Anyons and the Bose--Fermi Duality in the Finite-Temperature Thirring Model [Erratum]

Corrections to the paper published in Vol. 121, No. 1, October, 1999     

Rogue waves in the massive Thirring model

In this paper, general rogue wave solutions in the massive Thirring (MT) model are derived by using the Kadomtsev–Petviashvili (KP) hierarchy reduction method and these rational solutions are presented explicitly in terms of determinants whose matrix elements are elementary Schur polynomials. In the reduction process, three reduction conditions including one index- and two dimension-ones are proved to be consistent by only one constraint relation on parameters of tau-functions of the KP-Toda hierarchy. It is found that the rogue wave solutions in the MT model depend on two background parameters, which influence their orientation and duration. Differing from many other coupled integrable systems, the MT model only admits the rogue waves of bright-type, and the higher order rogue waves represent the superposition of fundamental ones in which the nonreducible parameters determine the arrangement patterns of fundamental rogue waves. Particularly, the super rogue wave at each order can be achieved simply by setting all internal parameters to be zero, resulting in the amplitude of the sole huge peak of order N being $2N+1$ times the background. Finally, rogue wave patterns are discussed when one of the internal parameters is large. Similar to other integrable equations, the patterns are shown to be associated with the root structures of the Yablonskii–Vorob'ev polynomial hierarchy through a linear transformation.     

基金使用的数学模型

对 2 0 0 1年全国大学生数学建模竞赛 C题作了详细的分析 ,给出了第 i( i=1 ,2 ,… ,n-1 )年末发放的奖金额需存的金额为 Mxi 和 Mxn( Mxn 到第 n年末的本息用于发放第 n年末的奖金后剩余原本金 M)的最佳投资方案 ,用线性代数和概率论的基础知识建立了数学模型 ,并给出了用于求解的 MATLAB程序 .     

投资的收益和风险的数学模型及算法研究

本文按照“满意解”、“多组解”的思路对投资的收益和风险问题进行了分析和处理 ,提出了将净收益与总体风险划分为若干等级 ,并按等级求出多组满意解的思想方法 ,最后对模型的数学性质与计算方法进行了初步研究     

一类相依风险模型的破产问题

研究了一类相依的双险种风险模型,其中第一类险种的索赔到达计数过程为E lang(2)过程,第二类险种的索赔到达计数过程为其p-稀疏过程.首先通过更新论证的方法得到罚金折现期望满足的积分-微分方程,然后推导拉普拉斯变换的表达式,并就索赔额服从指数分布的情形得到了罚金折现期望的精确表达式.     

航班登机口分配问题的数学建模

登机口作为机场的重要组成部分,其资源利用率直接影响航班服务的效率.针对不同的优先级建立多目标规划模型对航班进行优化分配,采用贪心算法和禁忌搜索算法,结合登机口类型、航班时间的约束,逐次对最大化分配航班问题、最小化中转旅客最短流程时间问题、最小化旅客总体紧张度问题进行建模求解.结果表明该算法不仅提升了求解速度,并且在航班登机口分配问题中展现了较好的综合寻优能力.这对民航机场实现经济效益、提高旅客满意度有一定的参考价值.     

Global strong solution to the Thirring model in critical space

We obtain a strong solution in charge critical space L²(R) of the Thirring system and Federbusch equations in one space dimension by using solution representation of the models. The uniqueness is obtained for the solution Ψ∈L^∞([0,T];L²(R)∩L⁴(R)). A decay of local charge and asymptotic behavior of the field can be shown directly.     

The Problem of Identifying the Model of Substitution of Production Factors

Computational Mathematics and Mathematical Physics - The generalized Houthakker–Johansen model that makes it possible to identify the substitution of production factors on the basis of the...     

研究生录取问题的优化模型与评述

针对2004年首届全国部分高校研究生数学建模竞赛的D题“研究生录取”问题的评卷情况,概括地介绍了这个问题的背景、评卷要点、答卷中存在的问题.并且给出了这个问题的一种有效的解决方法.     

Form-factors in the SU(2)-invariant Thirring model

In this paper we find explicit formulas for the matrix coefficient of the energy-momentum tensor and current operators in the SU(2)-invariant Thirring model. We show that the operators defined by these matrix coefficients commute on a space-like interval. For current operators we calculate the singularities of commutators at the origin.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 164, pp. 80–120, 1987     

Scattering theory for the Federbush,massless Thirring and continuum Ising models

The existence of the LSZ limits of the positive energy quantum fields of the Federbush, Thirring and Ising models is proved. The corresponding S-matrices are obtained explicitly, confirming previous formal results, and are shown to result from a large class of dynamics. The scattering theory for the Federbush and Thirring models on the classical and negative energy quantum levels is studied as well. The wave and scattering operators are shown to exist and are obtained explicitly, and they are proved to be shared by a large class of dynamics, containing in particular the polynomial conserved charges.     

Lieb–Thirring and Bargmann-type inequalities for circular arc

For measures on the unit circle with convergent Verblunsky coefficients we find relations in form of inequalities between these coefficients and the distances from mass points to the essential support of the measure.     

下料问题的优化模型及其快速算法

结合生产实际中具体的下料问题,本文建立了该类问题的优化模型,并提出下料方式的遴选三准则,即高利用率优先准则,长度优先准则和时间优先准则.运用本文的算法对一维下料的利用率高达99.6%,机器时间4秒.对二维的利用率为98.9%,机器时间约7秒.