二阶半线性常微分方程Robin边值问题的奇摄动

用基本方法讨论了一个半线性奇摄动Robin边值问题.利用微分不等式理论，证明了问题解的存在性，并得到了解的渐近估计.作为应用，给出了两个例子，一个是将结果应用于一个燃烧反应扩散问题的模型，另一个是得到了有关Dirichlet问题的相应结果.     

Tracking accuracy of a semi‐Lagrangian method for advection–dispersion modelling in rivers

There is an increasing need to improve the computational efficiency of river water quality models because: (1) Monte‐Carlo‐type multi‐simulation methods, that return solutions with statistical distributions or confidence intervals, are becoming the norm, and (2) the systems modelled are increasingly large and complex. So far, most models are based on Eulerian numerical schemes for advection, but these do not meet the requirement of efficiency, being restricted to Courant numbers below unity. The alternative of using semi‐Lagrangian methods, consisting of modelling advection by the method of characteristics, is free from any inherent Courant number restriction. However, it is subject to errors of tracking that result in potential phase errors in the solutions. The aim of this article is primarily to understand and estimate these tracking errors, assuming the use of a cell‐based backward method of characteristics, and considering conditions that would prevail in practical applications in rivers. This is achieved separately for non‐uniform flows and unsteady flows, either via theoretical considerations or using numerical experiments. The main conclusion is that, tracking errors are expected to be negligible in practical applications in both unsteady flows and non‐uniform flows. Also, a very significant computational time saving compared to Eulerian schemes is achievable. Copyright © 2006 John Wiley & Sons, Ltd.     

Structures of Wey1 Groups of Some Kac-Moody Algebras

ＳｔｒｕｃｔｕｒｅｓｏｆＷｅｙ１ＧｒｏｕｐｓｏｆＳｏｍｅＫａｃ┐ＭｏｏｄｙＡｌｇｅｂｒａｓ＊）ＬｕＣａｉｈｕｉ（卢才辉）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＣａｐｉｔａｌＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，Ｂｅｉｊｉｎｇ，１０００３７）Ｚ...     

Pointed shape and global attractors for metrizable spaces

In this paper we consider two notions of attractors for semidynamical systems defined in metric spaces. We show that Borsuk's weak and strong shape theories are a convenient framework to study the global properties which the attractor inherits from the phase space.Moreover we obtain pointed equivalences (even in the absence of equilibria) which allow to consider also pointed invariants, like shape groups.     

Simple Twisted Group Algebras of Dimension p4 and their Semi-Centers

For a simple twisted group algebra over a group G, if G^∣ is Hall subgroup of G, then the semi-center is simple. Simple twisted group algebras correspond to groups of central type. We classify all groups of central type of order p⁴ where p is prime and use this to show that for odd primes p there exists a unique group G of order p⁴, such that there exists simple twisted group algebra over G with a commutative semi-center. Moreover, if 1 < |G| <64, then the semi-center of simple twisted group algebras over G is noncommutative and this bounds are strict.     

The Method of Upper and Lower Solutions of Stochastic Differential Equations and Applications

Abstract

The purpose of this article is to consider a stochastic integral equation driven by semimartingale with discontinuous and increasing drift part. We discuss the existence of strong solutions using lower and upper solutions method and a fixed point theorem for ordered topological space. Finally we present some applications in finance.     

Shape Invariant Potential and Semi-Unitary Transformations (SUT) for Supersymmetry Harmonic Oscillator in <Emphasis Type="Italic">T</Emphasis><Superscript>4</Superscript>-Space

Constructing the Semi-Unitary Transformations (SUT) to obtain the supersymmetric partner Hamiltonians for a one dimensional harmonic oscillator, it has been shown that under this transformation the supersymmetric partner loses its ground state in T ⁴-space while its eigen functions constitute a complete orthonormal basis in a subspace of full Hilbert space.     

GPS／捷联惯性组合导航系统的一种半实时算法

本文讨论了ＧＰＳ／捷联惯性组合导航系统的原理和特点，针对其理论仿真和工程实现中的衔接问题，提出了一种半实时算法。该算法既继承了理论仿真方便、直接的优点；又充分利用了实测数据。系统调试成功后，可以直接将全套软件转换到导航计算机中。文中给出了半实时算法的原理和方案，讨论了组合卡尔曼滤波器的实现和ＧＰＳ仿真器、航迹仿真器、惯性器件等的设置。最后给出了有关结论。     

Semi‐linear wave models with power non‐linearity and scale‐invariant time‐dependent mass and dissipation

In this paper we will consider the semi‐linear Cauchy problem for wave models with scale‐invariant time‐dependent mass and dissipation and power non‐linearity. The goal is to study the interplay between the coefficients of the mass and the dissipation term to prove blow‐up results or global existence (in time) of small data energy solutions.     

New Intermetallic Compounds Ln2Ni2Mg (Ln = Y,La–Nd,Sm, Gd–Tm) with Mo2FeB2 Structure

The title compounds were synthesized by reacting the elements in sealed tantalum tubes in a high‐frequency furnace. They crystallize with the Mo₂FeB₂ structure, a ternary ordered variant of the U₃Si₂ type, space group P4/mbm. All compounds were characterized through Guinier powder patterns and the lattice parameters were obtained from least‐squares fits. Four structures were refined from single crystal X‐ray data: a = 740.5(1) pm, c = 372.5(1) pm, wR2 = 0.0430, 247 F values, 13 variables for Y₂Ni_1.90Mg, a = 764.5(1) pm, c = 394.39(9) pm, wR2 = 0.0371, 310 F values, 12 variables for La₂Ni₂Mg, a = 754.4(1) pm, c = 385.20(9) pm, wR2 = 0.0460, 295 F values, 12 variables for Pr₂Ni₂Mg, and a = 752.53(8) pm, c = 382.33(5) pm, wR2 = 0.0183, 291 F values, and 12 variables for Nd₂Ni₂Mg. A refinement of the occupancy parameters indicated small defects on the nickel site of the yttrium compound, resulting in the composition Y₂Ni_1.90Mg for the investigated single crystal. The compounds with cerium, samarium, and gadolinium to thulium as rare earth component were characterized through their Guinier powder patterns. The cell colume of Ce₂Ni₂Mg is smaller than that of Pr₂Ni₂Mg, indicating intermediate‐valent cerium. The structures can be considered as an intergrowth of distored AlB₂ and CsCl related slabs of compositions LnNi₂ and LnMg. Chemical bonding in La₂Ni₂Mg and isotypic La₂Ni₂In is compared on the basis of extended Hückel calculations.