I.I.D.序列最大部分和的精确渐近性

借助于截尾技术和强逼近原理,本文研究了独立同分布(i.i.d.)序列最大部分和的精确渐近性,给出了更加一般的结果.     

评V.I.Arnold问题

一、一个共同存在的问题 1976年V.I.Arnold提出:向量场是由固定次数带有有理系数多项式来给定,是否能给出—个稳定性的判定准则? 王联、王慕秋在文[2]中解决了当n=2情况下的V.I.Arnold问题,杨世藩同志在文[3]中对n=3的情况进行了研究。并得到很好的结果,但在对于系统:     

I.I.D.随机变量序列矩完全收敛的精确渐近性

{X,Xn;n≥1}为独立同分布的随机变量序列, EX=0,01 p/2满足E|X|r<∞,且E|X|3<∞,那么其中Z服从均值为0,方差为σ2的正态分布.     

I.I.D. STATISTICAL CONTRACTION OPERATORS AND STATISTICALLY SELF－SIMILAR SETS

I.i.d. random sequence is the simplest but very basic one in stochastic processes, and statistically self-similar set is the simplest but very basic one in random recursive sets in the theory of random fractal. Is there any relation between i.i.d. random sequence and statistically self-similar set? This paper gives a basic theorem which tells us that the random recursive set generated by a collection of i.i.d. statistical contraction operators is always a statistically self-similar set.     

I.I.D.随机变量两两乘积之和的Hsu-Robbins型定理(Ⅰ)

设随机变量Ｘ１，Ｘ２，…ｉｉｄ；称Ｕｎ＝１≤ｉ＜ｊ≤ｎＸｉＸｊ，为两两乘积之和，本文意在给出 Ｕｎ／ｎ~２→０即文中（０．３）式成立的充分必要条件．我们在这部分工作中虽未能彻底解决这个问题，但却揭示出这类条件与Ｓｎ／ｎ→０（Ｓｎ＝ｎｉ＝１Ｘｉ）之条件间的本质上的不同之处，就是说，这是一类不能完全用Ｘ１的矩来刻划的条件，它们要更为深层次地依赖于Ｘ１的尾分布性质．     

I.I.D.随机变量两两乘积之和的Hsu-Robbins型定理(Ⅱ)

在本部分中，采用由 Ｌｅｖｙ函数（４．ｌ）所确定的值ｂｎ取代（Ｉ）［１］中的１／ｎ“位点”ａｎ，使得（Ｉ）中定理１中的附加条件（Ａ）得以解除，从而获得了可以称之为Ｈｓｕ－Ｒｏｂｂｉｎｓ型的充分必要条件．作为推论，还给出了两个互为复制的ｉｉｄ随机变量三角阵对应行之和乘积的Ｋｏｌｍｏｇｏｒｏｖ强大数律．     

I.I.D.随机变量两两乘积之和的Hsu-Robbins型定理(Ⅰ)

设随机变量Ｘ１，Ｘ２，…ｉｉｄ；称Ｕｎ＝１≤ｉ＜ｊ≤ｎＸｉＸｊ，为两两乘积之和，本文意在给出 Ｕｎ／ｎ~２→０即文中（０．３）式成立的充分必要条件．我们在这部分工作中虽未能彻底解决这个问题，但却揭示出这类条件与Ｓｎ／ｎ→０（Ｓｎ＝ｎｉ＝１Ｘｉ）之条件间的本质上的不同之处，就是说，这是一类不能完全用Ｘ１的矩来刻划的条件，它们要更为深层次地依赖于Ｘ１的尾分布性质．     

I.J.Matrix定理的进一步推广

文献 [1]— [5 ]连续讨论了 I.J.Matrix定理的一些推广及应用 ,特别是文 [5 ]利用高阶微分的知识简明地给出了一个推广 ,本文给出其进一步的推广 .设 a0 ,a1 ,… ,an 是 n 1个互不相同且不为零的数 ,f ( x)是次数为 m的多项式 ,文 [5 ]讨论的是m相似文献   

I.J.Matrix定理的更广泛推广

Ｉ．Ｊ．Ｍａｔｒｉｘ定理的更广泛推广张之正（河南洛阳师专数学系４７１０２２）近年来，数学通报连续讨论了１．Ｊ．Ｍａｔｒｉｘ定理的一些推广及其应用（文［ｌ］，［２］用复交函数中的留数定理，文［３Ｊ用初等方法，文［４］用线性代数中的Ｖａｎｄｅｒｍｏｎｄｅ...     

Monotone factors of I.I.D. processes

LetB(p) andB(q) be Bernoulli shifts on {0, 1,...,d - 1}^ℤ. Ifh(p)>h(q), it is a classical theorem of Sinai that there is a factor map takingB(p) toB(q). If, in addition,p stochastically dominatesq, we can ask whether there is such a factor map ϕ which is monotone: ϕ(x) _i≤x_i for each coordinatei of almost every pointx. Here we show that there is a monotone finitary code fromB(p) toB(q) in the case whereB(q) is a shift on two symbols.     

