笛卡儿闭Domain范畴的两个重要性质

对于CONT的任意一个笛卡儿闭的满子范畴C,构造CONT的两个新的满子范畴R-C(以C对象的收缩为对象的范畴)和B-C(以C扩张序列的双极限为对象的范畴),并证明了它们都是笛卡儿闭范畴。由于R-C和B-C都包含C为其满子范畴,利用上述结果可得CONT的极大笛卡儿闭子范畴必对收缩和双极限封闭。本文还从范畴笛卡儿闭性的角度给出了Domain理论中一个公开问题的等价描述。     

Motion of test particles around domain walls

We present a detailed analysis of the motion of test particles around domain walls. The study of the trajectories of the test particles has been done using the Hamilton-Jacobi formalism. In most of the cases we show that the particles can not be trapped by the walls.     

Studies of an infinite element method for acoustical radiation

Infinite element computations are very efficient for predicting the vibro-acoustic response and sensitivities of a vibrating structure for an exterior acoustic domain. In addition, domain decomposition methods are very powerful algorithms for solving large linear systems in parallel. In this paper, an infinite element method is proposed and analyzed for parallel computations purpose. An original formulation of this method with Lagrange multipliers defined on (semi-)infinite space is presented. The implementation aspects of this method in an industrial acoustic software (SYSNOISE) are discussed. New numerical results illustrate the efficiency of the proposed method for realistic acoustical radiation problems.     

A finite-element approach in stream-tube method for solving fluid and solid mechanics problems

This paper presents a theoretical formulation in which the stream-tube method (STM) is examined through a variational approach for solving solid strain and fluid flow problems with finite elements. The analysis considers a reference domain, used as computational domain, related to the physical domain by an unknown transformation function to be determined numerically. Mass conservation is automatically verified by STM. The variational approach leads to eliminate the pressure in fluid problems and avoids to set up a mixed displacement–pressure procedure in the case of incompressible solids. Examples are given for fluid flows, applications and comparisons are also provided in the bending problem in elasticity.     

解与HJB方程相关的拟变分不等式的松弛法

本文对关于HJB方程的拟变分不等式提出了松弛算法，也给出了基于上述算法的区域分解方法，并建立了相应的收敛性定理。     

On the steady motions of a flat domain wall in a ferromagnet

A new derivation is presented of Walker's exact solution to Gilbert equation, a solution which mimicks the travelling-wave motion of a flat domain wall at 180^°. It is shown that a process during which the working of the applied magnetic field exactly compensates dissipation (the Walker condition) exists both under the constitutive circumstances considered in the standard Gilbert equation and when either the internal free-energy or the dissipation, or both, are generalized by the introduction of higher-gradient terms; but that such a process cannot solve the generalized Gilbert equation. It is also shown that, when dry-friction dissipation is considered and a suitable magnetic field is applied, the associated Gilbert equation has a Walker-type solution mimicking a flat wall, at 90^° this time, which however does not satisfy the Walker condition. Received 16 November 2001     

THE CONVERGENCE OF A DOMAIN DECOMPOSITION ALGORITHM FOR PARABOLIC PROBLEMS

At recent, Hourgat et gave a domain decomposition algorithm for elliptic problems which can be implemented in parallel. Many numerical experiments have illustrated its efficiency. In the present paper, we apply this algorithm to solve the discrete parabolic problems, analyse its convergence and show that its convergence rale is about (1 - 2p + σp2 ) which is nearly optimal and independent of the parameter τ, where σ τ O((1 +H )(1 + ln(H / h))2 ). 0 < p < 1 / σ,τ,h,H are the time step size, finite element parameter and subdomain diameter, respectively.     

Extremal stochastic integrals: a parallel between max-stable processes and α-stable processes

We construct extremal stochastic integrals of a deterministic function with respect to a random Fréchet () sup-measure. The measure is sup-additive rather than additive and is defined over a general measure space , where is a deterministic control measure. The extremal integral is constructed in a way similar to the usual stable integral, but with the maxima replacing the operation of summation. It is well-defined for arbitrary , and the metric metrizes the convergence in probability of the resulting integrals.This approach complements the well-known de Haan's spectral representation of max-stable processes with Fréchet marginals. De Haan's representation can be viewed as the max-stable analog of the LePage series representation of stable processes, whereas the extremal integrals correspond to the usual stable stochastic integrals. We prove that essentially any strictly stable process belongs to the domain of max-stable attraction of an Fréchet, max-stable process. Moreover, we express the corresponding Fréchet processes in terms of extremal stochastic integrals, involving the kernel function of the stable process. The close correspondence between the max-stable and stable frameworks yields new examples of max-stable processes with non-trivial dependence structures.This research was partially supported by a fellowship of the Horace H. Rackham School of Graduate Studies at the University of Michigan and the NSF Grant DMS-0505747 at Boston University.     

PIMD上一元多项式环的素理想分类

设R是主理想整环,若R有无穷多个极大理想,则称R是Principal Ideal Maximal Domain,简称为PIMD.设x是PIMD上的未定元,R[x]是R上的一元多项式环.依据整环的基本理论和唯一分解环的结构理论,研究R[x]的素理想和极大理想,推证了R[x]的任一主理想都不是极大理想,给出了构造R[x]的极大理想的一种方法,得到了R[x]的素理想是极大理想的条件,最终给出R[x]的素理想分类定理.     

The influence of wire width on the charge distribution of transverse domain walls and their stray field interactions

We present here a numerical study of the magnetostatic charge distribution of transverse Néel type domain wall in permalloy nanowires. The calculations indicate that not only is the distribution highly non-uniform within a given transverse wall but it also varies dramatically with respect to the wire width. The implications of this for magnetostatic domain wall pinning are analyzed by considering the stray field interaction between a wall and another extended magnetic body for a particular domain wall chirality, where two distinct depinning mechanisms are observed depending on the wire width.