超连续Domain与拟超连续Domian

讨论了超连续domain与拟超连续domain的相关性质,证明了超连续半格范畴为有性质M*的拟超连续domain范畴的反射子范畴。     

导算子连续和一致连续的充要条件

专著[1]论及导算子连续和一致连续的充要条件,给出过于下的定理。 设T_r={x|‖x-x_o‖0)有界.(见[1]36面定理3.8) 本文改进了以上结果。     

单子理论对拓扑等度连续与均匀连续的刻画及其应用

在扩大模型下,应用单子理论给出了拓扑等度连续和均匀连续的非标准刻画,并应用均匀连续的非标准特征证明了网收敛与均匀连续之间的关系,最后应用拓扑等度连续和均匀连续的非标准特征证明了拓扑等度连续和均匀连续之间的关系.     

I-fuzzy拓扑中的几乎连续与δ-连续

在I-fuzzy拓扑空间框架下引入了I-fuzzy正则开集、I-fuzzyδ-开集等基本概念,进一步,在此基础上又给出了I-fuzzy几乎连续、I-fuzzyδ-连续的概念,且分别研究了I-fuzzy几乎连续、I-fuzzyδ-连续的基本性质.     

连续信息代数

给出基于自由域信息代数和带论域信息代数上的连续性概念.证明在城集格有最大元的情况下,两种连续性之间是相互对应的.定义了连续信息代数之间的连续映射的概念,证得:若(φ,D),(ψ,E)都是强连续的信息代数.则([φ→ψ]c,D×E)也是强连续的.     

关于左连续蕴涵算子的连续逼近问题

从阿基米德型t-范定义的剩余型蕴涵算子是连续的蕴涵算子出发，研究关于左连续的蕴涵算子Ro和Godel蕴涵算子心'的连续逼近问题，从而进一步为模糊推理寻求理论基础。     

Wm2(Rn)中连续泛函及连续算子的神经网络逼近

本文主要讨论定义在Sobolev空间W2^m(R^n)中紧集上连续泛函及连续算子的逼近。     

交C-连续偏序集

利用偏序集上的半拓扑结构,引入了交C-连续偏序集概念,探讨了交C-连续偏序集的性质、刻画及与C-连续偏序集、拟C-连续偏序集等之间的关系.主要结果有:(1)交C-连续的格一定是分配格;(2)有界完备偏序集(简记为bc-poset)L是交C-连续的当且仅当对任意x∈L及非空Scott闭集S,当∨S存在时有x∧∨S=∨{x∧s:s∈S};(3)完备格是完备Heyting代数当且仅当它是交连续且交C-连续的;(4)有界完备偏序集是C-连续的当且仅当它是交C-连续且拟C-连续的;(5)获得了反例说明分配的完备格可以不是交C-连续格,交C-连续格也可以不是交连续格.     

相容连续Domain的不变性

引入了Scott相容连续映射与商相容Domain等概念,研究了Scott相容连续映射保局部基与保waybelow序及保局部基与保紧元之间的关系,证明了相容连续Domain或相容代数Domain在保局部基的Scott相容连续满映射下保持不变.     

ZC-连续格

对于广义理想子集系统Z,引入ZC-连续格和ZC-代数格的概念,讨论它们的一些性质。特别地,证明当ZC-连续格P中的关系Z满足插入性质时,P可嵌入到方体中。     

带有免疫和传染年龄的传染病模型

建立了带有免疫和传染年龄的传染病模型,这种传染病带有病原体Ⅰ或Ⅱ,病原体Ⅰ可发展为病原体Ⅱ,得到了无病平衡态全局稳定和局部稳定的条件.当病原体Ⅰ不发展为病原体Ⅱ时,得到了病原体Ⅰ类平衡态的稳定性依赖于病原体Ⅱ类的基本再生指数.     

Creep of polymer concrete in the nonlinear region

Two polyester-based polymer concretes with various volume content of diabase as an extender and aggregate are tested in creep under compression at different stress levels. The phenomenological and structural approaches are both used to analyze the experimental data. Common features of changes in the instantaneous and creep compliances are clarified, and a phenomenological creep model which accounts for the changes in the instantaneous compliance and in the retardation spectrum depending on the stress level is developed. It is shown that the model can be used to describe the experimental results of stress relaxation and creep under repeated loading. Modeling of the composite structure and subsequent solution of the optimization problem confirm the possibility of the existence of an interphase layer more compliant than the binder. A direct correlation between the interphase volume content and the instantaneous compliance of the composite is revealed. It is found that the distinction in nonlinearity of the viscoelastic behavior of the two polymer concretes under investigation can be due to the difference in their porosity. Submitted to the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000.) Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 2, pp. 147–164, 2000.     

Modelling and simulation of micro-well formation

Physico-chemical processes on the micro-scale require new modelling concepts because some effects become dominating that are negligible for macroscopic systems. This is illustrated by a new method for the production of micro-wells based on the placement of a small drop of toluene on a plate of polystyrene. After droplet evaporation, a micro-well is left. A mathematical model has been developed to understand the elementary processes of the micro-well formation. The model accounts for: (1) growth of the drop on the substrate, (2) evaporation process of the solvent, (3) dissolution of the substrate, (4) flow rate in the evaporating drop caused by the pinning effect, including the vertical velocity profile, and (5) increase in the concentration of dissolved material followed by precipitation. In the modelling and simulation process, it could be shown that the method of drop production also has a significant influence on the shape of the micro-wells.     

