Statistical mechanics and ocean circulation

We apply equilibrium statistical mechanics based upon the conservation of energy and potential enstrophy to the mass-density distribution within the ocean, using a Monte Carlo method that conserves the buoyancy of each fluid particle. The equilibrium state resembles the buoyancy structure actually observed.     

Statistical inference for detrended point processes

We consider a multivariate point process with a parametric intensity process which splits into a stochastic factor b_t and a trend function a_t of a squared polynomial form with exponents larger than . Such a process occurs in a situation where an underlying process with intensity b_t can be observed on a transformed time scale only. On the basis of the maximum likelihood estimator for the unknown parameter a detrended (or residual) process is defined by transforming the occurrence times via integrated estimated trend function. It is shown that statistics (mean intensity, periodogram estimator) based on the detrended process exhibit the same asymptotic properties as they do in the case of the underlying process (without trend function). Thus trend removal in point processes turns out to be an appropriate method to reveal properties of the (unobservable) underlying process – a concept which is well established in time series. A numerical example of an earthquake aftershock sequence illustrates the performance of the method.     

Computational applications of nonextensive statistical mechanics

Computational applications of the nonextensive entropy _Sq$S_q$ and nonextensive statistical mechanics, a current generalization of the Boltzmann–Gibbs (BG) theory, are briefly reviewed. The corresponding bibliography is provided as well.     

Statistical mechanics of choice: MaxEnt estimation of population heterogeneity

The paper studies heterogeneity of large populations of decision-makers in terms of their choice behavior. It is argued that heterogeneity measures may be deduced from the aggregate data by application of the Maximum Entropy (MaxEnt) formalism. The case of the aggregate data being comprised of value shares is studied in detail; it is shown that the estimate of heterogeneity belongs to the product-form family of probability distributions.     

Statistical analysis of dyadic stationary processes

In this paper we consider a multiple dyadic stationary process with the Walsh spectral density matrix f(), where is an unknown parameter vector. We define a quasi-maximum likelihood estimator % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-qqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xHapdbiqaaeGaciGaaiaabeqaamaabaabaaGcbaGabeiUdyaaja% aaaa!377D!\[{\rm{\hat \theta }}\] of , and give the asymptotic distribution of % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-qqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xHapdbiqaaeGaciGaaiaabeqaamaabaabaaGcbaGabeiUdyaaja% aaaa!377D!\[{\rm{\hat \theta }}\] under appropriate conditions. Then we propose an information criterion which determines the order of the model, and show that this criterion gives a consistent order estimate. As for a finite order dyadic autoregressive model, we propose a simpler order determination criterion, and discuss its asymptotic properties in detail. This criterion gives a strong consistent order estimate. In Section 5 we discuss testing whether an unknown parameter satisfies a linear restriction. Then we give the asymptotic distribution of the likelihood ratio criterion under the null hypothesis.This work is supported by Contract N00014-85-K-0292 of the Office of Naval Research and Contract F49620-85-C-0008 of the Air Force Office of Scientific Research. The United States Government is authorized to reproduce and distribute reprints for governmental purposes notwithstanding any copyright notations hereon.The work of this author was done at the Center for Multivariate Analysis. His permanent address is Department of Mathematics, Hiroshima University, Hiroshima 730, Japan.     

阳性药对照临床试验中非劣效性检验的统计分析方法及相关问题

现阶段所进行的新药临床试验设计方法中,由于以安慰剂为对照的优效性临床试验存在伦理方面的问题,以阳性药为对照的非劣效性临床试验在新药临床试验中的作用越来越重要。本文就现有几种非劣效性临床试验统计学方法进行回顾比较并附以实例。经比较,可信区间法在一类错误上相对于合成法较保守,而两阶段阳性对照试验法则可通过对阳性对照药的疗效的判断尽早的终止无效的非劣效试验。最后,探索分析了现有非劣效检验统计方法需要改进的地方。     

The varieties of mechanics by 1800

After an exploration of some of the basic categories attending mechanics, Newtonianism, and physics, a survey is given of the range of subjects covered by mechanics at the end of the 18th century, and the three main traditions operative in the subject are stressed. A few major French figures of that time are then noted, and also some views evident in certain other countries. The appendix of the paper is concerned with bibliographical questions; and an extensive bibliography, mostly of secondary literature, is appended.     

