一类新的关于(4+4+1)-体共轭套中心构型

本文研究R3中一类(4+4+1)-体中心构型.利用中心构型等价类的性质及代数、分析方法,得到了该构型构成中心构型的充分和必要条件,证明了对任意给定的质量比这类中心构型存在的结论,解决了给定不同质量比范围该类中心构型是否唯一的问题,推广了文[16]的结论.     

立方体套中心构型的存在唯一性

本文研究两层立方体套中心构型,运用中心构型等价类的性质结合分析方法,得到了立方体套构成中心构型等价类的充分与必要条件,并且证明了该等价类对于任意给定的质量比具有存在唯一性,推广了文[8]的结论.     

两层扭转正多边形构成的中心构型

研究了R³中的一类特殊的两层扭转正多边形构成的中心构型的存在性.     

五体问题的中心构型及其相对平衡解

N体问题的中心构型非常重要,但它们的分类很复杂.本文讨论了一类菱形五体问题的中心构型及其相对平衡解,证明了菱形五体问题的相对平衡解的存在唯一性.     

关于4-体问题中心构型的一点研究

N-体问题的中心构型是应用数学领域广泛研究的问题．关于N-体问题的中心构型已有许多研究结果．但是对于n≥4,其中心构型解的计算是比较困难的．作者运用Wu-Ritt零点分解方法和子结式序列研究了一般的平面4体中心构型问题,给出了这类4体中心构型问题的解析解,从而证明了一类平面牛顿4-体问题的中心构型个数是有限的．     

利用太阳光压力进行Halo轨道编队控制

利用太阳光压力可以实现地日限制性三体问题中L2点附近编队控制.该编队需要的控制力量级小,常规的推进方式难以实现.太阳帆能产生微小的连续光压力,可以用于Halo轨道附近的编队控制.由于太阳光压力的方向受到限制,只有部分编队构型可以利用太阳光压力实现.该文主要讨论了两种常见的编队构型--直线编队和圆编队,给出了太阳帆能实现的编队构型需要满足的条件.最后,对每种构型的编队进行了数值仿真,仿真结果表明太阳帆能有效的进行编队控制.     

约束矩阵方程的中心对称解及其在振动理论反问题中的应用

研究了中心主子矩阵约束下矩阵方程的中心对称解.利用矩阵向量化、Kronecker乘积及奇异值分解方法,得到了有解的充分必要条件及解的一般表达形式.同时,考虑了与之相关的对任意给定矩阵的最佳逼近问题.进而,给出在振动理论反问题中的应用,利用截断的主质量矩阵(或主刚度矩阵)、截断模态矩阵以及质量矩阵(或刚度矩阵)的中心主子阵,求系统的质量矩阵(或刚度矩阵).最后用两个例子说明文中方法的有效性.     

民用飞机发动机反推的空气动力学特性分析

建立了飞机发动机反推的数值计算方法,该方法针对低速不可压N-S方程组,通过SIMPLE算法对方程组进行解耦求解,采用强隐式方法迭代求解有限体积离散后的代数方程组,湍流模型为标准k-ε模型。选取30 m/s和71 m/s两种速度,对某型民机在两种反推构型下的空气动力学特性进行了计算,分析了反推气流分布及其对飞机的影响,对比了发动机流场畸变指数,总结了速度变化对反推流场性能的影响,发现反推构型Ⅱ的综合设计效果优于构型Ⅰ,为该飞机发动机反推设计提供了参考和支撑。     

边增加常返构型改变（英文）

研究图上Abelian沙堆模型的常返构型问题.刻画了当图的边增加时,图的常返构型如何改变.     

构成型顾客满意模型的偏最小二乘路径建模及其应用

本文研究了偏最小二乘路径建模在顾客满意模型中的应用,特别是引入了构成型关系的模型。本文首先比较了构成型模型和反映型模型的区别,并详尽阐述了构成型模型的偏最小二乘建模原理,接着构建了电信企业顾客满意度指数模型,并考虑了如何在指数模型中引入构成型外部关系.利用该电信企业的数据,比较分析了构成型模型(顾客期望和质量感知潜变量调整为构成型关系)和反映型模型(所有潜变量均为反映型关系)的实证结果,研究表明在为企业提供改善顾客满意水平的信息上两种模型具有较好的相似性,但是构成型模型能够提供更加稳定的结果,从而验证了顾客满意模型中引入构成型模型的可行性.     

Classification of four-body central configurations with three equal masses

It is known that a central configuration of the planar four body problem consisting of three particles of equal mass possesses a symmetry if the configuration is convex or is concave with the unequal mass in the interior. We use analytic methods to show that besides the family of equilateral triangle configurations, there are exactly one family of concave and one family of convex central configurations, which completely classifies such central configurations.     