A perturbed risk model with dependence between premium rates and claim sizes

This paper considers a dependent risk model with diffusion for the surplus of an insurer, in which a current premium rate will be adjusted after a claim occurs and the adjusted rate is determined by the amount of the claim. At the same time, the diffusion is changed correspondingly. Using Rouché’s theorem, we first derive the closed-form solution for the Laplace transform of the survival probability in the dependent risk model. Then, using the Laplace transform, we derive a defective renewal equation satisfied by the survival probability. For the exponential claim sizes, we present the explicit recursion expression for the survival probability, by which we can exactly solve the survival probability step-by-step. We also illustrate the influence of the model parameters in the dependent risk model on the survival probability by numerical examples.     

Multi‐dimensional Lotka–Volterra systems for carcinogenesis mutations

In the paper we consider three classes of models describing carcinogenesis mutations. Every considered model is described by the system of (n+1) equations, and in each class three models are studied: the first is expressed as a system of ordinary differential equations (ODEs), the second—as a system of reaction–diffusion equations (RDEs) with the same kinetics as the first one and with the Neumann boundary conditions, while the third is also described by the system of RDEs but with the Dirichlet boundary conditions. The models are formulated on the basis of the Lotka–Volterra systems (food chains and competition systems) and in the case of RDEs the linear diffusion is considered. The differences between studied classes of models are expressed by the kinetic functions, namely by the form of kinetic function for the last variable, which reflects the dynamics of malignant cells (that is the last stage of mutations). In the first class the models are described by the typical food chain with favourable unbounded environment for the last stage, in the second one—the last equation expresses competition between the pre‐malignant and malignant cells and the environment is also unbounded, while for the third one—it is expressed by predation term but the environment is unfavourable. The properties of the systems in each class are studied and compared. It occurs that the behaviour of solutions to the systems of ODEs and RDEs with the Neumann boundary conditions is similar in each class; i.e. it does not depend on diffusion coefficients, but strongly depends on the class of models. On the other hand, in the case of the Dirichlet boundary conditions this behaviour is related to the magnitude of diffusion coefficients. For sufficiently large diffusion coefficients it is similar independently of the class of models, i.e. the trivial solution that is unstable for zero diffusion gains stability. Copyright © 2009 John Wiley & Sons, Ltd.     

A necessary and sufficient condition for the existence of an exponential attractor

We give a necessary and sufficient condition for the existence of an exponential attractor. The condition is formulated in the context of metric spaces. It also captures the quantitative properties of the attractor, i.e., the dimension and the rate of attraction. As an application, we show that the evolution operator for the wave equation with nonlinear damping has an exponential attractor.     

ON NEWMAN-TYPE RATIONAL INTERPOLATION TO ｜x｜ AT THE CHEBYSHEV NODES OF THE SECOND KIND

Recently Brutman and Passow considered Newman-type rational interpolation to ｜x｜ induced by arbitrary set of symmetric nodes in [-1,1] and gave the general estimation of the approximation error.By their methods one could establish the exact order of approximation for some special nodes. In the present paper we consider the special case where the interpolation nodes are the zeros of the Chebyshev polynomial of the second kind and prove that in this case the exact order of approximation is O（1/n｜nn）     

面向远海岛屿的救助基地选址优化模型及其算法

为解决在远海海域选择岛屿建设救助基地的方案优化问题,建立了基于GIS和智能算法的双目标优化模型,采用自适应拉伸的拥挤距离计算公式,设计了自适应精英保留策略对算法进行改进,通过剖析决策者选择最优方案的基本原则,得到了性价比最高的优化方案。最后,以我国南海南沙群岛选择岛屿建设救助基地的方案优化为例进行分析,得到了较好结果。为验证文中改进算法的有效性,选取多个不同规模的方案进行分析比较,结果显示本文提出的算法在优化结果及解的分布性等方面均更优。本文研究为我国海上岛屿救助基地选址和在资源有限的情况下如何科学配置救助船队提供了分析方法。     

颤振分析中的特征值排序问题

颤振分析中判断颤振临界速度的重要依据是系统V-g和V-f图,即系统特征值随参数的变化曲线.在几乎所有商用软件及自编程序的输出结果中,有时会出现所谓的"窜支"现象,这给颤振临界速度和颤振穿越分支及耦合形式的判断带来很大不便.通过隐函数定理可以证明,除重特征值点以外,系统特征值连续依赖于系统参数变化.依据多元向量值函数连续性,建立对特征值的排列算法,给出系统特征根轨迹的正确曲线,再输出V-g和V-f图数据,从而避免"窜支"现象.编制应用程序,通过几个典型算例对算法进行了验证.该工作能够有效简化颤振分析的后处理工作,提高分析效率.     

Computing a closest bifurcation instability in multidimensional parameter space

Summary Engineering and physical systems are often modeled as nonlinear differential equations with a vector λ of parameters and operated at a stable equilibrium. However, as the parameters λ vary from some nominal value λ₀, the stability of the equilibrium can be lost in a saddle-node or Hopf bifurcation. The spatial relation in parameter space of λ₀ to the critical set of parameters at which the stable equilibrium bifurcates determines the robustness of the system stability to parameter variations and is important in applications. We propose computing a parameter vector λ_* at which the stable equilibrium bifurcates which is locally closest in parameter space to the nominal parameters λ₀. Iterative and direct methods for computing these locally closest bifurcations are described. The methods are extensions of standard, one-parameter methods of computing bifurcations and are based on formulas for the normal vector to hypersurfaces of the bifurcation set. Conditions on the hypersurface curvature are given to ensure the local convergence of the iterative method and the regularity of solutions of the direct method. Formulas are derived for the curvature of the saddle node bifurcation set. The methods are extended to transcritical and pitchfork bifurcations and parametrized maps, and the sensitivity to λ₀ of the distance to a closest bifurcation is derived. The application of the methods is illustrated by computing the proximity to the closest voltage collapse instability of a simple electric power system.