临界情况下奇环的稳定性

关于确定奇环稳定性的问题,目前仅有А.А.Андронов和Л.А.Черкас在粗情况下分别对n=1及任意n的结果及作者和钱敏在临界情况下对n=1的结果。对其它情况问题至今尚未解决。 本文对临界情况及任意的n解决了这一问题。本文的结果包括了А.А.Андронов,Л.А.Черкас,作者和钱敏的三个老的结果并对这些结果给予统一的证明。 本文最后讨论了利用奇环的稳定性确定极限环的存在性及从奇环分支出极限环的问题。     

一类Sturm-Liouville问题特征的渐近分析

考虑[0,1]上带第三类边界条件的S-L问题特征值的渐近表示.利用已有的渐近性结果及Fr啨chet导数技术,对特征值进行了精细的分析,清楚地给出了边界条件中的常数(h,H)对特征值的影响.本文的工作对S-L问题的一类反谱问题及相关微分方程反问题的唯一性结果有着重要的应用,也为专著[4,6]中的某些关键结果提供了一个简化的证明途径.     

解抛物问题的一类新的瀑布型多重网格法

本文推广石钟兹 ,许学军对椭圆问题提出的新的瀑布型多重网格法到抛物问题 ,建立了相应的理论结果 .     

某些差分多项式的亏量

Halburd和Korhonen指出研究复域差分的值分布问题对进一步研究复域差分与差分方程具有十分重要的意义.本文得到了关于有限级亚纯函数的差分多项式的亏量为一些结果,其中部分结果可视为微分多项式相应结果的差分模拟.同时,我们在一定条件下给出了经典的Valiron-Mohon'ko定理的一个差分模拟结果,并且作为本文中的一个重要工具出现.这些结果推广了前人已有结果.     

随机非线性算子的随机拓扑度的计算与应用

本文主要研究随机拓扑度的计算问题,获得随机不动点的一些结果,所得结果改进和推广了最近一些文献中所得结论.作为应用,本文研究了随机积分方程随机解的存在性问题.     

求解整数规划的单参数填充函数

本文给出了一个新的求解离散全局最优化问题的单参数填充函数,并给出了一个新的算法,同时给出了对几个测试问题的数据计算结果.     

两参数非线性发展方程的奇摄动尖层解

本文研究了一类具有非线性发展方程奇摄动问题.引入伸长变量和多重尺度,构造了初始边值问题外部解和尖层、边界层和初始层校正项,得到了问题形式解.利用不动点定理,证明了问题的解的一致有效性.推广了对两参数的奇摄动问题的研究结果.     

函数的可测性问题

讨论了函数的可测性问题 ,特别是函数的 Borel可测和 Lebesgue可测的关系 .对相应结论给出了明确和严格的证明 .利用本文的结果 ,我们严格证明了 Lebesgue积分的变量替换公式 .此外还明确指出了分布函数密度的等价唯一性问题 .     

多目标优化问题近似解的非线性标量化刻画

本文主要研究非线性标量化问题近似解与多目标优化问题近似解的关系.利用两种范数建立非线性标量化问题,得到了多目标优化问题近似有效解和近似真有效解的非线性标量化结果,并给出例子对主要结果进行了说明.     

基于最优D.C.分解的单二次约束非凸二次规划精确算法

本文提出一种基于最优D.C.分解的单二次约束非凸二次规划精确算法.本文首先对非凸二次日标函数进行D.C.分解,然后对D.C.分解中凹的部分进行线性下逼近得到一个凸二次松弛问题.本文证明了最优D.C.分解可通过求解一个半定规划问题得到,而原问题的最优解可以通过计算最优凸二次松弛问题的满足某种互补条件的解得到.最后,本文报告了初步数值计算结果.     

Numerical Optimization for the Location of Wastewater Outfalls

In this paper we solve a constrained optimal control problem related to the location of the wastewater outfalls in a sewage disposal system. This is a problem where the control is the position and the constraints are non-convex and pointwise, which makes difficult its resolution. We discretize the problem by means of a characteristics-Galerkin method and we use three algorithms for the numerical resolution of the discretized optimization problem: an interior point algorithm, the Nelder-Mead simplex method and a duality method. Finally, we compare the numerical results obtained by applying the described methods for a realistic problem posed in the ría of Vigo (Galicia, Spain).     

New algorithms for the split variational inclusion problems and application to split feasibility problems

ABSTRACT

In this paper, we suggest two new iterative methods for finding an element of the solution set of split variational inclusion problem in real Hilbert spaces. Under suitable conditions, we present weak and strong convergence theorems for these methods. We also apply the proposed algorithms to study the split feasibility problem. Finally, we give some numerical results which show that our proposed algorithms are efficient and implementable from the numerical point of view.     

