肿瘤生长的自由边界问题

本文介绍肿瘤生长的自由边界问题这一新兴研究方向的研究内容和进展状况.文章首先介绍肿瘤生长的数学建模历史、最新进展和一些重要的肿瘤生长模型,这些模型的数学形式是偏微分方程的自由边界问题.之后介绍近几年人们对这些自由边界问题所做严谨数学理论分析获得的一些主要成果,并简单介绍了证明这些成果用到的数学理论和方法.     

非稳定井流的自由边界问题

<正> 近年来 C.Baiocchi 在研究水坝的浸润面时,提出了一种 Baiocchi 变换,它成为研究一类稳定自由边界问题的有力工具.A.Torelli 在处理非稳定问题时发展了 Baioc-chi 变换.基于 Baiocchi 等人的工作,C.W.Cryer 和 H.Fetter 研究了稳定井流的自由边界问题.本文进一步讨论非稳定可压缩井流的自由边界问题.我们通过 Torelli 变换把它归结为一个发展型变分不等方程,证明了该方程的解存在唯一.     

一个肿瘤生长自由边界问题的研究

本文研究一个描述肿瘤生长的自由边界问题.这个自由边界问题是对Byrne和Chaplain相应肿瘤生长模型的一个改进,研究了该问题解当t→∞时的渐近状况,证明了未血管化的肿瘤体积不会无限制地增大,它或者趋于消失,或者趋于一个休眠态,依营养物浓度的大小和抑制物浓度的大小而定.     

一个肿瘤生长自由边界问题的研究

本文研究一个描述肿瘤生长的自由边界问题.这个自由边界问题是对Byrne和Chaplain相应肿瘤生长模型的一个改进,研究了该问题解当t→∞时的渐近状况,证明了未血管化的肿瘤体积不会无限制地增大,它或者趋于消失,或者趋于一个休眠态,依营养物浓度的大小和抑制物浓度的大小而定.     

关于非均质水坝问题

本文研究带有蒸发或降雨补给、底板不隔水且具有一般几何形状的非均质水坝自由边界问题,证明了解的存在性、唯一性及解和自由边界的其他性质.     

关于热传导自由边界问题的探讨

对钢锭冷凝过程的研究,归结为求解组合介质热传导自由边界问题.本文就未凝固的钢水中热传导问题进行了探讨.即讨论下面的定解问题:     

具有两种流体的轴对称渗流的一个自由边界问题

本文处理带有两种流体的轴对称的一个自由边界问题，其中在渗流区域的上部都是油，下部是水，这是同时取油注水的一个数学模型。下面，我们将用复分析方法求出此自由边界问题的一个解，并证明其解的唯一性。     

具有自由边界的二维渗流问题

渗流的自由边界问题是工程上很受关注的问题．现有的数值分析方法需事先估计边界形态，逐次逼近．本文采用“变分不等式”的模式，结合有限元方法研究有自由边界的渗流问题，在整个结构区域内作有限元剖分，避免了传统的有限元分析中估计自由边界、反复修正计算区域的迭代过程．本文方法为简单而快速地分析渗流自由边界问题提供了一条有效的途径．     

美式期权自由边界的计算方法

美式期权的自由边界问题在金融工程文献中已经引起了广泛的关注,然而,它的数值计算方法一直是一个难点.基于差分技巧,给出了满足具有有限到期日的美式期权自由边界的两种计算方法,即,根据股票期权价格和相应的偏导数来确定自由边界条件.数值结果表明了上述两种方法下自由边界是一致性的.此外研究结果对自由边界的计算提供很好的科学依据.     

无锚固储液罐提离的流-固多种非线性耦合的三维移动边界问题统一分析格式*

本文建立了在地震作用下无锚固储液罐提离的流-固多种非线性耦合的移动边界问题的统一格式的三维分析方法,其中建立了任意四边形标薄板壳拟协调非线性有限元的列式和分析移动边界问题的线性互补方程;提出了在ALE标架下用带压力项的时间分裂步法求解储液罐内含自由液面大幅晃动(移动边界问题)的非定常的三维粘性流体(N-S)问题的方法;其中没有利用轴称性和梁式模态假定等条件及未曾利用势函数理论;该方法适用于一般板壳-流体多种非线性耦合的多种移动边界问题.     

Production planning with discounting and stochastic demands

A general continuous review production planning problem with stochastic demand is considered. Conditions under which the stochastic problem may be correctly solved using an equivalent deterministic problem are developed. This deterministic problem is known to have the same solution as the stochastic problem. Moreover, conditions are established under which the deterministic equivalent problem differs from a commonly used deterministic approximation to the problem only in the interest rate used in discounting. Thus, solving the stochastic problem is no more difficult than solving a commonly used approximation of the problem.     

三种新变形的全一问题

该文研究三种新变形的全一问题及最小全一问题. 原始的全一问题可被形象的称为顶点点亮顶点问题, 而这三类新问题则分别被称为顶点点亮边问题,边点亮顶点问题,边点亮边问题. 顶点点亮顶点问题已经得到了广泛的研究. 比如,解的存在性问题和求解的有效算法已经被解决,一般图上的最小顶点点亮顶点问题已经被证明是NP- 完备的,树、单圈图和双圈图上的最小顶点点亮顶点问题的线性时间最优算法也已被给出等. 该文对于顶点点亮边问题,证明一个图有解当且仅当它是二部图,因此只可能有两组解和最优解. 对于边点亮顶点问题,证明一个图有解当且仅当它包含偶数个顶点,并通过将其最优问题多项式变换成最小权的完美匹配问题,得出一般图上的最小边点亮顶点问题可在多项式时间内求解. 边点亮边问题可归约成线图上的顶点点亮顶点问题.     

