weyl群的定义关系及其应用

首 先深化 Ｒ． Ｓｔｅｉｎｂｅｒｇ 关于 Ｗ ｅｙｌ 群定义 关系的一个定 理，作为应 用，对 Ｂｌ ， Ｃｌ 型 Ｗ ｅｙｌ群分别构造了一 个指数为２的正 规子群     

Quantum phenomena in magnetic nano clusters

One of the fascinating fields of study in magnetism in recent years has been the study of quantum phenomena in nanosystems. While semiconductor structures have provided paradigms of nanosystems from the stand point of electronic phenomena, the synthesis of high nuclearity transition metal complexes have provided examples of nano magnets. The range and diversity of the properties exhibited by these systems rivals its electronic counterparts. Qualitative understanding of these phenomena requires only a knowledge of basic physics, but quantitative study throws up many challenges that are similar to those encountered in the study of correlated electronic systems. In this article, a brief overview of the current trends in this area are highlighted and some of the efforts of our group in developing a quantitative understanding of this field are outlined.     

Solutions to the reflection equation and integrable systems for N = 2 SQCD with classical groups

Integrable systems underlying the Seiberg-Witten solutions for the N = 2 SQCD with gauge groups SO(n) and Sp(n) are proposed. They are described by the inhomogeneous XXX spin chain with specific boundary conditions given by reflection matrices. We attribute reflection matrices to orientifold planes in the brane construction and briefly discuss its possible deformations.     

Spectral reduction for control systems modeling passive integrated circuits

Linear control systems modeling passive integrated circuits are examined. A new algebraic method of spectral reduction equipped with efficient tools for preserving passivity is proposed and justified. For RC networks (circuits), this method is similar to and can be regarded as an extension of the well-known PACT method, which is based on congruence transforms. Up to now, such an extension seemed to be impossible, and different techniques were used for the reduction of RCL and RCLM networks. Some numerical results are presented.     

Consecutive customer losses in regular and oscillating <Emphasis Type="Italic">M</Emphasis><Superscript><Emphasis Type="Italic">X</Emphasis></Superscript>/<Emphasis Type="Italic">G</Emphasis>/1/<Emphasis Type="Italic">n</Emphasis> systems

We derive fast recursions to compute the probability that k or more consecutive customer losses take place during a busy period of a queue, the so called k-CCL probability, for regular and oscillating M ^X /G/1/n systems.     

Periodic Solutions and Approximate Symmetries

Assuming that a dynamical system (DS) has a periodic solutionwith period T in the neighborhood of an equilibrium, a newDS can be obtained which governs approximately the motion oftrajectories in the neighborhood of the periodic orbit. Approximatesymmetries and first integrals have been discussed for this DS. Theresults have been demonstrated on the Helmholtz oscillator.     

The Kinetic Theory of Simple Reacting Spheres: I. Global Existence Result in a Dilute-Gas Case

Existence of global-in-time, spatially inhomogeneous, and L ¹-renormalized solutions is proven for the model of simple reacting spheres under the assumptions that initially the system has a finite total mass, energy, and entropy.     

Self-quenched dynamics

We introduce a model for the slow relaxation of an energy landscape caused by its local interaction with a random walker whose motion is dictated by the landscape itself. By choosing relevant measures of time and potential this self-quenched dynamics can be mapped on to the “True” Self-Avoiding Walk model. This correspondence reveals that the average distance of the walker at time t from its starting point is , where for one dimension and 1/2 for all higher dimensions. Furthermore, the evolution of the landscape is similar to that in growth models with extremal dynamics. Received 8 August 2000     

Interaction of Two Charges in a Uniform Magnetic Field: II. Spatial Problem

The interaction of two charges moving in ℝ³ in a magnetic field B can be formulated as a Hamiltonian system with six degrees of freedom. Assuming that the magnetic field is uniform and the interaction potential has rotation symmetry, we reduce this system to one with three degrees of freedom. For special values of the conserved quantities, choices of parameters or restriction to the coplanar case, we obtain systems with two degrees of freedom. Specialising to the case of Coulomb interaction, these reductions enable us to obtain many qualitative features of the dynamics. For charges of the same sign, the gyrohelices either “bounce-back”, “pass-through”, or exceptionally converge to coplanar solutions. For charges of opposite signs, we decompose the state space into “free” and “trapped” parts with transitions only when the particles are coplanar. A scattering map is defined for those trajectories that come from and go to infinite separation along the field direction. It determines the asymptotic parallel velocities, guiding centre field lines, magnetic moments and gyrophases for large positive time from those for large negative time. In regimes where gyrophase averaging is appropriate, the scattering map has a simple form, conserving the magnetic moments and parallel kinetic energies (in a frame moving along the field with the centre of mass) and rotating or translating the guiding centre field lines. When the gyrofrequencies are in low-order resonance, however, gyrophase averaging is not justified and transfer of perpendicular kinetic energy is shown to occur. In the extreme case of equal gyrofrequencies, an additional integral helps us to analyse further and prove that there is typically also transfer between perpendicular and parallel kinetic energy.      

Generalized Halanay inequalities for dissipativity of Volterra functional differential equations

This paper is concerned with the dissipativity of theoretical solutions to nonlinear Volterra functional differential equations (VFDEs). At first, we give some generalizations of Halanay's inequality which play an important role in study of dissipativity and stability of differential equations. Then, by applying the generalization of Halanay's inequality, the dissipativity results of VFDEs are obtained, which provides unified theoretical foundation for the dissipativity analysis of systems in ordinary differential equations (ODEs), delay differential equations (DDEs), integro-differential equations (IDEs), Volterra delay-integro-differential equations (VDIDEs) and VFDEs of other type which appear in practice.