陀螺仪运动的混沌与KAM理论

本文建立了外环轴水平放置的重力对称陀螺仪的运动方程．将非自由陀螺仪转子的质心位置作为扰动，利用Ｍｅｌｎｉｋｏｖ方法和ＫＡＭ理论研究了陀螺仪的运动，研究结果表明：在 螺仪转子的质心与支架中心不重合且充分接近时，或 螺仪能量充分大时，陀螺仪运动的Ｐｏｉｎｃａｒｅ映射既出现Ｓｍａｌｅ马蹄意义下的混沌，又存在ＫＡＭ不变环面和不变闭曲线。     

数学问题解答

20 0 0年 1 0月号问题解答(解答由问题提供人给出 )1 2 76　设Ｉ为△ＡＢＣ的内心 ,Ｋ、Ｌ、Ｍ分别为△ＡＢＣ的内切圆在ＢＣ ,ＣＡ ,ＡＢ上的切点 .过Ｂ且与ＭＫ平行的直线分别与直线ＬＭ及ＬＫ交于Ｒ及Ｓ ,点Ｊ在ＢＩ上 ,试证明 :∠ＲＪＳ是锐角 ,当且仅当ＢＪ >12 (ＡＢ ＢＣ-ＡＣ) .(山东枣庄市立新学校　孔令恩　 2 771 0 2 )证明　如图所示 ,ＩＢ⊥ＭＫＲＳ∥ＭＫ ＩＢ ⊥ＲＳ∠ＡＢＩ=∠ＣＢＩ ∠ＲＢＭ =∠ＳＢＫ∠ＲＭＢ =∠ＡＭＬ =90°- Ａ2∠ＢＳＫ =∠ＭＫＬ =90°- Ａ2 ∠ＲＭＢ=∠ＢＳＫ △ＲＢＭ ∽△ＳＢＫ ＢＲＢＫ …     

第39届IMO-5的简证

题目　设Ｉ为△ＡＢＣ的内心,Ｋ、Ｌ、Ｍ分别为△ＡＢＣ的内切圆在ＢＣ、ＣＡ、ＡＢ上的切点,已知通过点Ｂ与ＭＫ平行的直线分别与直线ＬＭ及ＬＫ交于Ｒ、Ｓ两点,求证∠ＲＩＳ为锐角．证明　记△ＡＢＣ的内切圆半径为ｒ,∵　ＲＳ∥ＭＫ且△ＭＫＬ为切点三角形,故　∠ＲＳＫ＝∠ＭＫＬ＝∠ＬＭＡ,∴　Ｓ、Ｌ、Ｍ、Ｂ四点共圆．故　ＲＢ·ＲＳ＝ＲＭ·ＲＬ．但Ｒ是圆Ｉ外一点,ＲＭ·ＲＬ＝ＲＩ２－ｒ２,∴　　ＲＢ·ＲＳ＝ＲＩ２－ｒ２（１）同理可知　ＳＢ·ＳＲ＝ＳＩ２－ｒ２（２）由（１）、（２）有ＲＩ２＋ＳＩ２－２ｒ２＝ＲＳ…     

第41届国际数学奥林匹克题解

第一天大田 ,2 0 0 0年 7月 19日时间 :4小时 30分每题 7分　　问题 1 圆Γ1 和圆Γ2 相交于点Ｍ和Ｎ .设ｌ是圆Γ1 和Γ2 的两条公切线中距离Ｍ较近的那条公切线 .ｌ与圆Γ1 相切于点Ａ ,与圆Γ2 相切于点Ｂ .设经过点Ｍ且与ｌ平行的直线与圆Γ1 还相交于点Ｃ ,与圆Γ2 还相交于点Ｄ .直线ＣＡ和ＤＢ相交于点Ｅ ;直线ＡＮ和ＣＤ相交于点Ｐ ;直线ＢＮ和ＣＤ相交于点Ｑ .证明　ＥＰ =ＥＱ .解答　令Ｋ为ＭＮ和ＡＢ的交点 .根据圆幂定理 ,ＡＫ2 =ＫＮ·ＫＭ =ＢＫ2 ,换言之Ｋ是ＡＢ的中点 .因为ＰＱ∥ＡＢ ,所以Ｍ是ＰＱ的中点 .故只需证明Ｅ…     

三角域上Meyer－KOnig－Zeller算子

定义了一种三角域上Ｍｅｙｅｒ－Ｋ［ＡＫｏＤ］ｎｉｇ－Ｚｅｌｌｅｒ算子，并研究其在Ｃ度量下的逼近性质。     

三角域上Meyer－K?nig－Zeller算子

定义了一种三角域上Ｍｅｙｅｒ－Ｋ［ＡＫｏ‥Ｄ］ｎｉｇ－Ｚｅｌｌｅｒ算子，并研究其在Ｃ度量下的逼近性质。     

可压缩格子Boltzmann模型的启示性稳定理论

１引言格子Ｂｏｌｔｚｍａｎｎ方法（ＬＢＭ）是近几年发展起来的一种模拟复杂系统的新方法［１］［２］［３］这种方法已经在流体力学各领域得到应用．最近,许多研究工作集中于用ＬＢＭ模型计算可压缩流体流动．Ａｌｅｘａｎｄｅｒ和Ｃｈｅｎ等［４］提出了可以计算激波的等温模型,模型中的音速是可以选择的．Ｑｉａｎ和Ｏｒｓｚａｇ［５］分析了ＬＢＧＫ模型在可压缩区域内的非线性偏差,给出了激波结构的ＬＢＭ结果．Ｑｉａｎ和Ｏｒｓｚａｇ［６］也计算了弱可压缩的高Ｒｅ数问题,并用于计算Ｋｏｌ－ｍｏｇｏｒｏｖ流．Ａｎｃｏｎａ［…     

