非均匀调和函数的两类边值问题与积分表达式

本文给出非均匀指数函数的定义及性质,并且进一步引入了非均匀三角函数、非均匀双曲函数和非均匀对数函数.最后利用非均匀指数函数表达形式和非均匀解析函数的Cauchy积分理论,建立了非均匀泊松积分公式和非均匀施瓦茨积分公式,获得了非均匀调和函数在两类特殊边界上的狄利克雷问题和诺伊曼问题解的显示表达式.     

数据流的非平稳性度量——纪念李国平院士吴新谋教授诞辰100周年

该文融合遍历论、粗粒化方法和信息论的观点研究数据流的非平稳性度量问题. 引入了数据流的非平稳性度量的概念, 给出了数据流非平稳性度量的有效的近似算法. 数据流的非平稳性度量为该文融合遍历论、粗粒化方法和信息论的观点研究数据流的非平稳性度量问题. 引入了数据流的非平稳性度量的概念, 给出了数据流非平稳性度量的有效的近似算法. 数据流的非平稳性度量为该文融合遍历论、粗粒化方法和信息论的观点研究数据流的非平稳性度量问题. 引入了数据流的非平稳性度量的概念, 给出了数据流非平稳性度量的有效的近似算法. 数据流的非平稳性度量为$0$和$1$之间的实数,平稳性较好的数据流的非平稳性度量较小. 作者将数据流的非平稳性度量应用到模型选择问题中,提出残差序列非平稳性度量最小化的模型选择标准. 作者用数值试验检验了该文提出的数据流非平稳性度量的近似算法, 并检验了其作为模型选择标准的能力.数值试验的结果表明, 非平稳性度量是衡量数据流非平稳程度的一个合理指标, 可以很好地区分趋势平稳数据和差分平稳数据, 区分独立同分布序列、白噪声序列和鞅差序列.     

密度和刚度线性变化对非均匀地壳层中扭转表面波传播的影响

研究了覆盖在非均匀半无限空间上的非均匀地壳层中,扭转表面波传播的可能性.地壳层的非均匀性随着厚度线性变化,非均匀半无限空间的非均匀性表现为3种类型,即指数型、二次型和双曲型.采用封闭形式,可以分别推导出上述3种类型非均匀性的色散方程.对于覆盖在半空间上的同一地壳层,色散方程与经典案例的方程一致.研究发现,随着非均匀地壳层中密度线性变化的非均匀参数的增大,相速度减小,而由刚度引起的非均匀因素对相速度的影响相反.     

非Chetaev型非完整系统的Lie对称性与Noether对称性

研究非Ｃｈｅｔａｅｖ型非完整系统的Ｌｉｅ对称性与Ｎｏｅｔｈｅｒ对称性,具体研究了非Ｃｈｅｔａｅｖ型常 质量非完整系统和非Ｃｈｅｔａｅｖ型变质量非完整系统的Ｌｉｅ对称性与Ｎｏｅｔｈｅｒ对称性．给出Ｌｉｅ对称 性导致Ｎｏｅｔｈｅｒ对称性以及Ｎｏｅｔｈｅｒ对称性导致Ｌｉｅ对称性的条件．     

关于非凸的有限理性的稳定性

关于有限理性方面的文献, 大多数都是在满足凸性条件下研究有限理性的相关性质, 在一定程度上限制了其应用范围. 应用Ekeland变分原理, 减弱了有限理性模型的假设条件, 考虑在不满足凸性条件下的有限理性模型的稳定性问题. 具体给出了非凸的Ky Fan点问题解的稳定性, 非凸非紧的Ky Fan点问题解的稳定性, 非凸向量值函数Ky Fan点解的稳定性和非凸非紧向量值函数Ky Fan点解的稳定性. 作为应用, 还给出了非凸的n人非合作博弈有限理性模型解的稳定性和非凸的多目标博弈有限理性模型解的稳定性.     

预线性与对合非结合剩余格

非结合剩余格是非结合格值逻辑系统的代数抽象,本文研究几类特殊非结合剩余格的代数性质。证明了满足预线性条件的非结合剩余格必是分配格,并给出预线性非结合剩余格的充分必要条件。同时,引入对合和强对合非结合剩余格的概念,研究了它们的基本性质,并分别给出对合和强对合非结合剩余格的等价条件。最后,通过反例说明强对合预线性非结合剩余格不一定是蕴涵格。     

非自治动力系统拓扑压变分原理的一点注记

用类似于非自治熵的变分原理的方法,证明了非自治拓扑压的变分原理的一个不等式,推广了非自治熵的变分原理,丰富了非自治变分原理的内容.     

图和色多项式根2的阶

本文证明了3-连通非偶图的色多项式根2的阶为1;满足一定条件的非3-连通非偶图的色多项式根2的阶是图的非偶块和非偶可分块数.从而,把色多项式P(G)中1的阶是图G的非平凡块数这一结果进一步加以推广.     

非局部非对称弹性固体理论

本文基于非局部连续统场论和非线性连续体力学理论,建立了非局部非对称弹性固体的非线性理论.它完善和发展了Eringen等人所建立的非局部弹性场论.将文献[1]中所建立的非局部非对称弹性力学的线性理论推广到有限变形.证明了在非局部弹性固体中存在着非局部体力矩.非局部体力矩引起应力的非对称性,而非局部体力矩则由原子晶格相互作用形成的共价键所产生的.并应用本文建立的理论合理地解释了平面横波和纵波色散系关的不相似性.     

固定设计下非参数回归模型估计的渐近性质

考虑固定设计下具有非参数AR(1)的非参数回归模型,综合最小二乘和非参数核估计法,定义了非参数函数的估计量,在适当的条件下,研究了它们的渐近性质.     

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.