一类稀疏效应下捕食┐被捕食者系统极限环的存在性和唯一性

本文研究捕食者种群具有线性密度制约的一类稀疏效应下捕食－被捕食者系统ｘ＝ｘ（ａｘ－ｃｘ３－ｂｙ），ｙ＝ｙ（－α＋βｘ－γｙ）．（＊）得到：（１）当Ａ１＜Ａ１，Ａ２＜Ａ２，Ａ３＞Ａ３时，系统（＊）在第一象限内存在极限环；（２）当Ａ２＜Ａ２，Ａ３＞Ａ３时，系统（＊）在第一象限内存在唯一极限环     

Cycle and circle tests of balance in gain graphs: Forbidden minors and their groups

We examine two criteria for balance of a gain graph, one based on binary cycles and one on circles. The graphs for which each criterion is valid depend on the set of allowed gain groups. The binary cycle test is invalid, except for forests, if any possible gain group has an element of odd order. Assuming all groups are allowed, or all abelian groups, or merely the cyclic group of order 3, we characterize, both constructively and by forbidden minors, the graphs for which the circle test is valid. It turns out that these three classes of groups have the same set of forbidden minors. The exact reason for the importance of the ternary cyclic group is not clear. © 2005 Wiley Periodicals, Inc. J Graph Theory     

The number of limit cycles of cubic Hamiltonian system with perturbation

In this paper, by using qualitative analysis, we investigate the number of limit cycles of perturbed cubic Hamiltonian system with perturbation in the form of (2n+2m) or (2n+2m+1)th degree polynomials . We show that the perturbed systems has at most (n+m) limit cycles, and has at most n limit cycles if m=1. If m=1, n=1 and m=1, n=2, the general conditions for the number of existing limit cycles and the stability of the limit cycles will be established, respectively. Such conditions depend on the coefficients of the perturbed terms. In order to illustrate our results, two numerical examples on the location and stability of the limit cycles are given.     

Studying the process of ionization of hydrogen in conditions of its forced delivery to a porous nickel oxide electrode

The hydrogen ionization process is studied experimentally on an industrial sintered nickel oxide electrode in models of sealed nickel-metal hydride batteries. It is shown that the hydrogen ionization rates that are reached during overcharge by high current densities in conditions of forced gas delivery into the electrode pores (up to 40 mA cm^?2) exceed the self-discharge rate of a nickel-hydrogen battery by two orders of magnitude. Up to 70% of hydrogen delivered into the compact assembly block undergoes ionization during forced charge of models of sealed nickel-metal hydride batteries with a closed hydrogen cycle. Two independent methods (potentiostatic and manometric) are used to determine the relationship between rates of hydrogen ionization with the degree of the electrode filling with gas and perform estimation of the process intensity at a unit reaction surface. It is established that, in conditions of forced gas delivery, practically all the hydrogen oxidation current is generated at the surface of the nickel oxide electrode beneath thin films of an electrolyte solution at the rate of 4–5 mA cm^?2. It is shown that the hydrogen oxidation rate on a nickel oxide electrode filled in part by gas is independent of the electrode potential, probably because of a tangible contribution made by diffusion limitations to the overall hampering of the process.     

利用振幅调制器进行光电负反馈抑制激光强度噪声

采用振幅调制器作为抑制激光强度噪声的元件，首先对光电负反馈回路进行了简要的理论分析，然后利用该光电负反馈进行抑制激光二极管抽运全固化单频环形Nd:YVO4红外激光器强度噪声的实验。结果表明，在0－1MHz的低频段，强度噪声大幅度降低，最大降低约15dB。     

用能量法求多自由度振动系统的角频率

利用简谐振动能量方程，通过分析振幅矢量的关系，用能量法求多自由度振动系统的角频率或简正振动频率。     

一类高次系统极限环的存在与唯一性

本文对系统dxdt=-y(1-ax2n)(1-bx2n) δx-lx4n 1dydt=x2n-1(1-cx2n)(1-bx2n)进行定性分析,得出其极限环的存在性,不存在性及唯一性的一系列充分条件.     

Orthogonal double covers by super‐extendable cycles

An Orthogonal Double Cover (ODC) of the complete graph K_n by an almost‐hamiltonian cycle is a decomposition of 2K_n into cycles of length n?1 such that the intersection of any two of them is exactly one edge. We introduce a new class of such decompositions. If n is a prime, the special structure of such a decomposition allows to expand it to an ODC of K_n+1 by an almost‐hamiltonian cycle. This yields the existence of an ODC of K_p+1 by an almost‐hamiltonian cycle for primes p of order 3 mod 4 and its eventual existence for arbitrary primes p. © 2002 Wiley Periodicals, Inc. J Combin Designs 10: 283–293, 2002; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/jcd.10011     

关于圈的完全正矩阵实现

本文给出了一个关联图为圈的非负、半正定矩阵A为完全正的一个充要条件.我们还证明了这样的矩阵A（当A为完全正时）的分解指数即为A的阶数.