The inverse scattering problem for Schrödinger and Klein–Gordon equations with a nonlocal nonlinearity

We study the inverse scattering problem for the nonlinear Schrödinger equation and for the nonlinear Klein–Gordon equation with the generalized Hartree type nonlinearity. We reconstruct the nonlinearity from knowledge of the scattering operator, which improves the known results.     

On the null-controllability of the heat equation in unbounded domains

We make two remarks about the null-controllability of the heat equation with Dirichlet condition in unbounded domains. Firstly, we give a geometric necessary condition (for interior null-controllability in the Euclidean setting) which implies that one cannot go infinitely far away from the control region without tending to the boundary (if any), but also applies when the distance to the control region is bounded. The proof builds on heat kernel estimates. Secondly, we describe a class of null-controllable heat equations on unbounded product domains. Elementary examples include an infinite strip in the plane controlled from one boundary and an infinite rod controlled from an internal infinite rod. The proof combines earlier results on compact manifolds with a new lemma saying that the null-controllability of an abstract control system and its null-controllability cost are not changed by taking its tensor product with a system generated by a non-positive self-adjoint operator.     

A gas-kinetic scheme for shallow-water equations with source terms

In this paper, the Kinetic Flux Vector Splitting (KFVS) scheme is extended to solving the shallow water equations with source terms. To develop a well-balanced scheme between the source term and the flow convection, the source term effect is accounted in the flux evaluation across cell interfaces. This leads to a modified gas-kinetic scheme with particular application to the shallow water equations with bottom topography. Numerical experiments show better resolution of the unsteady solution than conventional finite difference method and KFVS method with little additional cost. Moreover, some positivity properties of the gas-kinetic scheme is established.     

Sur les grands quotients partiels du développement en fraction continue

In this paper we obtain some metrics results about large partial quotients in the continued fraction expansion.     

Laplacians and the Cheeger Inequality for Directed Graphs

We consider Laplacians for directed graphs and examine their eigenvalues. We introduce a notion of a circulation in a directed graph and its connection with the Rayleigh quotient. We then define a Cheeger constant and establish the Cheeger inequality for directed graphs. These relations can be used to deal with various problems that often arise in the study of non-reversible Markov chains including bounding the rate of convergence and deriving comparison theorems.Received September 8, 2004     

火焰原子吸收法测定霞石中的氧化钾和氧化钠

本方法用于测定霞石中的钾、钠，主要通过在溶样时加入氢氟酸除去二氧化硅，调整溶液中钾、钠的含量，消除互相之间的干扰，加入氯化铯消除电离因素的干扰，提高了分析结果的准确性和重现性，使测定结果更接近化学分析值。回收率为99．2％-101．6％。     

K-非常凸空间

本文引入了一种新的K凸空间K-非常凸空间,及其对偶空间K-非常光滑空间,它们分别是非常凸空间和非常光滑空间的推广但又严格弱于非常凸空间和非常光滑空间,因此它们又有许多独特的性质.本文讨论了它们的一些特性及与其它K凸性和K光滑性的关系,推广了[3]、[6]、[7]、[8]中的一些结果.     

一种新化合物K2Ti8O15纳米线

钛酸钾晶须通常是直径和长度在微米量级的无机晶须 ,可用Ｋ2 Ｏ·ｎＴｉＯ2 表示其组成 ,ｎ =1,2 ,4 ,6 ,8,[1] .六钛酸钾晶须具有耐高温、耐腐蚀、纤维拉伸强度高、导热系数小、红外反射率高 ,硬度低的特点 .在民用及工业方面有很多应用 .如催化剂载体、离子吸附交换材料、高温过滤器、绝热材料、耐摩擦材料等[2～ 5] .钛酸钾纳米线的合成尚未见报道 .我们在用电弧产生的Ｎ2 等离子体热解焦油时 ,生成了一种直径 9～ 2 0ｎｍ长约几百纳米线 .Ｘ射线能谱定量分析表明这种纳米线化学组成为Ｋ2 Ｔｉ8Ｏ15,是一种新的非化学计量化合物 .试验装…