Semigroups Generated by Ordinary Differential Operators in L 1(I)*

In this paper we give necessary and sufficient conditions for the existence of a C> ₀-semigroup in L ¹(I) (I real interval) generated by a second-order differential operator when suitable boundary conditions at the endpoints are imposed.     

Space-Time Topology (II)—Causality, the Fourth Stiefel–Whitney Class and Space-Time as a Boundary

We show that stable causality is related to the vanishing of the top Stiefel–Whitney class of a space-time manifold M, and that if M is a stably causal space-time manifold, then it is the boundary of a five-dimensional space-time. We then propose a scheme for making it both a necessary and sufficient condition.     

Benson真有效意义下集值优化的广义最优性条件

本文引入了关于集值映射的α-阶Clarke切导数、α-阶邻接切导数及α-阶 伴随切导数的概念,借此建立了约束向量集值优化Benson真有效解导数型的Kuhn- Tucker条件.     

一个耦合系统自由边界问题的整体古典解

§ 1　ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｔｈｉｓｐａｐｅｒｗｅｄｉｓｃｕｓｓｔｈｅｇｌｏｂａｌｃｌａｓｓｉｃａｌｓｏｌｕｔｉｏｎｏｆａｍｕｌｔｉｄｉｍｅｎｓｉｏｎａｌｑｕａｓｉｓｔａｔｉｏｎａｒｙｐｒｏｂｌｅｍ .Ｔｈｅｐｒｏｂｌｅｍｃｏｍｅｓｆｒｏｍｔｈｅｄｉｓｃｕｓｓｉｏｎｏｆａｇｒｏｗｔｈｍｏｄｅｌｏｆｓｅｌｆｍａｉｎｔａｉｎｉｎｇｐｒｏｔｏｃｅｌｌ(ｓｅｅ [1— 3])ｉｎｍｕｌｔｉｄｉｍｅｎｓｉｏｎａｌｃａｓｅ .Ｔｈｅｐｒｏｔｏｃｅｌｌｃａｎｂｅｖｉｓｕａｌｉｚｅｄａｓｈａｖｉｎｇａｐｏｒｏｕｓｓｔ…     

THE COUPLING OF NATURAL BOUNDARY ELEMENT AND FINITE ELEMENT METHOD FOR 2D HYPERBOLIC EQUATIONS

In this paper, we investigate the coupling of natural boundary element and finite element methods of exterior initial boundary value problems for hyperbolic equations. The governing equation is first discretized in time, leading to a time-step scheme, where an exterior elliptic problem has to be solved in each time step. Second, a circular artificial boundary FR consisting of a circle of radius R is introduced, the original problem in an unbounded domain is transformed into the nonlocal boundary value problem in abounded subdomain. And the natural integral equation and the Poisson integral formula are obtained in the infinite domainΩ2 outside circle of radius R. The coupled variational formulation is given. Only the function itself, not its normal derivative at artificial boundary ΓR, appears in the variational equation, so that the unknown numbers are reducedand the boundary element stiffness matrix has a few different elements. Such a coupled method is superior to the one based on direct boundary element method. This paper discusses finite element discretization for variational problem and its corresponding numerical technique, and the convergence for the numerical solutions. Finally, the numerical example is presented to illustrate feasibility and efficiency of this method.     

风冷热泵冷热水机组动态过程仿真

本文给出了风冷热泵冷热水机组动态过程模型。系统的高、低压段被分成制冷剂侧、管壁、以及水或空气侧三个控制容积。针对每个控制容积建立了质量和能量平衡的微分方程。由于压缩机、热力膨胀阀阀体、以及四通换向阀具有较小的热惯性,因而采用稳态模型描述压缩过程、膨胀过程、以及内泄露过程。膨胀阀感温包中的制冷剂温度对于蒸发器出口温度的延迟用一阶惯性环节来描述。通过“预测-校正”和“自适应步长”方法实现系统仿真。仿真结果与测试数据吻合良好。     

极低硫钢的精炼脱硫动力学模型

通过对影响脱硫反应限制性环节的分析,将持续接触和瞬时接触两种反应模式综合考虑,建立了精炼脱硫动力学模型,并通过实验室"极低硫钢精炼脱硫"实验数据对模型进行验证.结果表明,本模型的预测结果与实验结果比较吻合.     

Constructing Solutions of an Ill-Posed Nonlinear Singularly Perturbed Problem for an Equation of Elliptic Type

Mathematical Notes -     

Existence and boundary behavior for singular nonlinear differential equations with arbitrary boundary conditions

Existence theory is developed for the equation ?(u)=F(u), where ? is a formally self-adjoint singular second-order differential expression and F is nonlinear. The problem is treated in a Hilbert space and we do not require the operators induced by ? to have completely continuous resolvents. Nonlinear boundary conditions are allowed. Also, F is assumed to be weakly continuous and monotone at one point. Boundary behavior of functions associated with the domains of definitions of the operators associated with ? in the singular case is investigated. A special class of self-adjoint operators associated with ? is obtained.     

EXISTENCE AND UNIQUENESS OF THE SOLUTION FOR NONLINEAR THIRD-ORDER ROBIN BOUNDARY VALUE PROBLEM WITH A TURNING POINT

The paper aims to obtain existence and uniqueness of the solution as well as asymptotic estimate of the solution for singularly perturbed nonlinear third- order Robin boundary value problem with a turning point.In order to achieve this aim,existence and uniqueness of the solution for third-order nonlinear Robin boundary value problem is derived first based on the upper and lower solutions method under relatively weaker conditions.In this manner,the goal of this paper is gained by applying the existence and uniqueness results mentioned above.