多形性相变的分子动力学模拟

 本文利用分子动力学方法研究了KCl晶体在ρ＝ρ₀时的温度相变。面心立方（fcc）和体心立方（bcc）两种结构的径向分布函数随温度的变化的情况说明，在高压下，发生着bcc结构相fcc结构的转变，bcc结构是不稳定的。为了选取合理的势参数，利用了分子动力学程序在T＝0时的性质，计算了NaCl和KCl晶体的零温状态方程，研究了它们在压力作用下发生的多形性相变。计算表明，NaCl和KCl晶体将分别于18.8 GPa和5.9 GPa发生从fcc到bcc的多形性相变，这些值相当接近实验结果。着说明本文选用的势参数势有一定精度的。     

On Hilbert's type inequalities

By introducing two pairs of conjugate exponents and estimating the weight coefficients, we give generalizations of some Hilbert's type inequalities with the best constant factor. As applications, some particular results are considered.     

Inequalities for formal power series and entire functions

We present several integral and exponential inequalities for formal power series and for both arbitrary entire functions of exponential type and generalized Borel transforms. They are obtained through certain limit procedures which involve the multiparameter binomial inequalities, integral inequalities for continuous functions, and weighted norm inequalities for analytic functions. Some applications to the confluent hypergeometric functions, Bessel functions, Laguerre polynomials, and trigonometric functions are discussed. Also some generalizations are given.     

A Mann type iterative scheme for variational inequalities in noncompact subsets of Banach spaces

In this paper, we study the existence of solutions and approximation of the solutions by using a Mann type iterative scheme for variational inequalities in noncompact subsets of Banach spaces. The results presented in this paper generalize the corresponding results of J. Li [J. Li, On the existence of solutions of variational inequalities in Banach spaces, J. Math. Anal. Appl. 295 (2004) 115-126].     

2+1维SU(2)格点规范场胶球波函数的高阶RPA计算

采用无规相近似(RPA)耦合集团展开方法求解薛定谔本征值方程，计算高阶胶球波函数. 在计算中，用空心Wilson圈图作为试探波函数，对特殊Wilson圈图作近似处理，计算出的2+1维SU(2)格点规范场的六阶和七阶胶球波函数的μ0F和μ2F及相关参数z 在弱耦合区(β=4.8-9.6)出现较好的标度行为，七阶真空能量在整个区域(β=0.8-8.0)与六阶真空能量一致.     

High pressure phase transitions in organic solids II: X-ray diffraction study ofp-dichlorobenzene at high pressures

X-ray diffraction experiments onp-dichlorobenzene at high pressures show a transition at ～ 0.3 GPa, to a new phase, the diffraction pattern of which cannot be indexed on the anticipated low temperature monoclinic crystal structure. We have instead found an orthorhombic cell, very closely related to the low temperature monoclinic cell, for this new phase. This structure, which also occurs inp-diiodobenzene at ambient conditions, has cell constantsa =14.02,b = 6.06,c = 7.41Å andZ = 4. The space group is Pbca. This new phase has a non-β herring-bone structure, in contrast with the initialα phase which has aβ-structure with ribbon-like arrangement of molecules, with Cl-Cl contacts of ～ 4A between adjacent molecules. This implies that with pressure the halogen-halogen interaction in this compound plays a less dominant role in crystal engineering.     

高压下聚苯胺系高分子导体电学特性的研究

 本文研究了大共轭π键结构的聚苯胺等高聚物在高压下的电学性能，其结果表明PAn-H⁺的电阻值在p=3.2 GPa下出现极小值，可作3.2 GPa压力下的定标物质。并指出聚苯胺系列导体属于电子性导电物质，而且在不同的压力条件下电流和电压的关系均表现为非线性。     

New studies of X-ray diffraction line profiles from aggregates of distorted crystallites I

The fourth central moment of an X-ray diffraction profile from an aggregate of distorted crystallites has been expressed by Mitra (1964a) as a function of the crystallite size, strain and strain gradients in the specimen. While the usual methods of line profile analysis yield information regarding either the apparent strain or the rms strain, the present study provides additional information regarding strain distribution in the form of strain derivatives and rms displacements of atoms over a given distancet in the direction of study. The strain parameters like 〈ee′〉, 〈ee″〉 have been obtained from fourth moment of the strain profile against range plots. The strain parameters thus obtained have subsequently been used to determine the rms displacements of the atoms. Alloys of copper and zinc at different stages of cold working and annealing have been studied by this method. The results have been discussed in the light of dislocation distribution, polygonisation and grain growth as well as distortion waves in the distorted crystals.     

Extremal Theory for Spectrum of Random Discrete Schrödinger Operator. I. Asymptotic Expansion Formulas

We consider the spectral problem for the random Schrödinger operator on the multidimensional lattice torus increasing to the whole of lattice, with an i.i.d. potential (Anderson Hamiltonian). We obtain the explicit almost sure asymptotic expansion formulas for the extreme eigenvalues and eigenfunctions in the intermediate rank case, provided the upper distributional tails of potential decay at infinity slower than the double exponential function. For the fractional-exponential tails (including Weibull’s and Gaussian distributions), extremal type limit theorems for eigenvalues are proved, and the strong influence of parameters of the model on a specification of normalizing constants is described. In the proof we use the finite-rank perturbation arguments based on the cluster expansion for resolvents. The results of our paper illustrate a close connection between extreme value theory for spectrum and extremal properties of i.i.d. potential. On the other hand, localization properties of the corresponding eigenfunctions give an essential information on long-time intermittency for the parabolic Anderson model.