一个二次系统不存在极限环的新证法

<正> 本文研究二次微分系统 x=-y+lx~2+mxy+ny~2=P_2,y=x(1+by)=Q_2,(b≠0)(1)将证明下面定理. 定理1 系统(1)在相平面上不存在极限环. 在[1]中已证当m~2+4n(n+b)≥0时(1)在相平面上不存在极限环,那里是用找Dulac函数的方法来证明的,利用Dulac函数     

Dulac的构造及其应用(Ⅱ)

本文研究（Ⅱ）类系统Dulac函数的构造问题,作为应用,讨论此系统的极限环的不存在性问题,得到了一些新结果.     

一类具有Watt型功能性反应的捕食系统的极限环与稳定性

研究一类具有Watt型功能性反应的捕食模型.讨论了该系统正平衡点的存在性以及非负平衡点的性态,应用Poincare-Bendixson定理和张芷芬定理,证明了极限环的存在性和唯一性,并采用构造Dulac函数的方法,获得了正平衡点全局渐近稳定性的一个充分条件.     

关于二次系统中心积分,Dulac 函数与极限环(Ⅰ)

<正> 本文研究二次系统的中心积分与 Dulac 函数和极限环之间的关系,首先得到二次系统所有中心情况下的通积分,完全用初等函数表示,借此导出一系列的 Dulac 函数,用以证明不存在极限环和在两个奇点附近不同时存在极限环的定理,以及用来判定非粗焦点的稳定性.一个二次系统如果原点为焦点或中心型奇点,由[5],则此二次系统可以简化为:(?)=λ_1x-y-λ_3x~2+(2λ_2+λ_5)xy+λ_6y~2,(?)=x+λ_1y+λ_2x~2+(2λ_3+λ_4)xy-λ_2y~2. (1)得到存在中心的充要条件和由非粗焦点产生极限环的条件(见[5])取决于系     

Dulac函数的构造及其应用(I)

本文研究(I)和(II)类系统Dulac函数的构造问题,作为应用,讨论此两类系统的极限环的不存在性问题,得到了一些新结果.     

Dulac函数的构造及其应用(Ⅰ)

本文研究（Ⅰ）和（Ⅱ）类系统Dulac函数的构造问题,作为应用,讨论此两类系统的极限环的不存在性问题,得到了一些新结果．     

Dynamics Analysis of Cannibalistic Model With Density Dependence in Mature Stage北大核心CSCD

在考虑成熟阶段具有密度制约的基础上,建立了一类具有卵-成熟阶段的同类相食模型.该文从两个方面讨论了模型的动力学性态：当种群不存在同类相食时,构造Lyapunov函数证明平衡点的全局渐近稳定性;当种群存在同类相食时,利用中心流形定理证明同类相食使模型产生鞍结点分支,通过构造Dulac函数说明在二维自治系统中不存在极限环,得到了平衡点的全局稳定性.最后,利用数值模拟验证了所得相应结果的正确性.     

一类二维系统的极限环的个数

本文利用Dulac函数方法讨论一类二维系统在环城上的包围多个奇点的极限环的唯一性及在n连城上极限环的唯n-1性，并给出了两个多项式的例子，讨论了极限环的唯一性和唯二性．     

关于一类非多项式平面微分系统的极限环及分支问题

旨在讨论一类非多项式平面微分系统.通过使用Dulac准则和Bendixson准则获得极限环不存在性的充分条件,引入广义Liénard系统理论以研究极限环的存在性及稳定性,应用Hopf分岔理论证明自原点分岔出极限环的充分条件.此外,给出一个范例以验证分析和结果的有效性.     

关于杜拉克的《极限环论》

§1 法国数学家杜拉克(H.Dulac)(1870—1955)在1923年发表的长篇论文“极限环论”是一篇知名文献。在这篇论文中,杜拉克推广了邦加赖(H.Poincaré)关于极限环个数有限的定理,去掉了邦加赖所加的限制,即在无通过鞍点的极限环存在的这一限制之下有限性定理才能成立,当时许多数学家,包括知名的班狄克生(I var Bendixon)在内,都曾为去掉这个限制而努力,但统归无效,杜拉克这篇论文,却终于成功地去掉邦加赖的限制而证明了这个定理,并因此而名噪一时。     

On the linear piezoelectricity of composite materials

From the equations of the linear piezoelectricity for a composite material with a periodic structure we derive the dynamical solution by means of Bloch expansion techniques. This expression techniques. This expression allows, as a limit case, a comparison with the homogenization method, and the macroscopic coefficients are also deduced.     

环上矩阵的Moore-Penrose逆

本文研究环上矩阵的广义逆,得到其存在的充要条件,给出它的表达式,推广了以往文献的相应结果。     

Relativistic semi-classical theory of atom ionization in ultra-intense laser

A relativistic semi-classical theory (RSCT) of H-atom ionization in ultra-intense laser (UIL) is proposed. A relativistic analytical expression for ionization probability of H-atom in its ground state is given. This expression, compared with non-relativistic expression, clearly shows the effects of the magnet vector in the laser, the non-dipole approximation and the relativistic mass-energy relation on the ionization processes. At the same time, we show that under some conditions the relativistic expression reduces to the non-relativistic expression of non-dipole approximation. At last, some possible applications of the relativistic theory are briefly stated.     

Explicit Expression of Hermite Interpolation Basis Functions under the Ball Basis

In paper [1],it was shown that an explicit expression of the cardinal basis functions for two-point Hermite interpolation. This paper will show the explicit expression of Hermite interpolation under the Ball basis.     

Computation of rational interval functions

This paper presents a general algorithm for computing interval expressions. The strategy is characterized by a subdivision of the argument intervals of the expression and a recomputation of the expression with these new intervals. The precision of the result is limited only by the actual computer.     

GA算子的代数模型

采用矩阵形式表示遗传操作过程 ,可为遗传算法程序设计提供简明的数学模型     

Invariant curves and analytic integrability of a planar vector field

We give an expression of the irreducible invariant curves at the singular point. For analytically integrable systems, we provide an expression of its primitive first integral. This fact allows us to obtain necessary conditions of analytic integrability at degenerate singular points.     

Quantum effects in the transverse dielectric permittivity of a Maxwellian Plasma

We obtain an explicit analytic expression for the transverse permittivity of Maxwellian plasma. This expression considers quantum effects due both to spatial and frequency dispersion and to the presence of an intrinsic magnetic moment in the plasma particles.     

Biased detection of guanine-rich microRNAs by array profiling: Systematic error or biological phenomenon?

This article describes an unexpected phenomenon which was revealed during the study of microRNA expression profiles of breast tumors. Hierarchical clustering has distinguished two broad groups of microRNAs with different expression patterns. One of these groups, Group Q (“questionable”), was composed mainly of recently discovered microRNAs and contained a large number of viral microRNA species. This microRNA subset was found to be extremely rich in guanine. The above features suggest that the Group Q is an artifact of microRNA expression profiling. However, the latter explanation is not supported by the evidence for biologically relevant associations observed for the Group Q microRNAs.     

KdV方程的延拓结构

利用外微分形式系统和Lie代数表示理论提出了求解非线性波方程Lax对的延拓结构理论,该方法是构造非线性波方程Lax对的系统最有效的方法.其关键在于如何给出延拓代数的具体表示,如微分算子表示或矩阵表示.如果一个非线性波方程具有非平凡的延拓代数,则称其延拓代数可积,本篇论文主要利用延拓结构理论,讨论KdV方程的解,同时给出...