向量优化问题有效解的稳定性

运用标量化的方法,通过锥正定真有效解的上半连续性讨论了无限维赋范空间中锥有效解的部分上半连续性,证明了锥有效解的通有稳定性.在此基础上,进一步证明,在Baire纲的意义下,绝大多数的向量优化问题至少存在一个锥正定真有效解是本质的有效解,换句话说,绝大多数的向量优化问题锥有效解是几乎下半连续的.     

无限Fuzzy关系方程的解集

对(0,1)格上的无限Fuzzy关系方程,给出其可解的充要条件.利用可达解与不可达解的概念,给出方程存在可达解与不可达解的充要条件.进一步,在解集非空时,刻画了方程的解集的结构及性质.     

The optimal solution of multi-kernel regularization learning

In regularized kernel methods, the solution of a learning problem is found by minimizing a functional consisting of a empirical risk and a regularization term. In this paper, we study the existence of optimal solution of multi-kernel regularization learning. First, we ameliorate a previous conclusion about this problem given by Micchelli and Pontil, and prove that the optimal solution exists whenever the kernel set is a compact set. Second, we consider this problem for Gaussian kernels with variance σ∈(0,∞), and give some conditions under which the optimal solution exists.     

硅体中磷反应扩散系统解的整体存在性及渐近性

本文用上下解方法，研究了一类带混合非齐次边界条件的化学反应──硅体中磷反应扩散系统，采用避开△的特征函数构造上下解的方法，得到一类充分条件，以使其整体解渐近趋向于Ｓｔｅａｄｙ－ｓｔａｔｅ解．     

The string merging problem

The string merging problem is to determine a merged string from a given set of strings. The distinguishing property of a solution is that the total cost of editing all of the given strings into this solution is minimal. Necessary and sufficient conditions are presented for the case where this solution matches the solution to the string-to-string correction problem. A special case where deletion is the only allowed edition operation is shown to have the longest common subsequence of the strings as its solution.This research was supported by the U.S. Army Research Office.     

Regularization of the Solution of the Cauchy Problem: The Quasi-Reversibility Method

Some regularization algorithm is proposed related to the problem of continuation of the wave field from the planar boundary into the half-plane. We consider a hyperbolic equation whose main part coincideswith the wave operator, whereas the lowest term contains a coefficient depending on the two spatial variables. The regularization algorithm is based on the quasi-reversibility method proposed by Lattes and Lions. We consider the solution of an auxiliary regularizing equation with a small parameter; the existence, the uniqueness, and the stability of the solution in the Cauchy data are proved. The convergence is substantiated of this solution to the exact solution as the small parameter vanishes. A solution of an auxiliary problem is constructed with the Cauchy data having some error. It is proved that, for a suitable choice of a small parameter, the approximate solution converges to the exact solution.     

The Elementary Solution of Triple Integral Equations and The Solution of Triple Series Equations Involving Associated Legendre Polynomials and their Application

A method is developed for the formal solution of an important class of triple integral equations involving Bessel functions. The solution of the triple integral equations is reduced to two simultaneous Fredholm integral equations and the results obtained are simpler than those of other authors and also superior for the purposes of solution by iteration. In the same manner the formal solution of triple series equations involving associated Legendre polynomials is presented. The solution of the problem is reduced to that of solving a Fredholm integral equation of the first kind. Finally to illustrate the application of the results an electrostatic problem is discussed.     

反应扩散方程的渐近吸引子

本文考虑了反应扩散方程的渐近吸引子，即构造了一个有限维解序列。首先利用数学归纳法证明了该解序列不会远离方程的整体吸引子，其次证明了它在长时间后无限趋于方程的整体吸引子，并且给出了渐近吸引子的维数估计。     

The Existence of Almost Periodic Solution and Periodic Solutions

In this paper, it is obtained that a periodic system has an almost periodic solution if it has a solution x=\phi(t) uniformly stable with respect to \Omega_\phi ,and has a periodic solution if x=\phi(t) is weakly uniformly asymptotically stable with respect to \Omega_\phi. Meanwhile, it is also obtained that a uniformly almost periodic system has an almost periodic solution if it has a solution x=\phi(t) uniformly asymptotically stable with respect to A_\phi^j.     

The stationary solution of a one-dimensional bipolar quantum hydrodynamic model

In this paper, we consider the existence and uniqueness of stationary solution to the bipolar quantum hydrodynamic model in one dimensional space with general non-constant doping profile. The existence of the stationary solution is proved by Leray-Schauder fixed-point theorem and a crucial truncation technique is used to derive the positive upper and lower bounds of the stationary solution. The uniqueness of the stationary solution is shown by a delicate energy estimate.     

The bang-bang-bang problem revisited

The solution given by Isaacs to the bang-bang-bang problem is shown to be a solution in aweak sense only. A solution in a stronger sense is demonstrated involving the notions of extended closed-loop strategies and of extended value-function. The bang-bang-bang singular surface is interpreted in a new way.The author is grateful to Professor J. V. Breakwell for his criticism and valuable remarks.     

