非线性高阶抛物双曲型耦合方程组的第一边界问题

本文研究了一类广义Sine-Gordon型非线性高阶双曲方程组、非线性高阶拟双曲型方程组、非线性高阶拟抛物型方程组以及非线性高阶广义Sehrdinger型方程组的耦合方程组的第一边界问题,作者证明了此耦合方程组第一边界问题的整体广义解和整体古典解的存在性、唯一性和光滑性。     

非线性方程组的一种解法

文中给出了求非线性方程组的一种解法；它找到一个变换，可使原方程组变换成一个新的方程组，通过求变换后方程组的解求得原方程组的解．     

高阶非线性双曲型拋物型耦合方程组的周期边界问题和初值问题

本文研究了广义Sine—Gordon型非线性高阶双曲方程组、高阶非线性拟双曲型方程组、高阶非线性拟抛物型方程组以及高阶非线性Schrodinger型方程组的耦合方程组的周期边界问题和初值问题。证明了此耦合方程组的周期边界问题和初值问题整体广义解和整体古典解的存在性、唯一性和光滑性。     

二阶椭圆型方程组两种分类的等价性

论文讨论了二阶椭圆型方程组的分类的等价性的问题。论文证明了由丁夏畦所定义的强椭圆型方程组是和所定义的 E_2类椭圆型方程组是相互等价的、准椭圆型方程组是和 E_1、E_3类方程组相互等价的。     

形变Boussinesq方程的对称群及其行波解

讨论具有方程组形式的形变Boussinesq方程的对称群及其行波解.通过研究方程组所允许的Lie对称群得到该方程组的解有行波解,并将方程组约化为非线性的常微分方程组,再利用广义-Tanh方法,得到形变Boussinesq方程的行波解.     

神经传导方程组的门槛现象

我们知道,神经传导问题可用非线性方程组即所谓H-H方程组来描述,而作为H-H方程组的简化模型FitzHagh-Nagumo方程组既反映了神经传导问题的基本特性又给数学上的讨论带来了方便,其形式为     

含三角函数的一般形式复杂对偶积分方程组的理论解

本文基于Gopson法，进行研究，改进，推广，应用于一般形式，复杂的对偶积分方程组的求解，首先引入函数进行方程组变换，其次引入未知函数的积分变换实现退耦，应用Abel反演变换，使方程组正则化为Fredholm第二类积分方程组，并由此给出对偶积分方程组的一般性解，本文给出的解法和理论解，可供求解复杂的数学，物理，力学中的混合边值问题参考，选用．同时也提供求解复杂的对偶积分方程组另一种有效的解法。     

拟线性正对称方程组的边值问题及其对混合型方程的应用

<正> 1.引言 本文有两个目的.第一个目的是讨论拟线性正对称方程组的边值问题.如所知,线性的正对称方程组是一类相当广泛的偏微分方程组,许多常见的偏微分方程都可以化为正对称方程组去.对于这个方程组,可以利用能量不等式来证明许多边值问题的适定性.本文充分利用线性正对称方程组的结果,经过适当的估计,用压缩映照原理证明了拟线性正对称方程组的边值问题的解的存在性.对求解的区域而言,问题是大范围的,但     

旋度与磁场微极流方程的正则性

本文研究了速度场的旋度与三维磁场微极流方程组光滑解的整体存在性之间的关系,将Constantin与Fefferman关于Navier-Stokes方程组的成果推广到了一个相当完备的不可压缩流体方程组系统,使得相应的结果在微极流方程组以及MHD方程组中都成立.     

耦合KdV方程组的对称,精确解和守恒律

通过利用修正的CK直接方法建立了耦合KdV方程组的对称群理论.利用对称群理论和耦合KdV方程组的旧解得到了它们的新的精确解.基于上述理论和耦合KdV方程组的共轭方程组的理论,得到了耦合KdV方程组的守恒律.     

非线性退化时滞微分控制系统的函数能控性

本文讨论非线性退化时滞微分控制系统．首先就非线性退化时滞微分控制系统的一阶变分系统给出变易公式,然后就非线性退化时滞微分控制系统的一阶变分系统的函数能控性给出一些判据,最后给出关于非线性退化时滞微分控制系统的函数能控性的判据．     

Phase portraits of separable quadratic systems and a bibliographical survey on quadratic systems

Although planar quadratic differential systems and their applications have been studied in more than one thousand papers, we still have no complete understanding of these systems. In this paper we have two objectives.First we provide a brief bibliographical survey on the main results about quadratic systems. Here we do not consider the applications of these systems to many areas as in Physics, Chemist, Economics, Biology, …Second we characterize the new class of planar separable quadratic polynomial differential systems. For such class of systems we provide the normal forms which contain one parameter, and using the Poincaré compactification and the blow up technique, we prove that there exist 10 non-equivalent topological phase portraits in the Poincaré disc for the separable quadratic polynomial differential systems.     

