一类线性errors－in－variables模型的参数强相合估计及其a．s．收敛速度

本文讨论了如下一类线性ｅｒｒｏｒｓ－ｉｎ－ｖａｒｉａｂｌｅｓ模型——多元线性结构关系模型β′ｘｋ＋α＝０，ξｋ＝ｘｋ＋εｋ．｛ｋ＝１，２，…，ｎ．其中，｛ｘｋ：ｋ＝１，２，…，ｎ｝为一组ｉ．ｉ．ｄ．的ｍ维随机向量，｛εｋ：ｋ＝１，２，…，ｎ｝是ｉ．ｉ．ｄ．的随机误差，Ｅ（ε１）＝０，Ｖａｒ（ε１）＝σ２Ｉｍ．且｛ｘｋ：ｋ＝１，２，…，ｎ｝与｛εｋ：ｋ＝１，２，…，ｎ｝相互独立．在一些条件下，我们证明了估计量β，α，σ２的强相合性、唯一性，并给出了估计量的收敛速度为ｏ（ｎ－１－１ｑ），这里ｑ∈［１，２）．对于Ｅ（ｘ１）ｕ１和Ｖａｒ（ｘ１）Ｖｘ的估计也得出了同样的结果     

Poisson分布参数的渐近最优和可容许的经验Bayes估计

设Ｘ及（Ｘ１，Ｘ２…，Ｘｎ）分别为取自Ｐｏｉｓｓｏｎ分布Ｐ（θ）的当前样本和历史样本，参数θ的先验分布族Ｆ＝｛Γ（ｍ，β）：β＞０｝，其中ｍ＞０已知，Γ（ｍ，β）表示参数为（ｍ，β）的伽玛分布．对ｐ＞０，ｑ＞２的任意两个实数，记ｔｎ＝Ｘ＋∑ｎｉ＝１Ｘｉ＋ｐＸ＋∑ｎｉ＝１Ｘｉ＋ｐ＋ｑ＋（ｎ＋１）ｍ（Ｘ＋ｍ）则在平方损失函数ｌ（θ，ｄ）＝（θ－ｄ）２下，ｔｎ是θ的渐近最优和可容许的经验Ｂａｙｅｓ估计，而且收敛速度为Ｏ（１ｎ）．     

矩阵损失下均值向量的线性可容许估计

设Ｙ＝（Ｙ１，…，Ｙｎ）′相互独立，ＥＹ＝Ｘβ，ＣｏｖＹ＝Ｘｄｉａｇ（β１，…，βｎ）Ｘ′，β＝（β１，…，βｎ）′∈Ｒ＋ｎ为参数，Ｒ＋＝（０，＋∞），Ｘ为已知的元素非负且对角线元素为正的ｎ阶满秩矩阵，估计均值Ｘβ，选取损失函数为矩阵损失，估计类为Ｄ＝｛ＡＹ：Ａ为元素非负的ｎ阶矩阵｝．本文研究ＡＹ在Ｄ中的容许性，获得了ＡＹ在Ｄ中是Ｘβ的容许估计的充要条件．     

相依线性回归方程组的一种“朴实”两步估计的有效性

对于相依线性回归方程组Ｙｉ＝Ｘｉβｉ＋εｉ（ｉ＝１，２），我们提出了系数向量βｉ的一种较为简便的“朴实”的两步估计量，例如β１的估计量为β１（Ｔ）＝（Ｘ’１，Ｘ１）＾－１Ｘ‘１Ｙ１－σ１２σ２２（Ｘ’１Ｘ１）＾－１Ｘ‘１ＴＹ２。其中Σ＝（σｉｊ）的一种估计量，本文给出了Σ的一种新取法，通过均方误差矩阵的大小我们证明了这种简便两种估计有有限样本量下可优效于ＬＳ估计。     

一类离散型奇异积分算子

设｛αｋ｝∞ｋ＝－∞为正数缺项序列，满足ｉｎｆｋαｋ＋１／ｄｋ＝α＞１，Ω（ｙ′）为Ｂｅｓｏｖ空间Ｂ０，１１（Ｓｎ－１）上的函数，其中Ｓｎ－１为Ｒｎ（ｎ２）上的单位球面．本文证明：若∫Ｓｎ－１Ω（ｙ′）ｄσ（ｙ′）＝０，则离散型奇异积分ＴΩ（ｆ）（ｘ）＝∑∞ｋ＝－∞∫Ｓｎ－１ｆ（ｘ－αｋｙ′）Ω（ｙ′）ｄσ（ｙ′）和相关的极大算子ＴΩ（ｆ）（ｘ）＝ｓｕｐＮ∑∞ｋ＝Ｎ∫Ｓｎ－１ｆ（ｘ－αｋｙ′）Ω（ｙ′）ｄσ（ｙ′）均在Ｌ２（Ｒｎ）上有界．上述结果推广了Ｄｕｏａｎｄｉｋｏｅｔｘｅａ和ＲｕｂｉｏｄｅＦｒａｎｃｉａ［１］在Ｌ２情形下的一个结果     