Exact controllability of a spherical cap: Numerical implementation of HUM

This paper deals with the numerical implementation of the exact boundary controllability of the Reissner model for shallow spherical shells (Ref. 1). The problem is attacked by the Hilbert uniqueness method (HUM, Refs. 2–4), and we propose a semidiscrete method for the numerical approximation of the minimization problem associated to the exact controllability problem. The numerical results compare well with the results obtained by a finite difference and conjugate gradient method in Ref. 5.This work was done when the first two authors were at CNR-IAC, Rome, Italy as Graduate Students.     

Numerical solution of a minimax ergodic optimal control problem

In this work we consider an L^∞ minimax ergodic optimal control problem with cumulative cost. We approximate the cost function as a limit of evolutions problems. We present the associated Hamilton-Jacobi-Bellman equation and we prove that it has a unique solution in the viscosity sense. As this HJB equation is consistent with a numerical procedure, we use this discretization to obtain a procedure for the primitive problem. For the numerical solution of the ergodic version we need a perturbation of the instantaneous cost function. We give an appropriate selection of the discretization and penalization parameters to obtain discrete solutions that converge to the optimal cost. We present numerical results. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical approximations of a nonlinear eigenvalue problem and applications to a density functional model

In this paper, we study numerical approximations of a nonlinear eigenvalue problem and consider applications to a density functional model. We prove the convergence of numerical approximations. In particular, we establish several upper bounds of approximation errors and report some numerical results of finite element electronic structure calculations that support our theory. Copyright © 2010 John Wiley & Sons, Ltd.     

A method based on Rayleigh quotient gradient flow for extreme and interior eigenvalue problems

Recently, a continuous method has been proposed by Golub and Liao as an alternative way to solve the minimum and interior eigenvalue problems. According to their numerical results, their method seems promising. This article is an extension along this line. In this article, firstly, we convert an eigenvalue problem to an equivalent constrained optimization problem. Secondly, using the Karush-Kuhn-Tucker conditions of this equivalent optimization problem, we obtain a variant of the Rayleigh quotient gradient flow, which is formulated by a system of differential-algebraic equations. Thirdly, based on the Rayleigh quotient gradient flow, we give a practical numerical method for the minimum and interior eigenvalue problems. Finally, we also give some numerical experiments of our method, the Golub and Liao method, and EIGS (a Matlab implementation for computing eigenvalues using restarted Arnoldi’s method) for some typical eigenvalue problems. Our numerical experiments indicate that our method seems promising for most test problems.     

The C 1 wavelet method for numerical solutions of the Neumann problem

In this article we use the C ¹ wavelet bases on Powell-Sabin triangulations to approximate the solution of the Neumann problem for partial differential equations. The C ¹ wavelet bases are stable and have explicit expressions on a three-direction mesh. Consequently, we can approximate the solution of the Neumann problem accurately and stably. The convergence and error estimates of the numerical solutions are given. The computational results of a numerical example show that our wavelet method is well suitable to the Neumann boundary problem.     

Interaction of faults under slip‐dependent friction. Non‐linear eigenvalue analysis

We analyse the evolution of a system of finite faults by considering the non‐linear eigenvalue problems associated to static and dynamic solutions on unbounded domains. We restrict our investigation to the first eigenvalue (Rayleigh quotient). We point out its physical significance through a stability analysis and we give an efficient numerical algorithm able to compute it together with the corresponding eigenfunction. We consider the anti‐plane shearing on a system of finite faults under a slip‐dependent friction in a linear elastic domain, not necessarily bounded. The static problem is formulated in terms of local minima of the energy functional. We introduce the non‐linear (static) eigenvalue problem and we prove the existence of a first eigenvalue/eigenfunction characterizing the isolated local minima. For the dynamic problem, we discuss the existence of solutions with an exponential growth, to deduce a (dynamic) non‐linear eigenvalue problem. We prove the existence of a first dynamic eigenvalue and we analyse its behaviour with respect to the friction parameter. We deduce a mixed finite element discretization of the non‐linear spectral problem and we give a numerical algorithm to approach the first eigenvalue/eigenfunction. Finally we give some numerical results which include convergence tests, on a single fault and a two‐faults system, and a comparison between the non‐linear spectral results and the time evolution results. Copyright © 2004 John Wiley & Sons, Ltd.     

An efficient method for solving non-linear singularly perturbed two points boundary-value problems of fractional order

In this paper, we discuss a numerical solution of a class of non-linear fractional singularly perturbed two points boundary-value problem. The method of solution consists of solving reduced problem and boundary layer correction problem. A series method is used to solve the boundary layer correction problem, and then the series solutions is approximated by the Pade’ approximant of order [m, m]. Some theoretical results are established and proved. Two numerical examples are discussed to illustrate the efficiency of the present scheme.