模量有限元法。该模型的特点是其中含有一个被称为分裂因子的参数,通过算例说明:适当调整分裂因子的值,可以达到调整有限元模型的刚度、降低有限元刚度矩阵的谱条件数、克服常规有限元病态问题的目的,最后分析了克服病态问题的机理。     

一类高阶线性齐次递归数列的几个模性质

给出一类特殊的高阶线性递归序列的几个模性质.     

Linear maps preserving the minimum and surjectivity moduli of Hilbert space operators

Let B(H) be the algebra of all bounded linear operators on a complex infinite-dimensional Hilbert space H. For every T∈B(H), let m(T) and q(T) denote the minimum modulus and surjectivity modulus of T respectively. Let ?:B(H)→B(H) be a surjective linear map. In this paper, we prove that the following assertions are equivalent:

(i)

m(T)=m(?(T)) for all T∈B(H),

(ii)

q(T)=q(?(T)) for all T∈B(H),

(iii)

there exist two unitary operators U,V∈B(H) such that ?(T)=UTV for all T∈B(H).

This generalizes the result of Mbekhta [7, Theorem 3.1] to the non-unital case.     

Lp approximation by Bernstein-Kantorovich quasi-interpolants

Bernstein-Kantorovich quasi-interpolants K(2r-1) n (f, x) are considered and direct,inverse and equivalence theorems with Ditzian-Totik modulus of smoothness ω2rψ(f, t)p (1 ≤ p≤+∞) are obtained.     

L p approximation by Bernstein-Kantorovich quasi-interpolants

Bernstein-Kantorovich quasi-interpolants K^（2r-1）n（f, x） are considered and direct, inverse and equivalence theorems with Ditzian-Totik modulus of smoothness ω^2rφ（f, t）p （1 ≤ p ≤＋∞） are obtained.     

On Growth of Polynomials with Restricted Zeros

Let P(z) be a polynomial of degree n which does not vanish in |z| k, k ≥ 1.It is known that for each 0 ≤ s n and 1 ≤ R ≤ k,M (P~(s), R )≤( 1/(R~s+ k~s))[{d~((s)/dx(s))(1+x~n)}_(x=1)]((R+k)/(1+k))~nM(P,1).In this paper, we obtain certain extensions and refinements of this inequality by involving binomial coefficients and some of the coefficients of the polynomial P(z).     

PROPERTIES OF SOME SETS OF SEQUENCES DEFINED BY A MODULUS FUNCTION

In this article, the author introduces the generalized difference paranormed sequence spaces c （△v^m, f, p, q, s）, c0 （△v^m, f, p, q, s）, and l∞ （△v^m, f, p, q, s） defined over a seminormed sequence space （X, q）. The author also studies their properties like completeness, solidity, symmetricitv, etc.