截断和的弱大数律

投｛Ｘｎ，ｎ≥１｝ｉ．ｉ．ｄ．，Ｘｎ，１≤Ｘｎ，２≤…≤Ｘｎ，ｎ是Ｘ１，Ｘ２，…，Ｘｎ的次序统计量．对非负整数ｋ，ｒ，ｋ＋ｒ≤ｎ，令．本文研究当ｋ＝ｋｎ，ｒ＝ｒｎ满足ｍｉｎ（ｋ，ｒ）→∞，ｍａｘ（ｋ，ｒ）→０时截断和Ｓｎ（ｋ，ｒ）的弱大数律．设βｎ＞０，Ｃｎ∈Ｒ，文中给出了依概率收敛的充要条件．     

一类非线性中立型差分方程的振动性

本首先建立下列两类差分方程△（ｘｎ－ｒｎｒｎ－ｒｘｎ＋ｒ）＾ａ＋ｑｎｆ（ｎ－σ）＝０（＊）和△（ｒｎ△ｙ）＾ｎ＋τ＾－ａｑｎｆ（ｒｎ－σｙｎ）＝０（＊＊）振动性的等价性,然后给出方程（＊）振动性的一些判则。     

异方差回归模型近邻型估计的相合性

本文研究异方差回归模型Ｙｉ＾（ｎ）＝ｇ（ｘｉ＾（ｎ））＋εｉ＾（ｎ）,ｉ＝１,…,ｎ,其中ｇ是右实函数,ｘｉ＾（ｎ）是非随机设计点列,εｉ＾（ｎ）是随机误差,文中定义了一类ｇ（ｘ）的近邻型估计ｇｎ（ｘ）＝（ｎ）∑（ｉ＝１）Ｗｍ（ｘ）Ｙｉ＾（ｎ）,得到了ｒ阶平均相全和渐近正态性,特别,在（∞）∑（ｎ＝１）（ｎ）∑（ｉ＝１）Ｅ／εｉ＾（ｎ）／＾ｓ／（ｎｉ）＾ｓ／ｒ〈∞,ｍａｘＥ（１≤ｉ≤ｎ）／εｉ（＾     

二维渗流最低水平开穿透的宽度

在二维渗流中,设rn是矩形[O,n]2的最低水平开穿透,令ξn=max｛y：（xy）∈rn｝．本文证明了在临界状态p＝pc时,存在常数0＜C1＜C2＜1,当n充分大时有存在,而在上临界状态p＞pc时,有存在］＝0.     

Ramsey数r（k,l）的新下界公式

本文给出并证明了Ｒａｍｓｅｙ数ｒ（ｋ，ｌ）的一个新下界公式ｒ（ｋ，ｌ）≥１．５（ｋ－１）（ｌ－１），此下界公式与文献［１，２］所给出的下界公式ｒ（ｋ，ｌ）＞（ｎ２＾ｎ／２）／（ｅ√２，ｎ＝ｍｉｎ（ｋ，ｌ）相比，当ｋ，ｌ较小时，或ｋ，ｌ相差较大明要优越。     

指数和的不等式

指数和的不等式是指形如∑ｎｉ＝１ａｉｂｒｉ≤∑ｎｉ＝１ａｉｂｉ（１）的不等式，其中０＜ａ１＜…＜ａｎ＜∞，０＜ｂ１＜…＜ｂｎ＜∞，（ｒ１，ｒ２，…，ｒｎ）是（１，２，…，ｎ）的任何置换．今年春节过后不久，陈希孺院士向他的学生们指出一个挑战性的问题：对...     

不等式研究成果集锦(2)

１３．设ｓ、ｔ是两个非零实数,对正整数ｒ＝１,２,…,ｎ－１,定义ｎ元正实数组ａ＝（ａ１,ａ２,…,ａｎ）和正权数组λ＝（λ１,λ２,…,λｎ）的一类加权对称平均　Ｐｒ（ａ,λ;ｓ,ｔ）＝∑１≤ｉ１＜…＜ｉｒ≤ｎ（∑ｎｋ＝１λｎ－∑ｒｊ＝１λｉｊ）（ｒ－１∑ｒｊ＝１ａｓｉｊ）ｔｓＣｒｎ－１∑ｎｋ＝１λｋ１ｔ,则对ｒ＝１,２,…,ｎ－２,当ｓ＜ｔ时,有Ｐｒ（ｒ,λ;ｓ,ｔ）≥Ｐｒ＋１（ｒ,λ;ｓ,ｔ）;当ｓ＞ｔ时,上边不等式反号．（张志华,肖振纲,１９９８,３）１４．△ＡＢＣ三边长分别为ａ、ｂ、ｃ…     

一类四阶差分方程振动性的充分必要条件

本文给出了四阶差分方程△＾２（ｒｎ△＾２ｙｎ）＋ｆ（ｎ,ｙｎ）＝０,ｎ＝０,１,２,…的所有解（有界解）振动的一些充分条件和必要条件。     

变量满足多个线性关系且部分变量带误差的回归分析

考虑独立变量ａ１ｔ，ａｐｔ，它们满足ｍ（≥１）个线性回归关系，ｐΣｊ＝１ｂｉｊａｊｔ＝ｃｉ，ｉ＝１，ｍ，这些变量中的一些，比如ａｉｔ（ｉ＝ｒ＋１，ｐ）可以被确切观测到，而另一些变量的观测值带有误差。即ａｉｔ的观测值为ｘｉｔ＝ａｉｔ＋∈ｉｔ（ｉ＝１，ｒ，ｔ＝１，ｎ），而ｘｉｔ＝ａｉｔ（ｉ＝ｒ＋１，ｐ，ｔ＋１，ｎ），在?ｔ＝（∈１ｔ，∈ｒｔ）ｔ，ｔ＝１，ｎ为ｉｉｄ。且Ｅ∈ｔ＝０，Ｅ∈ｔ∈ｔｒ＝σ＾２Ｉ     

数学问题解答

１９９８年９月号问题解答（解答由问题提供人给出）１１５１设Ｓｎ＝１＋１２＋１３＋…＋１ｎ，求Ｓ１９９９的整数部分．解当ｒ为自然数时，显然有：ｒ＋１２＋ｒ－１２２＜ｒ＜ｒ＋１＋ｒ２，∴ｒ＋１－ｒ＜１２ｒ＜ｒ＋１２－ｒ－１２．在上式中令ｒ＝３，４，…，ｎ...     

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.     

On a class of self-similar processes with stationary increments in higher order Wiener chaoses

We study a class of self-similar processes with stationary increments belonging to higher order Wiener chaoses which are similar to Hermite processes. We obtain an almost sure wavelet-like expansion of these processes. This allows us to compute the pointwise and local Hölder regularity of sample paths and to analyse their behaviour at infinity. We also provide some results on the Hausdorff dimension of the range and graphs of multidimensional anisotropic self-similar processes with stationary increments defined by multiple Wiener–Itô integrals.     

A REPRESENTATION FORMULA RELATED TO SCHR(O)DINGER OPERATORS

Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.     

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.     

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.     

On a class of Riemann surfaces

It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary.     

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