包含伺服约束的非完整系统的Lie对称性与守恒量

利用代数方程和微分方程在无限小变换下的不变性,研究带有伺服约束的非完整系统的Lie 对称性.给出Lie对称性的确定方程、限制方程、结构方程,并给出守恒量的形式. 关键词： 非完整系统 伺服约束 Lie对称性 守恒量     

纵横波测已紧固螺栓轴向应力

本提出了用纵横波声时测已紧固螺栓轴向应力的一种新方法,解决了用超声精确地测已紧固螺栓应力问题,并且利用超声波沿轴向传播的波速同轴向应力以及三阶弹性常数的关系导出了螺栓应力同其材料声速特性、夹紧距离、温度及纵、横波声时的一种新关系,考虑了受应力作用时温度对声速的影响,简化了测量及计算过程,本还介绍了材料的声速特性实验及测量方法;实验结果表明应力低于２５０ＭＰａ,夹紧距离大于３０ｍｍ时,应力超声测     

灰色随机变量的熵和信息量

在定义灰随机变量的基础上,应用熵和信息量理论,研究了灰随机变量熵和随机量,得到若干公式和运算性质,拓展了胡庆贺在文[3]中对灰数信息量给出的定义和运算法则,揭示了灰随机变量两类不肯定性的特征及其相互关系,为进一步了解某些信息不完全事物的未知信息量提供了理论依据。     

On the Structure of Spectra of Modulated Travelling Waves

Modulated travelling waves are solutions to reaction-diffusion equations that are time-periodic in an appropriate moving coordinate frame. They may arise through Hopf bifurcations or essential instabilities from pulses o fronts. In this article, a framework for the stability analysis of such solutions is presented: the reaction-diffusion equation is cast as an ill-posed elliptic dynamical system in the spatial variable acting upon time-periodic functions. Using this formulation, points in the esolvent set, the point spectrum, and the essential spectrum of the linearization about a modulated travelling wave are related to the existence of exponential dichotomies on appopriate intervals for the associated spatial elliptic eigenvalue problem. Fredholm properties of the linearized operator are characterized by a relative Morse-Floe index of the elliptic equation. These results are proved without assumptions on the asymptotic shape of the wave. Analogous results are true for the spectra of travelling waves to parabolic equations on unbounded cylinders. As an application, we study the existence and stability of modulated spatially-periodic patterns with long-wavelength that accompany modulated pulses.     

A numerical method for the determination of weakly non‐hydrostatic non‐linear free surface wave propagation

A numerical method is described that may be used to determine the propagation characteristics of weakly non‐hydrostatic non‐linear free surface waves over a general, bottom topography. In shallow water of constant undisturbed depth, such waves are equivalent to the familiar cnoidal waves characterized by sharp crests and relatively flat troughs. For a certain range of parameters, these propagate without change of form by virtue of the weakly non‐hydrostatic balance in the vertical momentum equation. Effectively, this counters the tendency for the non‐linearity in a purely hydrostatic theory to lead to a continuously deforming surface wave profile. The realistic representation furnished by cnoidal wave theory of free surface waves in the shallow near‐shore zone has led to its utilization in evaluating their propagation characteristics. Nonetheless, the classic analytical theory is inapplicable to the case of wave propagation over a sloping beach or off‐shore sand bar topography. Under these conditions, a local change in form of the surface wave profile is anticipated before the waves break and knowing this is required in order to evaluate fully the propagation process. The efficacy of the numerical method is first demonstrated by comparing the solution for water of constant depth with the evaluation of the analytical solution expressed in terms of the Jacobian elliptic function cn. The general method described in the paper is then illustrated by experiments to determine the change in profile of weakly non‐hydrostatic non‐linear surface waves propagating over bed forms representative of those found in shallow coastal seas. Copyright © 2001 John Wiley & Sons, Ltd.     

Solvent‐free synthesis of polyacrylamide by frontal polymerization

Polymerization and characterization of polyacrylamide prepared by frontal polymerization are described. Frontally polymerized polyacrylamide is imidized and crosslinked during polymerization. Imide formation was determined by elemental analysis. The addition of commercial polyacrylamide or barium carbonate to the monomer (acrylamide) and initiator (potassium persulfate) decreased the reaction temperature from 235 °C to < 100 °C, thereby reducing imide formation. The commercial polyacrylamide‐diluted product, frontally polymerized polyacrylamide‐diluted product, and the barium carbonate‐diluted product were characterized by IR, TGA, and elemental analysis. Molecular weights of barium carbonate‐diluted samples were determined by light scattering and found to be on the order of one million. Conversion of the barium carbonate‐diluted product was determined to be 76 ± 6%, independent of the amount of diluent over the range 0.8:1–1.5:1. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 1129–1135, 2000     

Different approaches to the study of the gravitational radiation emitted by astrophysical sources

Stars and black holes are sources of gravitational radiation in many phases of their life, and the signals they emit exhibit features that are characteristic of the generating process. Emitted since the beginning of star formation, these signals also contribute to create a stochastic background of gravitational waves. We shall show how the spectral properties of this background can be estimated in terms of the energy spectrum of each single event and of the star formation rate history, which is now deducible from astronomical observations. We shall further discuss the process of scattering of masses by stars and black holes, showing that, unlike black holes, stars emit signals that carry a clear signature of the nature of the source.     

Propagation velocity of the reaction front in addition polymerization systems

Traveling polymerization fronts in unstirred solutions of methylmethacrylate, methacrylic acid, or acrylamide with some free radicals initiators (through thermal decomposition) have been observed experimentally. A local heating of the initial reactant mixture, under suitable conditions, leads to a reaction front that propagates along the space coordinate with a constant velocity. In this article, a physical interpretation of this phenomenon is provided through a mathematical model that accounts for the depolimerization reaction and is based on the constant pattern approach. Moreover, an approximate explicit analytic expression for the velocity of propagation of the polymerization front is proposed. The theoretical values are compared with those measured experimentally as a function of the initiator concentration for different addition polymerization systems. © 1997 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 35:1047–1059, 1997