Consistency of a linear system of inequalities

We show that a consistency check of a linear system of inequalitiesAxb reduces to check whetherQb0 for a certain matrixQ. It is a direct consequence of the Farkas-Minkowski theorem. Thus, when one has to check consistency for different values ofb, one need not run a numerical algorithm for eachb.On leave at the Electronics Research Laboratory of the University of California at Berkeley in a CNRS/NSF Exchange Program.     

柠檬酸铝/聚丙烯酰胺胶态分散凝胶反应动力学和机理的研究

采用粘度法研究了柠檬酸铝（AlCit)与部分水解取丙烯酰胺（HPAM）胶态分散凝胶体系的反应动力学。结果表明，胶态分散凝胶体系的交联反应是一级反应。并推导出胶态分散凝胶体系的反应动力学方程。     

Filter Diagonalization with Finite Fourier Transform Eigenfunctions

Below, we briefly report on the progress in the development of the Filter Diagonalization technique when filtering is carried out with the aid of Finite Fourier Transform (FFT) eigenfunctions. During recent years interest in these functions, also known as ‘prolates’, or ‘slepians’, has increased among scientists doing research in the field of signal processing. The main explanation to this follows from the set of very special extremal and orthogonality properties exibited by the FFT eigenfunctions. Recent results of Walter and Shen on sampling with prolate spheroidal functions will necessary produce a new wave of interest. In the presented, Filter diagonalization machinery, we show that the sampling formula of Walter and Shen simplifies essentially the computation of matrix elements as certain 2D–integrals involving FFT eigenfunctions.     

Generalized criterion of solvent polarity as a tool for control of chromatographic process

The generalized (reductive) criterion of solvent polarity was obtained by the method of multiparametric optimization of the Snyder index P", Hildebrand parameter _T , permittivity _r , and solvatochromism parameter E _T (30). Possibilities of employing this criterion for estimation of the elution power of normal and reversed mobile phases used in high-performance liquid chromatography were considered.     

病态分析体系有偏估计的研究

运用广义岭估计和Ｌｉｕｋｅｊｉａｎ提出的有偏估计，对病态分析体系进行了数值模拟和实际光度测定，结果表明，广义岭估计显优于最小二乘估计，Ｌｉｕｋｅｊｉａｎ法有功效，可和为解析病态分析体系的化学计量学方法。     

液晶光定向层材料

本文综述了近10年来液晶显示用光定向层材料领域的研究现状和进展情况，主要概述了光降解型、光致异构型、光交联型以及自组装等材料，并对目前报道的液晶光定向机理进行了总结和归纳。     

Permutation representations in molecular symmetry

The reducible representations of the point groups are generally studied because of their relevance to molecular orbital and vibration theory. Triple correlations within the polyhedra are described by group-theoretical invariants that are related to the permutation representations and termed polyhedral isoscalar factors. These invariants are applied in theorems on matrix elements referring to the symmetry-adapted bases at different centres. Further invariants or geometrical weight factors inter-relate different types of reduced matrix elements of irreducible tensors (generalization of the Wigner-Eckart theorem to the polycentric case). As a demonstration a complete tabulation is given for the point group C ₄.     

A re-statement of the Hohenberg–Kohn theorem and its extension to finite subspaces

Bearing in mind the insight into the Hohenberg–Kohn theorem for Coulomb systems provided recently by Kryachko (Int J Quantum Chem 103:818, 2005), we present a re-statement of this theorem through an elaboration on Lieb’s proof as well as an extension of this theorem to finite subspaces. Contribution to the Serafin Fraga Memorial Issue.     

The Hellmann-Feynman theorem applied to long-range forces

The relations between the Hellmann-Feynman forces in laboratory fixed (L-) and relative (R-) coordinate systems are clarified. In the usualL-coordinate system, the force is interpreted as force on nucleus, while in theR-coordinate system, it means force on whole particles consisting of the electrons and nuclei of each interacting subsystem. From a perturbation theoretical viewpoint, the concept of the force on whole particles correctly corresponds to the perturbation energy and is superior to the force on the nucleus.     

Zhang–Zhang Polynomials of Multiple Zigzag Chains Revisited: A Connection with the John–Sachs Theorem

Multiple zigzag chains Zm,n of length n and width m constitute an important class of regular graphene flakes of rectangular shape. The physical and chemical properties of these basic pericondensed benzenoids can be related to their various topological invariants, conveniently encoded as the coefficients of a combinatorial polynomial, usually referred to as the ZZ polynomial of multiple zigzag chains Zm,n. The current study reports a novel method for determination of these ZZ polynomials based on a hypothesized extension to John–Sachs theorem, used previously to enumerate Kekulé structures of various benzenoid hydrocarbons. We show that the ZZ polynomial of the Zm,n multiple zigzag chain can be conveniently expressed as a determinant of a Toeplitz (or almost Toeplitz) matrix of size m2×m2 consisting of simple hypergeometric polynomials. The presented analysis can be extended to generalized multiple zigzag chains Zkm,n, i.e., derivatives of Zm,n with a single attached polyacene chain of length k. All presented formulas are accompanied by formal proofs. The developed theoretical machinery is applied for predicting aromaticity distribution patterns in large and infinite multiple zigzag chains Zm,n and for computing the distribution of spin densities in biradical states of finite multiple zigzag chains Zm,n.