一类非线性外问题的数值解法

本文利用FEM-BEM方法研究平面上一类非线性外问题数值方法, 给出了基于非线性人工边界条件的耦合问题收敛性结果和误差估计.数值算例验证了我们的理论分析结果. 最后, 我们提出求解其耦合问题的一种区域分解算法.     

采用新方法研究非局部理论中Ⅰ-型裂纹的断裂问题

采用新的方法研究非局部理论中Ⅰ_型裂纹的断裂问题,进而确定裂纹尖端的应力状态,这种方法就是Schmidt方法·　所得结果比艾林根研究同样问题的结果准确和更加合理,克服了艾林根研究同样问题时遇到的数学困难·　与经典弹性解相比,裂纹尖端不再出现物理意义上不合理的应力奇异性,并能够解释宏观裂纹与微观裂纹的力学问题·     

多元统计分析方法的理论研究及应用分析

多元统计分析在多指标实际问题的研究中起着重要的作用.以往文献中,一般采用某一种多元统计方法对一个多指标实际问题进行研究,但其结果存在一定的偏差性.采用四种典型的多元统计方法:主成分分析法、因子分析法、分层聚类和K-均值聚类方法对同一个多指标银行问题进行研究,并对四种方法的不同结果进行比较综合分析,这样可以避免单一方法的偏差性,以便得到的结果更合理、更具有说服力.     

路径跟踪方法求解无界非凸区域上的不动点问题

给出了求解一类无界非凸区域上不动点问题的路径跟踪方法.在适当的条件下,给出了不动点存在性的构造性证明,从而得到了路径跟踪方法的全局收敛性结果.研究结果为计算无界非凸区域上不动点问题提供了一种全局收敛性方法.     

Helmholtz型方程柯西问题的修正Lavrentiev正则化方法（英文）

本文研究了带非齐次Dirichlet及Neumann数据的一类Helmholtz型方程柯西问题.文章在解的先验假设下建立问题的条件稳定性结果,利用修正L avrentiev正则化方法克服其不适定性,并结合正则化参数的先验与后验选取规则获得了正则化解的收敛性结果,相应的数值实验结果验证了所提方法是稳定可行的,推广了已有文献在Helmholtz型方程柯西问题正则化理论与算法方面的相关研究结果.     

时间依赖中子迁移方程离散纵标法的合理性

大家知道,解 Boltzmann 积分-微分方程有一定难度,人们通常采用近似方法求解,离散纵标法是常用的方法之一.此方法首先由 Wick,Chandraskhar 给出,后来得到很大发展.关于该方法的合理性已有很多结果,但研究的均是定态问题.在[14]中对非定态问题给出了一些研究结果.本文运用算子半群扰动论中的结果,给出单能多维     

Hilbert空间中带约束优化问题的广义Largrange泛函及乘子方法

Bertsekas总结了有限维空间的乘子方法。Rockafellar对线性矢量空间中带有限个不等式的凸规划问题提出了相应的乘子方法。Wierzbicki和Kurcyusz研究了Hilbert空间中带算子不等式优化问题,只给出弱逼近极小序列的结果。本文讨论Hilbert空间中带约束优化问题的广义Lagrange泛函以及乘子方法,给出了鞍点方面收敛性的结果。     

一类求解分片延迟微分方程的线性多步法的散逸性

本文研究分片延迟微分方程本身及数值方法的散逸性问题．给出了一个关于此类问题本身散逸性的充分条件,同时得到了一类求解此类问题的线性多步法的数值散逸性结果,此结果表明所考虑的数值方法继承了方程本身的散逸性．数值试验进一步验证了理论结果的正确性．     

关于Columbus问题大扰动情形的完全解

本文在大扰动普遍情形下,按照连续系统的直接方法解答了Columbus问题。所得理论结果和Kelvin实验结果精确一致。至此,Columbus问题得到较完善的解决。     

基于正交多项式下的数值微分任意阶稳定逼近

本文研究了数值微分问题.利用基于正交多项式理论下的积分算子方法,获得了可以稳定逼近已知函数任意阶导数的结果,推广了Lanczos积分方法的结果.     

Monotonic bounds in multistage mixed-integer stochastic programming

Multistage stochastic programs bring computational complexity which may increase exponentially with the size of the scenario tree in real case problems. For this reason approximation techniques which replace the problem by a simpler one and provide lower and upper bounds to the optimal value are very useful. In this paper we provide monotonic lower and upper bounds for the optimal objective value of a multistage stochastic program. These results also apply to stochastic multistage mixed integer linear programs. Chains of inequalities among the new quantities are provided in relation to the optimal objective value, the wait-and-see solution and the expected result of using the expected value solution. The computational complexity of the proposed lower and upper bounds is discussed and an algorithmic procedure to use them is provided. Numerical results on a real case transportation problem are presented.     

