中心条件推导的间接方法

对于一类多项式系统,给出两类对称条件的推导算法,具体讨论了一类三次系统的中心条件;对于Poincare型系统,给出一类等时中心的充分条件．     

一类时间可逆三次微分系统的代数条件

作者曾给出时间可逆微分系统代数条件推导的算法,并给出了一类时间可逆三次微分系统的系数条件,但其中含有一个实参数.为了消去这个参数,这里使用具有投影性质的三角序列和标准基等消元手段,得到了不含参数的完整代数条件.     

一类五次多项式系统原点等时中心的分析

研究了一类五次系统原点复等时中心的问题.先通过一种最新算法求出了这类五次系统原点的周期常数,从而得到复等时中心的必要条件,并利用一些有效途径证明它们的充分性.这实际上解决了这类五次系统的伴随系统原点等时中心问题与其自身为实系统时鞍点可线性化的问题.     

一类时间可逆三次微分系统的代数条件

作者曾给出时间可逆微分系统代数条件推导的算法,并给出了一类时间可逆三次微分系统的系数条件,但其中含有一个实参数.为了消去这个参数,这里使用具有投影性质的三角序列和标准基等消元手段,得到了不含参数的完整代数条件.     

次线性可逆系统的Aubry-Mather集

通过引进合适的作用-角变量变换并结合新的估计方法,对次线性可逆系统的Poincare映射,应用推广的平面可逆系统的Aubry-Mather定理,在系统光滑性为C~1的情形下,获得了一类次线性可逆系统的Aubry-Mather集存在的充分条件.     

时间可逆系统的等时中心问题

若在中心附近的闭轨线都具有相同的周期,则此中心称为等时中心. 时间可逆多项式系统的等时中心问题是一类公开问题. 为了构造性地解决这一难题,讨论一类范围更广的时间可逆解析动力系统, 给出相应横截交换系统的递推公式,此公式可以用于等时中心条件的推导. 在递推公式的基础上,以吴特征集方法为工具,给出一类时间可逆三次系统具有横截交换系统的充要条件.     

R3中一类四次可逆系统的周期轨与极限环问题

本文研究了R3中一类四次可逆系统及其扰动系统的周期轨与极限环问题,利用Poincáre紧化理论讨论了相关平面系统的定性性质,证明了所考虑的系统存在无穷多对称周期轨的结论.然后借助一系列技巧性变换,并利用平均方法证明了R3中这类四次可逆系统的扰动系统在其某周期轨邻域至少存在两个具有不同稳定性的极限环的结论.     

一类二次可逆系统周期函数的单调性

利用Picard-Fuchs方程,研究了一类二次可逆系统周期函数的单调性问题,获得了在首次积分曲线是亏格1时的二次可逆系统周期函数单调的结论.     

一类五次多项式系统无穷远点等时中心条件与极限环分支

研究一类五次系统无穷远点的中心、拟等时中心条件与极限环分支问题.首先通过同胚变换将系统无穷远点转化成原点,然后求出该原点的前8个奇点量,从而导出无穷远点成为中心和最高阶细焦点的条件,在此基础上给出了五次多项式系统在无穷远点分支出8个极限环的实例.同时通过一种最新算法求出无穷远点为中心时的周期常数,得到了拟等时中心的必要条件,并利用一些有效途径一一证明了条件的充分性.     

可逆系统的KAM定理的一个应用

本文利用可逆系统的KAM定理证明了一类既不保守也不耗散的二阶非线性微分方程解的有界性、不变环面和拟周期解以及次调和解的存在性。     

Charpit System of Partial Differential Equations with Algebraic Constraints

In this paper the Charpit system of partial differential equations with algebraic constraints is considered. So, first the compatibility conditions of a system of algebraic equations and also of the Charpit system of partial differential equations are separately considered. For the combined system of equations of both types sufficient conditions for the existence of a solution are found. They lead to an algorithm for reducing the combined system to a Charpit system of partial differential equations of dimension less than the initial system and without algebraic constraints. Moreover, it is proved that this system identically satisfies the compatibility conditions if so does the initial system.     