SQUARE AND RHOMBUS CENTRAL CONFIGURATIONS

In this paper, we consider the flat central configurations of bodies using the characteristic set method. We completely solve two special cases of four planets, namely,the square and the rhombus. For the square case, we obtain that a square is a central configuration only in the case where the masses are equal and there exactly are two different square central configurations determined by the mass and the angular velocity; for the rhombus case, we obtain that if a rhombus is a central configuration, then the masses of the diagonal vertices must be equal. Furthermore, there are two or three or four different rhombus central configurations determined by the masses and the angular velocity.     

Some Enumeration Problems on Central Configurations at the Bifurcation Points

In “Counting central configurations at the bifurcation points,” we proposed an algorithm to rigorously count central configurations in some cases that involve one parameter. Here, we improve our algorithm to consider three harder cases: the planar \((3+1)\)-body problem with two equal masses; the planar 4-body problem with two pairs of equal masses which have an axis of symmetry containing one pair of them; the spatial 5-body problem with three equal masses at the vertices of an equilateral triangle and two equal masses on the line passing through the center of the triangle and being perpendicular to the plane containing it.While all three problems have been studied in two parameter cases, numerical observations suggest new results at some points on the bifurcation curves. Applying the improved version of our algorithm, we count at those bifurcation points. As a result, for the \((3+1)\)-body problem, we identify three points on the bifurcation curve where there are 8 central configurations, which adds to the known results of \(8,9,10\) ones. For our 4-body case, at the bifurcation points, there are 3 concave central configurations, which adds to the known results of \(2,4\) ones. For our 5-body case, at the bifurcation point, there is 1 concave central configuration, which adds to the known results of \(0,2\) ones.     

The central configurations of four masses x, −x, y, −y

The configuration of a homothetic motion in the N-body problem is called a central configuration. In this paper, we prove that there are exactly three planar non-collinear central configurations for masses x, −x, y, −y with x≠y (a parallelogram and two trapezoids) and two planar non-collinear central configurations for masses x, −x, x, −x (two diamonds). Except the case studied here, the only known case where the four-body central configurations with non-vanishing masses can be listed is the case with equal masses (A. Albouy, 1995-1996), which requires the use of a symbolic computation program. Thanks to a lemma used in the proof of our result, we also show that a co-circular four-body central configuration has non-vanishing total mass or vanishing multiplier.     

正四面体套中心构型的存在唯一性

Two cases of the nested configurations in R^3 consisting of two regular quadrilaterals are discussed. One case of them do not form central configuration, the other case can be central configuration. In the second case the existence and uniqueness of the central configuration are studied. If the configuration is a central configuration, then all masses of outside layer are equivalent, similar to the masses of inside layer. At the same time the following relation between r(the ratio of the sizes) and mass ratio b = m/m must be satisfied b=24(3的立方根)（3r^2 2r 3）^-3/2-8（1-r）|1-r|^-3-3(6r的立方根)/24(3的立方根)（3 r）（3r^2 2r 3）^-3/2-8r（1-r）|1-r|^-3-3(6r^-2的立方根)in which the masses at outside layer are not less than the masses at inside layer, and the solution of this kind of central configuration is unique for the given ratio (b) of masses.     

On the central configurations of the planar restricted four-body problem

This article is devoted to answering several questions about the central configurations of the planar (3+1)-body problem. Firstly, we study bifurcations of central configurations, proving the uniqueness of convex central configurations up to symmetry. Secondly, we settle the finiteness problem in the case of two nonzero equal masses. Lastly, we provide all the possibilities for the number of symmetrical central configurations, and discuss their bifurcations and spectral stability. Our proofs are based on applications of rational parametrizations and computer algebra.     

On the distribution of mass in collinear central configurations

Moulton's Theorem says that given an ordering of masses, , there exists a unique collinear central configuration with center of mass at the origin and moment of inertia equal to 1. This theorem allows us to ask the questions: What is the distribution of mass in this standardized collinear central configuration? What is the behavior of the distribution as ? In this paper, we define continuous configurations, prove a continuous version of Moulton's Theorem, and then, in the spirit of limit theorems in probability theory, prove that as , under rather general conditions, the discrete mass distributions of the standardized collinear central configurations have distribution functions which converge uniformly to the distribution function of the unique continuous standardized collinear central configuration which we determine.

     

Planar central configurations as fixed points

Planar central configurations can be seen as critical points of the reduced potential or solutions of a system of equations. By the homogeneity of the potential and its O(2)-invariance it is possible to see that the SO(2)- orbits of central configurations are fixed points of a map f. The purpose of the paper is to define and study this map and to derive some properties using topological fixed point theory. The generalized Moulton–Smale theorem for collinear configurations is proved, together with some estimates on the number of central configurations in the case of three bodies, using fixed point indices. Well-known results such as the compactness of the set of central configurations follow easily in this topological framework. Dedicated to Professor Albrecht Dold and Professor Edward Fadell