On the Lévy-Khintchine decomposition of conditionally positive definite functions

Summary The main aim of the paper is to prove still another version of the Lévy--Khintchine decomposition of conditionally positive definite functions on a general locally compact Abelian group. The exposition is based on the two-cones theorem proved by N. Drumm in 1976. Application of the main result to the Euclidean group shows the novelty of the approach.     

控制系统实的第二标准型绝对稳定的显式准则

本文给出的非线性控制系统实的第二标准型绝对稳定的显式准则,包含并改进了文[1]所得到的判别准则。将本文准则应用于着名的飞机纵向运动方程,所得结果包含并改进了文[1,2,3,4]中所得到的相应结论。     

Orthogonal Decompositions in Hilbertian Subspaces, Error Functions and Optimal Extensions of Interpolation Systems

We address the question of optimal extensions of a fixed set S of measurement points for an interpolation system in a reproducing kernel Hilbert space of R . By considering the interpolation error function obtained from the reproducing kernel, we introduce different criteria of optimal extensions. We highlight the orthogonal decomposition of the space based on the subspace associated with the set S. The connection to the classical Schur decomposition of the Gram matrix of the interpolation problem is established. All the theory extends to conditionally positive functions and for this case, we give a result on the spectrum of the matrix of the interpolation problem.     

Some concepts of positive dependence for bivariate interchangeable distributions

In this work we consider some familiar and some new concepts of positive dependence for interchangeable bivariate distributions. By characterizing distributions which are positively dependent according to some of these concepts, we indicate real situations in which these concepts arise naturally. For the various families of positively dependent distributions we prove some closure properties and demonstrate all the possible logical relations. Some inequalities are shown and applied to determine whether under- (or over-) estimates, of various probabilistic quantities, occur when a positively dependent distribution is assumed (falsely) to be the product of its marginals (that is, when two positively dependent random variables are assumed, falsely, to be independent). Specific applications in reliability theory, statistical mechanics and reversible Markov processes are discussed. This work was partially supported by National Science Foundation GP-30707X1. It is part of the author's Ph.D. dissertation prepared at the University of Rochester and supervised by A. W. Marshall. Now at Indiana University.     

从一道习题的推广看矩阵的标准形理论

通过一道简单习题的多重推广,串联起了实对称阵与实反对称阵的正交相似标准形理论.     

The Canonical Basis for the Quantum Group of Type B2

We use the Ringel-Hall algebra approach to study the canonical basis elements for the quantum group of type B₂ which are characterized in Xi [12]. However, our approach simplifies several computations there.     

Perfectness of Conelike *–Semigroups in ℚk

Let S be an abelian *–semigroup in ℚ^k. We give a sufficient condition for every positive definite function on S to have a unique representing measure on the dual semigroup of S (i.e. S is perfect). To characterize perfectness for any abelian *–semigroupis a challenging, but not yet generally solved problem. In this paper, we characterize the structure of involutions on an abelian *–semigroup which is a subset of ℚ^k, and show that any conelike *–semigroups in ℚ^k are perfect.     

Recurrence of the integral of a smooth conditionally periodic function

We prove that the integral of a smooth multifrequency conditionally periodic function with zero mean oscillates. Translated fromMatematicheskie Zametki, Vol. 63, No. 5, pp. 737–748, May, 1998. The author wishes to express his deep gratitude to S. V. Konyagin for fruitful discussions, verification of the results, and the correction of some misprints. This research was supported by the Russian Foundation for Basic Research under grants No. 96-01-00378 and No. 96-15-96072 and by the EFAKOD Foundation.     

On the Marginal Automorphisms of a Group

Let W be a nonempty subset of a free group. We call an automorphism α of a group G a marginal automorphism if x ^?1α(x) ∈ W*(G) for each x ∈ G, where W*(G) is the marginal subgroup of G. In this article, we give some results on marginal automorphisms of a group.     

Random Walks on the Affine Group of a Homogeneous Tree in the Drift-Free Case

The affine group of a homogeneous tree is the group of all its isometries fixing an end of its boundary. We consider a random walk with law μ on this group and the associated random processes on the tree and its boundary. In the drift-free case there exists on the boundary of the tree a unique μ-invariant Radon measure. In this paper we describe its behaviour at infinity.     

