关于Schur-Frobenius求逆公式的一般化

对于（１，…，ｉ）－逆诸情形，本文证得了非交换主理想整环Ｒ上分块矩阵的Ｓｃｈｕｒ－Ｆｒｏｂｅｎｉｕｓ求逆公式的一般化定理，进而将广义Ｓｃｈｕｒ补的Ｈａｙｎｓｗｏｒｔｈ商公式开拓到Ｒ上     

一般化合成模糊对策的势指标

定义了一种新的合成模糊对策模型，我们称之为一般化合成模糊对策模型．并研究了这种模型的Shapley值和Banzhaf-Coleman势指标。     

交通分配模型的经济学含义及模型的扩展

本文首先分析了各类交通分配模型依赖的经济学理论和概念．然后应用宏观经济学非瓦尔拉斯均衡理论对模型进行了一般化扩展，最后利用扩展模型进行了数例演算     

“调配问题”的动态规划模型与计算

本给出了调配问题的动态规划模型与计算,该表征更具一般化,且便于计算机计算。     

考虑利率因素的保险破产模型研究

本文首先介绍了在一般化破产模型基础上够造的保险费收取次数为Poisson过程的破产模型,并进一步在此模型上考虑了利率因素,使得相应的破产概率更具有实际意义。     

缠绕方程和DNA模型

一般化了DNA重组的缠绕模型的缠绕方程的求解方法, 同时利用有理缠绕和二桥纽结 的关系给出了某些缠绕方程的解.     

流水中重物运动过程的数学建模与分析

围绕与封堵溃口有关的重物落水后的运动问题,通过分析落水重物的受力,确定了影响其在水中运动的主要因素.建立了大实心方砖落水后竖直位移-时间、水平位移-时间的运动模型.在此基础上,通过建立包含形状因素的水流力系数模型,将各种形状试件折算为球体,建立了适应不同情况的描述重物水中运动过程的一般化模型,并对一般化模型进行合理性检验和误差分析.结合建立的模型,提出了"最有效位置触底"的猜想以及需要进行的验证试验.最后,结合相似性理论对模型进行了推广.     

一般化凸空间上的一个连续选择定理(英文)

本文研究一般化凸空间上的连续选择定理.利用在D■X的条件下,一般化凸空间(X,D;Γ)上Γ-凸子集的概念,得到了两类一般化凸空间之间,以及φ映射和Γ-凸映射之间的关系,并且得到了一个连续选择定理.本文推广了一般化凸空间上凸子集的概念.     

产出为Cobb-Dauglas函数的 Holmstrom-Milgrom委托代理模型

Holmstrom-Milgrom模型是在委托代理理论一般化模型的基础上提出的一个简化模型,引入代理人的能力水平,将产出函数从一维的线性函数扩展到二维的非线性Cobb-Dauglas生产函数,分析求解了新的模型.与原模型相比,新的最优解中代理人的努力程度有所提高,风险成本有所降低,委托人的期望收益有所改善.     

基于RBC模型的动态随机一般均衡的数值解

以一般均衡为框架,引入随机变量的动态随机一般均衡系统,由于模型的庞大和函数形式的复杂,往往不能给出明确的数值解.本文给出几种操作性强的、有效的寻求一般化模型数值解的方法,并通过介绍模型参数确定的办法,使得理论的模型有了现实的含义.     

EXISTENCE AND ATTRACTIVITY OF k-ALMOST AUTOMORPHIC SEQUENCE SOLUTION OF A MODEL OF CELLULAR NEURAL NETWORKS WITH DELAY

In this paper we discuss the existence and global attractivity of k-almost automorphic sequence solution of a model of cellular neural networks.We consider the corresponding difference equation analogue of the model system using suitable discretization method and obtain certain conditions for the existence of solution.Almost automorphic function is a good generalization of almost periodic function.This is the first paper considering such solutions of the neural networks.     