Building correct estimation algorithms as a constrained optimization problem

For estimation algorithms, the problem of building correct algorithms by modifying weights of features and weights of objects is examined. Criteria for the possibility to build a correct algorithm are obtained for certain cases. Conditions of the possibility to build a correct algorithm are obtained in terms of solving a constrained optimization problem. An optimization method is proposed. Under these conditions, the proposed method significantly reduces the computational complexity of synthesizing a correct algorithm.     

焦点量算法与中心条件推导

对于一般情形, 基于后继函数法给出焦点量计算的递推公式;基于形式级数法给出焦点量计算和化简的Maple算法;给出了时间可逆条件的推导算法,给出了一类五次系统时间可逆的充要条件.     

A constrained optimization approach to solving certain systems of convex equations

This research presents a new constrained optimization approach for solving systems of nonlinear equations. Particular advantages are realized when all of the equations are convex. For example, a global algorithm for finding the zero of a convex real-valued function of one variable is developed. If the algorithm terminates finitely, then either the algorithm has computed a zero or determined that none exists; if an infinite sequence is generated, either that sequence converges to a zero or again no zero exists. For solving n-dimensional convex equations, the constrained optimization algorithm has the capability of determining that the system of equations has no solution. Global convergence of the algorithm is established under weaker conditions than previously known and, in this case, the algorithm reduces to Newton’s method together with a constrained line search at each iteration. It is also shown how this approach has led to a new algorithm for solving the linear complementarity problem.     

Asymptotic estimation of states of linear nonautonomous systems with scalar output

For a linear nonautonomous system with one output, the existence conditions for an identifier that estimates the current state with exponential rate are established. An algorithm for constructing such an identifier is described and its dependence on small perturbations of coefficients is studied.     

Conditional sampling for max-stable processes with a mixed moving maxima representation

This paper deals with the question of conditional sampling and prediction for the class of stationary max-stable processes which allow for a mixed moving maxima representation. We develop an exact procedure for conditional sampling using the Poisson point process structure of such processes. For explicit calculations we restrict ourselves to the one-dimensional case and use a finite number of shape functions satisfying some regularity conditions. For more general shape functions approximation techniques are presented. Our algorithm is applied to the Smith process and the Brown-Resnick process. Finally, we compare our computational results to other approaches. Here, the algorithm for Gaussian processes with transformed marginals turns out to be surprisingly competitive.     

Modified inertial Mann algorithm and inertial CQ-algorithm for nonexpansive mappings

In this article, we first introduce a modified inertial Mann algorithm and an inertial CQ-algorithm by combining the accelerated Mann algorithm and the CQ-algorithm with the inertial extrapolation, respectively. This strategy is intended to speed up the convergence of the given algorithms. Then we established the convergence theorems for two provided algorithms. For the inertial CQ-algorithm, the conditions on the inertial parameters are very weak. Finally, the numerical experiments are presented to illustrate that the modified inertial Mann algorithm and inertial CQ-algorithm may have a number of advantages over other methods in computing for some cases.     

Inverse Problem for Quasi-Periodic Differential Pencils with Jump Conditions Inside the Interval

Non-self-adjoint second-order differential pencils on a finite interval with non-separated quasi-periodic boundary conditions and jump conditions are studied. We establish properties of spectral characteristics and investigate the inverse spectral problem of recovering the operator from its spectral data. For this inverse problem we prove the corresponding uniqueness theorem and provide an algorithm for constructing its solution.     

Construction of covering maps between orientable surfaces

Consider the following problem. Can a set of numbers be realized as boundary covering indices of a covering map between surfaces? How to realize them? A set of equivalent criteria for this problem are found, which can be checked by a finite algorithm. Furthermore, the algorithm will also construct a solution if such one exists. As an application, a well_known group of necessary conditions are shown to be not sufficient in infinitely many cases, while in most cases, numbers satisfying them are realizable.