LOOP GROUP ACTIONS AND THE RIBAUCOUR TRANSFORMATIONS FOR FLAT LAGRANGIAN SUBMANIFOLDS

The Ribaucour transformations for flat Lagrangian submanifolds in Cn and CPn via loop group actions are given. As a consequence, the authors obtain a family of new flat Lagrangian submanifolds from a given one via a purely algebraic algorithm. At the same time, it is shown that such Ribaucour transformation always comes with a permutability formula.     

MOMENT GENERATING FUNCTIONS OF RANDOM VARIABLES AND ASYMPTOTIC BEHAVIOUR FOR GENERALIZED FELLER OPERATORS

1. Introduction and NotationsThe generalized Feller operators which include many famous operators, such ajsBernstein, Szasz-Mirakjan, BaskakoV, Meyer--K5nig and Zeller operators, can be constructed by making use of the probabilistic method. In the paper [1][2], Xu JihuaPr(--lvjdetl a general scheme f(,r its construction, and Zhao Jillghui showed that theFeller type operators are of good approximations f'or unbounded functions.Our purpose is to present representation of moment generating …     

ESTIMATIONS OF THE CONSTANTS IN INVERSE INEQUALITIES FOR FINITE ELEMENT FUNCTIONS

In this paper, we estimate the constants in the inverse inequalities for the finite ele- ment functions. Furthermore, we obtain the least upper bounds of the constants in inverse inequalities for the low-order finite element functions. Such explicit estimates of the con- stants can be used as computable error bounds for the finite element method.     

一类不依赖于局部极小解个数的填充函数

求解无约束总体优化问题的一类单参数填充函数需要假设问题的局部极小解的个数只有有限个,而且填充函数中参数的选取与局部极小解的谷域的半径有关.本文对填充函数的定义作适当改进,而且对已有的这一类填充函数作改进,构造了一类双参数填充函数.新的填充函数不仅无须对问题的局部极小解的个数作假设,而且其中参数的选取与局部极小解的谷域的半径无关.     

含随机参数非线性方程组解的存在性、唯一性及算法与效用函数计算公式的导出

1 引 言在决策分析及若干非确定性经济分析中,如何确定行为人效用函数及其计算公式,是迄今仍未解决的重大问题.近些年有多项研究均涉及此问题[1,2,3,4].Multiple Degree RiskAversion模型[5,6],可通过鉴别行为人风险性质,把上述效用函数及其参数的确定归结为求解由所定义函数构造的一种非线性方程组.这里,用途最广也最具代表性的风险性质为递减风险厌恶[7].其效用函数及其参数可由关于未知量ψ1,ψ2的两个联立非线性方程     

关于偏微分方程解的规模,恰当解,形式幂级数解和序的优化

基于Reid标准型,楔子(盒子)理论,吴方法解决了一些偏微分方程组的维数问题 -即解的规模,并给出了形式幂级数解并编制了算法．最重要的是给出了验证恰当解的优序-即Ⅱ-型序。     

THE IMPROVED FOURIER SPLITTING METHOD AND DECAY ESTIMATES OF THE GLOBAL SOLUTIONS OF THE CAUCHY PROBLEMS FOR NONLINEAR SYSTEMS OF FLUID DYNAMICS EQUATIONS

Consider the Cauchy problems for an n-dimensional nonlinear system of fluid dynamics equations. The main purpose of this paper is to improve the Fourier splitting method to accomplish the decay estimates with sharp rates of the global weak solutions of the Cauchy problems. We will couple together the elementary uniform energy estimates of the global weak solutions and a well known Gronwall''s inequality to improve the Fourier splitting method. This method was initiated by Maria Schonbek in the 1980''s to study the optimal long time asymptotic behaviours of the global weak solutions of the nonlinear system of fluid dynamics equations. As applications, the decay estimates with sharp rates of the global weak solutions of the Cauchy problems for $n$-dimensional incompressible Navier-Stokes equations, for the $n$-dimensional magnetohydrodynamics equations and for many other very interesting nonlinear evolution equations with dissipations can be established.