无限秩典型根系的自同构

所谓一个无限秩典型根系△是指型A∞,A+∞,B∞,C∞或D∞的无限秩根系的一种.对任一非负整数l,△包含一个有限根系△l,使得△0△l…且本文的工作是求出△的保持每一△ni的所有自同构,其中ni属于集合{ni},集合{ni|i=1,2,…}是任一给定的非负整数序列且n1<n2<….这是有限根系的自同构群的推广.     

States of Infinite Equilibrium Classical Systems

We construct a measure that corresponds to the correlation functions of equilibrium states of infinite systems of classical statistical mechanics. The correlation functions satisfy the Bogolyubov compatibility conditions. We also construct measures that correspond to the correlation functions of nonequilibrium states of infinite systems for the Boltzmann hierarchy and the Bogolyubov–Strel'tsova diffusion hierarchy.     

具无穷时滞退化中立型微分系统的周期解(英文)

In this paper,we discuss the periodic solutions of the nonlinear singular neutral differential systems with infinite delay.By using matrix measure and Krasnoselskii＇s fixed point theorem,we obtained the suffcient conditions of the existence of periodic solutions.     

Some Long-Range Dependence Processes Arising from Fluctuations of Particle Systems

Several long-range dependence, self-similar Gaussian processes arise from asymptotics of some classes of spatially distributed particle systems and superprocesses. The simplest examples are fractional Brownian motion and sub-fractional fractional Brownian motion, the latter being intermediate between Brownian motion and fractional Brownian motion. In this paper we focus mainly on long-range dependence processes that arise from occupation time fluctuations of immigration particle systems with or without branching, and we study their properties. Some long-range dependence non-Gaussian processes that appear in a similar way are also mentioned. Mathematics Subject Classifications (2000) Primary 60G15, 60G18; secondary 60F17, 60G20, 60J80.Research partially supported by CONACyT grant 37130-E (Mexico).     

Dynamics of Lotka-Volterra Competition Systems with Large Interaction

We show that under certain additional hypothesis, two population competing species models in bounded domains with diffusion and large interaction have simple dynamics. In particular, the solutions approach stationary states as t tends to infinity.     

Continuous Limits of Classical Repeated Interaction Systems

We consider the physical model of a classical mechanical system (called “small system”) undergoing repeated interactions with a chain of identical small pieces (called “environment”). This physical setup constitutes an advantageous way of implementing dissipation for classical systems; it is at the same time Hamiltonian and Markovian. This kind of model has already been studied in the context of quantum mechanical systems, where it was shown to give rise to quantum Langevin equations in the limit of continuous time interactions (Attal and Pautrat in Ann Henri Poincaré 7:59–104, 2006), but it has never been considered for classical mechanical systems yet. The aim of this article is to compute the continuous limit of repeated interactions for classical systems and to prove that they give rise to particular stochastic differential equations (SDEs) in the limit. In particular, we recover the usual Langevin equations associated with the action of heat baths. In order to obtain these results, we consider the discrete-time dynamical system induced by Hamilton’s equations and the repeated interactions. We embed it into a continuous-time dynamical system and compute the limit when the time step goes to 0. This way, we obtain a discrete-time approximation of SDE, considered as a deterministic dynamical system on the Wiener space, which is not exactly of the usual Euler scheme type. We prove the L ^p and almost sure convergence of this scheme. We end up with applications to concrete physical examples such as a charged particle in a uniform electric field or a harmonic interaction. We obtain the usual Langevin equation for the action of a heat bath when considering a damped harmonic oscillator as the small system.     

On Infinite Disjoint Congruence Covering Systems

In this paper we show that for any α∈(0,l] there exists an infinite disjoint covering system {a1(modni)}i=1∞ such that     

在有限部分具有四个奇点二次系统的无穷远奇点

为了研究具有四个奇点二次系统的结构,本文研究了这类系统的无穷远奇点。 一般来说,二次系统的无穷远奇点是比较复杂的。但是在有限范围内具有四个奇点的次系统,它的无穷远奇点则具有某些特殊性质。为了方便,下面以E_2~4表示这种系统。     

On the Variety of Solutions of Generalized Cauchy-Riemann Systems with a Singular Line

In the article it is proved that a specific generalized Cauchy-Riemann system with singularity on a circle has only the trivial solution in the class of infinitely differentiable functions.     

On Stability and Stabilizability of Singular Stochastic Systems with Delays

This paper deals with the class of continuous-time singular linear systems with Markovian jump parameters and time delays. Sufficient conditions on the stochastic stability and stochastic stabilizability are developed. A design algorithm for a state feedback controller which guarantees that the closed-loop dynamics will be regular, impulse free, and stochastically stable is proposed in terms of the solutions to linear matrix inequalities. The research of this author was supported by NSERC Grant RGPIN36444-02. The research of this author was supported by the Program for a New Century of Excellent Talents in the Universities and by the Foundation for the Authors of National Excellent Doctoral Dissertations of P. R. China, Grant 200240. The research of this author was supported by HKU Grant RGC 7029/05P.     

