General Solutions of Relativistic Wave Equations II: Arbitrary Spin Chains

A construction of relativistic wave equations on the homogeneous spaces of the Poincaré group is given for arbitrary spin chains. Parametrizations of the field functions and harmonic analysis on the homogeneous spaces are studied. It is shown that a direct product of Minkowski space time and two-dimensional complex sphere is the most suitable homogeneous space for the physical applications. The Lagrangian formalism and field equations on the Poincaré and Lorentz groups are considered. A boundary value problem for the relativistically invariant system is defined. General solutions of this problem are expressed via an expansion in hyperspherical functions defined on the complex two-sphere. PACS numbers: 02.30.Gp, 02.60.Lj, 03.65.Pm, 12.20.-m     

The atomic and molecular reaction statics

This work presents a new science called atomic and molecular reaction statics (AMRS). There are four parts for AMRS, i.e. the group theoretical derivation of molecular electronic states, the principle of microscopic reversibility, the principle of microscopic transitivity and the optimum energy process rule. AMRS has been developed for about twenty years.     

Poincaré Semigroup Symmetry as an Emergent Property of Unstable Systems

The notion that elementary systems correspond to irreducible representations of the Poincaré group is the starting point for this paper, which then goes on to discuss how a semigroup for the time evolution of unstable states and resonances could emerge from the underlying Poincaré symmetry. Important tools in this analysis are the Clebsch-Gordan coefficients for the Poincaré group.     

Scaling,Renormalization and Statistical Conservation Laws in the Kraichnan Model of Turbulent Advection

We present a systematic way to compute the scaling exponents of the structure functions of the Kraichnan model of turbulent advection in a series of powers of ξ, adimensional coupling constant measuring the degree of roughness of the advecting velocity field. We also investigate the relation between standard and renormalization group improved perturbation theory. The aim is to shed light on the relation between renormalization group methods and the statistical conservation laws of the Kraichnan model, also known as zero modes.     

变压器寄生参数和负载特性对高压脉冲波形的影响

构建了输出电压幅值为0～20 kV、脉冲重复频率为0.25～20 kHz的双极性高压脉冲电源实验平台,研究了变压器寄生参数与负载特性对输出脉冲波形的影响。采用等效电路复频域解析方法,分析了变压器寄生参数对输出脉冲波形的上升沿、平顶及下降沿的影响规律,并通过改变变压器绕线方案间接验证。发现变压器分布电容和漏感越大,输出脉冲波形上升沿与下降沿越平缓,过冲电压幅值越大,并采用脉冲变压器二次侧均匀密绕、一次侧均匀疏绕、高匝数的方案进行优化。进一步分析了纯阻性、阻容性或阻感性负载特性对输出高压脉冲波形的影响规律,发现电阻值增大（5～50 kΩ）,过冲电压幅值增大,脉冲上升沿和下降沿变陡;当负载电阻回路串联小电容时,过冲电压幅值显著增大,而电容值高于一定值时输出脉冲波形恢复至与纯电阻波形一样;当负载电阻回路串联电感时,输出脉冲波形下降沿变平缓。     

Generating Quadratic Pseudo-Anosov Homeomorphisms of Closed Surfaces

In this note, we show that given a closed, orientable genus-g surface S _g , any hyperbolic toral automorphism has a positive power which induces a quadratic, orientable pseudo-Anosov homeomorphism on S _g . To show this, we lift Anosov toral automorphisms through a ramified topological covering and present the lifted homeomorphism via a standard set of Lickorish twists. This construction provides a general method of producing pseudo-Anosov maps of closed surfaces with predetermined orientable foliations and quadratic dilatation. Since these lifted automorphisms have orientable foliations, this construction is a sort of converse to that of Franks and Rykken [Trans. Amer. Math. Soc. 1999], who established that one can associate to a quadratic pseudo-Anosov homeomorphism with oriented unstable foliation a hyperbolic toral automorphism.     

左联合谱的一个刻划及其应用

In this paper we characterize the left joint spectrum of an n-tuple T =(T1,... ,Tn) of dominant bounded linear operators on a complex Hilbert space H and the unital C^*-algebra C^*(T) generated by T1,… , Tn and I; moreover, we give an application of this characterization.     

Exploiting Electrostatics To Generate Unsaturation: Oxidative GeE Bond Formation Using a Non π‐Donor Stabilized [R(L)Ge:]+ Cation

The two‐coordinate germanium cation [(IDipp){(Me₃Si)₂CH}Ge:]⁺ has been synthesized, which lacks π‐donor stabilization of the metal center and consequently has a very small HOMO–LUMO gap (187 kJ mol^?1). It undergoes a variety of facile oxidative bond‐forming reactions, most notably allowing access to the first examples of Group 14 metal cations containing M?E multiple bonds (E=C, N). The use of an electrostatic (rather than purely steric) strategy to discourage aggregation means that less bulky systems (for example, containing a primary alkylidene fragment, ?CHR) are accessible.     

用等效网络方法求均匀弹簧纵振动的本征频率

利用机电类比方法导出了均匀质量弹簧在几种特定边界条件下的本征频率方程,并给出了相应的本征频率公式。体现了等效网络理论分析机械振动问题的优越性。     

Some New uniform frames with block size four and index one or three

In this paper, some new uniform frames with block size four and index one or three are obtained. The known existence results for (4,1)‐frames and (4,3)‐frames are both improved to the extent that only a finite number of possible exceptions remain. © 2003 Wiley Periodicals, Inc.