较多约束多目标规划的最优性条件

本文研究较多约束多目标规划的最优性条件.借助于所给问题的较多约束集结构表示,定义了较多约束规划问题的较多约束Pareto有效解和较多约束Pareto弱有效解,给出较多约束Pareto有效解和较多约束Pareto弱有效解要满足的Fritz John条件和Kuhn-Tucker条件,最后给出在凸性条件下它的一些最优性充分条件.     

多目标规划的ακ—较多有效性

本文先讨论带两个参数的ακ－较多锥的个性质，借助它们研究了多目标规划问题的ακ－较多有效解和ακ－较多最优解之间以及它们与Pareto有效解之间的关系，同时，还各自给出这两类解存在的两个充要条件。     

多目标规划的αk-较多有效性

本文先讨论带两个参数的αk-较多锥的几个性质,借助它们研究了多目标规划问题的αk-较多有效解和αk-较多最优解之间以及它们与Pareto有效解之间的关系.同时,还各自给出这两类解存在的两个充要条件.     

较多约束规划及其最优性条件

本文研究了文[1]中提出的较多约束规划的基本问题，在给出问题的较多约束集结构表示的基础上，证明了这类问题的较多约束最优解要满足的Fritz John条件和Kuhn-Tucker条件。     

多目标规划ak-较多有效解类的有效性充分条件

在文［３］引进多目标规划问题的带双参数ａ和ｋ的ａｋ－较多有效解, 并且给出了此类解的有效性必要条件。本文在一定凸性的假设下证明了ａｋ－较多 有效解和ａｋ－弱较多有效解的几个有效性充分条件．     

多目标规划αk-较多有效解类的有效性充分条件

在文[3]引进多目标规划总是的带双参数α和k的αk-较多有效解,并且给出了此类解的有效性必要条件。本文在一定凸性的假设下证明了αk-较多有效解和αk-弱较多有效解的几个有效性充分条件。     

非光滑多目标规划的最优性

本文给出了一种新的右上导数定义,利用这一右上导数定义了几类广义凸性条件,进而讨论了非光滑多目标规划的最优性．包括Ｆｒｉｔｚ－Ｊｏｈｎ条件和Ｋｕｈｎ－Ｔｕｃｋｅｒ条件．     

不可微多目标规划的最优性条件

众所周知,Clarke、Ioffe和Aubin对非光滑分析做出了开创性的奠基工作,然而当应用它们解决有关实际问题时,在不少情况下还不很理想,特别是,他们所定义的向量函数广义梯度都比较难计算,这常造成相应不可微多目标规划算法在具体实现时的困难。     

非光滑多目标规划的最优性条件

近年来,关于非光滑最优化问题的研究十分活跃,尤其是对单目标规划,出现了很多成果.关于非光滑多目标规划,也有不少工作.然而,以前的研究,多是利用次微分(凸规划情形)或广义梯度进行讨论的.文[1]利用古典方向导数给出了非光滑无约束单目标规划的最优性条件,并指出,在广泛的非光滑函数类中,方向导数是存在的.本文则以更     

关于多目标数学规划的最优性条件

本文讨论定义于Ｂａｎａｃｈ空间的多目标数学规划，得到一些ε－最优解和（弱）有效解的必要条件，充分条件和必要充分条件。     

LOCAL INEQUALITIES FOR SIDON SUMS AND THEIR APPLICATIONS

The authors consider Sidon sets of first kind. By comparing them with the Steinhaus sequence, they prove a local Khintchine-Kahane inequality on compact sets. As consequences, they prove the following results for Sidon series taking values in a Banach space: the summability on a set of positive measure implies the almost everywhere convergence; the contraction principle of Billard-Kahane remains true for Sidon series. As applications, they extend a uniqueness theorem of Zygmund concerning lacunary Fourier series and an analytic continuation theorem of Hadamard concerning lacunary Taylor series. Some of their results still hold for Sidon sets of second kind.     

单种群离散模型的全局和局部稳定性

本文概述了关于单种群离散模型稳定性研究的成果,在此基础上,给出一些新的结果.     

