汽车电磁悬架系统的Noether对称性及其应用

研究了含有电磁悬架汽车振动系统的Noether对称性,给出了系统的守恒量,并通过守恒量求得系统的对称性解.以能量形式,建立汽车不同振动形式下的Lagrange(拉格朗日)方程.选取位移坐标为广义坐标,研究了各种振动形式下系统的Noether对称性,并给出相应的Noether恒等式、Killing方程和广义Noether定理.研究系统守恒量,运用存在的守恒量,给出一种新的求解汽车振动系统响应的方法;并应用到具体的车体振动系统计算中,给出了系统在转弯、制动或加速等情况下的位移响应和速度响应曲线.     

汽车车体振动系统的对称性与守恒量研究

用Lie群方法研究汽车车体振动系统的对称性,寻找其存在的守恒量.以汽车车体做上下垂直振动和绕其质心的前后俯仰振动,采用Lagrange函数的方法,构建汽车车体振动系统.以此系统为对象,引入Lie群方法,给出该振动系统的Noether对称性理论与Lie对称性理论;由此推导该汽车系统存在的Noether对称性与Lie对称性,并得到系统相应的的守恒量.该方法对车体振动问题提出了新的对称性解法,同时扩大了Lie群方法的应用范围.     

约束Hamilton系统的Lie对称性及其在场论中的应用

研究了约束Hamilton系统的Lie对称性,得到了场论系统的守恒量.首先给出约束Hamilton系统的正则运动方程和固有约束方程;其次构建了约束Hamilton 系统的Lie对称性确定方程和结构方程;然后给出了约束Hamilton系统的Lie守恒定理和守恒量;最后研究了复标量场与Chern-Simons项耦合系统的Lie对称性和另外一个例子以说明此方法在场论中的应用.     

约束Hamilton系统的积分因子和守恒量及其在场论中的应用

在约束Hamilton系统的研究中,场论系统一直是重要且难度大的一部分.近年来,场论系统已经成为一个热门的研究领域.论文基于积分因子方法给出了构造场论系统守恒量的一般性方法.首先,构造了约束Hamilton系统的广义Hamilton正则方程;其次,给出了场论系统积分因子的定义和守恒定理;然后,建立了场论系统的广义Killing方程,从而导出系统的积分因子和守恒量;最后,给出了几个场论中的例子以说明这种方法的可行性和有效性.显然,与Noether对称性理论和Lie对称性理论相比较,这种方法具有步骤清晰,计算简便,限制条件少等优点.     

变质量Chetaev型非完整系统的共形不变性

研究变质量Chetaev型非完整系统的共形不变性与守恒量.推导共形因子表达式,得到系统共形不变性同时是Lie对称性的充要条件,给出系统弱Lie对称性和强Lie对称性的共形不变性,导出系统相应的守恒量,并举例说明结果的应用.     

非Chetaev型变质量非完整系统的Lie对称性与Noether对称性

研究非Chetaev型变质量非完整系统的Lie对称性与Noether对称性以及其间的 关系,给出Lie对称性导致Noether对称性以及Noether对称性导致Lie对称性的条件.     

非完整非有势系统相对于非惯性系的广义Noether定理

本文构造了力学系统相对运动的Lagrange函数,建立了非线性非完整非有势系统相对于非惯性系的Jourdain型变分原理,提出并证明了这类力学系统相对于非惯性系的广义Noether定理,研究了其守恒量.     

覆冰输电导线舞动的Noether对称性和守恒量

为克服传统输电导线非线性振动响应数值模拟的非保结构缺点,研究了输电导线在覆冰和大风激励条件下双向舞动中的Noether对称性和守恒量.首先,考虑空气动力和导线几何的非线性,依据分析力学方法建立了垂向与扭振两自由度舞动模型;其次,引进群分析理论,根据不变性原则给出了系统存在Noether对称性的条件以及相应守恒量的形式;...     

转动相对论系统的Lie对称性和守恒量

研究转动相对论性完整与非完整力学系统的Lie对称性和守恒量.定义转动相对论力学系统的无限小变换生成元,利用微分方程在无限小变换下的不变性,建立转动相对论性力学系统的Lie对称确定方程,得到结构方程和守恒量的形式,并给出应用实例.     

