On zeros of polynomials orthogonal over a convex domain

We establish a discrepancy theorem for signed measures, with a given positive part, which are supported on an arbitrary convex curve. As a main application, we obtain a result concerning the distribution of zeros of polynomials orthogonal on a convex domain.     

Polynomial inequalities on measurable sets and their applications

We study Pólya-and Remez-type inequalities for univariate and multivariate polynomials and discuss their applications to Nikolskii-type inequalities and upper estimates of trigonometric integrals.     

Asymptotics of Differentiated Bernstein Polynomials

It is shown that the m th-order derivative of the n th-order Bernstein polynomial of a function f satisfying a certain Lipschitz condition, can be written for n\rightarrow +∈fty as a singular integral of Gauss—Weierstrass type, m times differentiated (in a certain sense) under the integral sign. The theorem is applied to yield an overdifferentiation formula, involving p times differentiated Bernstein polynomials of functions that are not C ^p . December 1, 1998. Dates revised: July 22, 1999 and January 11, 2000. Date accepted: February 1, 2000.     

Approximation in L p (R d ) from a space spanned by the scattered shifts of a radial basis function

A new multivariate approximation scheme on R ^d using scattered translates of the “shifted” surface spline function is developed. The scheme is shown to provide spectral L _p -approximation orders with 1 ≤ p ≤ ∞, i.e., approximation orders that depend on the smoothness of the approximands. In addition, it applies to noisy data as well as noiseless data. A numerical example is presented with a comparison between the new scheme and the surface spline interpolation method.     

Lifting chains of prime ideals to paravaluation rings

Résumé  SoitR ⊂T une extension des anneaux commutatifs et soit {P _α :α ∈I} une cha?ne croissante des idéaux premiers deR (I étant un ensemble totalement ordonné, peut-être infini). Alors il existe un anneau de paravaluationV deT et une cha?ne {Q _α} des idéaux premiers deV de sorte queR ⊂V etQ _α ∩R =P _α pour toutα ∈I. Tout d’abord, on établit le cas spécial dans lequelT est un corps; dans ce cas, on trouve en effet un tel anneau de valuationV deT. Ensuite, l’assertion ci-dessus pour le cas général découle comme conséquence. Dans le cas général, on peut aussi remplacer le mot “paravaluation” avec le mot “valuation” siR est un anneau de Marot etT est son anneau total de fractions.      

First Alexandroff Decomposition Theorem for Topological Lattice Group Valued Measures

Let (X, F) be an Alexandroff space, let A(F) be the Boolean subalgebra of 2 ^X generated by F, let G be a Hausdorff commutative topological lattice group and let rba_F(A(F), G) denote the set of all order bounded F-inner regular finitely additive set functions from A(F) into G. Using some special properties of the elements of rba_F(A(F), G), we extend to this setting the first decomposition theorem of Alexandroff.     

Finite-dimensional approximation of the inverse frame operator

A frame in a Hilbert space allows every element in to be written as a linear combination of the frame elements, with coefficients called frame coefficients. Calculations of those coefficients and many other situations where frames occur, requires knowledge of the inverse frame operator. But usually it is hard to invert the frame operator if the underlying Hilbert space is infinite dimensional. In the present paper we introduce a method for approximation of the inverse frame operator using finite subsets of the frame. In particular this allows to approximate the frame coefficients (even inl ²) using finite-dimensional linear algebra. We show that the general method simplifies in the important cases of Weil-Heisenberg frames and wavelet frames.     

Co掺杂对YBa_2Cu_3O_(7-δ)电阻率与塞贝克系数的影响

用固态反应法制备了YBa2Cu3-xCoxO7-δ(x=0.0,0.1,0.2,0.5)样品,研究了Co掺杂对YBa2Cu3O7-δ高温区的电阻率和塞贝克系数的影响。随着Co含量的增加,样品的电阻率和塞贝克系数逐渐增大,从金属性导电转变为p型半导体导电。x=0.2和0.5样品的电导活化能在500K处发生突变,高温区的活化能大于低温区的活化能。通过塞贝克系数与温度的关系,计算出x=0.2和0.5样品的费米能级分别为0.02和0.12 eV。当温度高于650-700K时,氧脱附显著影响样品的电输运性质,导致电阻率和塞贝克系数随温度增加而增大。     

三唑磷-鲁米诺-H2O2发光体系的研究与应用

研究了碱性介质中三唑磷-鲁米诺-H2O2体系的化学发光特征,建立了三唑磷流动注射化学发光分析方法,并对反应机理进行了探讨.研究了三唑磷-鲁米诺-H2O2体系的化学发光反应动力学,考察了pH、流速、鲁米诺-H2O2配比等因素对化学发光的影响.在最佳条件下,过氧化氢HOO-负离子可能与三唑磷的磷原子反应生成磷的过氧化合自由基,与鲁米诺作用使得体系化学发光得到增强,3s内达到了最大值;应用于三唑磷的测定,在1.0×10-8-1.0×10-5g/mL范围内呈良好的线性关系,检出限(S/N=3)为6.7×10-9g/mL;测定蔬菜样品,三唑磷浓度分别为1.0-5.0μg/mL时,测定回收率为82.3%-108.6%,测定偏差为1.6%-4.7%.     

晶粒间界相对纳米Nd_2Fe_(14)B各向异性和矫顽力的影响

本文采用立方晶粒结构模型研究了晶粒间界相对纳米硬磁材料各向异性和矫顽力的影响.结果表明:晶粒间界相减弱了交换耦合作用.当晶粒尺寸D为定值时,随着晶粒间界相厚度d的增加,晶粒平均各向异性单调增加,而材料的有效各向异性Keff、矫顽力单调减小.我们计算的矫顽力随晶粒尺寸的变化与相关理论和实验结果基本一致.