Birkhoff系统的一类新型守恒量

给出了Birkhoff系统的一类新型守恒量。首先，建立了Birkhoff系统的运动方程及其Mei对称性的定义和判据；其次，给出了系统的一类新型守恒量的存在定理，并导出了用于确定无限小生成元的广义Killing方程；最后，建立了守恒定理的逆定理     

相对论Birkhoff系统的形式不变性与Noether守恒量

研究相对论Birkhoff系统的形式不变性,寻求系统的守恒量。在群的无限小变换下,给出相对论Birkhoff系统的形式不变性的定义和判剧。基于相对论Pfaff-Birkhoff-D'Alembert原理在群的无限小变换下的变形形式,建立相对论Birkhoff系统的Noether对称性理论。通过研究形式不变性与Noether对称性之间的关系,得到相对论Birkhoff系统的守恒量。研究结果表明:在一定的条件下,相对论Birkhoff系统的形式不变性导致Noether对称性的守恒量。     

Birkhoff系统的Poincare—Cartan积分不变量

基于现代微分几何学，分析了作为保守系统和非保守系统的推广－Birkhoff系统的辛结构。构造Birkhoff系统的Poincare-Cartan积分不变量。最后，将一维阻尼振动作为示例，求出其Poincare积分不变量。     

Birkhoff系统的一类新型守恒量

给出了Birkhoff系统的一类新型守恒量。首先,建立了Birkhoff系统的运动方程及其Mei对称性的定义和判据;其次,给出了系统的一类新型守恒量的存在定理,并导出了用于确定无限小生成元的广义Killing方程;最后,建立了守恒定理的逆定理     

自治Birkhoff系统的广义正则变换和辛算法研究

研究了自治Birkhoff系统的广义正则变换,将Hamilton系统的辛算法推广到Birkhoff系统,通过引入凯莱变换和生成函数法构造Birkhoff方程的Birkhoff的辛差分格式,同时讨论了Birkhoff差分格式的辛算法.     

约束Birkhoff系统的形式不变性

约束Birkhoff系统的形式不变性是约束Birkhoff方程在无限小变换下的一种不变性。给出约束Birkhoff系统形式不变性的定义与判据,并研究了这种形式不变性与Noether对称性之间的关系。     

Birkhoff 猜想在高维空间中的实现

<正> G.D.Birkhoff 引进了回复运动的概念.Markhoff 首次在二维环面上作出一个微分方程,使得它的解包含有回复的而非几乎周期的运动.G.D.Birkhoff 希望作出的微分方程是解析的.他猜想这种系统是存在的.L.Auslander,F.Hahm,L.Markus 在三维紧致流形 M 上构造了一个动力系统,使得 M 是非几乎周期运动组成的极小集合.但     

相对论性Birkhoff系统的变分方程与积分不变量

建立了相对论性Birkhoff系统的变分方程，并且利用系统的Birkhoff方程及其变分方程证明了可由第一积分直接构造该系统的一类积分不变量。文中举例说明了结果的应用。     

对Birkhoff猜想的一个解答

<正> 1)在动力系统的研究中,G.D.Birkhoff最先引进了回复运动的概念,并且构造了微分方程的例子,说明回复运动不同于几乎周期运动。不过,这些例子(包括后来Markhoff的例子)都是不解析的.为了想说明回复运动的概念是自然而不是矫揉造作的,Birkhoff希望作出一个解析的微分方程,使得它有回复而非几乎周期的运动;他猜想这种系统是存在的。十七年之后,到1929年,P.Franklin再一次提到这个问题.在1949年,B.B.提出在动力系统中寻找这种运动;认为它可能提供寻找所需微分方     

Birkhoff系统的Poincaré-Cartan积分不变量

基于现代微分几何学,分析了作为保守系统和非保守系统的推广——Birkhoff系统的辛结构.构造Birkhoff系统的Poincar-Cartan积分不变量.最后,将一维阻尼振动作为示例,求出其Poincar-Cartan积分不变量.     

