具有进位吸引子的区间映射

对于一个具有n-进位吸引子的区间连续映射,证明了"n不是2的方幂"是该映射具有正拓扑熵的充分条件但不是必要条件;探讨了函数方程f3(λx)=λf(x)的一类解,并证明这类解中的每一个成员都有3-进位吸引子.     

3阶非单谷Feigenbaum映射的拟极限集

一个从闭区间到自身的连续映射被称为3阶非单谷Feigenbaum映射,如果它是函数方程f~3(λx)=λf(x)的解．本文讨论了3阶非单谷Feigenbaum映射的拟极限集及其Hausdorff维数．3阶非单谷Feigenbaum映射必然产生混沌,混沌的产生使得拟极限集的存在性问题复杂化．文中采用分形几何中的知识方法证明了此类映射的拟极限集的存在性,并相应的对其Hausdorff维数作出了估计．最后给了一个具体的例子,说明确实存在这样的3阶非单谷Feigenbaum映射．     

Fengenbaum映射的搓揉序列与特征集

设f为Feigenbaum映射,亦即函数方程fp(λx)=λf(x)满足一定条件的单峰解．f的搓揉序列为0-1无限序列,f的特征集是临界点轨迹的闭包．本文研究f的性质进而证明．f的搓揉序列是某代换在符号空间中的不动点,f在特征集上的限制是某代换子移位的一个因子．     

三角代数上的交换零点ξ-Lie可导映射

设u是数域F上的一个三角代数,δ是u上的一个线性映射,ξ∈F且ξ≠1证明了:如果对任意的x,y∈u且xy=yx=0有δ([x,y]_ξ)=[δ(x),y]_ξ+[x,δ(y)]_ξ,则在u上存在一个导子Φ和一个中心元λ使得对任意的x∈u,有δ(x)=Φ(x)+λx.     

一个加性混合幂丢番图不等式(Ⅰ)

本文证明了如果λ1,…,λ6是非零实数,并且不同一符号,至少有一个λi/λj(1≤i,j≤3)是无理数,那么对任意实数η和ε＞0,不等式|λ1x21+λ2x22+λ3x23+λ4x44+λ5x45+λ6x46+η|＜ε有无穷多正整数解x1,…,x6.     

三角代数上的零点(m,n)-弱可导映射

设m和n是任意固定的非零整数且m+n≠0,u是一个|mn(m+n)|-无挠的三角代数,δ是u上的一个线性映射.本文证明了:如果对任意的x,y∈u且xy=yx=0有mδ(xy)+nδ(yx)=mδ(x)y+mxδ(y)+nδ(y)x+nyδ(x),则在u上存在一个导子Φ和一个中心元λ使得对任意的x∈u,有δ(x)=Φ(x)+λx.     

一个加性混合幂丢番图不等式(Ⅰ)

本文证明了:如果λ1,…,λ6是非零实数,并且不同一符号,至少有一个λi/j(1≤i,j≤3) 是无理数,那么对任意实数η和ε>0,不等式|λ1x12 λ2x22 λ3x32 λ4s44 λ5x54 λ6x64 η|<ε有无穷多正整数解x1,…,x6．     

非自治Ginzburg-Landau方程的有限维行为

本文研究Ω(с)Rn(n=1,2,3)上具有几乎周期外力的非自治Ginzburg-Landau方程的有限维行为.证明了非自治Ginzburg-Landau系统存在紧的一致吸引子A1.当外力是时间拟周期时,得到了吸引子A1的Hausdorff维数的上界估计.当外力是时间周期时,证明了吸引子里一定含有周期解,而且当耗散系数λ满足适当条件时,系统在空间H=L2(Ω)上存在唯一周期解,该周期解指数吸引H中的任何有界集.     

三维静态Landau-Lifshitz方程组多重正则解的存在性

对三维Landau-Lifshitz方程u×(-△u+λ(u,n)n)=o,|u|=1,x∈ΩR3的Dirichlet常边值问题,证明了当λ＞λ1时,存在两个正则解,当λ＞max(λ1,λ*)时,存在三个正则解,除常数外,还有一个是非轴对称极小解,另一个是轴对称解,其中λ1是-△算子齐次Dirichlet问题的第一特征值,     

非自治Ginzburg-Landau方程的有限维行为

本文研究Ω R~n(n=1,2,3)上具有几乎周期外力的非自治Ginzburg-Landau方程的有限维行为。证明了非自治Ginzburg-Landau系统存在紧的一致吸引子A_1。当外力是时间拟周期时,得到了吸引子A_1的Hausdorff维数的上界估计,当外力是时间周期时,证明了吸引子里一定含有周期解,而且当耗散系数λ满足适当条件时,系统在空间H=L~2(Q)上存在唯一周期解,该周期解指数吸引H中的任何有界集。     

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.