具有独立贡献的相依回归模型

考虑相依回归（ＳＵＲ）模型ｙｉ＝Ｘｉβｉ＿ｅｉ，ｉ＝１，２，…，ｍ，Ｅｅｉ＝０，ｉ，ｊ＝１；２，…ｍ，其中ｙｉ和ｅｉ是ｎ×１维随机向量，Ｘｉ是ｎ×ｐｉ已知矩阵，βｉ是ｐｉ×１维参数向量，∑＝（σｉｊ）ｍ×ｍ＞０．文中给出了两个概念：独立贡献和简洁估计．主要结果是如下五种叙述等价：（１）ＳＵＲ模型具有独立贡献；（２）βｉ的ＢＬＵＥ是简洁估计；（３）协方差改进估计是ＢＬＵＥＺ（４）βｉ的ＢＬＵＥ具有形式其中，ｊ＝１，２，…，ｍ；（５）ＰｋＮｉＮｊ＝０，ｉ≠ｊ，ｋ，Ｉ，ｊ＝１，２，…，ｍ     

图中含有D—闭迹的一个充分条件

设Ｇ是一个简单图，Ｌ＝ｕ１ｕ２…ｕｔ是Ｇ中的一个路，定义Ｌ的度ｄ（Ｌ）＝∑ｔｉ＝１ｄ（ｕｉ），其中ｄ（ｕｉ）为ｕｉ在Ｇ中的度数．本文证明了：若Ｇ是ｎ≥３阶几乎无桥的简单连通图，ＧＫ１，ｎ－１，且对Ｇ中任何两个无公共点的二长路Ｌ１，Ｌ２，有ｄ（Ｌ１）＋ｄ（Ｌ２）≥２ｎ－１，则Ｇ有一个Ｄ－闭迹，从而Ｇ的线图Ｌ（Ｇ）是Ｈａｍｉｌｔｏｎ图．     

相依样本下非参数回归函数递推型核估计的渐近分布

设（Ｘｉ，Ｙｉ）１≤ｉ≤ｎ为来自二元总体（Ｘ，Ｙ）的平稳，φ－混合样本，记ｍ（ｘ）△Ｅ（Ｙ│Ｘ＝ｘ），ｍ（ｘ）的一种递推型核估计为ｍｎ（ｘ）＝ｎ∑ｉ＝１ｈｉ＾－１Ｙｉｋ（（ｘ－Ｘｉ）／ｈｉ）／ｎ∑ｊ＝１ｈ＾－１ｊｋ（ｘ－Ｘｊ）／ｈｊ）。本文在一定的条件下证明了（ｎ／（ｎ∑ｊ＝１ｈ＾－１ｊ）＾１／２）（ｍｎ（ｘ１）－ｍ（ｘ１），ｍｎ（ｘ２）－ｍ（ｘ２），．．．ｍｎ（ｘｒ０）－ｍ（ｘｒ０））′依分布收     

Finite Dimensional Lie Superalgebras W(m,n,t) and S(m,n,t) of Cartan Type

设Ｌ＝Ｗ或Ｓ，Ｆ是特征数大于２的域．本文证明了Ｆ上的有限维单李超代数Ｌ（ｍ，ｎ，ｔ）的自然滤过是不变的．进而得出了Ｌ（ｍ，ｎ，ｔ）与Ｌ（ｍ′，ｎ′，ｔ′）同构的充要条件是ｍ＝ｍ′，ｎ＝ｎ′和ｔｉ＝τ（ｔ′ｉ），ｉ＝１，２，…，ｍ，这里τ是｛１，２，…，ｍ｝的一个置换．     

关于Thue方程的解数

设ｍ是正整数，ｆ（Ｘ，Ｙ）＝ａ０Ｘｎ＋ａ１Ｘ（ｎ－１）Ｙ＋．．．＋ａｎＹｎ∈Ｚ［Ｘ，Ｙ］是Ｑ上不可约化的叫ｎ（ｎ≥３）次齐次多项式。本文证明了：当ｇｃｄ（ｍ，ａ０）＝１，ｎ≥４００且ｍ≥１０（３５）时，方程｜ｆ（ｘ，ｙ）｜＝ｍ，ｘ，ｙ∈ｚ，ｇｃｄ（ｘ，ｙ）＝１，至多有６ｎｖ（ｍ）组解（ｘ，ｙ），其中ｖ（ｍ）是同余式Ｆ（ｚ）＝ｆ（ｚ，１）≡０（ｍｏｄｍ）的解数。特别是当ｇｃｄ（ｍ，ＤＦ）＝１时，该方程至多有６ｎ（ω（ｍ）＋１）组解（ｘ，ｙ），其中ＤＦ是多项式Ｆ的判别式，ω（ｍ）是ｍ的不同素因数的个数．     

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