Universal series induced by approximate identities and some relevant applications

We prove the existence of series ∑a_nψ_n, whose coefficients (a_n) are in ∩_p>1?^p and whose terms (ψ_n) are translates by rational vectors in R^d of a family of approximations to the identity, having the property that the partial sums are dense in various spaces of functions such as Wiener’s algebra W(C₀,?¹), C_b(R^d), C₀(R^d), L^p(R^d), for every p∈[1,∞), and the space of measurable functions. Applying this theory to particular situations, we establish approximations by such series to solutions of the heat and Laplace equations as well as to probability density functions.     

一个与Dedekind和相关的新和式及其在特殊点的值

本文利用正整数模q的正则数的定义以及解析方法研究一类与Dedekind和有关的和式的计算问题,并给出这个和式在一些特殊点上有趣的恒等式.     

Dynamic Picone's identity and its applications

We prove some Picone-type identities and inequalities for a class of first-order nonlinear dynamic systems and derive various weighted inequalities of Wirtinger type and Hardy type on time scales. As applications we study oscillatory and related properties of these systems including Reid's roundabout theorem on disconjugacy, Sturm's separation and comparison theorems, as well as a variational method in the oscillation theory.     

基于吴方法的几何定理证明的恒等式方法

多年来通常认为以吴方法为代表的几何定理机器证明的坐标法给出的证明不可读,或不是图灵意义下的类人解答.其实,只要对吴氏的算法做不多的改进,即将命题的结论多项式表示为其条件多项式的线性组合,就能获得不依赖于理论、算法和大量计算过程的恒等式明证.这样的恒等式可以转化为其他更简明且更有直观几何意义的点几何形式或向量及其他形式,从而获得多种证明方法.这也证明了点几何恒等式明证方法对等式型几何命题的普遍有效性.     

密度矩阵重正化群的异构并行优化

密度矩阵重正化群方法（DMRG）在求解一维强关联格点模型的基态时可以获得较高的精度,在应用于二维或准二维问题时,要达到类似的精度通常需要较大的计算量与存储空间.本文提出一种新的DMRG异构并行策略,可以同时发挥计算机中央处理器（CPU）和图形处理器（GPU）的计算性能.针对最耗时的哈密顿量对角化部分,实现了数据的分布式存储,并且给出了CPU和GPU之间的负载平衡策略.以费米Hubbard模型为例,测试了异构并行程序在不同DMRG保留状态数下的运行表现,并给出了相应的性能基准.应用于4腿梯子时,观测到了高温超导中常见的电荷密度条纹,此时保留状态数达到10⁴,使用的GPU显存小于12 GB.     

Another proof of Bianchi's identity in arbitrary bundles

In this paper we relate the group of automorphisms of a principal fibre bundle with the (second) Bianchi identity generalizing a result of Kazdan.During the preparation of this paper the author was supported by a fellowship of theGraduiertenkolleg Geometrie und Mathematische Physik at the Ruhr-Universität Bochum.     

Dissipation and Decoherence in a Quantum Oscillator

The time development of the reduced density matrix for a quantum oscillator damped by coupling it to an ohmic environment is calculated via an identity of the Debye-Waller form. Results obtained some years ago by Hakim and the author in the free-particle limit⁽¹⁰⁾ are thus recovered. The evolution of a free particle in a prepared initial state is examined, and a previously published exchange^(5,9) is illuminated with figures showing no decoherence without dissipation. PACS number: 03.75.Ss     

Some Hardy Type Inequalities in R~n

Some Hardy type inequalities on the ball and its complementary set in the Euclidean space are established by using the Picone type identity and constructing suitable auxiliary functions.     

相空间路径积分中的Feynman规则和广义Ward恒等式

基于Green函数的相空间生成泛函,导出了广义正则Ward恒等式.指出无须作出相空间生成泛函中对正则动量的路径积分,即可求得树图近似下的Feynman规则.对场的拉氏量添加一个四维散度项后,场的传播子发生了改变.     

The Asymptotic Behavior of Certain Birth Processes

We describe a connection between discrete birth process and a certain family of multivariate interpolation polynomials. This enables us to compute all asymptotic moments of the birth process, generalizing previously known results for the mean and variance. Received July 15, 2004