Shock formation in a chemotaxis model

In this paper, we establish the existence of shock solutions for a simplified version of the Othmer–Stevens chemotaxis model (SIAM J. Appl. Math. 1997; 57 :1044–1081). The existence of these shock solutions was suggested by Levine and Sleeman (SIAM J. Appl. Math. 1997; 57 :683–730). Here, we consider the general Riemann problem and derive the shock curves in parameterized forms. By studying the travelling wave solutions, we examine the shock structure for the chemotaxis model and prove that the travelling wave speed is identical to the shock speed. Moreover, we explicitly derive an entropy–entropy flux pair to prove the uniqueness of the weak shock solutions. Some discussion is given for further study. Copyright © 2007 John Wiley & Sons, Ltd.     

某些偏微分方程的定向振荡解

本文研究了在应用中颇为重要的几类非线性偏微分方程的振荡解。首先,我们讨论了修正KdV方程、二维KdV方程和Boussinesq方程,利用Jacobl椭圆函数作出了这些方程转化后的常微分方程的解,从而证明了原方程行波振荡解的存在性。其次,我们研究了高维约比波动方程。对所归结的微分方程构造了它的一个幂级数解,导出了此解与Bessel函数的关系,然后由Bessel函数的实零点的分布结果证明了高维约化波动方程的柱面振荡解的存在性。     

On the basic transcendental functions appearing in the dielectric tensor of a weakly relativistic Maxwellian plasma

Summary It is shown how to deduce in a straightforward way the class of transcendental functions which appear in the elements of the dielectric tensor of a weakly relativistic thermal plasma. The deduction is made directly from the second form of Trubnikov integrals and is valid for arbitrarily large values of the wave perpendicular refractive index.

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Riassunto Si mostra come sia possibile dedurre in modo molto diretto la famiglia di trascendenti che appare negli elementi della matrice dielettrica di un plasma debolmente relativistico in condizioni di equilibrio termico. Il procedimento parte direttamente dalla così detta seconda forma degli integrali di Trubnikov ed è valido per valori arbitrariamente grandi dell’indice di rifrazione perpendicolare al campo magnetico nel quale è immerso il plasma.

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Резюме Мы показываем, как вывести непосредственным образом класс трансцендентных функций, которые появляются в элементах диэлектрического тензора для слабо релятивистской плазмы в условиях теплового равновесия. Вывод проводится непосредственно из второй формы интегралов Трубникова и справедлив для произвольно больших величин показателя преломления для волны, перпендикулярной магнитному полю, в которое помещена плазма.

     

LOCAL WELL-POSEDNESS AND ILL-POSEDNESS ON THE EQUATION OF TYPE □u = u^k（δu）^α

This paper undertakes a systematic treatment of the low regularity local wellposedness and ill-posedness theory in H^s and H^s for semilinear wave equations with polynomial nonlinearity in u and δu. This ill-posed result concerns the focusing type equations with nonlinearity on u and δtu.     

女性艰难的独立史——从《伤逝》、《倾城之恋》到《试婚》

从男女之间的婚恋关系可以判断出一个社会的文明程度。鲁迅《伤逝》的子君、张爱玲《倾城之恋》的白流苏、安宁《试婚》的宝贝的婚恋史,构成了一部女性争取独立的艰难史。在女性争取独立的征途中,既需要女性提高自身素质,拥有独立的经济地位,也需要社会做出很多改变。     

惰性气体和H_2分子碰撞截面计算研究

用T .T(K .T .TangJ.Peter .Toennies)势模型和公认精密度较高的密耦 (Close -Coupling)近似方法计算了E =0 .0 5ev时 0 0 - 0 0弹性碰撞 0 0 - 0 2非弹性碰撞 ,得出氢分子转动激发分波截面 ,并研究了原子与分子碰撞弹性分波截面和非弹性激发截面随量子数增加的变化规律 .     

微机控制阶梯波慢扫描电路

本文介绍了在相对论电子束起初发射度测量系统中我们研制的微机控制阶梯波慢扫描电路工作原理     

Analytical approximation solutions for 3-D optical waveguides: Review

The rectangular dielectric waveguide is the most commonly used structure in integrated optics, especially in semi-conductor diode lasers. Demands for new applications such as high-speed data backplanes in integrated electronics, waveguide filters, optical multiplexers and optical switches are driving technology toward better materials and processing techniques for planar waveguide structures. The infinite slab and circular waveguides that we know are not practical for use on a substrate because the slab waveguide has no lateral confinement and the circular fiber is not compatible with the planar processing technology being used to make planar structures. The rectangular waveguide is the natural structure. In this review, we have discussed several analytical methods for analyzing the mode structure of rectangular structures, beginning with a wave analysis based on the pioneering work of Marcatili. We study three basic techniques with examples to compare their performance levels. These are the analytical approach developed by Marcatili, the perturbation techniques, which improve on the analytical solutions and the effective index method with examples. T Srinivas received the B.Sc. (Hon.) degree from Nehru Science College, Hydrabad and M.E. (Int.) and Ph.D. dgrees from the Indian Institute of Science, Bangalore, India. He was a Postdoctoral Research Fellow at Toyohashi University of Technology, Japan from 1992 to 1996. He is currently an Associate Professor with the Department of Electrical Communication Engineering, Indian Institute of Science. His areas of interests are optical communication networks, integrated optics, micro-opto-electrical-mechanical systems (MOEMS) and fiberoptic sensors     

山东地区地震波衰减特点及其应用

利用山东地震台网记录到的构造地震与塌陷地震所激发的地震波横波（S波）波列中的最大振幅随距离的衰减进行研究。采用逐步回归法进行计算，得出S波最大振幅随距离的关系式。     

从相对论的两条基本原理论证电磁波的相位不变性

根据相对论的两条基本原理和时空洛仑兹变换的推导思路，论证了普遍的电磁波相位不变性．清楚地揭示出电磁波的相位不变性和相对论的基本原理及时空洛仑兹变换的内在联系