Homogeneous nilmanifolds with prescribed isotropy

We describe a family of homogeneous nilmanifolds whose isotropy group has a prescribed compact Lie algebra.     

On Schurity of Finite Abelian Groups

A finite group G is called a Schur group, if any Schur ring over G is associated in a natural way with a subgroup of Sym(G) that contains all right translations. Recently, the authors have completely identified the cyclic Schur groups. In this article, it is shown that any abelian Schur group belongs to one of several explicitly given families only. In particular, any noncyclic abelian Schur group of odd order is isomorphic to ?₃ × ?_{3 ^k} or ?₃ × ?₃ × ? _p where k ≥ 1 and p is a prime. In addition, we prove that ?₂ × ?₂ × ? _p is a Schur group for every prime p.     

齐次可列马尔科夫链幂收敛性的注记

给出齐次可列马尔科夫键转移矩阵的一种置换相似标准型，并用之来讨论键的极限性态，分别明确给出转移矩阵益收敛于零矩阵、非零矩阵、随机矩阵、常随机矩阵和正的常随机矩阵的充分必要条件．     

Homogeneous weak solenoids

A (generalized) weak solenoid is an inverse limit space over manifolds with bonding maps that are covering maps. If the covering maps are regular, then we call the inverse limit space a strong solenoid. By a theorem of M.C. McCord, strong solenoids are homogeneous. We show conversely that homogeneous weak solenoids are topologically equivalent to strong solenoids. We also give an example of a weak solenoid that has simply connected path-components, but which is not homogeneous.

     

14阶循环拉丁方型均匀设计

本文利用电子计算机求得全部１４阶循环拉丁方型均匀设计。这些设计的均匀性比现有的均匀设计Ｕ１４（１４＾ｓ）有显著改进，且参数ｓ的范围从ｓ≤８扩大到ｓ≤１４。     

Homogeneous varieties under split solvable algebraic groups

We present a modern proof of a theorem of Rosenlicht, asserting that every variety as in the title is isomorphic to a product of affine lines and punctured affine lines.     

Latin bitrades derived from groups

A Latin bitrade is a pair of partial Latin squares which are disjoint, occupy the same set of non-empty cells, and whose corresponding rows and columns contain the same set of entries. In [A. Drápal, On geometrical structure and construction of Latin trades, Advances in Geometry (in press)] it is shown that a Latin bitrade may be thought of as three derangements of the same set, whose product is the identity and whose cycles pairwise have at most one point in common. By letting a group act on itself by right translation, we show how some Latin bitrades may be derived directly from groups. Properties of Latin bitrades such as homogeneity, minimality (via thinness) and orthogonality may also be encoded succinctly within the group structure. We apply the construction to some well-known groups, constructing previously unknown Latin bitrades. In particular, we show the existence of minimal, k-homogeneous Latin bitrades for each odd k≥3. In some cases these are the smallest known such examples.     

On the Number of Elementary Submodels of an Unsuperstable Homogeneous Structure

We show that if M is a stable unsuperstable homogeneous structure, then for most κ ? |M|, the number of elementary submodels of M of power κ is 2^κ.     

On Nonstructure of Elementary Submodels of an Unsuperstable Homogeneous Structure

In the first part of this paper we let M be a stable homogeneous model and we prove a nonstructure theorem for the class of all elementary submodels of M, assuming that M is ‘unsuperstable’ and has Skolem functions. In the second part we assume that M is an unstable homogeneous model of large cardinality and we prove a nonstructure theorem for the class of all elementary submodels of M.     

Homogeneous and strictly homogeneous criteria for partial structures

The Galois closure on the set of relations invariant to all finite partial automorphisms (automorphisms) of a countable partial structure is established via quantifier-free infinite predicate languages (infinite languages with finite string of quantifiers respectively). Based on it the homogeneous and strictly homogeneous criteria for a countable partial structure as well as an ultrahomogeneous criterion for a countable relational structure are found. Next it is shown that infinite languages with a finite string of quantifiers cannot determine the corresponding Galois closure for relations invariant to all automorphisms of an uncountable partial structure.     

Homogeneous factorisations of Johnson graphs

For a graph Γ, subgroups , and an edge partition of Γ, the pair is a (G, M)-homogeneous factorisation if M is vertex-transitive on Γ and fixes setwise each part of , while G permutes the parts of transitively. A classification is given of all homogeneous factorisations of finite Johnson graphs. There are three infinite families and nine sporadic examples. This paper forms part of an ARC Discovery grant of the last two authors. The second author holds an Australian Research Council Australian Research Fellowship.     

Morrey Estimates for Nondivergence Parabolic Operators with Discontinuous Coefficients on Homogeneous Groups

In this paper, by establishing the boundedness of singular integral operators with variable kernels and their commutators with BMO functions on Morrey spaces of homogeneous groups, we prove a local a prior estimate in Sobolev-Morrey space for solutions to the nondivergence parabolic equation with discontinuous coefficients.     

New Hardy Spaces Associated with Herz Spaces and Beurling Algebras on Homogeneous Groups

The author introduces the Hardy spaces associated with the Herz spaces and the Beurling algebras on homogeneous groups and establishes their atomic decomposition characterizations. As the applications of this decomposition, the duals of these Hardy spaces and the boundedness of the central δ-Calderón-Zygmund operators on these Hardy spaces are studied. Received January 13, 2000, Accepted July 26, 2000     

On Involutions Which Generate Mathieu Groups M 11 and M 12

Abstract

We will give an elementary construction of the Mathieu groups M ₁₁ and M ₁₂.     

一类广义齐次Moran集的Hausdorff维数

本文构造了一类具有类似高维Moran结构的集合,给出一些充分条件来计算其Hausdorff维数.     

完备可分度量群上的齐次Levy过程的复合Poisson逼近

该文利用算子半群的方法给出了取值于具有左不变度量的完备可分群的齐次Levy过程是复合Poisson过程的弱极限这一结论．     

Eigenvalues under the Backward Ricci Flow on Locally Homogeneous Closed 3-manifolds

In this paper, we study the evolving behaviors of the first eigenvalue of the Laplace–Beltrami operator under the normalized backward Ricci flow, construct various quantities which are monotonic under the backward Ricci flow and get upper and lower bounds. We prove that in cases where the backward Ricci flow converges to a sub-Riemannian geometry after a proper rescaling, the eigenvalue evolves toward zero.