关于复归一化反射系数不变性定理

本文通过对给定阻抗的Darlington等效网络的单位归一化散射矩阵的研究,提出了一个n端口网络对n个非Foster正实阻抗复归一化散射矩阵和其增广网络单位归一化散射矩阵之间的关系,这里Darlington等效网络是互易的,也可以是非互易的。从而进一步证明了Carlin-Yarman复归一化反射系数不变性定理是不正确的。

集值严格Φ-压缩映象的一致极限场的区域不变性定理及其满射性定理

本文是[1]的继续。借助[4,5]的方法,证明了一致极限场的区域不变性定理和满射性定理,改进和推广了[2,3]中相应的某些结果。

论参数曲线曲面的几何不变性

本文在揭示一般参数曲线、曲面总可以采用完全或部分规范基函数表示的基础上,给出了几何不变性定理:空间参数曲线、平面参数曲线、参数曲面经过与坐标系的相对运动后,形状保持不变,且其完全或部分规范基函数表示不变。并介绍了几何不变性在计算机辅助几何设计(CAGD)与计算机绘图中的应用及一些实例。

一类两点边值问题的可解性

本文研究了一类半线性二阶常微分方程的两点边值问题的可解性。利用 Leray- Schauder度的同伦不变性定理 。

一类非线性常微分方程边值问题解的存在性

在假设一类常微分方程边值问题中的非线性项有界的条件下,运用同伦映射不变性定理,得出了解的存在性结论。当非线性项为零时,边值条件将保证对应问题零解的唯一性,所以,边值条件是特殊的,但非唯一的形式。所采用的方法也适用于某些高阶常微分方程边值问题的解的存在性的研究。

流形的维数浅谈

微分流形是数学领域中的一个重要分支,也是研究数学的重要基础和工具。它的诞生,给数学物理开辟了广阔的前景。因此,我们有必要学习微分流形,有必要掌握流形的概念及性质,本文就流形中的维数作一点浅析。

Fluid–solid coupling analysis of rock pillar stability for concealed karst cave ahead of a roadway based on catastrophic theory

In order to study the mechanism of water inrush from a concealed, confined karst cave, we established a fluid–solid coupling model of water inrush from a concealed karst cave ahead of a roadway and a strength reduction method in a rock pillar for preventing water inrush based on catastrophic theory. Fluid–solid coupling effects and safety margins in a rock pillar were studied. Analysis shows that rock pillar instability, exerted by disturbance stress and seepage stress, is the process of rock pillar catastrophic destabilization induced by nonlinear extension of plastic zones in the rock pillar. Seepage flow emerges in the rock pillar for preventing water inrush, accompanied by mechanical instability of the rock pillar. Taking the accident of a confined karst cave water-inrush of Qiyi Mine as an example, by studying the safety factor of the rock pillar and the relationship between karst cave water pressure and thickness of the rock pillar,it is proposed that rock pillar thickness with a safety factor equal to 1.5 is regarded as the calculated safety thickness of the rock pillar, which should be equal to the sum of the blasthole depth, blasting disturbance depth and the calculated safety thickness of the rock pillar. The cause of the karst water inrush at Qiyi Mine is that the rock pillar was so small that it did not possess a safety margin. Combining fluid–solid coupling theory, catastrophic theory and strength reduction method to study the nonlinear mechanical response of complicated rock engineering, new avenues for quantitative analysis of rock engineering stability evaluation should be forthcoming.

内P-反动态信息特征与信息恢复

P-集合(packet sets)是一个动态模型,P-集合是由内P-集合x^F(internal packet set X^F)与外P-集合XF(~Fouter packet set X^F)构成的元素集合对;或者(X^F,X^F)是P-集合.利用内P-集合的结构,给出内P-信息,内P-反动态信息,信息的内P-反动态恢复概念,给出内P-反动态信息的属性合取收缩生成,给出内P-反动态信息与内P-信息同属性定理,给出内P-反动态信息存在与属性合取范式定理,给出信息的内P-反动态恢复属性定理.这些基本理论结果是把内P-集合与一类信息系统故障状态识别交叉,渗透研究得到的.

HEAT KERNEL AND HARDY'S THEOREM FOR JACOBI TRANSFORM

In this paper, the authors obtain sharp upper and lower bounds for the heat kernel associatedwith Jacobi transform, and get some analogues of Hardy's Theorem for Jacobi transform byusing the sharp estimate of the heat kernel.