Uniqueness for a Historical SDE with a Singular Interaction

We consider a measure-valued process that models a self-repelling or self-attracting population. The process is found as the unique solution to an equation driven by historical Brownian motion. The main result is pathwise uniqueness for a historical stochastic differential equation with a singular drift coefficient.     

奇异k紧整数的无限族

设n，s1，s2是3个正整数，使得s1〈s2〈n，gcd（n．s1，s2）=1，G（n；s1，s2）是n个结点的步长为s1和s2的双环网，d（n；s1，s2）是其直径．设d（n）=min{d（n；s1，s2）│s1〈s2〈n}，d1（n）=min{d（n；1，s）│1〈s〈n}．已知d1（n）≥d（n）≥[√3n]-2=lb（n）．若d（n；s1，s2）=d（n）=lb（n）＋k，k≥0，则称双环网G（n；s1，s2）是k紧优双环网．若d1（n）〉d（n）=lb（n）＋k，则n称为奇异k紧整数．本文给出构造奇异k紧整数无限族的方法，并对于k=1，2．…，20．构造出这样的无限族．     

The Coordinate of the Singular Point of Generating Functions of Clusters in the High-Temperature Dynamics of Spin Lattice Systems with Axially Symmetric Interaction

We investigate generating functions for equipped trees composed of double bonds of two sorts on a hypercubic lattice of dimension d with built-in fragments. Rules for constructing these clusters are chosen to ensure the estimate for coefficients of power series in time for the longitudinal and transverse autocorrelation functions of the spin system with axially symmetric interaction. We derive a system of two equations for the tree-generating functions and an equation for the generating functions of chains leading from the root to a fragment in a tree using the Bethe approximation and under the condition that mainly bonds of one sort are taken into account. For the face-centered hypercubic lattice, we find the first terms of the 1/d expansion for the coordinate of the singular point of the generating function in both the anisotropic and the isotropic cases taking fragments in the forms of a triangle from four bonds and a four-fold bound pair into account. The obtained result is written in terms of ratios of lattice sums and is generalized to nuclear spin systems with dipole–dipole interaction. The theoretical value of the singular-point coordinate agrees well with the experimental value calculated from the tail of the absorption spectrum of the nuclear magnetic resonance in a barium fluoride monocrystal.     

On Some Quasilinear Elliptic Systems with Singular and Sign-Changing Potentials

Using variational methods, we study the existence and nonexistence of nontrivial weak solutions for the quasilinear elliptic system $$\left\{\begin{array}{ll}- {\rm div}(h_1(|\nabla u|^2)\nabla u) = \frac{\mu}{|x|^2}u + \lambda F_u(x, u, \upsilon)\quad {\rm in}\,\Omega,\\- {\rm div}(h_2(|\nabla \upsilon|^2)\nabla \upsilon) = \frac{\mu}{|x|^2}\upsilon + \lambda F_\upsilon(x,u,\upsilon)\quad {\rm in}\,\Omega,\\u = \upsilon = 0 \qquad \qquad \qquad \qquad \qquad \qquad {\rm in}\, \partial\Omega, \end{array}\right.$$ where \({\Omega \subset \mathbb{R}^N,N \geq 3}\) , is a bounded domain containing the origin with smooth boundary \({\partial \Omega ; h_i, i = 1, 2}\) , are nonhomogeneous potentials; \({(F_u, F_v) = \nabla F}\) stands for the gradient of a sign-changing C ¹-function \({F : \Omega \times \mathbb{R}^2 \to \mathbb{R}}\) in the variable \({{w = (u, v) \in \mathbb{R}^2}}\) ; and λ and μ are parameters.     

On State Feedback Stabilization of Singular Systems with Random Abrupt Changes

This paper deals with the class of continuous-time singular linear systems with random abrupt changes. The state feedback stabilization and its robustness for this class of systems with norm-bounded uncertainties are tackled. Sufficient conditions for designing either a stabilizing controller or a robust stabilizing controller are developed in the LMI setting. The developed sufficient conditions are used to synthesize the state feedback controller that guarantees that either the nominal system or the uncertain system is piecewise regular, impulse free and stochastically stable or robust stochastically stable. The research of this author was supported by NSERC, Grant RGPIN36444-02.     

Asymptotic Analysis for a Class of Infinite Systems of First-Order PDE: Nonlinear Parabolic PDE in the Singular Limit

Abstract

We study the asymptotic behavior of solutions of the Cauchy problem for a functional partial differential equation with a small parameter as the parameter tends to zero. We establish a convergence theorem in which the limit problem is identified with the Cauchy problem for a nonlinear parabolic partial differential equation. We also present comparison and existence results for the Cauchy problem for the functional partial differential equation and the limit problem.     

On Dynamics Related to a Class of Numeration Systems

 In this paper, we investigate the class of numeration systems and we study the associated dynamical systems, called odometers. It is shown that these odometers are measure-theoretically isomorphic to rank one transformations on the unit interval, constructed by a cutting-stacking method. Furthermore, a symbolic coding leads to isomorphic shift systems arising from substitutions. Some skew products of the odometers by cocycles related to the sum of digits are shown to be ergodic.