On the principle of invariance in the theory of inhomogeneously ageing shells

It is proved that a general governing relationship results for an inhomogeneously ageing hereditary medium under fairly broad assumptions from the principle of material independence from the reference system /1/, also later called the principle of invariance.     

The principle of material frame-indifference and cylindrical couette flow of a rarified gas

The problem of a free molecular cylindrical Couette flow in a rotating coordinate system at different temperatures and the same angular velocities of the walls is considered. It is proved that, in an approximation which is linear in the angular velocities, the azimuthal thermal flux is proportional to the angular velocities of the walls in a fixed system of coordinates. An example of the flow of a gas which does not satisfy the principle of material frame-indifference (PMI) in the axiomatic theory of the mechanics of continuous media is thereby constructed and, consequently, the above-mentioned principle is not a universal principle of mechanics.     

ADirect Method for the Problem of the Solid Cylinder in Elasticity

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流域可持续发展系统的协调控制

流域可持续发展是以流域作为特殊区域的一种可持续发展模式,本将流域可持续发展视为一个整体,提出了“流域可持续发展系统”的研究框架,讨论了流域可持续发展系统协调控制的指导原则和协调控制的主要内容,详细研究分析了流域可持续发展系统在技术层次上协调控制的技术路线。     

Application of the principle of possible displacements to problems of the dynamics of a “shell-fluid” system

We state in general form the principle of possible displacements for a “shell-fluid” mechanical system, on the basis of which it is possible to solve dynamic problems taking account of a geometrically nonlinear process of deformation of the shell and nonpotential motions of a viscous fluid. It is shown that this principle yields the equations of motion of the shell and fluid as components of this system, confirming the reliability of the principle. The conditions of force contact are taken into account as a load term in the equations of motion of the shell. Bibliography: 5 titles. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 26, 1996, pp. 117–123.     

优化矿井通风系统方案的灰色关联模型

考虑到在矿井通风系统方案的评价中其众多的技术经济指标所具有的不同属性 ,根据灰色系统理论关联度原理 ,将灰色关联度多层次分析方法应用于矿井通风系统方案的优化 ,为矿井通风方案优选提供了一种科学的方法 ,进而拓宽了灰色关联度分析的应用领域 .     

The frames of application of the reflection principle

The formal system S₁ is considered in the language of set theory with an extremely strong reflection principle. It is proved that the principle is incompatible with the Gödel-Bernays theory. In S₁, however, we drop the assumption that each set is a class, and replace it by a weaker statement through which the consistency of S₁ seems somewhat credible. In this system, all theorems ZF, as well as some statements on the existence of large cardinals, are provable. It is also shown that if S₁ is consistent then it is compatible with the constructibility axiom.     

Bellman最优性原理——论动态规划(Ⅰ)

对于Bellman最优性原理,本文举出实例表明:(1)策略不一定有(合理的)子策略;(2)子策略不一定存在最优子策略;(3)最优策略不一定有最优子策略;(4)用最短路与反证法来论述最优性原理的正确性,不能肯定成立;(5)Bellman最优性原理与其递推公式并不等价。 讨论四类最优策略之后,给出最优性原理与递推公式等价的一个充分性定理。     

Averaging principle and hyperbolic evolution equations

An averaging principle is derived for the abstract nonlinear evolution equation where the almost periodic right hand-side is a continuous perturbation of the time-dependent family of linear operators determining a linear evolution system. It generalizes classical Henry’s results for perturbations of sectorial operators on fractional spaces. It is also proved that the main hypothesis of the nonlinear averaging principle is satisfied for general hyperbolic evolution equations introduced by Kato.     

The maximum principle for the nonlinear stochastic optimal control problem of switching systems

The aim of this paper is to present a stochastic maximum principle for an optimal control problem of switching systems. It presents necessary conditions of optimality in the form of a maximum principle for stochastic switching systems, in which the dynamic of the constituent processes takes the form of stochastic differential equations. The restrictions on transitions for the system are described through equality constraints.