Grünwald插值算子的L_p收敛速度

讨论了以第二类 Ｔｃｈｅｂｙｃｈｅｆｆ多项式的零点为插值结点纽的 Ｇｒǖｎｗａｌｄ 插值于Ｌｐ下 的收敛性．当１≤ｐ＜２时,给出了收敛速度的一个精确估计;当Ｐ≥２时,说明了其于Ｌｐ下不 是收敛算子列．给出了一种以第二类Ｔｃｈｅｂｙｃｈｅｆｆ多项式的零点为插值结点组的修改的 Ｇｒｕｎｗａｌｄ插值,证明了其于 Ｌｐ（１≤ｐ＜∞）下是收敛的．     

Grünwald插值算子的Lp收敛速度

讨论了以第二类 Ｔｃｈｅｂｙｃｈｅｆｆ多项式的零点为插值结点纽的 Ｇｒǖｎｗａｌｄ 插值于Ｌ_p下 的收敛性．当１≤ｐ＜２时,给出了收敛速度的一个精确估计;当Ｐ≥２时,说明了其于Ｌ_p下不 是收敛算子列．给出了一种以第二类Ｔｃｈｅｂｙｃｈｅｆｆ多项式的零点为插值结点组的修改的 Ｇｒｕｎｗａｌｄ插值,证明了其于 Ｌ_p（１≤ｐ＜∞）下是收敛的．     

Grünwald插值算子的L_1收敛速度

先给出了以第二类Ｔｃｈｅｂｙｃｈｅｆ多项式的零点为插值结点组的Ｇｒｕｎｗａｌｄ插值多项式于Ｌ１下的收敛速度，然后给出了一种修改的Ｇｒｕｎｗａｌｄ插值多项式及其于Ｌ１下的收敛速度．     

Gruenwald插值算子的L1收敛速度

先给出了以第二类Ｔｃｈｅｂｙｃｈｅｆｆ多项式的零点为插值结点组的Ｇｒｕｎｗａｌｄ插值多项式于Ｌ１下的收敛速度，然后给出了一种修改的Ｇｒｕｎｗａｌｄ插值多项式及其于Ｌ１下的收敛速度。     

二元Jackson插值多项式及其在Orlicz空间中的逼近阶

本文引进了Ｋａｎｔｏｒｏｖｉｔｃｈ算子型的二元修正Ｊａｃｋｓｏｎ三角插值多项式，给出了其在Ｏｒｌｉｃｚ空间中的收敛阶，作了推论，给出了二元修正Ｈｅｒｍｉｔｅ－Ｆｅｊｅｒ插值算子在带Ｏｒｌｉｃｚ空间中的逼近的量化估计。     

Grunwald插值算子的Lp收敛速度

讨论了以第二类Tchebycheff多项式的零点为插值结点组的Grünwald插值于Lp下的收敛性.当1≤p＜2时,给出了收敛速度的一个精确估计;当p≥2时,说明了其Lp下不是收敛算子列.给出了一种以第二类Tchebycheff多项式的零点为插值结点组的修改的Grünwald插值,证明了其于Lp(1≤p＜∞)下是收敛的.     

关于Lagrange平均插值过程的逼近阶估计

本文以多项式（１＋ｘ）Ｖｎ（ｘ）Ｖｎ（ｘ）＝ｃｏｓ２ｎ＋１２θｃｏｓθ２，ｘ＝ｃｏｓθ的零点作为插值的节点，构造了一个Ｌａｇｒａｎｇｅ插值多项式算子过程Ｃｎ（ｆ，ｘ），给出了其逼近阶估计．同时证明Ｃｎ（ｆ，ｘ）亦满足Ｄｉｔｚｉａｎ－Ｔｏｔｉｋ定理．     

扩充的Hermite-Fejér插值算子平均收敛性

讨论了以Ｊａｃｏｂｉ正交多项式零点为插值结点的扩充Ｈｅｒｍｉｔｅ－Ｆｅｊｅｒ插值算子在Ｌｐｕ空间的平均收敛性。首先给出了算子加权平均收敛的条件,进一步得到了收敛阶。     

