一类超椭圆方程有正整数解的必要条件的问题

研究一类超椭圆方程(n d)(n 2d)…(n kd)=y3有正整数解的必要条件,利用数论的一些基本方法,给出了一个新的结果,推进了Erd(o)s和Selfridge的猜想的证明.     

一类超椭圆曲线的整点个数

设ｎ是大于２的工整数,Ｄ是无平方因子正整数,分别是Ｋ的理想类群和类数．对于正整数ｍ,设ｇｋ（ｍ）是Ｉｘ中阶数等于ｍ的理想类的个数．本文证明了：超椭圆曲线ｆ（ｘ,ｙ）＝Ｄｘ２－４ｙｎ＋１＝０上整数点（ｘ,ｙ）的个数不超过ｍａｘ（８,２１６４Ｐ８１ｇｋ（Ｐ））,其中ｐ是ｎ的奇素因数．     

关于二次域理论求解一类Diophantus方程的整数解

本文研究了两个典型Diophantus方程在实二次域中整数解的问题.利用二次域中的理论和二次代数整数环中算术基本定理,得到了该类方程的一般解法和在实二次域中的所有整数解的相关结论,推广了文献[1]和[2]的结果.     

一类半线性椭圆方程正稳定解的唯一性

讨论一类具有Dirichlet边值的半线性椭圆方程(?)其中Ω(?)R~n,主要利用Liouville及re-scaling等方法探讨,当n=2,3时,这类方程正稳定解的唯一性.     

Euclid域中Diophantus方程的整数解

本文研究了两个典型Diophantus方程的整数解的问题.利用二次域中的重要理论和二次代数整数环中算术基本定理,获得了两个典型Diophantus方程在Euclid域中的所有整数解,推广了文献[6]的结果.     

一类半线性椭圆方程的正径向解

本文以关于非线性全连续算子的锥不动点定理为工具，研究半线性椭圆边值问题上Δu λa(|x|)u f(|x|,u)=0(x∈Ω)，u|=0及Δu λf(|x|,u)=0(x∈Ω)，u|=0．在不假定f单调的情况下，本文得出了上述问题存在正径向解的若干充分条件．     

一类拟线性椭圆方程整体解的不存在性

这篇文章主要利用常微分技术讨论了一个二阶拟线性椭圆方程Lpu≡div（｜Du｜^p-2Du）=f（x,u）,x∈R^N的整体解的不存在性.我们只考虑2≤p〈N的情況并且在假设f（x,u）关于第二个变量u没有单调性的情况下得到整体解的不存在性结果.     

一类非线性奇异椭圆方程的非平凡解

讨论一类非线性奇异椭圆方程边值问题,运用正则化方法,经过取两次极限,得到了这个问题的一个非平凡解.     

R^n中一类半线性椭圆方程的k—NODE解的唯一性

本文主要讨论了R~n中超线性椭圆方程边值问题的k-node解的唯一性,在条件 p1(n)<-(ι+2)/(p-1)1,同时给出了 -△u+a(|x|)u=sum from t=1 to m a_i(|x|)|u|p~(i-1)u,u→0 (|x|→∞)的k-node解的唯一性结果。     

拟线性椭圆方程的衰减正解

本文建立了一类拟线性椭圆方程具有高度衰减阶正解的存在性，并对此类正解的最大值进行了上下界估计。     

Column generation based heuristic for tactical planning in multi-period vehicle routing

The periodic vehicle routing problem (PVRP) consists in establishing a planning of visits to clients over a given time horizon so as to satisfy some service level while optimizing the routes used in each time period. The tactical planning model considered here restricts its attention to scheduling visits and assigning them to vehicles while leaving sequencing decisions for an underlying operational model. The objective is twofold: to optimize regional compactness of the routes in a desire to specialize routes to restricted geographical area and to balance the workload evenly between vehicles. Approximate solutions are constructed using a truncated column generation procedure followed by a rounding heuristic. This mathematical programming based procedure can deal with problems with 50–80 customers over five working days which is the range of size of most PVRP instances treated in the literature with meta-heuristics. The paper highlights the importance of alternative optimization criteria not accounted for in standard operational models and provides insights on the implementation of a column generation based rounding heuristic.     

