The number of periodic solutions of polynomial differential equations

We estimate the number of periodic solutions for special classes ofnth-order ordinary differential equations with variable coefficients. Translated fromMatematicheskie Zametki, Vol. 64, No. 5, pp. 720–727, November, 1998. The author thanks Yu. S. Il'yashenko for setting the problems, permanent advice, and overall support. The author is also thankful to D. A. Panov for numerous discussions. This research was supported by the CRDF Foundation under grant MR1-220, by the INTAS Foundation under grant No. 93-05-07, and by the Russian Foundation for Basic Research under grant No. 95-01-01258.     

Itô-Wiener Chaos Expansion with Exact Residual and Correlation, Variance Inequalities

We give a formula of expanding the solution of a stochastic differential equation (abbreviated as SDE) into a finite Itô-Wiener chaos with explicit residual. And then we apply this formula to obtain several inequalities for diffusions such as FKG type inequality, variance inequality and a correlation inequality for Gaussian measure. A simple proof for Houdré-Kagan's variance inequality for Gaussian measure is also given.     

一个非严格双曲型方程组粘性逼近解的收敛性

本文讨论非严格双曲型方程组的粘性逼近解的收敛性，当ｆ满足一定条件，初值为有界可测函数时，利用补偿紧致的理论及对前进熵波的分析，在没有对粘性解导数一致界估计的情况下，证明了粘性逼近解存在一个子序列在强拓扑意义下收敛．     

GLOBAL ATTRACTIVITY IN A PERIODIC COMPETITION SYSTEM WITH FEEDBACK CONTROLS

ＷＥＮＧＰＥＩＸＵＡＮ（翁佩萱）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＳｏｕｔｈＣｈｉｎａＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，Ｇｕａｎｇｚｈｏｕ５１０６３１，Ｃｈｉｎａ）ＧＬＯＢＡＬＡＴＴＲＡＣＴＩＶＩＴＹＩＮＡＰＥＲＩＯＤＩＣＣＯＭＰＥＴ...     

A Novel Fabrication Technique of Long Period Fiber Gratings

１ＩｎｔｒｏｄｕｃｔｉｏｎＳｉｎｃｅｔｈｅｄｉｓｃｏｖｅｒｙｏｆｐｈｏｔｏｓｅｎｓｉｔｉｖｉｔｙｉｎｇｅｒｍａｎｏｓｉｌｉｃａｔｅｏｐｔｉｃａｌｆｉｂｅｒｓｂｙＨｉｌｅｔａｌ．ｉｎ１９７８［１］，ｓｉｇｎｉｆｉｃａｎｔｐｒｏｇｒｅｓｈａｓｂｅｅｎｍａ...     

On a sequential selection procedure of Bechhofer,Kiefer, and Sobel

We give an elementary proof of a theorem of Bechhofer, Kiefer, and Sobel concerning their sequential procedure $\text{P}{}_{\mathrm{B}}{}^1$ for selecting the highest probability in binomial or multinomial trials. Our proof uses the change of measure approach. An error in the original proof is pointed out and corrected.     

基于多层次特征的跨场景服装检索

针对跨场景服装检索如何提取更有表述力的服装特征问题,提出了一种新的基于高层公共特征约束的相似性度量算法。首先,通过类别空间学习提取不同场景域的类别信息;然后,在场景域空间网络用类别信息约束传统对比损失函数,增大对类间负样本对的惩罚以减轻过拟合;最后,融合类别公共特征和域特定特征并通过类别判断进行辅助检索。分析和实验结果表明,新算法对跨场景服装检索的准确度要优于当前前沿的方法。     

GLOBAL EXISTENCE OF POSITIVE PERIODIC SOLUTION FOR A NEUTRAL DELAY COMPETITIVE SYSTEM

In this paper, by means of Mawhin's coincidence degree theory and somenew techniques, sufficient conditions for the global existence of positive periodicsolution to a class of neutral type competitive system with delays are obtained.