关于Hadamard乘积矩阵的一些性质的注记

对文 [1 ]的主要结论作了说明 ,给出 Hadamard乘积矩阵有关性质的更一般的结果 .     

一个矩阵分解算法的推广及应用

对样本相关系数矩阵等行和分解算法作了简化和推广,使算法不仅可以应用在基于正态总体非独立样本的假设检验问题,也可以有效地运用在最优化算法中牛顿法等与二次函数极小化有关的问题上.     

A Remark on the Positive Definite Problem of a Binary Quartic Form

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｔｈｅｓｔｕｄｙｏｆｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓａｎｄｏｔｈｅｒｍａｔｈｅｍａｔｉｃａｌｆｉｅｌｄｓ,ｏｎｅｕｓｕａｌｌｙｎｅｅｄｔｏｄｅａｌｗｉｔｈｔｈｅｐｏｓｉｔｉｖｅｄｅｆｉｎｉｔｅ,ｎｅｇａｔｉｖｅｄｅｆｉｎｉｔｅｐｒｏｂｌｅｍｓｏｆｂｉｎａｒｙｑｕａｒｔｉｃｆｏｒｍｓ,ｓｅｅ［１,２］．Ｉｔｉｓｗｅｌｌ－ｋｎｏｗｔｈａｔｉｎｔｈｅｃａｓｅｏｆｑｕａｄｒａｔｉｃｆｏｒｍ,ｔｈｅｒｅｅｘｉｓｔｍａｎｙｃｒｉｔｅｒｉｏｎｓｆｏｒｔｈｅｐｏｓｉ…     

Canonical and Boundary Representations on a Hyperboloid of One Sheet

For the hyperboloid of one sheet X=G/H, G=SO₀(1,2), H=SO₀(1,1), canonical representations R _,, C, =0,1, are defined as the restrictions to G of representations of the overgroup =SO₀(2,2) associated with a cone. They act on the torus containing two copies of X as open G-orbits. We study boundary representations generated by R _,. For some , they contain Jordan blocks. The decomposition of R _, into irreducible constituents includes a finite number (depending on ) of irreducible parts of the boundary representations.     

Degenerate Principal Series Representations of U(p, q) and Spin0(p, q)

Let p>q and let G be the group U(p, q) or Spin₀(p, q). Let P=LN be the maximal parabolic subgroup of G with Levi subgroup where

Canonical Representations and Overgroups for Hyperboloids of One Sheet and Lobachevsky Spaces

We define canonical representations for the hyperboloid of one sheet and for the Lobachevsky space =G/K where G=SO₀(1,n–1), H=SO₀(1,n–2) and K=SO(n–1), as the restriction to G of representations associated with a cone of overgroups and for and respectively. We determine explicitly the interaction of Lie operators of with operators intertwining canonical representations and representations of G associated with a cone.Mathematics Subject Classifications (2000) 43A85, 22E46, 53D55.V. F. Molchanov: Supported by grants of the Netherlands Organization for Scientific Research (NWO): 047-008-009, the Russian Foundation for Basic Research (RFBR): 01-01-00100-a, the Minobr RF: E00-1.0-156, the NTP Univ. Rossii: ur04.01.037.     

Symplectic Automorphisms and the Picard Group of a K3 Surface

We consider the symplectic action of a finite group G on a K3 surface X. The Picard group of X has a primitive sublattice determined by G. We show how to compute the rank and discriminant of this sublattice. We then investigate the classification of symplectic actions by a fixed finite group, using moduli spaces of K3 surfaces with symplectic G-action.     

流形上矩阵方程AX=B的正定及半正定阵的反问题

文[1-5]中研究了对称、对称半正定及流形上的对称半正定的反问题,并说明了其应用背景.本文研究线性流形上的正定及半正定阵的反问题,说明了文[1-3]中的一些结果为本文的特例.     

四次函数实零点的完全判据和正定条件

本文给出了四次函数实零点的完全判据和正定条件,这一结果在研究多项式系统的奇点分析和分支问题时给出了可以实用的判据．