Dubins’ problem on surfaces. I. nonnegative curvature

Let M be a complete, connected, two-dimensional Riemannian manifold. Consider the following question: Given any (p₁,v₁) and (p₂, v₂) in T M, is it possible to connect p₁ to P₂ by a curve y in M with arbitrary small geodesic curvature such that, for i = 1, 2, y is equal to v_i at p_i? In this article, we bring a positive answer to the question if M verifies one of the following three conditions: (a) M is compact, (b) M is asymptotically flat, and (c) M has bounded nonnegative curvature outside a compact subset.     

Linear Systems on Fano Threefolds. I

Abstract

In this note, we classify all the polarized Fano threefold (X, H) with Bs|H|¬ = ∅. As corollaries we obtained that (1) the very ample part of the conjecture of Fujita holds for smooth Fano threefolds and (2) global Seshadri constants of ample divisors on Fano threefolds are bounded from below by 1 except three types of polarized Fano threefolds.     

Localization,completion and the AR property in Noetherian P.I. rings

Given a prime idealP in a noetherian ringR we examine the following two properties: (1)P is Ore localizable. (2) The completion ofR atP is Noetherian. For rings satisfying the 2nd layer condition a strong connection is discovered between (1) and (2) and consequently questions by Goldie and McConnell are answered. As a corollary we also obtain a new characterization for non-maximal primitive idealP inR to satisfy (1), whereR is the enveloping algebra of complex solvable finite dimensional Lie algebra Dedicated to the memory of Shimshon Amitsur     

Algebraic multilevel preconditioning methods. I

Summary A recursive way of constructing preconditioning matrices for the stiffness matrix in the discretization of selfadjoint second order elliptic boundary value problems is proposed. It is based on a sequence of nested finite element spaces with the usual nodal basis functions. Using a nodeordering corresponding to the nested meshes, the finite element stiffness matrix is recursively split up into two-level block structures and is factored approximately in such a way that any successive Schur complement is replaced (approximated) by a matrix defined recursively and thereform only implicitely given. To solve a system with this matrix we need to perform a fixed number (v) of iterations on the preceding level using as an iteration matrix the preconditioning matrix already defined on that level. It is shown that by a proper choice of iteration parameters it suffices to use \left( {1 - \gamma ^2 } \right)^{ - \tfrac{1}{2}} $$ " align="middle" border="0"> iterations for the so constructedv-foldV-cycle (wherev=2 corresponds to aW-cycle) preconditioning matrices to be spectrally equivalent to the stiffness matrix. The conditions involve only the constant in the strengthened C.-B.-S. inequality for the corresponding two-level hierarchical basis function spaces and are therefore independent of the regularity of the solution for instance. If we use successive uniform refinements of the meshes the method is of optimal order of computational complexity, if . Under reasonable assumptions of the finite element mesh, the condition numbers turn out to be so small that there are in practice few reasons to use an accelerated iterative method like the conjugate gradient method, for instance.Dedicated to the memory of Peter HenriciThe research of the second author reported here was supported in part by the Committee of Science, Bulgaria, under Grant No. 55/26.03.87     

Topological regular variation: I. Slow variation

Motivated by the Category Embedding Theorem, as applied to convergent automorphisms (Bingham and Ostaszewski (in press) [11]), we unify and extend the multivariate regular variation literature by a reformulation in the language of topological dynamics. Here the natural setting are metric groups, seen as normed groups (mimicking normed vector spaces). We briefly study their properties as a preliminary to establishing that the Uniform Convergence Theorem (UCT) for Baire, group-valued slowly-varying functions has two natural metric generalizations linked by the natural duality between a homogenous space and its group of homeomorphisms. Each is derivable from the other by duality. One of these explicitly extends the (topological) group version of UCT due to Bajšanski and Karamata (1969) [4] from groups to flows on a group. A multiplicative representation of the flow derived in Ostaszewski (2010) [45] demonstrates equivalence of the flow with the earlier group formulation. In companion papers we extend the theory to regularly varying functions: we establish the calculus of regular variation in Bingham and Ostaszewski (2010) [13] and we extend to locally compact, σ-compact groups the fundamental theorems on characterization and representation (Bingham and Ostaszewski (2010) [14]). In Bingham and Ostaszewski (2009) [15], working with topological flows on homogeneous spaces, we identify an index of regular variation, which in a normed-vector space context may be specified using the Riesz representation theorem, and in a locally compact group setting may be connected with Haar measure.     

QUANTUM SUPERGROUPS I. FOUNDATIONS

In this part one of a series of papers, we introduce a new version of quantum covering and super groups with no isotropic odd simple root, which is suitable for the study of integrable modules, integral forms, and the bar involution. A quantum covering group involves parameters q and π with π²?=?1, and it specializes at π?=??1 to a quantum supergroup. Following Lusztig, we formulate and establish various structural results of the quantum covering groups, including a bilinear form, quasi- $ \mathcal{R} $ -matrix, Casimir element, character formulas for integrable modules, and higher Serre relations.