On Melnikov functions of a homoclinic loop through a nilpotent saddle for planar near-Hamiltonian systems

The first-order Melnikov function of a homoclinic loop through a nilpotent saddle for general planar near-Hamiltonian systems is considered. The asymptotic expansion of this Melnikov function and formulas for its first coefficients are given. The number of limit cycles which appear near the homoclinic loop is discussed by using the asymptotic expansion of the first-order Melnikov function. An example is presented as an application of the main results.     

Optical multistability in nonlinear negative index Fibonacci multilayers

We have demonstrated numerically that the nonlinear negative index Fibonacci multilayer can exhibit optical multistability and offer a wide variety of switching between states of various contrasts. The stepwise up-switch and one-step or stepwise down-switch operations can take place in such structures. It is also shown that multistable operations and contrasts can be controlled by regulating the width of the negative index slabs.     

盐酸二乙胺与己二酸、癸二酸的相关系

在电子工业中,盐酸二乙胺常与己二酸或癸二酸等二羧酸配合用作有机软钎剂的活性成份[1].文献中极少报道有关有机物的相图研究[2],上述(C2H5)2NH·HCl-C6H10O4和(C2H5)2NH·HCl-C10H18O4的相图,特别是它们混和物的热分解尚未见报道,这给有关钎剂的合成和应用带来很大的盲目性.本文用DTA,DSC,TGA和目测变温法[3]研究了(C2H5)2NH·HCl-C6H10O4和(C2H5)2NH·HCl-C10H18O4两个二元系的相图及其各组成点的热分解温度和行为.1　实验部分(C2H5)2NH·HCl[2],C6H10O4[4](化学纯)在二次去离子水中重结晶,C10H18O4(化学纯)在无水…     

Inequalities for irregular Gabor frames

In [C.K. Chui and X.L. Shi, Inequalities of Littlewood-Paley type for frames and wavelets, SIAM J. Math. Anal., 24 (1993), 263–277], the authors proved that if {e^imbxg(x-na): m,n ? \Bbb Z}\{e^{imbx}g(x-na): m,n\in{\Bbb Z}\} is a Gabor frame for L²(\Bbb R)L^2({\Bbb R}) with frame bounds A and B, then the following two inequalities hold: A ￡ \frac2pb?_{n ? \Bbb Z}|g(x-na)|² ￡ B,     a.e.A\le \frac{2\pi}{b}\sum_{n\in{\Bbb Z}}\vert g(x-na)\vert^2\le B, \quad a.e. and A ￡ \frac1a?_{m ? \Bbb Z}|[^(g)](w-mb)|² ￡ B,     a.e.A\le \frac{1}{a}\sum_{m\in{\Bbb Z}}\vert \hat{g}(\omega-mb)\vert^2\le B, \quad a.e. . In this paper, we show that similar inequalities hold for multi-generated irregular Gabor frames of the form è_{1 ￡ k ￡ r}{e^{iáx, l?}g_k(x-m): m ? D_k, l ? L_k }\bigcup_{1\le k\le r}\{e^{i\langle x, \lambda\rangle}g_{k}(x-\mu):\, \mu\in \Delta_k, \lambda\in\Lambda_k \} , where Δ _k and Λ _k are arbitrary sequences of points in \Bbb R^d{\Bbb R}^d and g_k ? L²(\Bbb R^d)g_k\in{L^2{(\Bbb R}^d)} , 1 ≤ k ≤ r.     

Ramsey functions involving with large

For fixed integers m,k2, it is shown that the k-color Ramsey number r_k(K_m,n) and the bipartite Ramsey number b_k(m,n) are both asymptotically equal to k^mn as n→∞, and that for any graph H on m vertices, the two-color Ramsey number is at most (1+o(1))n^m+1/(logn)^m-1. Moreover, the order of magnitude of is proved to be n^m+1/(logn)^m if H≠K_m as n→∞.     

Application of time reversal to passive acoustic remote sensing of the ocean

This paper investigates a novel approach to processing records of ambient noise in the ocean that are measured concurrently in spatially separated locations. The approach is a synthesis of two well-known phase-coherent signal processing techniques. At the first stage of processing, an approximation to the transient acoustic Green function is found by the method of noise interferometry. At the second stage, the approximate Green function is time reversed and back propagated from the location of one of the receivers, thereby producing a focus in the vicinity of the other receiver. Unlike the earlier work, measurements at just two points (rather than vertical array measurements) are used when the sound-propagation range is large compared to the ocean depth. The requirement for optimal focusing of the back-propagated field is shown to lead to extraction of estimates of the unknown physical parameters of the waveguide and, hence, to passive acoustic remote sensing of the ocean.     

磁性斯格明子的研究现状和展望

磁性斯格明子是具有拓扑保护性质的纳米尺度涡旋磁结构.斯格明子主要存在于非中心对称的手性磁性材料以及界面镜面对称性破缺的磁性薄膜材料中.因具有实空间的非平庸拓扑性,磁性斯格明子展现出丰富新奇的物理学特性,例如拓扑霍尔效应,新兴电磁动力学等,为研究拓扑自旋电子学提供了新的平台.另一方面,由于其具有尺寸小,高稳定性和易操控的特性,磁性斯格明子在未来高密度,低能耗,非易失性计算和存储器件中也具有潜在应用.现阶段的研究已经初步发现一系列磁斯格明子材料,并证明能够通过电流操控室温下稳定的磁性斯格明子,但是室温下单个斯格明子的精确产生、湮灭以及探测在实验上仍具有挑战性.本文阐述了磁性斯格明子的基础理论以及动力学研究现状,并对现有的斯格明子材料和斯格明子的产生,湮灭以及探测方法进行了总结,最后还对未来磁性斯格明子的物理理论研究以及应用发展中的挑战和机遇进行了讨论.     

丁基锡系列化合物与脱氧核糖核酸的相互作用

通过紫外（ultraviolet,UV）光谱和圆二色（circular dichroism,CD）光谱,研究了丁基锡化合物（一丁基锡、二丁基锡和三丁基锡）与脱氧核糖核酸（deoxyribonucleic acid,DNA）的作用方式以及时间和浓度的影响。结果显示丁基锡化合物与DNA的作用是双重的,既作用于DNA的碱基,对双螺旋结构有一定影响,又作用于DNA的磷酸基团,使构象发生变化。但是,丁基锡化合物与脱氧核糖核酸作用的程度和方式与丁基锡种类、时间和浓度等因素有关。一丁基锡倾向于与磷酸基团作用,三丁基锡倾向于与碱基作用,而二丁基锡与两者作用程度相近。短时间内,丁基锡化合物的作用位点通常是DNA的碱基;长时间时,则作用位点往往是DNA的磷酸基团。低浓度的丁基锡化合物倾向与DNA的碱基结合,高浓度的丁基锡化合物倾向与DNA的磷酸基团结合。