On common linear copositive Lyapunov functions for pairs of stable positive linear systems

We study the common linear copositive Lyapunov functions of positive linear systems. Firstly, we present a theorem on pairs of second order positive linear systems, and give another proof of this theorem by means of properties of geometry. Based on the process of the proof, we extended the results to a finite number of second order positive linear systems. Then we extend this result to third order systems. Finally, for higher order systems, we give some results on common linear copositive Lyapunov functions.     

线性连续衰退记忆系统的可分性

为逼近建模和辨识问题的需要,讨论线性时变连续有界输入有界输出稳定衰退记忆系统的不同子类．从衰退记忆系统的子类包括概周期系统,渐近周期系统,渐近强周期系统,找到了LTV系统的可分子空间即渐近强周期系统．     

THE V-FUNCTIONAL METHOD FOR THE STABILITY OF DEGENERATE DIFFERENTIAL SYSTEMS WITH DELAYS

1 IntroductionStability is an important perfermance index of concrete systems such asmanagement systems, power systems, engineering systems and so on. Forthe stability V--functional criterion method of functional differential systems,have had many results in recent years, see) for example, [1] and [2]. Andfor degenerate systems, papers [41-[81 have carefully discussed and given someimportant results. But we note that (see [9]) many concrete systems, besidescontain delay, are degenerate. So, f…     

非线性系统的线性对称结构

非线性系统的线性对称结构洪奕光，程代展（中国科学院系统科学研究所，北京１０００８０）１９９１年１２月２０日收到．１９９３年９月１６日收到压缩稿，一、引言近年来，人们对非线性控制系统对称性问题的研究很感兴趣．这主要是因为现实世界存在着大量的对称现象，而...     

对角形拟线性椭圆方程组的一般特征问题

本文对拟线性椭圆方程组的一般特征问题得到极小解在L∞中的界,并利用变分方法证明了它的极小解的存在性.     

On the equivalence of differential systems

In this article. First, we construct some nonlinear differential systems which are equivalent to some known systems. Second, we discuss, in a different method, the equivalence between some linear differential systems. And then we apply the obtained results to the study of the qualitative properties of these systems simultaneously.     

Hypercomplex analysis and integration of systems of ordinary differential equations

We review the theory of hypercomplex numbers and hypercomplex analysis with the ultimate goal of applying them to issues related to the integration of systems of ordinary differential equations (ODEs). We introduce the notion of hypercomplexification, which allows the lifting of some results known for scalar ODEs to systems of ODEs. In particular, we provide another approach to the construction of superposition laws for some Riccati‐type systems, we obtain invariants of Abel‐type systems, we derive integrable Ermakov systems through hypercomplexification, we address the problem of linearization by hypercomplexification, and we provide a solution to the inverse problem of the calculus of variations for some systems of ODEs. Copyright © 2016 John Wiley & Sons, Ltd.     

A survey on piecewise-linear models of regulatory dynamical systems

Recent developments in understanding the various regulatory systems, especially the developments in biology and genomics, stimulated an interest in modelling such systems. Hybrid systems, originally developed for process control applications, provide advances in modelling such systems. A particular class of hybrid systems which are relatively simpler to analyze mathematically but still capable of demonstrating the essential features of many non-linear dynamical systems is piecewise-linear systems. Implementation of piecewise-linear systems for modelling of regulatory dynamical systems requires different considerations depending on the status of the problem. In this work we considered three different cases. Firstly, we consider the inferential modelling problem based on the empirical observations and study the discrete piecewise-linear system, whose inverse problem is solvable under some assumptions. Secondly, we considered the problem of obtaining some complex regulatory systems by tractable piecewise-linear formulations and study the qualitative dynamic features of the systems and their piecewise-linear models. Finally, we considered Boolean delay equations for building abstract models of regulatory systems, which might be the simplest models demonstrating the essential qualitative features of our interest underlying adaption, learning and memorization.