Analytic continuation and identities involving heat,Poisson, wave and Bessel kernels

In this article we use classical formulas involving the K–Bessel function in two variables to express the Poisson kernel on a Riemannian manifold in terms of the heat kernel. We then use the small time asymptotics of the heat kernel on certain Riemannian manifolds to obtain a meromorphic continuation of the associated Poisson kernel to all values of complex time with identifiable singularities. This result reproves in a different setting by different means a well–known theorem due to Duistermaat and Guillemin [DG 75]. Also, we develop analytic expressions for the heat kernel beyond asymptotic expansions. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

ROS3P—An Accurate Third-Order Rosenbrock Solver Designed for Parabolic Problems

In this note we present a new Rosenbrock solver which is third-order accurate for nonlinear parabolic problems. Since Rosenbrock methods suffer from order reduction when they are applied to partial differential equations, additional order conditions have to be satisfied. Although these conditions have been known for a longer time, from the practical point of view only little has been done to construct new methods. Steinebach modified the well-known solver RODAS of Hairer and Wanner to preserve its classical order four for special problem classes including linear parabolic equations. His solver RODASP, however, drops down to order three for nonlinear parabolic problems. Our motivation here was to derive an efficient third-order Rosenbrock solver for the nonlinear situation. Such a method exists with three stages and two function evaluations only. A comparison with other third-order methods shows the substantial potential of our new method.This revised version was published online in October 2005 with corrections to the Cover Date.     

关于椭圆曲线E_D:y~2=x~3-D~2x的BSD猜想

本文证明了形如ｙ~２＝ｘ~３－ｐ-１~２…ｐ-ｎ~２ｘ的一类椭圆曲线的Ⅲ群２-分支在一定条件下同构于 Ｚ／２Ｚ × Ｚ／２Ｚ,其阶为 ４,与Ｌ函数部分的相应结果和 Ｒｕｂｉｎ Ｋ．关于有复乘的椭圆曲线的重要结果一起,我们知道ＢＳＤ猜想对本文定理中的椭圆曲线成立．     

Convergence de mesures spectrales aléatoires et applications à des principes d'invariance

Nous présentons un cadre unificateur pour un certain nombre de résultats connus de convergence en loi pour des processus admettant une représentation linéaire par rapport à un bruit blanc faible pour lequel il existe un principe dinvariance faible. Nous montrons que ce principe dinvariance est équivalent à la convergence dune suite de mesures aléatoires spectrales. Ceci permet daffaiblir les hypothèses usuelles et donc dobtenir des résultats nouveaux de convergence en loi, notamment pour des processus à longue portée.     

Group activity selection problem with approval preferences

We consider a setting where one has to organize one or several group activities for a set of agents. Each agent will participate in at most one activity, and her preferences over activities depend on the number of participants in the activity. The goal is to assign agents to activities based on their preferences in a way that is socially optimal and/or stable. We put forward a general model for this setting, which is a natural generalization of anonymous hedonic games. We then focus on a special case of our model where agents’ preferences are binary, i.e., each agent classifies all pairs of the form ‘(activity, group size)’ into ones that are acceptable and ones that are not. We formulate several solution concepts for this scenario, and study them from the computational point of view, providing hardness results for the general case as well as efficient algorithms for settings where agents’ preferences satisfy certain natural constraints.     

Phase transition,dielectric and piezoelectric properties of NaNbO3–Bi0.5Li0.5TiO3 lead-free ceramics

Lead-free ceramics (1?x)NaNbO₃–xBi_0.5Li_0.5TiO₃ have been fabricated by an ordinary sintering technique, and their electric properties and temperature characteristics have been studied. All the ceramics possess a perovskite structure with orthorhombic symmetry, indicating that (Bi_0.5Li_0.5)TiO₃ diffuses into NaNbO₃ lattices to form a new solid solution. A low (Bi_0.5Li_0.5)TiO₃ doping level transforms the NaNbO₃ ceramics from antiferroelectric to ferroelectric. The ceramics with x ≤ 0.075 are normal ferroelectric, and the ferroelectric-paraelectric phase become diffusives with the doping level of Bi_0.5Li_0.5TiO₃ increasing. As x increases, the Curie temperature of the ceramics decreases linearly, while the relative permittivity ε_r increases. 0.925NaNbO₃–0.075(Bi_0.5Li_0.5)TiO₃ ceramic exhibits the relatively large piezoelectric constant (d₃₃ = 58 pC/N), high Curie temperature (T_C = 228 °C) and good temperature stability, suggesting that the ceramics are one of new possible candidates for lead-free piezoelectric materials.     

自聚焦透镜的傅里叶变换性质及成像性质

对自聚焦透镜的二维傅里叶变换性质,成像性质以及脉冲响应作了系统论述.并从理论上对自行研制的自聚焦透镜的光斑尺寸进行了计算.在不考虑像差的情况下,直径为1.8 mm的透镜其出射光斑直径为1.2 μm,利用狭缝扫描法进行了实际测量,测量值为1.5 μm,理论值与实验值基本吻合,从而说明理论分析的合理性.     

分压与限流线路特性分析

在电学实验的创新设计类问题中,常常涉及到滑线变阻器的分压线路和限流线路。本文对滑线变阻器的分压线路和限流线路的特性作一较系统的分析,对涉及到此类问题的实际工作具有指导意义。     

Symmetry reduction and exact solutions of the (3+1)-dimensional Zakharovben Kuznetsov equation

By means of the classical method, we investigate the (3+1)-dimensional Zakharov-Kuznetsov equation. The symmetry group of the (3+1)-dimensional Zakharov-Kuznetsov equation is studied first and the theorem of group invariant solutions is constructed. Then using the associated vector fields of the obtained symmetry, we give the one-, two-, and three-parameter optimal systems of group-invariant solutions. Based on the optimal system, we derive the reductions and some new solutions of the (3+1)-dimensional Zakharov-Kuznetsov equation.