Bis(2-(1H-imidazol-2-yl)-pyridine)copper(II): Effects of counteranions on the molecular and supramolecular structures

The synthesis and physical properties of bis(2-(1H-imidazol-2-yl)-pyridine)copper(II) with chloride, nitrate and perchlorate as counteranions have been described. Microanalysis, magnetic susceptibility, conductivity and various spectroscopic measurements have been used for the characterization of the complexes. The crystal structures of all three complexes have been determined. Intermolecular hydrogen-bonding interactions and the resulting self-assembly patterns for each of the species have been scrutinized. The chloride containing complex crystallizes as a trihydrate, where the metal ion is in a tetragonally elongated cis-N₄Cl₂ coordination sphere. This complex provides a three-dimensional honeycomb-like structure through N–H?Cl, O–H?Cl and O–H?O hydrogen bonds. In the nitrate containing species, one of the two counteranions coordinates to the metal centre to provide an irregular N₄O₂ coordination sphere, while the other counteranion, with the help of a lattice water molecule, assembles a ladder-like structure via N–H?O and bifurcated O–H?O,O hydrogen bonds. A one-dimensional polymeric species has been formed when perchlorate is the counteranion. Here one of the two perchlorates acts as a bridge between the metal centres that are in tetragonally elongated trans-N₄O₂ coordination spheres. This polymeric chain, together with the second perchlorate and a water molecule, form a ribbon-like structure due to N–H?O and O–H?O hydrogen bonds.     

Spectroscopic Studies of a Three-dimensional, Five-coordinated Copper(Ⅱ) Complex via Hydrogen Bonds: [Cu(PDA)(H_2O)_2](H_2PDA=Pyridine-2,6-dicarboxylic Acid)

IntroductionFive- coordinated complexes with d9- configuredcations have received much attention stereochemi-cally,spectrochemically and biologically,and havebeen comprehensively discussed[1] . Usually thereare two stable configurations for the copper( )complexes with five equal coordinating atoms:anapically elongated square pyramid( SP) and a com-pressed trigonal bipyramid( TBP) ,with an obviousenergetic preference for the latter coordination.When the ligands are rigid and provide angular d…     

在不加对称性限制的条件下采用不同的半经验方法研究酞菁的电荷分布和几何构型

在不加对称性限制的条件下采用不同的半经验方法CNDO,INDO,MINDO/3,MNDO和Pm3对自由酞菁(H₂Pc)进行几何构型最优化和电荷密度布居分析，并将所得结果与Am1方法以及X射线衍射和中子衍射数据的数据进行比较。结果表明只有从INDO方法得到的是桥式构型，而从CNDO,MINDO/3,MNDO,Am1,Pm3方法得到的都是键式构型。除INDO之外所有的这几种方法都对先前报道的几何构型扭曲给出进一步的支持证据。新近建立的半经验方法如MNDO,Am1,Pm3等看起来更适合于用     

考虑剪切效应层合板的Hamilton体系及辛几何方法

基于ＹＮＳ层合板理论,通过对混合能变分原理的修正,建立了层合板问题的Ｈａｍｉｌｔｏｎ正则方程。在辛几何数学框架下,采用共轭辛正交归一关系给出精确解。并与经典层板理论进行了比较。     

非线性水波Hamilton系统理论与应用研究进展

概述了辛几何理论与辛算法在Hamilton力学中的应用，综述非线性水波的Hamilton理论研究进展．阐述非线性水波Hamilton变分原理与方法的优越性与局限性，探讨KdV方程和BBM方程的Hamilton描述、对称性与守恒律，提出非线性水波Hamilton描述研究中有待进一步研究的问题和解法设想．     

Generalized Einstein manifolds

A Finslerian manifold is called a generalized Einstein manifold (GEM) if the Ricci directional curvature R(u,u) is independent of the direction. Let F⁰(M, g_t) be a deformation of a compact n-dimensional Finslerian manifold preserving the volume of the unitary fibre bundle W(M). We prove that the critical points g₀ F⁰(g_t) of the integral I(g_t) on W(M) of the Finslerian scalar curvature (and certain functions of the scalar curvature) define a GEM. We give an estimate of the eigenvalues of Laplacian Δ defined on W(M) operating on the functions coming from the base when (M, g) is of minima fibration with a constant scalar curvature H admitting a conformal infinitesimal deformation (CID). We obtain λ ≥ H/(n − 1) (Δf = λf). If M is simply connected and λ = H/(n − 1), then (M, g) is Riemannian and is isometric to an n-sphere. We first calculate, in the general case, the formula of the second variationals of the integral I (g_t) for G = g₀, then for a CID we show that for certain Finslerian manifolds, I″(g₀) > 0. Applications to the gravitation and electromagnetism in general relativity are given. We prove that the spaces characterizing Einstein-Maxwell equations are GEMs.     

三维电阻抗成像的体积元方法的数值模拟和分析

电阻抗成像是一类椭圆方程反问题,本文在三维区域上对其进行数值模拟和分析.对于椭圆方程Neumann边值正问题,本文提出了四面体单元上的一类对称体积元格式,并证明了格式的半正定性及解的存在性;引入单元形状矩阵的概念,简化了系数矩阵的计算;提出了对电阻率进行拼接逼近的方法来降低反问题求解规模,使之与正问题的求解规模相匹配;导出了误差泛函的Jacobi矩阵的计算公式,利用体积元格式的对称性和特殊的电流基向量,将每次迭代中需要求解的正问题的个数降到最低.一系列数值实验的结果验证了数学模型的可靠性和算法的可行性.本文所提出的这些方法,已成功应用于三维电阻抗成像的实际数值模拟.     

Geometry of Differential Equations: A Concise Introduction

A short introduction to geometrical theory of nonlinear differential equations is given to provide a unified overview to the collection 'Symmetries of differential equations and related topics'.     

一类半对称图的构造

称一个有限简单无向图X是半对称图,如果图X是正则的且边传递但非点传递.主要利用仿射几何构造了一类2p~n阶连通p~3。度的半对称图的无限族,其中p≥n≥8.     

一种奇异临界椭圆方程的非平凡解

该文研究了一类带有Sobolev-Hardy临界指数的半线性椭圆方程,运用变分理论中的环绕定理证明了方程非平凡解的存在性