On the uniform convergence of trigonometric series

In this paper, we obtain sufficient conditions for the uniform convergence of trigonometric series with monotone (in the extended sense) coefficients.     

Some new sequence spaces defined by lacunary sequences

It is natural to expect that lacunary almost convergence must be related to the some concept of lacunary almost bounded variations in the some view as almost convergence is related to almost bounded variation. The purpose of this paper is to examine this new concept in some details. Some inclusion theorems have been established. Communicated by Pavel Kostyrko     

基于自组装生成[Bi_2W_(21)O_(70)(OH)_3]~(11-)配体的双核Ce(Ⅳ)配合物合成、结构及电化学性质

使用[β-B-BiW_9O_(33)]~(9-)作为基本建筑单元,成功合成了多酸做配体的双核Ce(Ⅳ)配合物(Na_6H_(10){Ce(H_2O)_3(μ_2-OH)[Bi_2W_(21)O_(70)(OH)_3]}_2·40H_2O),通过元素分析、X-射线单晶衍射、XRD、IR和TG表征技术确定了其组成和结构.两核Ce(Ⅳ)离子配合物是通过2个μ_2-OH~-连接构成的,每个Ce(Ⅳ)离子除了与2个μ_2-OH~-配位外,还与3个H_2O以及[Bi_2W_(21)O_(70)(OH)_3]~(11-)中4个缺位O原子配位,形成三帽三棱柱.[Bi_2W_(21)O_(70)(OH)_3]~(11-)多酸阴离子是通过3个W(Ⅵ)连接形成新的多酸阴离子物种,在缺位结构上留有一个空位恰好与Ce(Ⅳ)离子配位.通过对配合物的电化学分析发现,与硝酸铈铵对比,配合物中Ce(Ⅳ/Ⅲ)的阳极峰电势由0.857减小至0.772V,表明多酸阴离子配体有稳定Ce(Ⅳ)的作用.     

Refined theorems of approximation theory in the space of p-absolutely continuous functions

In this paper, we prove direct and inverse theorems of approximation theory in the space of p-absolutely continuous functions which generalize Terekhin’s results in the same way as Timan’s results in L _p generalize the classical theorems of approximation theory. The main theorems are refined for functions with quasimonotone Fourier coefficients and, in a number of cases, the resulats are shown to be sharp.     

一个双周期缺项整插值问题

本文研究等距结点上双周期（０，ｍ）整插值问题，得到了它在Ｂ_σ²中有唯一解的充要条件，给出这种插值函数的明显表达式，还讨论了收敛性和收敛速度．     

On a Class of Generalized Lacunary Difference Sequence Spaces Defined by Orlicz Functions

In this article we introduce the generalized lacunary difference sequence spaces [N_θ,M,Δ~m]_0,[N_θ,M,Δ~m]_1 and [N_θ,M,Δ~m]_∞using m~(th)- difference.We study their properties like completeness,solidness,symmetricity.Also we obtain some inclusion relations involving the spaces [N_θ,M,Δ~m]_0,[N_θ,M,Δ~m]_1 and[N_θ,M,Δ~m]_∞and the Cesàro summable and strongly Cesàro summable sequences.     

A Cantor-Lebesgue theorem with variable ``coefficients'

If is a lacunary sequence of integers, and if for each , and are trigonometric polynomials of degree then must tend to zero for almost every whenever does. We conjecture that a similar result ought to hold even when the sequence has much slower growth. However, there is a sequence of integers and trigonometric polynomials such that tends to zero everywhere, even though the degree of does not exceed for each . The sequence of trigonometric polynomials tends to zero for almost every , although explicit formulas are developed to show that the sequence of corresponding conjugate functions does not. Among trigonometric polynomials of degree with largest Fourier coefficient equal to , the smallest one ``at' is while the smallest one ``near' is unknown.

     

The minimality properties of chebyshev polynomials and their lacunary series

By considering four kinds of Chebyshev polynomials, an extended set of (real) results are given for Chebyshev polynomial minimality in suitably weighted Hölder norms on [?1, 1], as well as (L _∞ minimax properties, and bestL ₁ sufficiency requirements based on Chebyshev interpolation. Finally we establish bestL _p,L _∞ andL ₁ approximation by partial sums of lacunary Chebyshev series of the form ∑ ₁₌₀ ^∞ a ⁱ ? _b ⁱ (x) where? _x (x) is a Chebyshev polynomial andb is an odd integer ≥3. A complete set of proofs is provided.     

Markov-Type Inequalities for Products of Müntz Polynomials

Let Λ(λ_j)^∞_j=0 be a sequence of distinct real numbers. The span of {x^λ₀, x^λ₁, …, x^λ_n} over is denoted by M_n(Λ)span{x^λ₀, x^λ₁, …, x^λ_n}. Elements of M_n(Λ) are called Müntz polynomials. The principal result of this paper is the following Markov-type inequality for products of Müntz polynomials. T 2.1. LetΛ(λ_j)^∞_j=0andΓ(γ_j)^∞_j=0be increasing sequences of nonnegative real numbers. Let

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Then

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18(n+m+1)(λ_n+γ_m).In particular ,

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Under some necessary extra assumptions, an analog of the above Markov-type inequality is extended to the cases when the factor x is dropped, and when the interval [0, 1] is replaced by [a, b](0, ∞).