广义相对论的几个问题

介绍了爱因斯坦如何建立广义相对论,以及人们应该如何理解这一关于时间、空间和引力的理论.     

Classical Versus Quantum Equivalence Between Sine-Gordon,Liouville and Other Solitons

In this work we present a mapping between the classical solutions of the sine-Gordon, Liouville, ⁴ and other kinks in 1+1 dimensions. This is done by using an invariant quantity which relates the models. It is easily shown that this procedure is equivalent to that used to get the so called deformed solitons, as proposed recently by Bazeia et al. [Phys. Rev. D. 66 (2002) 101701(R)]. The classical equivalence is explored in order to relate the solutions of the corresponding models and, as a consequence, try to get new information about them. We discuss also the difficulties and consequences which appear when one tries to extend the deformation in order to take into account the quantum version of the models.     

Numerical analysis of the Gran methods. A comparative study

The paper concerns mainly the modified Gran methods, considered as extrapolative standard addition methods. Particularly, the approximation:

     

A Grobman–Hartman Theorem for Control Systems

We consider the problem of locally linearizing a control system via topological transformations. According to [2,3], there is no naive generalization of the classical Grobman–Hartman theorem for ODEs to control systems: a generic control system, when viewed as a set of under-determined differential equations parametrized by the control, cannot be linearized using pointwise transformations on the state and the control values. However, if we allow the transformations to depend on the control at a functional level (open loop transformations), we are able to prove a version of the Grobman–Hartman theorem for control systems.     

Mbone仿真骨压缩及扭转生物力学等效性研究

在临床应用及骨力学研究中,尸体骨样品稀缺且一致性较差,因此力学等效仿真骨不可或缺。美国Sawbones合成骨是目前世界上最具认可度的力学等效仿真骨,但其模型基于西方人开发,与中国人骨型有差异,尤其是股骨前弓角和前倾角与中国人有较大不同。本文旨在通过生物力学实验,研究基于中国人骨特点自研的新型力学等效仿真骨Mbone股骨的压缩及扭转力学性能,验证其力学等效性。本文测试并对比了新型自研力学等效仿真骨Mbone股骨和Sawbones股骨的压缩及扭转力学性能,结果显示：受压时,Mbone股骨压缩刚度比Sawbones略高7.2%,且其压缩破坏载荷在尸体骨范围内,破坏后呈现出与临床相符的股骨颈骨折;Mbone股骨内侧中段偏后方的压应变明显高于Sawbones,其他15个区域压应变与Sawbones高度一致。受扭时,Mbone股骨内旋扭转刚度比Sawbones略低6.7%,外旋扭转刚度比Sawbones低18.3%。Mbone力学等效仿真股骨在压缩及扭转力学性能上均表现出良好的力学等效性,且更贴合中国人骨型,因此认为其可以替代进口产品作为尸体骨的力学等效模型。     

Transverse disks, symbolic dynamics, homology direction vectors, and Thurston-Nielson theory

We review some properties of transverse disks and use symbolic dynamics to determine rotation vectors from the return map to a transverse disk. We also prove connections between the symbolic dynamics and Nielson equivalence of orbits.     

New light on the optical equivalence theorem and a new type of discrete diagonal coherent state representation

In many instances we find it advantageous to display a quantum optical density matrix as a generalized statistical ensemble of coherent wave fields. The weight functions involved in these constructions turn out to belong to a family of distributions, not always smooth functions. In this paper we investigate this question anew and show how it is related to the problem of expanding an arbitrary state in terms of an overcomplete subfamily of the overcomplete set of coherent states. This provides a relatively transparent derivation of the optical equivalence theorem. An interesting by-product is the discovery of a new class of discrete diagonal representations. Work supported in part by the Energy Research and Development Administration, Contract No. E(40-I)3992.     

关于有限群模范畴的商范畴及其等价函子

将所有能被p-可除kG-模分解的同态映射做成一个理想,利用该理想构造了有限群G的模范畴的商范畴,分析了该商范畴中的零对象,并得到该商范畴的3个等价函子。     

Kac-系统与Morita等价

本文讨论与Hilbert C~*-模相关的Kac-系统在C~*-代数上的作用的性质,给出了两个Morita等价的C~*-代数(在Kac-系统的作用下得到的C~*-代数的余交叉积是Morita等价的)。从而,Baaj和Skandalis等人的结论是本文定理的特殊情况。