一类哈密顿系统的Abel积分之比单调性的判据

研究了一类哈密顿系统的两个Abel积分比值的单调性的条件,指出这个单调性条件可由文中给出的两个判定函数直接确定.     

关于算子多项式的一点注记

本注记应用Ｇｅｌｆａｎｄ表示定理，推广了文「１，２」中关于算子多项式正性的两个主要结果，并且给出更直接和简单和证明。     

怎样利用集合元素的性质解题

在学习集合概念时,同学们对元素的性质,即元素的确定性、互异性、无序性这些性质记得住、背得过,就是不会用.为了帮助同学们解决这个问题,本文对其进行研究.这个问题往往与两个集合相等相联系,两个集合相等指的是两个集合中元素对应相等.要判断集合中元素相等自然要用到元素的性质.一、直接求解检验法     

最优可测耦合的存在性与Markov过程的遍历性

证明了一般完备可分距离可测空间上两个概率核最优可测耦合总是存在的 .据此得到了Markov过程的一个一般性遍历性定理 ,作为它的直接结果 ,对先前的粒子系统平稳分布的唯一性定理的结果作了补充 ,指出该定理同时蕴涵平稳分布的存在性 .     

隐含的函数单调性和奇偶性

<正>单调性和奇偶性是函数的两条重要性质,而它们自身又有许多性质,比如说:两个增函数相加在公共定义域中仍为增函数;若f(x)为偶函数,则f(-x)=f(x)=f(|x|)等.函数中许多问题的解答,都要从这两方面分析问题,寻求解题方法.有的问题,题目条件中已直接给出函数的单调性或奇偶性,可以利用它们的性质处理;而有的问题,并没有直接     

具有不确定性的分数阶时滞复值神经网络无源性

该文研究了一类具有不确定性和时滞的分数阶复值神经网络无源性问题,未将复值神经网络模型拆分成两个实值系统,而是将复值系统当成一个整体直接进行处理.通过构造恰当的Lyapunov函数,并利用矩阵不等式技巧,建立了网络无源性的线性矩阵不等式判据.给出的数值例子和仿真验证了获得结论的可行性和有效性.     

一类多线性相关摄动系统的性能鲁棒性

对于经平移和旋转后的一类多线性相关摄动系统族,其严格正实性可由系统族中的顶点系统的严格正实性所保证.利用这一结论还证明了经平移后的系统族的H^∞范数的最大值在其顶点系统上达到.关于区间系统族性能鲁棒性的两个著名的强Kharitonov型定理是上述结果的直接推论.     

LD设计的存在谱

在解决斯坦纳三元系大集存在性问题时,陆家羲引入LD设计和LD^*设计的概念,建立这两类设计的若干递推构造和直接构造,在构作斯坦纳三元系大集过程中发挥重要作用.为了构造陆家羲遗留的六个小阶数的斯坦纳三元系大集,Teirlinck依然借助LD设计,使用PBD进行递推构造,最终确定斯坦纳三元系大集的存在谱.本文将彻底解决LD设计存在的充分必要条件,对LD^*设计的存在性仅余四个可能例外值.     

勒贝格积分可加性的严格证明

文[1]在建立勒贝格积分理论体系时,勒贝格积分可加性是作为从定义出发直接导出的最基本结果,而两个变量和的上确界不小于各自上确界的和这一结果成为完成证明的关键.本文指出了该教材在证明过程中运用的上述上确界大小关系存在反例,并提出了勒贝格积分可加性的新的证明方法,避开了上述上确界大小关系.首先从定义出发证明了非负可测函数勒贝格积分加法的一个次线性性,从而给出了勒贝格积分可加性的严格证明.     

Banach空间二阶非线性积分-微分方程组两点边值问题

直接利用混合单调迭代法,研究了Banach空间二阶非线性积分-微分方程组两点边值问题解的存在性.     

Bounding the number of zeros of certain Abelian integrals

In this paper we prove a criterion that provides an easy sufficient condition in order for any nontrivial linear combination of n Abelian integrals to have at most n+k−1 zeros counted with multiplicities. This condition involves the functions in the integrand of the Abelian integrals and it can be checked, in many cases, in a purely algebraic way.     

两个Abel积分的比值单调性的判别条件

用直接计算的方法对文献中给出的第三类函数的一种特殊形式给出其积分比值单调性的判别条件.     

一类双中心平面二次系统的Abel积分零点个数

利用Abel积分与第一、第二型完全椭圆积分,本文研究一类具有两个中心奇点的平面二次系统在n次小扰动下的Abel积分零点个数上界问题,得到了较小的上界估计．     

Algebraic independence of the periods of abelian integrals

Abelian integrals of the first and the second kind are proved to have two algebraically independent periods. Some corollaries concerning the algebraic independence of the values of Euler's beta and gamma functions at rational points are derived.Translated fromMatematicheskie Zametki, Vol. 60, No. 5, pp. 681–691, November, 1996.     

The nef cone of the moduli space of sheaves and strong Bogomolov inequalities

The paper is devoted to generic translation flows corresponding to Abelian differentials with one zero of order two on flat surfaces of genus two. These flows are weakly mixing by the Avila–Forni theorem. Our main result gives first quantitative estimates on their spectrum, establishing the Hölder property for the spectral measures of Lipschitz functions. The proof proceeds via uniform estimates of twisted Birkhoff integrals in the symbolic framework of random Markov compacta and arguments of Diophantine nature in the spirit of Salem, Erd?s and Kahane.     

一类可积非Hamilton系统的Abel积分的零点估计

讨论了一类含参可积非Hamilton系统在一般二次多项式扰动下的Abel积分的零点,得出了不同参数范围下的Abel积分的零点数目的估计.     

The monodromy problem and the tangential center problem

We consider families of Abelian integrals arising from perturbations of planar Hamiltonian systems. The tangential center-focus problem asks for conditions under which these integrals vanish identically. The problem is closely related to the monodromy problem, which asks when the monodromy of a vanishing cycle generates the whole homology of the level curves of the Hamiltonian. We solve both of these questions for the case in which the Hamiltonian is hyperelliptic. As a by-product, we solve the corresponding problems for the 0-dimensional Abelian integrals defined by Gavrilov and Movasati.     

Monotonicity of the ratios of two Abelian integrals for Hamiltonian systems with parameters

We study the monotonicity of the ratios of two Abelian integrals $\oint_{\gamma_{i}(h)}ydx$ $\backslash$ $\oint_{\gamma_{0i}(h)}xydx$ over three period annuli $\{\gamma_i(h)\}$, for $i=1, 2, 3$, defined by a seventh-degree hyperelliptic Hamiltonian $H(x,y)=y^2+\Psi(x)$ with a parameter. The parameter makes the problem more challenging to analyze. To over the difficulty, we apply some criterion with the help of transformations, tools in computer algebra such as boundary polynomial theory to determine the monotonicity of the ratios. Our results establish the existence and uniqueness of limit cycle bifurcated from each period annulus.     

Level lines of harmonic functions related to some Abelian integrals

The geometry of level lines of harmonic functions being real parts of some Abelian integrals is studied. Such harmonic functions appear in the study of asymptotics of solutions to second-order differential equations, and the corresponding level lines are related both to the distribution of eigenvalues of a non-self-adjoint Sturm–Liouville problem and to location of trajectories of the corresponding quadratic differentials.