广义Toda链的τ-函数解与表示论

本文由Semenov-Tian-Shansky 约化定理所给出的完全可积Hamilton 系统的求解框架出发,利用Lie群、Lie代数表示论的方法;求得了广义Toda链的τ-函数解.     

A REPRESENTATION FORMULA RELATED TO SCHR(O)DINGER OPERATORS

Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.     

Qualitative Analysis of Bifurcating Solutions in the Lengyel-Epstein Model

One of the most fundamental problems in theoretical biology is to explain the mechanisms by which patterns and forms are created in the＇living world. In his seminal paper ＂The Chemical Basis of Morphogenesis＂, Turing showed that a system of coupled reaction-diffusion equations can be used to describe patterns and forms in biological systems. However, the first experimental evidence to the Turing patterns was observed by De Kepper and her associates（1990） on the CIMA reaction in an open unstirred reactor, almost 40 years after Turing＇s prediction. Lengyel and Epstein characterized this famous experiment using a system of reaction-diffusion equations. The Lengyel-Epstein model is in the form as follows     

On a class of self-similar processes with stationary increments in higher order Wiener chaoses

We study a class of self-similar processes with stationary increments belonging to higher order Wiener chaoses which are similar to Hermite processes. We obtain an almost sure wavelet-like expansion of these processes. This allows us to compute the pointwise and local Hölder regularity of sample paths and to analyse their behaviour at infinity. We also provide some results on the Hausdorff dimension of the range and graphs of multidimensional anisotropic self-similar processes with stationary increments defined by multiple Wiener–Itô integrals.     

(0,1 ;0)-INTERPOLATION ON INFINITE INTERVAL (-∞, +∞)

In this paper, we study the explicit representation and convergence of (0, 1; 0)-interpolation on infinite interval, which means to determine a polynomial of degree ≤ 3n - 2 when the function values are prescribed at two set of points namely the zeros of Hn(x) and H′n(x) and the first derivatives at the zeros of H′n(x).     

On a class of Riemann surfaces

It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary.     

CONTENTS OF VOLUME 30

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Instructions for contributions

正Applied Mathematics-A Journal of Chinese Universities,Series B(Appl.Math.J.Chinese Univ.,Ser.B)is a comprehensive applied mathematics journal jointly sponsored by Zhejiang University,China Society for Industrial and Applied Mathematics,and Springer-Verlag.It is a quarterly journal with     

Journal of Mathematical Research with Applications Guide for Authors

正Journal overview:Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,one of the transactions of China Society for Industrial and Applied Mathematics,is a home for original research papers of the highest quality in all areas of mathematics with applications.The target audience comprises:pure and applied mathematicians,graduate students in broad fields of sciences and technology,scientists and engineers interested in mathematics.     

Staircase transportation problems with superadditive rewards and cumulative capacities

A cumulative-capacitated transportation problem is studied. The supply nodes and demand nodes are each chains. Shipments from a supply node to a demand node are possible only if the pair lies in a sublattice, or equivalently, in a staircase disjoint union of rectangles, of the product of the two chains. There are (lattice) superadditive upper bounds on the cumulative flows in all leading subrectangles of each rectangle. It is shown that there is a greatest cumulative flow formed by the natural generalization of the South-West Corner Rule that respects cumulative-flow capacities; it has maximum reward when the rewards are (lattice) superadditive; it is integer if the supplies, demands and capacities are integer; and it can be calculated myopically in linear time. The result is specialized to earlier work of Hoeffding (1940), Fréchet (1951), Lorentz (1953), Hoffman (1963) and Barnes and Hoffman (1985). Applications are given to extreme constrained bivariate distributions, optimal distribution with limited one-way product substitution and, generalizing results of Derman and Klein (1958), optimal sales with age-dependent rewards and capacities.To our friend, Philip Wolfe, with admiration and affection, on the occasion of his 65th birthday.Research was supported respectively by the IBM T.J. Watson and IBM Almaden Research Centers and is a minor revision of the IBM Research Report [6].