SCDA for 3D lattice gases with repulsive interaction

The selfconsistent diagram approximation (SCDA) is generalized for three-dimensional lattice gases with nearest neighbor repulsive interactions. The free energy is represented in a closed form through elementary functions. Thermodynamical (phase diagrams, chemical potential and mean square fluctuations), structural (order parameter, distribution functions) as well as diffusional characteristics are investigated. The calculation results are compared with the Monte Carlo simulation data to demonstrate high precision of the SCDA in reproducing the equilibrium lattice gas characteristics. It is shown that similarly to two-dimensional systems the specific statistical memory effects strongly influence the lattice gas diffusion in the ordered states. Received 7 August 2002 / Received in final form 22 January 2003 Published online 24 April 2003     

Rook theory and cycle-counting permutation statistics

A statistic is found to combinatorially generate the cycle-counting q-hit numbers, defined algebraically by Haglund [Adv. in Appl. Math. 17 (1996) 408–459]. We then define the notion of a cycle-Mahonian pair of statistics (generalizing that of a Mahonian statistic), and show that our newly discovered statistic is part of such a pair. Finally, we note a second example of a cycle-Mahonian pair of statistics which leads us to define the stronger property of being a cycle-Euler–Mahonian pair.     

Modeling Language Evolution

We describe a model for the evolution of the languages used by the agents of a society. Our main result proves convergence of these languages to a common one under certain conditions. A few special cases are elaborated in more depth.     

Shifting the Superparamagnetic Limit of Nanosized Copper Iron Spinel

In this paper we analyze trend of EFG values measured at Cd impurity in a group of semiconducting delafossites with chemical formula CuBO₂ (B = Al, Fe, Cr, Nd). We conclude that this trend reveals one of the most subtle details in electronic spectrum of the compounds: if impurity states are formed within or out of the band gap. In CuAlO₂ and CuFeO₂ the Cd EFG exhibits larger value than in CuCrO₂ and CuNdO₂, when Cd substitutes the Cu atom. This occurs because in the first two compounds the Cd forms shallow band within the gap, and in the second two compounds does not. When Cd occupies the B position it exhibits almost the same EFG in all delafossites. In this case, Cd does not form its states within the gap in none of the compounds. To arrive to these conclusions we analyzed and calculated various systems (Cd-doped CuAlO₂ and CuCrO₂ compounds, fictitious molecules), using the FP-LAPW method.     

Parametric Centers for Trigonometric Abel Equations

This article is devoted to one-dimensional perturbative theory on R × S ¹. There is a recursive formula for the successive obstructions to parametric center at any order of the perturbation parameter. The first obstruction is studied by means of complex analysis techniques. This extends to the trigonometric case what was done previously for the polynomial case (Israel J. Math. 142, 273–283, 2004). This article is dedicated to Professor Zhang Zhi-Fen on the occasion of her 80th Birthday     

半导体与超晶格的数学模型及其分析Ⅰ:模型

本文论及半导体与超晶格的数学模型方法的一些新近发展动态。介绍了半导体与超晶格的一些背景材料并给出了半导体宏观模型间的层次框架。超晶格中载流子传输的SHE扩散模型也被观察。     

Convex central configurations for the n-body problem

We give a simple proof of a classical result of MacMillan and Bartky (Trans. Amer. Math. Soc. 34 (1932) 838) which states that, for any four positive masses and any assigned order, there is a convex planar central configuration. Moreover, we show that the central configurations we find correspond to local minima of the potential function with fixed moment of inertia. This allows us to show that there are at least six local minimum central configurations for the planar four-body problem. We also show that for any assigned order of five masses, there is at least one convex spatial central configuration of local minimum type. Our method also applies to some other cases.     

紧急输送策略的线性规划模型

以美国南弗洛里达州递避飓风袭击为例建立了紧急输送情况下的线性规划模型。其中具体建立了以SCEPD(美国南弗洛里达州紧急情况预防部门)提出的公路反向，地区分块撤离，使用小路等三个最受人们关注的策略的模型。模型的灵敏度分析能很好地解释建立更多的临时避难所、限制车辆等策略对撤离的影响。在相近的环境下，中模型解得的结果很接近官方预测的结果，并且本的模型能对更广泛的情况进行分析．可给SCEPD提供一定参考。