一类指数型整函数插值算子的逼近性质

设（Ｕσｆ）（ｘ）＝∑ｋ∈Ｚｆ（Ｘｋ）Ａσ（Ｘ－Ｘｋ）,Ｘｋ＝２ｋπσ,ｋ∈Ｚ,σ＞０,ｆ是Ｒ上的有界函数,而Ａσ（ｙ）＝２σ∫σ０ｓｉｎｍ（σ－Ｘ）ｈｓｉｎｍ（σ－Ｘ）ｈ＋ｓｉｎｍｘｈｃｏｓｘｙｄｘ,ｍ为奇自然数,０＜ｈ＜πσ,本文研究了此插值算子的收敛与饱和问题．     

一类高阶拟Hermite－Fejer多项式插值问题

本文首先证明了二个Ｍａｒｅｉｎｋｅｗｉｃｚ－Ｚｙｇｍｕｎｄ型不等式，然后将它们应用到一类新的高阶拟Ｈｅｒｍｉｔｅ－Ｆｅｊｅｒ插值问题上，得到了该插值问题的一致及加权平均收敛性和逼近阶．此外，文中还得到了该插值一种典型情况时的点态逼近阶．     

Rates of Convergence of Means of Euclidean Functionals

Let L be the Euclidean functional with p-th power-weighted edges. Examples include the sum of the p-th power-weighted lengths of the edges in minimal spanning trees, traveling salesman tours, and minimal matchings. Motivated by the works of Steele, Redmond and Yukich (Ann. Appl. Probab. 4, 1057–1073, 1994, Stoch. Process. Appl. 61, 289–304, 1996) have shown that for n i.i.d. sample points {X ₁,…,X _n } from [0,1] ^d , L({X ₁,…,X _n })/n ^(d−p)/d converges a.s. to a finite constant. Here we bound the rate of convergence of EL({X ₁,…,X _n })/n ^(d−p)/d . Y. Koo supported by the BK21 project of the Department of Mathematics, Sungkyunkwan University. S. Lee supported by the BK21 project of the Department of Mathematics, Yonsei University.     

Polarizations of Prym varieties of pairs of coverings

To any pair of coverings f_i:X → X_i, i=1, 2, of smooth projective curves one can associate an abelian subvariety of the Jacobian J_X, the Prym variety P(f₁, f₂) of the pair (f₁, f₂). In some cases we can compute the type of the restriction of the canonical principal polarization of J_X. We obtain 2 families of Prym-Tyurin varieties of exponent 6. Received: 2 September 2004     

Galois Structure of K-Groups of Rings of Integers

N/Kbe a Galois extension of number fields with finite Galois group G.We describe a new approach for constructing invariants of the G-module structure of the K groups of the ring of integers of N in the Grothendieck group of finitely generated projective Z[G]modules. In various cases we can relate these classes, and their function field counterparts, to the root number class of Fröhlich and Cassou-Noguès.     

Exact values of relative widths of classes of differentialbe functions

We study relative widths in the spacesC andL of classes of periodic differentiable functionsW ^r,r=1,2,…, when in contrast to the Kolmogorov widths it is additionally required that the approximating functions belong to the classMW ^r with a given majorantM of the norm of the derivative of orderr. It is proved that ifM satisfies the estimate

Enumeration of perfect matchings of a type of Cartesian products of graphs

Let G be a graph and let Pm(G) denote the number of perfect matchings of G.We denote the path with m vertices by P_m and the Cartesian product of graphs G and H by G×H. In this paper, as the continuance of our paper [W. Yan, F. Zhang, Enumeration of perfect matchings of graphs with reflective symmetry by Pfaffians, Adv. Appl. Math. 32 (2004) 175-188], we enumerate perfect matchings in a type of Cartesian products of graphs by the Pfaffian method, which was discovered by Kasteleyn. Here are some of our results:1. Let T be a tree and let C_n denote the cycle with n vertices. Then Pm(C₄×T)=∏(2+α²), where the product ranges over all eigenvalues α of T. Moreover, we prove that Pm(C₄×T) is always a square or double a square.2. Let T be a tree. Then Pm(P₄×T)=∏(1+3α²+α⁴), where the product ranges over all non-negative eigenvalues α of T.3. Let T be a tree with a perfect matching. Then Pm(P₃×T)=∏(2+α²), where the product ranges over all positive eigenvalues α of T. Moreover, we prove that Pm(C₄×T)=[Pm(P₃×T)]².     

