一类带积分边界条件的弹性梁微分方程边值问题正解的存在性和唯一性（英文）

本文主要研究一类带积分边界条件的四阶弹性梁微分方程边值问题正解的存在性和唯一性,通过广义凹算子不动点定理获得边值问题正解的存在性和唯一性,最后给出一个例子.     

一类高阶中立型微分方程的最终正解的存在性

研究了一类高阶中立型泛函微分方程的最终正解的存在性,获得了其存在最终正解的充要条件.     

β-内酰胺类抗生素/β-内酰胺酶抑制剂合剂临床应用专家共识

本文讨论一类非线性分数阶微分方程积分边值问题正解的存在性.借助于Green函数有关的不等式,通过Krasnoselskii-Zabreiko不动点定理获得该问题正解的存在性结果,并在非线性项无穷远处次线性增长的情况下给出解的迭代序列.     

一类带有p-Laplacian算子的分数阶积分边值问题的正解与逐次迭代方法

本文研究一类带有p-Laplacian算子并且非线性项f中含有分数阶导数项的分数阶微分方程边值问题的正解的存在性.通过构造上解和下解并利用单调迭代方法,获得该边值问题存在正解的充分条件,并给出一个具体的例子作为应用.     

一类分数阶微分方程m点边值问题正解的存在性

给出了一类分数阶微分方程m点边值问题的格林函数,通过讨论其性质,运用uo有界算子和不动点指数理论,在与相应的线性算子第一特征值有关的条件下获得了分数阶微分方程多点边值问题正解及多个正解的存在性结果.     

具变号非线性项三阶多点边值问题的正解与多个正解

本文研究了一类非线性项变号的三阶常微分方程多点边值问题正解存在性问题.利用Banach空间锥上不动点定理及非线性泛函分析方法,获得了该问题正解的存在性结论.推广了已有文献的结果.     

一类非线性共形分数阶微分方程的边值问题和脉冲初值问题（英文）

本文研究一类非线性共形分数阶微分方程的边值问题和脉冲初值问题,利用基于锥理论的和型算子不动点定理和混合单调算子不动点定理,获得共形分数阶微分方程边值问题和脉冲初值问题正解的存在性和唯一性定理,并且得到一组可以逼近唯一正解的单调迭代序列,最后给出一个实例用来验证结论的有效性.     

一类含积分边界条件的分数阶微分方程的正解的存在性北大核心CSCD

本文研究了一类含积分边界条件的分数阶微分方程的边值问题,利用格林函数的性质和Krasnoselskii不动点定理,得到了至少有一个,两个正解存在以及正解不存在的充分条件.     

一类带p-Laplacian算子分数阶微分方程边值问题的正解

本文应用凸锥上的不动点定理,讨论了一类带p-Laplacian算子分数阶微分方程边值问题的正解的存在性,分别得到了这类边值问题至少存在一个正解和多个正解的充分条件.最后,给出了两个具体的例子.     

一类带有偏差量及两个参数的非线性分数阶积分边值问题的正解及其性质

本文研究一类分数阶非线性微分方程边值问题,其中微分方程里含有一个偏差量和一个参数,且边界条件中含有一个非线性积分项及一个扰动参数.利用锥理论及带有参数的算子不动点定理获得了该边值问题存在唯一正解的充分条件,并讨论了唯一正解对参数的连续依赖性.作为应用,给出一个具体的例子.     

Complete monotonicity of a function involving the divided difference of digamma functions

In the paper, necessary and sufficient conditions are provided for a function involving the divided difference of two psi functions to be completely monotonic. Consequently, a class of inequalities for sums are presented, the logarithmically complete monotonicity of a function involving the ratio of two gamma functions are derived, and two double inequalities for bounding the ratio of two gamma functions are discovered.     

Tensor conditions for the existence of a common solution to the Lyapunov equation

Necessary and sufficient conditions for the existence of a common solution to the Lyapunov equation for two stable complex matrices are derived. These conditions are applied to the cases when a common weak solution to the Lyapunov equation exists. Conditions for the existence of a common solution to the Lyapunov equation for two complex 2 × 2 and two complex 3 × 3 matrices are derived.     