THE NECESSARV AND SUFFICIENT CONDITIONS FOR LIPSCHITZ LOCAL HOMEOMORPHISM

For a locally Lipschitz map f:$R^{n}\rightarrow R^{n}$,the well known inverse functin theorem gives a sufficient condition for f to be a Lipschitz local homeomorphims at a point $x_{0}$,that is,$\partial f(x_{0}$ is invertible.In this paper,it is showed that this condition is not necessary and some necessary and sufficient conditions are given.     

两指标局部鞅的停止变换及Wiener过程的鞅刻划

本文主要讨论两指标局部平方可积鞅的停止变换问题及Ｗｉｅｎｅｒ过程的鞅刻划和停止问题。     

LOCAL AND PARALLEL FINITE ELEMENT ALGORITHMS FOR THE NAVIER-STOKES PROBLEM

Based on two-grid discretizations, in this paper, some new local and parallel finiteelement algorithms are proposed and analyzed for the stationary incompressible Navier-Stokes problem. These algorithms are motivated by the observation that for a solutionto the Navier-Stokes problem, low frequency components can be approximated well by arelatively coarse grid and high frequency components can be computed on a fine grid bysome local and parallel procedure. One major technical tool for the analysis is some locala priori error estimates that are also obtained in this paper for the finite element solutionson general shape-regular grids.     

LOCAL C-SEMIGROUPS AND LOCAL C-COSINE FUNCTIONS

0IntroductionLetB(X)betheBanachspaceofallboundedlinearoperatorsonaBanachspaceX.CEB(X)isinjective.Alloperatorsarelinear.D(A),Im(A),andP(A)denotethedomain,theimage,andtheresolventsetofoperatorA,respectivelyNandRdenotethesetofallnaturalnumbersandthesetofallrealnumbers.TheconceptoflocalC-sernigroupsalldlocalC-cosinefunctionwereintroducedbyTanakaandOkazawain[1]tF.HuangandT.Huangin[21,respectively.Aspointedoutin[3]and[2]thatnotalllocalC-sendgroups(C--cosinefunctions)canbeextendedtobeC-se…     

对积分恒等式的一点补充和有限元的局部校正结果

１．积分恒等式简介其中ｈ＝ｍａｘ｛ｈｅ,ｋｅ｝, 易见用 Ｑ１（ｅ）表示 ｅ上全体双线性函数,ｕＩ∈ Ｑ１（ｅ）为ｕ在 ｅ上的双线性插值．文［１, ２］曾给出了一系列的积分恒等式,列举如下： Ａ：二阶恒等式,用于超收敛估计：对任给ｖ∈Ｑ１（ｅ）,有以及由于Ｉｅ１２的展开式中含有因子б１б２ｖ,将破坏超收敛估计,故对此项关于ｙ分部积分,得展开式其中τ１,τ２分别为ｅ的上下边.（１．３）,（１．４）和（１．６）是作导数超收敛估计的基本展开式．当然我们更有０次项的展开式．在下一节将讨论林氏积分表． 为了进一步…     

LOCAL WELL-POSEDNESS OF INTERACTION EQUATIONS FOR SHORT AND LONG DISPERSIVE WAVES

The well-posedness of the Cauchy problem for the system{iδtu+δx^2u=uv+|u|^2u,t,x∈IR，δtv+δxHδxv=δx|u|^2,u(0,x)=u0(x),v(0,x)=v0(x),is considered. It is proved that there exists a unique local solution (u(x,t), v(x,t))∈C（[0,T);H^s)×C([0,T);Hs^-1/2) for any initial data (u0,v0)∈H^s(IR)×H^s-1/2(IR)(s≥1/4) and the solution depends continuously on the initial data.     

LOCAL THEORY IN CRITICAL SPACES FOR COMPRESSIBLE VISCOUS AND HEAT-CONDUCTIVE GASES

We are concerned with local existence and uniqueness of solutions for a general model of viscous and heat-conductive gases with low regularity assumptions on the initial data (the velocity and the temperature may be discontinuous). Local well-posedness is showed to hold in spaces which are critical with respect to the scaling of the equations, provided that the initial density is close enough to a positive constant. When initial data are a trifle more regular, local well-posedness holds for any initial density bounded away from zero. This former result lies on new estimates for linear heat equations with a non constant diffusion coefficient.