ON SOLVABILITY OF A BOUNDARY VALUE PROBLEM FOR A NONHOMOGENEOUS BIHARMONIC EQUATION WITH A BOUNDARY OPERATOR OF A FRACTIONAL ORDER

This paper is concerned with the solvability of a boundary value problem for a nonhomogeneous biharmonic equation. The boundary data is determined by a differential operator of fractional order in the Riemann-Liouville sense. The considered problem is a generalization of the known Dirichlet and Neumann problems.     

Equivalence group of a fourth-order evolution equation unifying various non-linear models

A fourth-order non-linear evolutionary partial differential equation containing several arbitrary functions of the dependent variable is considered. This equation arises as a generalization of various non-linear models describing a non-linear heat diffusion, the dynamics of thin liquid films, etc. Equivalence transformations give more flexibility to the unified model. We determine the generators of the equivalence group and use them for specifying certain types of arbitrary functions when the model equation has additional symmetries, and hence admits non-trivial group invariant solutions.     

粘弹性厚板的动力方程

本文导出了一般粘弹性厚板含剪切、挤压和转动惯性效应的动力方程,它是弹性厚板动力方程的推广.据此方程还可退化得到若干种类型的中厚度粘弹性板的动力方程.     

On a boundary value problem for a p‐Dirac equation

The p‐Laplace equation is a nonlinear generalization of the Laplace equation. This generalization is often used as a model problem for special types of nonlinearities. The p‐Laplace equation can be seen as a bridge between very general nonlinear equations and the linear Laplace equation. The aim of this paper is to solve the p‐Laplace equation for 1 < p < 2 and to find strong solutions. The idea is to apply a hypercomplex integral operator and spatial function theoretic methods to transform the p‐Laplace equation into the p‐Dirac equation. This equation will be solved iteratively by using a fixed‐point theorem. Applying operator‐theoretical methods for the p‐Dirac equation and p‐Laplace equation, the existence and uniqueness of solutions in certain Sobolev spaces will be proved. Copyright © 2016 John Wiley & Sons, Ltd.     

Connection between an Exactly Solvable Stochastic Optimal Control Problem and a Nonlinear Reaction-Diffusion Equation

We present an exactly soluble optimal stochastic control problem involving a diffusive two-states random evolution process and connect it to a nonlinear reaction-diffusion type of equation by using the technique of logarithmic transformations. The work generalizes the recently established connection between the non-linear Boltzmann-like equations introduced by Ruijgrok and Wu and the optimal control of a two-states random evolution process. In the sense of this generalization, the nonlinear reaction-diffusion equation is identified as the natural diffusive generalization of the Ruijgrok–Wu and Boltzmann model.     

FRACTIONAL DIFFUSION EQUATIONS WITH INTERNAL DEGREES OF FREEDOM

We present a generalization of the linear one-dimensional diffusion equation by com-bining the fractional derivatives and the internal degrees of freedom. The solutions areconstructed from those of the scalar fractional diffusion equation. We analyze the in-terpolation between the standard diffusion and wave equations defined by the fractionalderivatives. Our main result is that we can define a diffusion process depending on theinternal degrees of freedom associated to the system.     

THE COMPARISON OF GREEN FUNCTION FOR QUASI-LINEAR ELLIPTIC EQUATION

A generalization of the usual Green function to a kind of nonlinear elliptic equation of divergence form is discussed. The regularity and comparison principle of Green function in the sense of distribution are shown.     

一类Riccati方程的推广

把 Riccati方程 y′=Py2 + Qy+ R推广成 Riccati型方程 :f′( y) dydx=Pf 2 ( y) + Qf ( y) + R.并给出其可积的条件及其对应的通积分 .     

Integral transform approach to solving Klein–Gordon equation with variable coefficients

In this paper we describe the integral transform that allows to write solutions of the time‐dependent partial differential equation via solution of a simpler equation. This transform was suggested by the author in the case when the last equation is a wave equation, and then it was used to investigate several well‐known equations such as Tricomi‐type equation, the Klein–Gordon equation in the de Sitter and Einstein‐de Sitter spacetimes. A generalization given in this paper allows us to consider also the Klein–Gordon equations with coefficients depending on the spatial variables.