A survey for the quadratic assignment problem

The quadratic assignment problem (QAP), one of the most difficult problems in the NP-hard class, models many real-life problems in several areas such as facilities location, parallel and distributed computing, and combinatorial data analysis. Combinatorial optimization problems, such as the traveling salesman problem, maximal clique and graph partitioning can be formulated as a QAP. In this paper, we present some of the most important QAP formulations and classify them according to their mathematical sources. We also present a discussion on the theoretical resources used to define lower bounds for exact and heuristic algorithms. We then give a detailed discussion of the progress made in both exact and heuristic solution methods, including those formulated according to metaheuristic strategies. Finally, we analyze the contributions brought about by the study of different approaches.     

Solving the maximum edge weight clique problem via unconstrained quadratic programming

The unconstrained quadratic binary program (UQP) is proving to be a successful modeling and solution framework for a variety of combinatorial optimization problems. Experience reported in the literature with several problem classes has demonstrated that this approach works surprisingly well in terms of solution quality and computational times, often rivaling and sometimes surpassing more traditional methods. In this paper we report on the application of UQP to the maximum edge-weighted clique problem. Computational experience is reported illustrating the attractiveness of the approach.     

关于广义Ramanujan-Nagell方程x~2+D=k~n的解数

设D、k是互素的正整数．本文运用初等方法证明了：当D是素数时,方程x2＋D＝kn至多有8组正整数解（x,n）.     

关于Thue方程的解数

设ｍ是正整数,ｆ（Ｘ,Ｙ）＝ａ０Ｘｎ＋ａ１Ｘ（ｎ－１）Ｙ＋．．．＋ａｎＹｎ∈Ｚ［Ｘ,Ｙ］是Ｑ上不可约化的叫ｎ（ｎ≥３）次齐次多项式。本文证明了：当ｇｃｄ（ｍ,ａ０）＝１,ｎ≥４００且ｍ≥１０（３５）时,方程｜ｆ（ｘ,ｙ）｜＝ｍ,ｘ,ｙ∈ｚ,ｇｃｄ（ｘ,ｙ）＝１,至多有６ｎｖ（ｍ）组解（ｘ,ｙ）,其中ｖ（ｍ）是同余式Ｆ（ｚ）＝ｆ（ｚ,１）≡０（ｍｏｄｍ）的解数。特别是当ｇｃｄ（ｍ,ＤＦ）＝１时,该方程至多有６ｎ（ω（ｍ）＋１）组解（ｘ,ｙ）,其中ＤＦ是多项式Ｆ的判别式,ω（ｍ）是ｍ的不同素因数的个数．     

广义Ramanujan-Nagell方程x~2+D~m=p~n的解数

设a是正整数,D=3a2+1,P=4a2+1,其中p是素数.本文证明了:如果a不是4的倍数,则除了当(D,p)=(4,5)时方程x2+Dm=pn恰有3组正整数解(x,m,n)=(1,1,1),(3,2,2),(11,1,3)以外,该方程恰有2组正整数解(x,m,n)=(a,1,1)和(8a3+3a,1,3).     

Finite checkability for integer rounding properties in combinatorial programming problems

LetA be a nonnegative integral matrix with no zero columns. Theinteger round-up property holds forA if for each nonnegative integral vectorw, the solution value to the integer programming problem min{1 y: yA w, y 0, y integer} is obtained by rounding up to the nearest integer the solution value to the corresponding linear programming problem min{1 y: yA w, y 0}. Theinteger round-down property is similarly defined for a nonnegative integral matrixB with no zero rows by considering max{1 y: yB w, y 0, y integer} and its linear programming correspondent. It is shown that the integer round-up and round-down properties can be checked through a finite process. The method of proof motivates a new and elementary proof of Fulkerson's Pluperfect Graph Theorem.Research partially supported by NSF Grants ENG76-09936 and ENG78-09882.     

An aggressive reduction scheme for the simple plant location problem

Pisinger et al. introduced the concept of ‘aggressive reduction’ for large-scale combinatorial optimization problems. The idea is to spend much time and effort in reducing the size of the instance, in the hope that the reduced instance will then be small enough to be solved by an exact algorithm.