非线性刚性微分-代数系统的波形松弛离散法

研究基于Runge-Kutta方法的波形松弛离散过程,得到新的刚性微分-代数系统的收敛理论,及该类系统解的存在性和惟一性,并用具体算例测试该理论的有效实用性.     

Nonequilibrium statistical thermodynamics of positronium atoms moving in solids

We calculate the quasitemperature of positronium atoms moving in a solid in the framework of nonequilibrium statistical thermodynamics. We represent the quasitemperature in the form of the renormalized temperature of the thermostat. The renormalization results from taking the positronium formation rate, the kinetic effects of interaction, and the dynamical effects of collisions into account. We obtain an expression for the thermalization time of positronium atoms.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 142, No. 1, pp. 112–126, January, 2005.     

Non-homogeneous quantum Markov states and quantum Markov fields

The program relative to the investigation of quantum Markov states for general one-dimensional spin models is carried on, following a strategy developed in the last years. In such a way, the emerging structure is fully clarified. This analysis is a starting point for the solution of the basic (still open) problem concerning the construction of a satisfactory theory of quantum Markov fields, i.e. quantum Markov processes with multi-dimensional indices.     

基于统计过程控制技术的项目管理可视化控制系统

概述IMCS-SPC模型的总体框架、组成部分以及两大核心技术(多变量统计过程控制技术和虚拟现实可视化技术);详细讨论项目管理者构建IMCS-SPC模型的基本步骤。作为一种采用多元统计分析进行过程控制的可视化决策支持系统,IMCS-SPC为项目管理者提供了一种十分清晰、直观的过程控制方法和工具,可有效提高项目管理效率,以确保项目过程的正常运行。     

Overlapping Schwarz waveform relaxation method for the solution of the reaction-diffusion equation

We are interested in solving time dependent problems using domain decomposition methods. In the classical approach, one discretizes first the time dimension and then one solves a sequence of steady problems by a domain decomposition method. In this article, we treat directly the time dependent problem and we study a Schwarz waveform relaxation algorithm for the convection diffusion equation. We study the convergence of the overlapping Schwarz waveform relaxation method for solving the reaction-diffusion equation over multi-overlapped subdomains. Also we will show that the method converges linearly and superlinearly over long and short time intervals, and the convergence depends on the size of overlap. Numerical results are presented from solutions of a specific model problems to demonstrate the convergence, linear and superlinear, and the role of the overlap size.     

A CLASS OF GENERALIZED MULTISPLITTING RELAXATION METHODS FOR LINEAR COMPLEMENTARITY PROBLEMS

In this paper,a class of generalized parallel matrix multisplitting relaxation methods for solving linear complementarity problems on the high-speed multiprocessor systems is set up. This class of methods not only includes all the existing relaxation methods for the linear complementarity problems ,but also yields a lot of novel ones in the sense of multisplittlng. We establish the convergence theories of this class of generalized parallel multisplitting relaxation methods under the condition that the system matrix is an H-metrix with positive diagonal elements.     

A state-of-the-art review of the X-FEM for computational fracture mechanics

This paper presents a review of the extended finite element method X-FEM for computational fracture mechanics. The work is dedicated to discussing the basic ideas and formulation for the newly developed X-FEM method. The advantage of the method is that the element topology need not conform to the surfaces of the cracks. Moreover, X-FEM coupled with LSM makes possible the accurate solution of engineering problems in complex domains, which may be practically impossible to solve using the standard finite element method.     

A combined relaxation method for variational inequalities with nonlinear constraints

A simple iterative method for solving variational inequalities with a set-valued, nonmonotone mapping and a convex feasible set is proposed. This set can be defined by nonlinear functions. The method is based on combining and extending ideas contained in various relaxation methods of nonsmooth optimization. Also a modification of the averaging method for the problem under consideration is proposed. © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.This research was supported in part by RFFI grant No. 95-01-00061.     

A Gauss-Seidel type solver for special convex programs,with application to frictional contact mechanics

An iterative method is described that solves the constrained minimization of a convex function, when the constraintsg _j(x ₁,...,x _n)0 are functions of only a few variables and can be partitioned in some way. A proof of convergence is given which is based on the fact that the function values that are generated decrease. The relation to the nonlinear equation solver TanGS is shown (Ref. 1), together with some new results for TanGS. Finally, the solver is applied to the solution of tangential traction in contact mechanics.