Corners of self-conjugate (s,s + 1)-cores and (s‾,s+1‾)-cores

In this paper, we describe a result on self-conjugate $(s,s+1)$-core partitions with the fixed number of corners. We also define shifted corners of a distinct partition and find formulas for the number of $(\stackrel{￣}{s},\stackrel{￣}{s+1})$-core partitions and the number of $(s,s+1)$-core shifted Young diagrams with the fixed number of shifted corners.     

Banach空间中优化问题的最优性条件

首先在Contingent切锥意义下界定了Banach空间中非空集合的伪切锥和伪凸性的概念，并讨论了相应的性质，然后针对可微优化问题，在广义凸性假设下，建立了最优性条件。     

平面分拆的矢量控制方法：列严格梯形平面分拆

作为移位平面分拆的自然拓广,本文引入了梯形平面分拆的概念.应用矢量控制技巧,建立了给定形状和行(列)分部约束的列严格梯形平面分拆集合之枚举函数的初等对称函数行列式表达式.其中之一的重要特例构成了关于循环对称平面分拆的Macdonald猜想的证明基础.     

The one-dimensional Hubbard model for large or infiniteU

The magnetic properties of the one-dimensional Hubbard model with a hardcore interaction on a ring (periodic boundary conditions) are investigated. At finite temperatures it is shown to behave up to exponentially small corrections as a pure paramagnet. An explicit expression for the ground-state degeneracies is derived. The eigenstates of this model are used to perform a perlurbational treatment for large but finite interactions. In first order inU ¹ an effective Hamiltonian for the one-dimensional Hubbard model is derived. It is the Hamiltonian of the one-dimensional Hcisenberg model with antiferromagnetic couplings between nearest neighbor spins. An asymptotic expansion for the ground-state energy is given. The results are valid for arbitrary densities of electrons.     

Scale Invariance Properties in the Simulated Annealing Algorithm

The Boltzmann distribution used in the steady-state analysis of the simulated annealing algorithm gives rise to several scale invariant properties. Scale invariance is first presented in the context of parallel independent processors and then extended to an abstract form based on lumping states together to form new aggregate states. These lumped or aggregate states possess all of the mathematical characteristics, forms and relationships of states (solutions) in the original problem in both first and second moments. These scale invariance properties therefore permit new ways of relating objective function values, conditional expectation values, stationary probabilities, rates of change of stationary probabilities and conditional variances. Such properties therefore provide potential applications in analysis, statistical inference and optimization. Directions for future research that take advantage of scale invariance are also discussed.     

An Algebraic Method for the Exact Solution of the Partition Function of the Canonical Ensemble in Nuclear Multifragmentation

We propose a unified method for deducing recursive relations for the canonical partition function of a system of noninteracting particles with charge conservation if the particles follow the Bose–Einstein, Fermi–Dirac, or Maxwell–Boltzmann statistics or parastatistics. For all these types of statistics, we find recursive relations for the partition function of a new statistical model of nuclear multifragmentation with electric charge and baryon number conservation, accounting for the internal degrees of freedom of the nuclear fragments.     

用PM3量化参数预测多氯代二苯并呋喃的logKow

从现有的PCDFs分子的正辛醇 /水分配系数 (logKow)实验数据出发 ,建立定量结构 性质关系方程(QSPR) .采用G98W程序包中的PM3方法对 13 5个多氯代二苯并呋喃 (PCDFs)分子和二苯并呋喃进行了优化计算 ,作业命令为 #pPM3optfreqscf(conver =9) ,以计算所得的分子轨道能量、碳原子电荷作为PCDFs分子结构描述符 ,运用多元线性回归技术建立了PCDFs的logKow与分子结构描述符的四元方程 ,最优相关系数为 0 .95 0 7,标准偏差为 0 .173 7,经检验该模型的稳健性好 ,并对未有实验数据的 85个PCDFs的logKow进行预测     

THE EXISTENCE THEOREM OF THE CONE-WEAK SUBDIFFERENTIAL OF SET-VALUED MAPPING

In this paper, the existence theorem of the cone-weak subdiflerential of set-valued mapping in locally convex topological vector space is proved.     

关于多正解问题的某些研究

本文以ｆｐ 同伦方法为工具，借助于一些适当的变换，研究有序的（Ｂ）空间中的集值映象方程的多正解问题；在文中的有关工作中，还使用了集值映象的拟导数的某些性质．     

Multinomial permutations on a circle

Multinomial permutations on a circle are considered in the framework of combinatorics. Different cases are presented and shown to agree with previously derived formula for the number of cyclic necklaces. Two applied examples are discussed with a view to illustrate the implications of derived formulas. Copyright © 2006 John Wiley & Sons, Ltd.