Müntz spaces and special Bloch type inequalities

Abstract

In this paper, we are interested in classical Müntz spaces and their properties. We first reprove Müntz theorem and obtain the Clarkson–Erdös–Schwartz expansion in the nondense case for some general abstract Müntz spaces without invoking any blow up property, but using classical complex variables tools. We introduce new Bloch type Müntz spaces and investigate the validity of Bloch type inequalities in this framework.     

多金属氧酸盐/介孔分子筛杂化材料的制备与表征

采用嵌段共聚物模板P123和缺位Keggin结构的多金属氧酸盐K₈SiW₁₁O₃₉•12H₂O, 由溶胶-凝胶法合成了具有类六方结构的SiW₁₁/SBA-15杂化介孔分子筛材料, 并通过X射线衍射(XRD)、傅立叶变换红外光谱(FT-IR)、紫外漫反射光谱(UV/DRS)、电感耦合等离子原子发射光谱(ICP-AES)、低温N₂吸附、透射电子显微镜(TEM)等手段对其进行了表征. 结果表明, 杂化材料中不仅规整均一的类六方介孔结构得以保持, 而且多金属氧酸盐的Keggin单元保留完整(含量达25%左右), 并共价键联于介孔材料的孔道内部. 稳定性实验表明, 杂化材料中多金属氧酸盐在水中的流失率远低于一般浸渍法制备的样品.     

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 best L ₁ sufficiency requirements based on Chebyshev interpolation. Finally we establish best L _p , L and L ₁ approximation by partial sums of lacunary Chebyshev series of the form _i=0 a ⁱ _b ⁱ(x) where _n (x) is a Chebyshev polynomial and b is an odd integer 3. A complete set of proofs is provided.     

Remarks on Mean Convergence (Boundedness) of Partial Sums of Trigonometric Series

Fairly general conditions on the coefficients of even and odd trigonometric Fourier series under which L-convergence (boundedness) of partial sums of the series is equivalent to the relation are given.     

Small Blocking Sets in PG(2, p3)

In this paper we show that a small minimalblocking set in PG(2,p³), with p 7,is of Rédei type.     

Keggin型缺位硅钨杂多阴离子的电化学性质及电催化还原H2O2

应用循环伏安、方波伏安和交流阻抗法研究了Keggin型缺位硅钨杂多阴离子SiW11O398-(SiW11)在0.1mol.L-1NaHSO4+Na2SO4溶液中的电化学性质及其对H2O2还原的间接电催化作用.结果表明,SiW11的酸性水溶液在玻碳(GC)电极上显示两对可逆的还原-氧化波,对应的电荷迁移数均为1,且有2个质子参与反应.根据第1对波的还原峰电流与扫描速率平方根关系得到SiW11在溶液中的扩散系数DO为8.92×10-6cm2.s-1.SiW11对H2O2的还原具有明显的电催化活性,催化峰电位随溶液pH的降低而正移,峰电流增大.质子H+在催化反应中起协同促进作用.实验测定该电催化过程的均相准一级反应速率常数为0.30 s-1.SiW11电催化还原H2O2的机理被认为是经过形成所谓"七配位过氧化物"而发生的.     

The law of the iterated logarithm for discrepancies of {θ n x}

It is proved that two types of discrepancies of the sequence {θ ⁿ x} obey the law of the iterated logarithm with the same constant. The appearing constants are calculated explicitly for most of θ > 1. Dedicated to the memory of Professor Walter Philipp