Business–Cycle Models and the Dangers of Linearizing

This paper studies the consequences of linearizing nonlinear business–cycle models near their interior steady state. It is shown that dynamic objects, created for example in a Bogdanov-Takens bifurcation, may be lost in the linearization procedure. Sufficient conditions are provided ensuring the absence of various dynamic features in the nonlinear version of the model. The authors thank Andy Atkeson and Hal Cole for useful comments and suggestions. They also thank three anonymous referees who have helped to greatly improve the exposition of this paper. Part of this research was done while the author was affiliated with the University of Cergy Pontoise (THEMA) and during visits at DELTA. Part of this research has been done while the author was working as a Marie Curie Fellow at INSEE/CREST and during visits at the University of Warwick.     

对《二维六角形晶格伊辛模型的重正化群解》一文的进一步计算

针对《二维六角形晶格伊辛模型的重正化群解》一文中有关〈V〉0的计算进行了修正,给出了新的重正化群的变换、重正化群的线性化变换矩阵以及临界指数.     

重复率气体火花开关绝缘恢复特性的实验研究

 在自行设计的气体火花开关上，利用双脉冲回路，对纳秒脉冲作用下N₂和H₂的绝缘恢复特性进行了实验研究。结果表明，在静态不吹气情况下，H₂的绝缘恢复时间明显比N₂短。在吹气情况下，适当的气流速度即可使绝缘恢复时间明显缩短。     

Piecewise optimal linearization method for nonlinear stochastic differential equations

A method for estimating the dynamical statistical properties of the solutions of nonlinear Langevin-type stochastic differential equations is presented. The non-linear equation is linearized within a small interval of the independent variable and statistical properties are expressed analytically within the interval. The linearization procedure is optimal in the sense of the Chebyshev inequality. Long-term behavior of the solution process is obtained by appropriately matching the approximate solutions at the boundaries between intervals. The method is applied to a model nonlinear equation for which the exact time-dependent moments can be obtained by numerical methods. The calculations demonstrate that the method represents a significant improvement over the method of statistical linearization in time regimes far from equilibrium.Supported in part by the National Science Foundation under Grants CHE77-16307 and PHY76-04761.     

Mixed-integer bilinear programming problems

This paper addresses a class of problems called mixed-integer bilinear programming problems. These problems are identical to the well known bilinear programming problems with the exception that one set of variables is restricted to be binary valued, and they arise in various production, location—allocation, and distribution application contexts. We first identify some special cases of this problem which are relatively more readily solvable, even though their continuous relaxations are still nonconvex. For the more general case, we employ a linearization technique and design a composite Lagrangian relaxation-implicit enumeration-cutting plane algorithm. Extensive computational experience is provided to test the efficacy of various algorithmic strategies and the effects of problem data on the computational effort of the proposed algorithm.     

Successive Linearization Methods for Nonlinear Semidefinite Programs

We present a successive linearization method with a trust region-type globalization for the solution of nonlinear semidefinite programs. At each iteration, the method solves a quadratic semidefinite program, which can be converted to a linear semidefinite program with a second order cone constraint. A subproblem of this kind can be solved quite efficiently by using some recent software for semidefinite and second-order cone programs. The method is shown to be globally convergent under certain assumptions. Numerical results on some nonlinear semidefinite programs including optimization problems with bilinear matrix inequalities are reported to illustrate the behaviour of the proposed method.The research of the fourth author was supported in part by a Grant-in-Aid for Scientific Research from Japan Society for the Promotion of Science. The research of the second author was supported by the DFG (Deutsche Forschungsgemeinschaft).     

An Alternative Way of Utilizing Fixed Point Theory

The author proposes an alternative way of using fixed point theory to get the existence for semilinear equations. As an example, a nonlocal ordinary differential equation is considered. The idea is to solve homogeneous equations in the linearization. One feature of this method is that it does not need the equation to have special structures, for instance, variational structures, maximum principle, etc. Roughly speaking, the existence comes from good properties of the suitably linearized equation. The idea may have wider application.     

求解二次分配问题的新的流量模型

二次分配问题是具有广泛应用背景的经典组合优化难题之一。本文在二次分配问题已有线性化模型的基础上,提出了一种新的基于流量的线性化模型。数值试验结果表明,新模型无论从时间上还是计算节点数都更具有优势。     

Equations of state for solids under strong compression

Abstract

The historical and theoretical background for the different mathematical forms commonly used to represent equations of state (EOS) for solids is reviewed and some criteria are discussed which allow to select some specific forms, which are not only convenient mathematical forms but bring out the physical meaning of the data. Some examples are discussed with emphasis on recent experimental and theoretical data including noble gas solids, simple metals and a few metals with special “anomalies” to illustrate the differences involved in the use of different EOS forms and to point out the specific physical reasons for differences in specific EOS forms.