湍流相干结构的机理研究（Ⅱ）——粗糙壁边界层相干结构的物理模型

本文主要分析了粗糙壁面相干结构的特性以及与光滑壁面相干结构的区别，讨论了从光滑壁到粗糙壁过渡的问题，在此基础上建立了粗糙壁面相干结构的物理模型，从理论上得到了慢条宽度、猝发时间等物理量与动量厚度雷诺数的关系，其结果与实验结果是相符合的。     

湍流相干结构的机理研究（Ⅱ）─粗糙壁边界层相干结构的物理模型

本文主要分析了粗糙壁面相干结构的特性以及与光滑壁面相干结构的区别，讨论了从光滑壁到粗糙壁过渡的问题，在此基础上建立了粗糙壁面相干结构的物理模型，从理论上得到了慢条宽度、猝发时间等物理量与动量厚度雷诺数的关系，其结果与实验结果是相符合的．     

湍流相干结构与小尺度结构之间的相互作用

本文首先对切变湍流场中存在大尺度相干结构与小尺度结构和不同尺度结构之间的相互作用进行了试验研究，得到了一些特征值，其次，在试验的基础上，建立了考虑不同尺度结构之间的相互作用后相干结构的数学描述和模式识别方法，并对光滑壁面与均匀密集加糙壁面条件下湍流边界层中的相干结构进行了模式识别．结果表明，文中所建立的计算方法是可行的。     

湍流边界层底层相干结构的一个理论模型

本采用非线性稳定性分析方法，研究了湍流边界层底层相干结构的成因。计算得到的增长最快的不稳定波的展向尺度与纵向尺度都与实验相符。这一分析的特点是采用了不同于湍流平均速度剖面的更合理的速度剖面作为稳定性分析的基础，并采用了新的非线性理论。中结果有助于理解湍流边界层底层相干结构的拟有序现象。     

湍流边界层近壁区相干结构起因的研究

利用流动稳定性理论中的一般共振三波的概念,提出了一种湍流边界层近壁区相干结构产生机理的理论模型。由此所得的相干结构的空间形态,展向尺度,传播速度等都与数值模拟所得结果相近。特别是计算了多数是不对称的各种流向涡对环量差的概率密度分布曲线,得到了与数值模拟结果相比基本满意的结果。     

压力梯度对湍流边界层相干结构的影响

利用流动稳定性理论中一般共振三波的概念,对有压力梯度湍流边界层的相干结构进行研究。通过计算得出顺压梯度能够抑制相干结构的产生和发展,而逆压梯度对之有激励和促进的作用。此外,与无压力梯度相比,相干结构的尺度、形状以及传播速度等都已改变,理论分析所得变化趋势与实验结果相一致。计算流向涡对无量纲环量差概率密度分布曲线发现逆压梯度下流向涡对较无压梯度更趋于对称。     

湍流边界层外区大尺度相干结构的理论模型及与实验的比较

本文基于流动稳定性理论,提出了一种解释湍流边界层外区大尺度相干结构产生机理的理论模型.将计算所得流线、等涡线分布及利用相干结构理论模型计算湍流边界层中平均温度分布的结果与实验比较,结果是比较满意的.     

用局部平均速度结构函数检测湍流边界层多尺度相干结构

测量风洞中平板湍流边界层不同法向位置的流向速度时间序列信号，提出了基于局部多尺度平均意义的湍流多尺度局部平均结构函数的概念，以描述湍流多尺度结构的伸缩变形和相对运动；基于多尺度局部平均结构函数的概念与Harr子波变换的一致性，提出了用湍流多尺度局部平均结构函数的平坦因子检测湍流边界层多尺度相干结构及其间歇性的检测方法，提取近壁区域不同法向位置处多尺度相干结构的条件相位平均波形，以研究多尺度相干结构猝发的动力学过程及其对湍流统计性质的影响．     

湍流边界层外区扰动激发近壁区相干结构的一种机制

应用直接数值模拟的方法，研究了湍流边界层近壁区由于外区扰动的作用而导致相干结构产生的问题．结果表明：在湍流边界层近壁区的上边界存在的速度扰动，可以在近壁区内激发出相干结构，从而完善了单个相干结构的理论模型。     

湍流边界层近壁区单个相干结构的模拟 *

提出了湍流边界层近壁区单个相干结构的理论模型 .用数值模拟的方法研究了它们的演化 ,结果发现在很多方面它们与实验观测到的特性相符 .     

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.