On a generalized $L_2$ projection and some related stability estimates in Sobolev spaces

Summary. In this paper we investigate a stability estimate needed in hybrid finite and boundary element methods, especially in hybrid coupled domain decomposition methods including mortar finite elements. This stability estimate is equivalent to the stability of a generalized projection in certain Sobolev spaces. Using piecewise linear trial spaces and appropriate piecewise constant test spaces, the stability of the generalized projection is proved assuming some mesh conditions locally. Received April 11, 2000 / Revised version received February 15, 2001 / Published online July 25, 2001     

N2（A）及N（2D）对IF（X）的传能研究

在微波放电系统中,对NH_3-F-F_2-CF_3I体系进行研究,结果表明,向IF(X)传能的诸多媒介中,N_2(A)及N(~2D)起着主要作用,并且这一结论在经微波激发后的N_2与CF_3I的直接反应中得到了进一步证实。     

三维射频加速腔程序包MAFIA的开发和应用

介绍了三维射频加速器计算机辅助设计(CAD)程序包MAFIA的特点、功能及其应用。用CAD的方法实现了射频加速器特别是非轴对称带耦合腔的加速器的三维腔形设计。同时介绍了节省内存、节约机时的模型方法,使得在中小型机器上运行大程序(八万条)成为可能。文章主要对L波段的加速腔进行了数值模拟,并和实验进行了比较,结果符合较好;通过三维数值模拟及图形模拟的方法比较了各种形状谐振腔的性能;计算分析了输入耦合腔及高阶模耦合器对加速腔电磁场分布等参量的影响;提出了加耦合器后谐振频率改变的补偿方法。     

U-statistics in danach spaces

U-statistics in Banach spaces are considered and thoroughly investigated. The martingale structure, estimates of moments, the law of large numbers, the central limit theorem, the invariance principle, estimates of the rate of convergence, and large deviations are established     

NMR study of products of thermal transformation of substituted N-aryl-o-quinoneimines

Products of thermal transformation of substituted N-aryl-o-quinoneimines were studied using NMR spectroscopy. The formation of 4aH-phenoxazine, which was further dimerized by the Diels—Alder reaction, was established.     

Finite-dimensional Leavitt path algebras

We classify the directed graphs E for which the Leavitt path algebra L(E) is finite dimensional. In our main results we provide two distinct classes of connected graphs from which, modulo the one-dimensional ideals, all finite-dimensional Leavitt path algebras arise.     

Flips and the Hilbert scheme over an exterior algebra

We study the tangent space at a monomial point M in the Hilbert scheme that parameterizes all ideals with the same Hilbert function as M over an exterior algebra.     

Explicit bounds on some new nonlinear integral inequalities with delay

The purpose of the present note is to establish some new delay integral inequalities, which provide explicit bounds on unknown functions and generalize some results of Li et al. [Some new delay integral inequalities and their applications, J. Comput. Appl. Math. 180 (2005) 191–200]. The inequalities given here can be used to investigate the qualitative properties of certain delay differential equations and delay integral equations.     

Symplectic Yang–Mills theory,Ricci tensor,and connections

A Yang–Mills theory in a purely symplectic framework is developed. The corresponding Euler–Lagrange equations are derived and first integrals are given. We relate the results to the work of Bourgeois and Cahen on preferred symplectic connections.     

About the Linear Stability of the Spherically Symmetric Solution for the Equations of a Barotropic Viscous Fluid under the Influence of Self-Gravitation

This paper is concerned with the question of linear stability of motionless, spherically symmetric equilibrium states of viscous, barotropic, self-gravitating fluids. We prove the linear asymptotic stability of such equilibria with respect to perturbations which leave the angular momentum, momentum, mass and the position of the center of gravity unchanged. We also give some decay estimates for such perturbations, which we derive from resolvent estimates by means of analytic semigroup theory.