HILBERTIAN INVARIANCE PRINCIPLE FOR EMPIRICAL PROCESS ASSOCIATED WITH A MARKOV PROCESS

The authors establish the Hilbertian invariance principle for the empirical process of astationary Markov process, by extending the forward-backward martingale decomposition ofLyons-Meyer-Zheng to the Hilbert space valued additive functionals associated with generalnon-reversible Markov processes.

SOLVABILITY OF VECTOR KY FAN INEQUALITIES WITH APPLICATIONS

This paper aims to study the solvability of vector Ky Fan inequalities and the compactness of its solution sets.For vector-valued functions with the cone semicontinuity and the cone quasiconvexity in infinite dimensional spaces,the authors prove some existence results of the solutions and the compactness of the solution sets.Especially,some results for the vector Ky Fan inequalities on noncompact sets are built and the compactness of its solution sets are also discussed.As applications,some existence theorems of the solutions of vector variational inequalities are obtained.

Global properties of nonlinear humoral immunity viral infection models

In this paper, we consider two nonlinear models for viral infection with humoraL immu- nity. The first model contains four compartments; uninfected target cells, actively infected cells, free virus particles and B cells. The second model is a modification of the first one by including the latently infected cells. The incidence rate, removal rate of infected cells, production rate of viruses and the latent-to-active conversion rate are given by more general nonlinear functions. We have established a set of conditions on these general functions and determined two threshold parameters for each model which are sufficient to determine the global dynamics of the models. The global asymptotic stability of all equilibria of the models has been proven by using Lyapunov theory and applying LaSalle＇s invariance principle. We have performed some numerical simulations for the models with specific forms of the general functions. We have shown that, the numerical results are consistent with the theoretical results.

Stability and Hopf bifurcation for a logistic SIR model with a stage -- Structure

A SIR model of epidemiological dynamics with stage-structure and a type of nonlinear incidence rate is considered under the assumption that the susceptible individual satisfy the logistic equation. The global attractivity of the model is studied using Lyapunov functions and LaSalle＇s invariance principle. By the uniform persistence theories, the permanence of the system and the existence of the positive equilibrium are obtained. Moreover, by the normal form theory and the center manifold presented by Hassard, a stability and Hopf bifurcation analysis of the system around positive equilibrium from a local perspective are performed. Numerical simulation is carried out to illustrate our results.

Unanswered questions in unsaturated soil mechanics

The last two to three decades have seen significant advances in the mechanics of unsaturated soils.It is now widely recognized that the fundamental principles in soil mechanics must cover both saturated and unsaturated soils.Nevertheless,there is still a great deal of uncertainties in the geotechnical community about how soil mechanics principles well-established for saturated soils can be extended to unsaturated soils.There is even wide skepticism about the necessity of such extension in engineering practice.This paper discusses some common pitfalls related to the fundamental principles that govern the volume change,shear strength and hydromechanical behaviour of unsaturated soils.It also attempts to address the issue of engineering relevance of unsaturated soil mechanics.

A smoothing trust region filter algorithm for nonsmooth least squares problems

We propose a smoothing trust region filter algorithm for nonsmooth nonconvex least squares problems. We present convergence theorems of the proposed algorithm to a Clarke stationary point or a global minimizer of the objective function under certain conditions. Preliminary numerical experiments show the efficiency of the proposed algorithm for finding zeros of a system of polynomial equations with high degrees on the sphere and solving differential variational inequalities.

STABILITY OF DISCONTINUOUS NONLINEAR SINGULAR SYSTEMS

This paper studies a class of nonlinear singular systems with discontinuous right-hand sides,it develops nonsmooth Lyapunov stability theory as well as LaSalle invariance principle.In this paper,LaSalle invariance principle of the discontinuous nonlinear singular systems is presented firstly.Furthermore,some sufficient conditions for stability and asymptotic stability of the given systems based on Filippov differential inclusion and Clarke's generalized gradient are given.Finally,these results are illustrated by the given example.

Some Open Problems on Simultaneous Stabilization of Linear Systems

Simultaneous stabilization of linear systems is a fundamental issue in the system and control theory, and is of theoretical and practical significance. In this paper, the authors review the recent research progress and the state-of-art results on simultaneous stabilization of single-input single-output linear time-invariant systems. Especially, the authors list the ever best results on the parameters involved in the well known ＂French Champagne Problem＂ and ＂Belgian Chocolate Problem＂ from the point of view of mathematical theoretical analysis and numerical calculation. And the authors observed that Boston claimed the lower bound of 5 can be enlarged to 0.976461 in 2012 is not accurate. The authors hope it will inspire further study on simultaneous stabilization of several linear systems.