一类特殊广义Kac—Moody代数虚根决定的反射与Weyl群间的关系

对有限型李代数ｇ（Ａ）,相应于每个根ａ的反射ｒａ均在ｇ（Ａ）的Ｗｅｙｌ群Ｗ中,当ｇ（Ａ）为可对称化的不定型Ｋａｃ－Ｍｏｏｄｙ代数时,若ａ为一虚根且（ａ,ａ）〈０,则亦可定义反射ｒａ,并有ｒａ∈－Ｗ或ｒａ是－Ｗ中元与一个图自同构之积,本文给出了一类秩为３的广义Ｋａｃ－Ｍｏｏｄｙ代数的虚根系,然后讨论了一类特殊的广义Ｋａｃ－Ｍｏｏｄｙ代数的虚根决定的反射与Ｗｅｙｌ群之间的关系。     

Reliability bounds in DFRA class with known mean and variance

ＲＥＬＩＡＢＩＬＩＴＹＢＯＵＮＤＳＩＮＤＦＲＡＣＬＡＳＳＷＩＴＨＫＮＯＷＮＭＥＡＮ　ＡＮＤ　ＶＡＲＩＡＮＣＥＣＨＥＮＧＫＡＮ（程侃）（ＩｎｓｔｉｔｕｔｅｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ,ｔｈｅＣｈｉｎｅｓｅＡｃａｄｅｍｙｏｆＳｃｉｅｎｃｅ,Ｂ...     

扭转映射的Aubry—Mather理论及其应用

本文介绍Ａｕｂｒｙ－Ｍａｔｈｅｒ理论近年来的发展情况。文章讨论了该理论与ＫＡＭ理论、保面积映射不动点理论的联系，简单地介绍了它的一些推广。作为该理论的应用，对平面Ｈａｍｉｌ－ｔｏｎ系统Ｍａｔｈｅｒ集的存在性给出了一些结果。     

RECENT PROGRESS ON SPHERICAL HARMONIC APPROXIMATION MADE BY BNU RESEARCH GROUP ——In memory of Professor Sun Yongsheng

As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years （2001-2005）. The main topics are： convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths.     

A unified approach to certain problems of best local approximation

In this paper we study best local quasi-rational approximation and best local approximation from finite dimensional subspaces of vectorial functions of several variables. Our approach extends and unifies several problems concerning best local multi-point approximation in different norms.     

Boundedness for commutators of multipliers on Hardy type spaces

In this paper, we study the commutators generalized by multipliers and a BMO function. Under some assumptions, we establish its boundedness properties from certain atomic Hardy space Hb^p（R^n） into the Lebesgue space L^p with p 〈 1.     

THE 8~(th) INTERNATIONAL CONGRESS ON INDUSTRIAL AND APPLIED MATHEMATICS

<正>August 10-14,2015Beijing,ChinaThe International Congress on Industrial and Applied Mathematics(ICIAM)is the premier international congress in the field of applied mathematics held every four years under the auspices of the International Council for Industrial and Applied Mathematics.From August 10 to 14,2015,mathematicians,scientists     

Towards Excellence in Science Chinese Academy of Sciences

<正>May 26,2014,Beijing Science is a human enterprise in the pursuit of knowledge.The scientific revolution that occurred in the 17th Century initiated the advances of modern science.The scientific knowledge system created by     

Bounds for the zeros of polynomials

Let P(z)=∑↓j=0↑n ajx^j be a polynomial of degree n. In this paper we prove a more general result which interalia improves upon the bounds of a class of polynomials. We also prove a result which includes some extensions and generalizations of Enestrǒm-Kakeya theorem.     

Boundedness of commutators related to Marcinkiewicz integrals on hardy type spaces

In this paper, the authors study the boundedness of the operator [μΩ, b], the commutator generated by a function b ∈ Lipβ(Rn)(0 ＜β≤ 1) and the Marcinkiewicz integrals μΩ, on the classical Hardy spaces and the Herz-type Hardy spaces in the case Ω∈ Lipα(Sn-1)(0 ＜α≤ 1).     

Jacobi polynomials used to invert the laplace transform

Given the Laplace transform F(s) of a function f(t), we develop a new algorithm to find an approximation to f(t) by the use of the classical Jacobi polynomials. The main contribution of our work is the development of a new and very effective method to determine the coefficients in the finite series expansion that approximation f(t) in terms of Jacobi polynomials. Some numerical examples are illustrated.     

Generalization of the interaction between Haar approximation and polynomial operators to higher order methods

In applications it is useful to compute the local average empirical statistics on u. A very simple relation exists when of a function f（u） of an input u from the local averages are given by a Haar approximation. The question is to know if it holds for higher order approximation methods. To do so, it is necessary to use approximate product operators defined over linear approximation spaces. These products are characterized by a Strang and Fix like condition. An explicit construction of these product operators is exhibited for piecewise polynomial functions, using Hermite interpolation. The averaging relation which holds for the Haar approximation is then recovered when the product is defined by a two point Hermite interpolation.