The method of fundamental solutions for linear diffusion-reaction equations

The paper presents an extension of the solution procedure based on the method of fundamental solutions proposed earlier in the literature for solving linear diffusion reaction equations in nonregular geometries in two and three dimensions. The solution procedure utilizes the fundamental solution to the problem along with boundary collocation to result in a grid-free numerical scheme. A new heuristic for source location is utilized along with orthogonal collocation in nonsmooth domains to improve the accuracy of the solution. The efficacy of the solution procedure is demonstrated for a variety of problems in nonregular simply and multiply connected geometries with nonuniform boundary conditions.     

The inverses of Toeplitz band matrices

The elements of the inverse of a Toeplitz band matrix are given in terms ofthe solution of a difference equation. The expression for these elements is a quotient of determinants whose orders depend the number of nonzero superdiagonals but not on the order of the matrix. Thus, the formulae are particularly simple for lower triangular and lower Hessenberg Toeplitz matrices. When the number of nonzero superdiagonals is small, sufficient conditions on the solution of the abovementioned difference equation can be given to ensure that the inverse matrix is positive. If the inverse is positive, the row sums can be expressed in terms of the solution of the difference equation.     

The analysis of sequential measurements of bones

Analysing sequential bone measurements obtained in experiments in which the duration of observation varies between individuals is a common problem. Two solutions are presented which estimate the population mean rate of change in different ways. The first solution provides a least squares estimate and involves calculating a weighting factor for each individual observation which increases nonlinearly with the observation period. Computation of this solution requires knowledge of the measurement error and also the true variability in the rate of change between individuals, which is rarely if ever known. The second solution, based on cumulative sums, is much simpler, involving a weighting factor which is equal to the observation period. No prior knowledge of the measurement error or variability in the rate of change is required. An expression for the standard error of the computed mean rate of change is also derived. Monte Carlo simulations of a large number of experiments have confirmed that, within the limits of the model parameters tested, the second solution produces valid estimates of the mean rate of change and its standard error.     

一类串联可修复系统的稳态解

本文讨论了一类具有两不同部件串联的可修复系统。利用系统算子生成的Banach空间中的正压缩C_o半群的性质,证明了系统的非负稳态解恰是系统算子的0本征值所对应的规范化后的本征向量；同时通过对系统算子谱点分布情况的分析,证明了系统算子的谱点均位于复平面左半平面且在虚轴上除0点外无其它谱,作为线性算子半群稳定性的—个直接结果,得出了该串联可修复系统的渐近稳定性。     

The Effects of Modelling on Log Bucking Solution Techniques

Log bucking is an industrial problem of subdividing longer logs into smaller logs such that potential revenue is maximized. The model has been solved using dynamic programming predominately, and branch-and-bound to a lesser extent. This research considers the effect of modelling assumptions that have been used to accommodate the solution techniques. Three levels of increasing model detail are considered. An examination of the nature and amount of error is made by using a model of lesser detail instead of a more precise model. The main experiment is used to show the differences in solution accuracy for the three dynamic programming strategies when compared with the accuracy of solutions generated by using branch-and-bound. The final analysis considers the cost in terms of time to solution for each solution technique to produce highly comparable solution accuracy.     

非线性群体发展方程的整体性态

本文研究一类非线性群体动力学模型,证明了C~1解的整体存在唯一性,并在特殊情形下讨论了解的渐近性态和平衡解的稳定性.     

常均曲率热流的存在性

给出常均曲率热流的Dirichlet边值问题存在唯一和正则的解,并且这个解可以一直达到某个能量集中的时刻.如果这个解还满足一定的能量不等式,那么可以得到在除有限个奇点的全局解.我们所使用的方法有别于文献[2].     

Logistic型方程周期解和概周期解的存在性

In this paper, we study the Logistic type equation x= a（t）x -b（t）x^2＋ e（t）. Under the assumptions that e（t） is small enough and a（t）, b（t） are contained in some positive intervals, we prove that this equation has a positive bounded solution which is stable. Moreover, this solution is a periodic solution if a（t）, b（t） and e（t） are periodic functions, and this solution is an almost periodic solution if a（t）, b（t） and e（t） are almost periodic functions.     

The proportional solution for rights problems

Recently there have been several studies to provide axiomatic characterizations of solutions to rights problems. However, these studies do not give a satisfactory answer to the question why the proportional solution is the most widely used. This is the question addressed in this paper. To that purpose, we adopt the axiomatic approach; we suggest a set of axioms which a desirable solution should satisfy and we show that the proportional solution is the only solution to satisfy these axioms. Our main axioms are no advantageous reallocation and additivity. A solution satisfies no advantageous reallocation if no subgroup of claimants ever benefits by transferring parts of their claims between themselves. A solution satisfies additivity if it yields the same allocation whether the total estate is divided at once or in several steps.