Elastic and Thermophysical Properties of Poly(Vinyl Chloride) and Chlorinated Polyethylene Blends

The results of experimental and theoretical investigations of elastic and thermophysical properties of poly(vinyl chloride) (PVC) and chlorinated polyethylene (CPE) blends are presented. Eight types of specimens with different ratios of weight contents of PVC and CPE (PVC/CPE = 100/0, 90/10, 80/20, 60/40, 40/60, 20/80, 10/90, and 0/100) were tested. The effect of blend composition on the elastic constants (tensile and shear modulus) is discussed. The data on the thermal conductivity, thermal diffusivity, and heat capacity of the blends investigated are also presented.     

How to Express a Parallel Sum of k Matrices

We present an alternative expression for the parallel sum of k Hermitian nonnegative definite matrices by using the Moore-Penrose inverse of a block matrix.     

双金属氧化物和氧化物载体组分间的相互作用

讨论了一些过渡金属氧化物（NiO,CuO或MoO3)在经改性所得复合载体（TiO2-γ-Al2O3，MoO3-t-ZrO2或NiO-t-ZrO2)上的分散作用，这些三地体系中实验测定的氧化物分散容量与研究负载型二元氧化物体系所得嵌入模型的估算值基本相符；样品的表面组成、结构和性能与载体的表面结构、过渡金属氧化物的负载量和加料顺序以及焙烧温度密切相关。     

赋权矩阵及其性质

本文给出了以S为行权和向量的权矩阵类T_＋(S)中每个权矩阵都可逆的一个充要条件．     

Density Correlations in the Two-Dimensional Coulomb Gas

We consider a two-dimensional Coulomb gas of positive and negative pointlike unit charges interacting via a logarithmic potential. The density (rather than the charge) correlation functions are studied. In the bulk, the form-factor theory of an equivalent sine-Gordon model is used to determine the density correlation length. At the surface of a rectilinear plain wall, the universality of the asymptotic behavior of the density correlations is suggested. A scaling analysis implies a local form of the compressibility sum rule near a hard wall. A symmetry of the Coulomb system with respect to the Möbius conformal transformation, which induces a gravitational source acting on the particle density, is established. Among the consequences, a universal term of the finite-size expansion of the grand potential is derived exactly for a disk geometry of the confining domain.     

Sums of Two Exact Powers

An asymptotic formula is obtained for the number of representations of an element of a finite field as a weighted sum of two prescribed powers of primitive elements. This generalises previous work on sums of primitive elements, including that relating to some conjectures of Golomb.     

Optimality conditions and duality theory for minimizing sums of the largest eigenvalues of symmetric matrices

The sum of the largest eigenvalues of a symmetric matrix is a nonsmooth convex function of the matrix elements. Max characterizations for this sum are established, giving a concise characterization of the subdifferential in terms of a dual matrix. This leads to a very useful characterization of the generalized gradient of the following convex composite function: the sum of the largest eigenvalues of a smooth symmetric matrix-valued function of a set of real parameters. The dual matrix provides the information required to either verify first-order optimality conditions at a point or to generate a descent direction for the eigenvalue sum from that point, splitting a multiple eigenvalue if necessary. Connections with the classical literature on sums of eigenvalues and eigenvalue perturbation theory are discussed. Sums of the largest eigenvalues in the absolute value sense are also addressed.This paper is dedicated to Phil Wolfe on the occasion of his 65th birthday.The work of this author was supported by the National Science Foundation under grants CCR-8802408 and CCR-9101640.The work of this author was supported in part during a visit to Argonne National Laboratory by the Applied Mathematical Sciences subprogram of the Office of Energy Research of the U.S. Department of Energy under contract W-31-109-Eng-38, and in part during a visit to the Courant Institute by the U.S. Department of Energy under Contract DEFG0288ER25053.     

Some Invariance Principles for Random Vectors in the Generalized Domain of Attraction of the Multivariate Normal Law

For independent identically distributed random vectors belonging to the generalized Domain of Attraction of the multivariate normal law, we define two partial sum processes analogous to that of Donsker's Theorem. We prove that each converges in distribution to a Brownian Motion in the space of continuous functions. One process uses nonrandom operator normalization, and the other is a studentization of the first, using normalization by the empirical covariance operator.     

关于有限Abel群直接因子的平均数

对于有限Ａｂｅｌ群Ｇ，ｔ（Ｇ）定义为其直接因子的个数，在［５］中，Ｅ．Ｋｒａｔｚｅｌ对于和式得到一渐近公式，对应余项为△＿１（ｘ）．本文利用Ｅ．Ｆｏｕｖｒｙ和Ｈ　．Ｉｗａｎｉｅｃ的方法，得到了关于△＿１（ｘ）的一个新的估计，改进了Ｈ．Ｍｅｎｚｅｒ等人的结果．     

Thermal conductivity of poly(vinyl chloride)/polycaprolactone blends

Thermal diffusivity, heat capacity, and density of polyvinyl chloride/polycaprolactone (PVC/PCL) blends were measured by the laser flash method, DSC, and pycnometry, respectively. The thermal conductivity of the PVC/PCL blends was determined from the results. The miscibility of the blend and crystallinity of PCL were determined by DSC. The effect of blend structure on thermal conductivity is discussed. The phase compositions of the PVC/PCL blends are of three types depending on PCL content: i.e., up to 33%, from 33 to 70%, and above 70% PCL by weight. Thermal conductivity, thermal diffusivity, and heat capacity of the PVC/PCL blends are strongly affected by the phase composition of the blend, which changes in a complicated way with PCL content. © 1994 John Wiley & Sons, Inc.