On the simple energy relation between the RHF,UHF and closed-shell SCF methods

The simple energy relation between the RHF and UHF methods are obtained by expanding these orbital sets by the closed-shell orbital with the same geometry of the open-shell systems. The results are also applied to higher spin states.     

The statistics of dimers on a three-dimensional lattice. I. An exactly solvable model

A three-dimensional lattice model is proposed for which the constant occurring in the dimer problem can be evaluated exactly.     

Concerning exact analytical STFT solutions to some families of inverse problems in engineering material theory

The problem of finding the exact analytical closed-form solution of some families of transcendental equations, which describe two different physical phenomenon, thermionic emission and electrical conductivity in semiconductors, is studied, in some detail, by the Special Trans Functions Theory (STFT). The mathematical genesis of the analytical closed-form solution is presented, and the structure of the theoretical derivation, proofs and numerical results confirm the validity and base principle of the STFT. Undoubtedly, the proposed analytical approach implies the qualitative improvement of the conventional analytical and numerical methods.     

Natural Geometry of Nonzero Quaternions

It is shown that the group of nonzero quaternions carries a family of natural closed Friedmann-Lemaître-Robertson-Walker metrics.     

l-群的凸-子群格的极小条件

设G是l-群,C(G)是G的凸l-子群格.称C(G)满足极小条件,如果C(G)中每个元均包台一个原子元.本文将C(G)的链条件(见文[1])推广到极小条件,主要结果是:C(G)满足极小条件且C(G)中每个原子元均是G的基数直和项当且仅当∑λ∈ΛRλ(∩)G(∩)Пλ∈ΛRλ(其中每个Rλ≌实数加群R的某个子群).     

Asymptotic Geometry and Growth of Conjugacy Classes of Nonpositively Curved Manifolds

Let X be a Hadamard manifold and Γ⊂Isom(X) a discrete group of isometries which contains an axial isometry without invariant flat half plane. We study the behavior of conformal densities on the limit set of Γ in order to derive a new asymptotic estimate for the growth rate of closed geodesics in not necessarily compact or finite volume manifolds. Mathematics Subject Classifications (2000): 20E45, 53C22, 37F35     

Adaptive optics optical coherence tomography for retina imaging

When optical coherence tomography (OCT) is used for human retina imaging, its transverse resolution is limited by the aberrations of human eyes. To overcome this disadvantage, a high resolution imaging system for living human retina, which consists of a time domain OCT system and a 37-elements adaptive optics (AO) system, has been developed. The AO closed loop rate is 20 frames per second, and the OCT has a 6.7-μm axial resolution. In this paper, this system is introduced and the high resolution imaging results for retina are presented.     

Cardy–Frobenius extension of the algebra of cut-and-join operators

Motivated by the algebraic open–closed string models, we introduce and discuss an infinite-dimensional counterpart of the open–closed Hurwitz theory describing branching coverings generated both by the compact oriented surfaces and by the foam surfaces. We manifestly construct the corresponding infinite-dimensional equipped Cardy–Frobenius algebra, with the closed and open sectors being represented by the conjugation classes of permutations and of pairs of permutations, i.e. by the algebras of Young diagrams and of bipartite graphs respectively.     

On rotating circular disks with varying material properties

Taking Young’s modulus, thermal expansion coefficient and density to be the functions of the radial coordinate, a closed form solution of rotating circular disks made of functionally graded materials subjected to a constant angular velocity and a uniform temperature change is proposed in this paper. Excellent agreement with the solution from Mathematica 5.0 indicates the correctness of the proposed closed form solution. Distributions of the radial displacement and stresses in the disks are determined with the proposed approach and how material properties, temperature change, geometric size and different material coefficients affect deformations and stresses is investigated.     

球外部区域上非线性椭圆型方程的正径向解

本文讨论球外部区域Ω={x∈RN||x|>R}上非线性椭圆边值问题正径向解的存在性,其中g(r),f(u)为非负连续函数.在g(r)满足条件0<∫R∞rg(r)dr<∞,f(u)关于u超线性或次线性增长的情形,获得了该问题正径向解的存在性.