分数布朗运动的美式障碍期权定价

假定标的股票服从分数布朗运动,应用二次近似法和偏微分方程方法求出了美式下降敲出看涨、看跌障碍期权价格近似解以及最佳实施边界.最后,通过显式差分法比较近似解的准确性,并分析Hurst参数对期权价格和最佳实施边界S*的影响.     

Analysis of an elliptic-parabolic free boundary problem modelling the growth of non-necrotic tumor cord

We study a free boundary problem modelling the growth of a tumor cord in which tumor cells live around and receive nutrient from a central blood vessel. The evolution of the tumor cord surface is governed by Darcy's law together with a surface tension equation. The concentration of nutrient in the tumor cord satisfies a reaction-diffusion equation. In this paper we first establish a well-posedness result for this free boundary problem in some Sobolev-Besov spaces with low regularity by using the analytic semigroup theory. We next study asymptotic stability of the unique radially symmetric stationary solution. By making delicate spectrum analysis for the linearized problem, we prove that this stationary solution is locally asymptotically stable provided that the constant c representing the ratio between the diffusion time of nutrient and the birth time of new cells is sufficiently small.     

Stability analysis of a coupled system of nonlinear implicit fractional anti‐periodic boundary value problem

In this article, we study the existence and uniqueness of solution for a coupled system of nonlinear implicit fractional anti‐periodic boundary value problem. Further, we investigate different kinds of stability such as Ulam‐Hyers stability, generalized Ulam‐Hyers stability, Ulam‐Hyers‐Rassias stability, and generalized Ulam‐Hyers‐Rassias stability. We develop conditions for existence and uniqueness by using the classical fixed point theorem. Also, two examples are provided to illustrate the obtained results.     

A hierarchy of bounds for stochastic mixed-integer programs

We consider general two-stage SMIPs with recourse, in which integer variables are allowed in both stages of the problem and randomness is allowed in the objective function, the constraint matrices (i.e., the technology matrix and the recourse matrix), and the right-hand side. We develop a hierarchy of lower and upper bounds for the optimal objective value of an SMIP by generalizing the wait-and-see solution and the expected result of using the expected value solution. These bounds become progressively stronger but generally more difficult to compute. Our numerical study indicates the bounds we develop in this paper can be strong relative to those provided by linear relaxations. Hence this new bounding approach is a complementary tool to the current bounding techniques used in solving SMIPs, particularly for large-scale and poorly formulated problems.     

压电材料空间轴对称问题的通解及其应用

本文根据横观各向同性压电材料空间轴对称问题场方程的结构特点,利用逐次引进势函数的方法,最后得到将位移分量和电势函数用满足特定偏微分方程的单一势函数表示的所谓通解,推导过程表明这种形式的通解是完备的,作为应用举例,文中用通解求解了压电材料半无限体表面受集中力的问题,得到位移、应力、电位移分量及电势函数的解析表达式,本文所提供的通解可作为分析含空腔、夹杂或币形裂纹等缺陷的压电材料的机-电耦合行为的工具,算例所得结果可直接用于求解压电体相互间或压电体与普通弹性体间的接触问题。     

分数次布朗运动的欧式障碍期权定价

假定标的股票服从分数次布朗运动,应用偏微分方程的方法求出下降敲出欧式看涨障碍期权价格显示解,以及看涨-看跌的平价关系式.最后,通过有限差分法比较了显示解的准确性,分析了Hurst参数对期权价格和风险特征参数的影响.     

Asymptotic stability of fractional impulsive neutral stochastic partial integro-differential equations with infinite delay

In this article, we investigate the existence and asymptotic stability in p-th moment of a mild solution to a class of neutral stochastic integro-differential equation of fractional order involving non-instantaneous impulses with infinite delay in a Hilbert space. A new set of sufficient conditions proving existence and asymptotic stability of mild solution is derived by utilizing solution operator, functional analysis, stochastic analysis and fixed point technique. Finally, an example is provided to illustrate the obtained abstract result.     

ON VERY WEAK SOLUTIONS OF A-HARMONIC EQUATION WITH VERY WEAK BOUNDARY VALUES

1 IntroductionLet fl be a boulided regular domain in n". By regUlar domain we understand any domainof finite measure for which tlie estli11ates fOr Hodge decomposition in (2.6) and (2.7) are justilied.See, fOr example, N, [7], [2]. A Lipscl1tiz dolllain, for example,is regular.We consider solutionsiL Of a quasi1inear second order equation:divA(x, Vu) = 0, (1.1)where A: fl x n" - n" satisfies the usua1 nreasuability conditions(Caratheodory conditions)and that fOr sonle 1 < p < x,the follo…