Complexities and algorithms for synchronized scheduling of parallel machine assembly and air transportation in consumer electronics supply chain

In this paper, we study the problem of synchronized scheduling of assembly and air transportation to achieve accurate delivery with minimized cost in consumer electronics supply chain. This problem was motivated by a major PC manufacturer in consumer electronics industry. The overall problem is decomposed into two sub-problems, which consist of an air transportation allocation problem and an assembly scheduling problem. The air transportation allocation problem is formulated as an integer linear programming problem with the objective of minimizing transportation cost and delivery earliness tardiness penalties. The assembly scheduling problem seeks to determine a schedule ensuring that the orders are completed on time and catch the flights such that the waiting penalties between assembly and transportation is minimized. The problem is formulated as a parallel machine scheduling problem with earliness penalties. The computational complexities of the two sub-problems are investigated. The air transportation allocation problem with split delivery is shown to be solvable. The parallel machine assembly scheduling problem is shown to be NP-complete. Simulated annealing based heuristic algorithms are presented to solve the parallel machine problem.     

On an optimal shape design problem to control a thermoelastic deformation under a prescribed thermal treatment

A shape optimization problem concerned with thermal deformation of elastic bodies is considered. In this article, measure theory approach in function space is derived, resulting in an effective algorithm for the discretized optimization problem. First the problem is expressed as an optimal control problem governed by variational forms on a fixed domain. Then by using an embedding method, the class of admissible shapes is replaced by a class of positive Borel measures. The optimization problem in measure space is then approximated by a linear programming problem. The optimal measure representing optimal shape is approximated by the solution of this finite-dimensional linear programming problem. Numerical examples are also given.     

The zero-one knapsack problem with equality constraint

The zero-one knapsack problem is a linear zero-one programming problem with a single inequality constraint. This problem has been extensively studied and many applications and efficient algorithms have been published. In this paper we consider a similar problem, one with an equality instead of the inequality constraint. By replacing the equality by two inequalities one of which is placed in the economic function, a Lagrangean relaxation of the problem is obtained. The relation between the relaxed problem and the original problem is examined and it is shown how the optimal value of the relaxed problem varies with increasing values of the Lagrangean multiplier. Using these results an algorithm for solving the problem is proposed.The paper concludes with a discussion of computational experience.     

Characterization of duality for a generalized quasi-equilibrium problem

In this paper, the duality theory of a generalized quasi-equilibrium problem (also called generalized Ky Fan quasi-inequality) is investigated by using the image space approach. Generalized quasi-equilibrium problem is transformed into a minimization problem. The minimization problem is further reformulated as an image problem by virtue of linear/nonlinear separation function. The dual problem of the image problem is constructed in the image space, then zero duality gap between the image problem and its dual problem is derived under saddle point condition as well as the equivalent regular linear/nonlinear separation condition. Finally, some more sufficient conditions guaranteeing zero duality gap are also proposed.     

现代物流技术中装卸工问题的拟多项式时间可解情况

装卸工问题是从现代物流技术中提出的一个实际问题，这个问题的雏形早在上个世纪60年代中国科学院数学研究所就提出和研究过。现代物流业的迅速发展，促成和推动装卸工问题的提出和研究。装卸工问题是一个新的NP困难的组合优化问题，本文研究限制情形下的装卸工问题，并证明是拟多项式时间可解的。     

一类偏积分-微分方程中的反问题

对一类偏积分-微分方程中参数校准的反问题进行研究.在弱解的框架下,原问题可转化为含具体正则化项的最优化问题.文中证明了该最优化问题的解的存在性和稳定性,并考察了最优解存在的一阶必要条件.另外,证明了当正则化参数足够大时,该最优化问题关于参数a的凸性性质.基于偏积分-微分方程反问题的研究对于金融市场中的模型校准问题具有重要的意义.     

The Complexity Analysis of the Inverse Center Location Problem

Given a feasible solution, the inverse optimization problem is to modify some parameters of the original problem as little as possible, and sometimes also with bound restrictions on these adjustments, to make the feasible solution become an optimal solution under the new parameter values. So far it is unknown that for a problem which is solvable in polynomial time, whether its inverse problem is also solvable in polynomial time. In this note we answer this question by considering the inverse center location problem and show that even though the original problem is polynomially solvable, its inverse problem is NP–hard.     

A new heuristic algorithm solving the linear ordering problem

The linear ordering problem is an NP-hard combinatorial problem with a large number of applications. Contrary to another very popular problem from the same category, the traveling salesman problem, relatively little space in the literature has been devoted to the linear ordering problem so far. This is particularly true for the question of developing good heuristic algorithms solving this problem.In the paper we propose a new heuristic algorithm solving the linear ordering problem. In this algorithm we made use of the sorting through insertion pattern as well as of the operation of permutation reversal. The surprisingly positive effect of the reversal operation, justified in part theoretically and confirmed in computational examples, seems to be the result of a unique property of the problem, called in the paper the symmetry of the linear ordering problem. This property consists in the fact that if a given permutation is an optimal solution of the problem with the criterion function being maximized, then the reversed permutation is a solution of the problem with the same criterion function being minimized.