均值混合正态分布统计量的性质

这篇文章基于基因遗传背景,提出了一类均值混合正态分布,它不同于通常所讨论的方差混合正态分布. 作者研究了这类均值混合正态分布统计量的性质,给出了平移变换群下不变量的稳健性,即它与正态分布下该统计量有相同的性质, 并且讨论了其它统计量的分布.     

Some Properties of Certain Subgroups of Tensor Squares of p-Groups

Let G be a finite p-group of order p ⁿ and ?(G) be the subgroup of the tensor square of G generated by all symbols x ? x, for all x in G. In the present article, we construct an upper bound for the order of ?(G) and any extra special p-group. It is also shown that ?(G) ? ?(G/G′). Using our result, we obtain the explicit structure of the tensor square of G and π₃ SK(G, 1). Finally, the structure of G will be characterized when the bound is attained.     

Bayes estimation of number of signals

Bayes estimation of the number of signals, q, based on a binomial prior distribution is studied. It is found that the Bayes estimate depends on the eigenvalues of the sample covariance matrix S for white-noise case and the eigenvalues of the matrix S ₂ (S ₁+A)^–1 for the colored-noise case, where S ₁ is the sample covariance matrix of observations consisting only noise, S ₂ the sample covariance matrix of observations consisting both noise and signals and A is some positive definite matrix. Posterior distributions for both the cases are derived by expanding zonal polynomial in terms of monomial symmetric functions and using some of the important formulae of James (1964, Ann. Math. Statist., 35, 475–501).     

Joint Distributions of Numbers of Runs of Specified Lengths in a Sequence of Markov Dependent Multistate Trials

Let Z ₀, Z ₁,...,Z _n be a sequence of Markov dependent trials with state space Ω = {F ₁,...,F _λ, S ₁,...,S _ν}, where we regard F ₁,...,F _λ as failures and S ₁,...,S _ν as successes. In this paper, we study the joint distribution of the numbers of S _i -runs of lengths k _ij (i = 1,2,...,ν, j = 1,2,...,r _i ) based on four different enumeration schemes. We present formulae for the evaluation of the probability generating functions and the higher order moments of this distribution. In addition, when the underlying sequence is i.i.d. trials, the conditional distribution of the same run statistics, given the numbers of success and failure is investigated. We give further insights into the multivariate run-related problems arising from a sequence of the multistate trials. Besides, our results have potential applications to problems of various research areas and will come to prominence in the future. This research was partially supported by the ISM Cooperative Research Program (2004-ISM·CRP-2007).     

Ideals of identities of representations of nilpotent lie algebras

Let L be a Lie algebra, nilpotent of class 2, over an infinite field K, and suppose that the centre C of L is one dimensional; such Lie algebras are called Heisenberg algebras. Let ρ:L→hom _KV be a finite dimensional representation of the Heisenberg algebra L such that ρ(C) contains non-singular linear transformations of V, and denote l(ρ) the ideal of identities for the representation ρ. We prove that the ideals of identities of representations containing I(ρ) and generated by multilinear polynomials satisfy the ACC. Let sl ₂(L) be the Lie algebra of the traceless 2×2 matrices over K, and suppose the characteristic of K equals 2. As a corollary we obtain that the ideals of identities of representations of Lie algebras containing that of the regular representation of sl ₂(K) and generated by multilinear polynomials, are finitely based. In addition we show that one cannot simply dispense with the condition of multilinearity. Namely, we show that the ACC is violated for the ideals of representations of Lie algebras (over an infinite field of characteristic 2) that contain the identities of the regular representation of sl ₂(K).