模糊数四则运算的交点-间断点法

对模糊数的四则运算提出了一种交点-间断点法:将模糊数的加法、减法和除法运算,化为求两个函数在某区间上其交点处的值;当交点不存在且两函数在该区间上的间断点为有限个时,将其运算化为求一函数在这些间断点处及区间的两端点处的最大值;将模糊数的乘法运算,化为用交点法或间断点法分别在两个区间上求出相应的值,然后取它们中最大者。     

The Gerber-Shiu penalty functions for two classes of renewal risk processes

In this paper, we study the Gerber-Shiu functions for a risk model with two independent classes of risks. We suppose that both of the two claim number processes are renewal processes with phase-type inter-claim times. By re-composing and analyzing the Markov chains associated with two given phase-type distributions, we obtain systems of integro-differential equations for two types of Gerber-Shiu functions. Explicit expressions for the Laplace transforms of the two types of Gerber-Shiu functions are established, respectively. And explicit results for the Gerber-Shiu functions are derived when the initial surplus is zero and when the two claim amount distributions are both from the rational family. Finally, an example is considered to illustrate the applicability of our main results.     

关于两个伪硬币问题的一些新结果

下面的问题被称为n个外观不可区分硬币的分组测试问题,每个硬币可以是伪硬币或是标准硬币.本文所涉及的问题是:已知一个由n个硬币组成的集合中有两个伪(较重的)硬币,用一台天平以最小的称重次数,从这n个硬币组成的集合中探测出两个伪(较重的)硬币. 我们构造了找出两个伪(较重的)硬币的两个算法,并且这两个算法是最优的.     

Existence of solutions of two generalized riccati operator equations and their representation

The solutions of two generalized Riccati operator equations are discussed in terms of two critical parameter values, which are related to the application of optimal control under unknown disturbances. Explicit formulas for calculating these two critical parameters as well as the closedform solutions of these two generalized Riccati operator equations are given. The connection between these two parameters and a zero-sum differential game is also investigated.     

Optimal design of elastic structures for multipurpose loading

The optimal design of elastic beams subjected to two alternative loading systems is considered for compliance constraints and a minimum-cross-section constraint. Sufficient conditions for optimality are established, and a technique for determining the optimal design is presented. Two examples are given. Generalizations to more than two loading systems and more complex structures are straightforward.     

THE CLASSIFICATION AND PERIOD OF STATES FOR MARKOV CHAIN IN RANDOM ENVIRONMENT

This paper is a continuation of [8]. In Section 1, three kinds of communication are introdnced for two states and the relations among them are investigated. In Section 2, two kinds of period of a state are introdnced and it is obtained that the period is a “class property” ,i.e. two states x and y belong to same class implies the period of x is equal to the period of y.     

Fourier transform of symmetric gauss measures on the Heisenberg group

An explicit form is derived for the Fourier transform of symmetric Gauss measures on the Heisenberg group at the Schrödinger representation. Using this explicit formula, necessary and sufficient conditions are given for the convolution of two symmetric Gauss measures to be a symmetric Gauss measure and for commutability of two symmetric Gauss measures. Moreover, necessary and sufficient conditions are presented for the convolution of two symmetric Gauss convolution semigroups to be a convolution semigroup.     

Robust synchronization of singular complex switched networks with parametric uncertainties and unknown coupling topologies via impulsive control

This paper presents a general model of singular complex switched networks, in which the nodes can be singular dynamic systems and switching behaviors act on both nodes and edges. The parametric uncertainties and unknown coupling topologies are also considered in this model. Two robust synchronization schemes are discussed respectively. In one scheme, the network is synchronized to a homogeneous orbit and in the other one the network is synchronized to a weighted average of all the nodes. Based on the Lyapunov stability theory, different robust synchronization conditions for the two schemes are obtained for this singular complex switched network model via impulsive control. The similarities and differences between these synchronization conditions for the two schemes are discussed. In addition, three useful robust results for the special cases of the singular complex switched networks are presented. Two systematic-design procedures are presented for the two schemes, and three numerical examples are provided for illustrations.