In the past thirty years, algebraic topologists have developed a great body of knowledge concerning the category of topological spaces. By contrast, corresponding problems in the category of uniform spaces have been barely touched. Lubkin [8] studied the notion of a covering space in the category of generalized uniform spaces, and suggested that much of algebraic topology could be profitably studied in this category. Deming [2] discussed the fundamental group of a generalized uniform space, and related it to the first Čech homology group. A slightly different version of Cech cohomology was defined by Kuzminov and Svedov in [7] and related to the dimension theory of uniform spaces.

Creation of mass processes were treated lately by several authors. The idea was to find some generalized Markov process that will correspond to a semigroup of operators which are not necessarily contraction operators (or equivalently to a quasi transition function which is not submarkov). It was G. A. Hunt [6] who first suggested the idea of Markov processes in which both the starting time and the terminal time are random. Such processes were constructed by Helms [4] and treated also by Nagasawa [12] and the author [10].

Let Y be a complex Banach space, U an open subset of Y, f a mapping of U into Y. Then f is said to be complex analytic if for each pair of elements x and y of Y with x in U, the function f(x + ξy) of the single complex variable ξ is analytic in ξ on some neighbourhood of the origin.

Gp = (V, X) is a graph on p vertices, with vertex set V and edge set X. Occasionally, to avoid ambiguity, V and X will be written V(GP) and X(GP), respectively.

In this paper the character table of GL(3, q) (U(3, q2)), the group of all nonsingular n × n (unitary) matrices over GF(q) (GF(q2)), is used to obtain the character tables for the related subgroups SL(3, q), PSL(3, q) (SU(3, q2), PSU(3, q2)), the corresponding groups of matrices of determinant unity and the projective group respectively. There are very few abstract character tables which hold for entire families of groups. Such tables are of much greater value than tables for specific groups because, among other things, they enable one to discern various patterns common to the whole family.

Nous reprenons le problème des secrétaires tel que considéré en particulier par Chow, Moriguti, Robbins et Samuels [2]. Nous commençons par dégager une formule sur le rendement de certains temps d'arrêt dans le problème des secrétaires. Nous faisons voir comment une certaine fonction d'une infinité de variables est étroitement reliée aux temps d'arrêt optimaux. Enfin, nous étudions le comportement asymptotique du rendement de certains temps d'arrêt pour le problème des n secrétaires lorsque n tend vers l'infini.

In this paper we show that the common points of any nonempty “family“ of normal functions form a normal function and from this we derive various significant consequences such as Theorem 2 below.

A sequence space is a vector subspace of the space ω of all real (or complex) sequences. A sequence space E with a locally convex topology τ is called a K- space if the inclusion map E → ω is continuous, when ω is endowed with the product topology . A K-space E with a Frechet (i.e., complete, metrizable and locally convex) topology is called an FK-space; if the topology is a Banach topology, then E is called a BK-space.

In [6], Pierce studied the modules over a commutative regular ring R by using the representation of R as the global sections of a sheaf which we call the Pierce sheaf. When the stalks of the Pierce sheaf are regular, Magid gave a Galois theory and some properties for a central separable R-algebra [4, (2.4), (2.5), (2.6) and (2.7)]. When the stalks of the Pierce sheaf are semi-local, DeMeyer presented a Galois theory for a central separable R-algebra [3, sections 2 and 3] and the author characterized the finitely generated and projective modules over a central separable R-algebra in terms of the R-modules in [7] and [8].

Let M be an n-dimensional connected topological manifold. Let ξ : M → Rn+1 be a continuous map with the following property: to each x ∈ M there is an open set x ∈ Ux ⊂ M, and a convex body Kx ⊂ Rn+1 such that ξ(UX) is an open subset of ∂Kx and such that is a homeomorphism onto its image. We shall call such a mapping ξ a locally convex immersion and, along with Van Heijenoort [8] we shall call ξ(M) a locally convex hypersurface of Rn+1.

The aim of this paper is to characterize the finite simple group PSp4(3) by the structure of the centralizer of an element of order three contained in the center of its Sylow 3-subgroup. More precisely, we shall prove the following results.

Let X be a given complex matrix of order n. If f(z) is analytic at the eigenvalues of X, one may define the primary matrix function f(X) with stem function f(z) by using any of several well-known methods: for instance, canonical forms, power series, or interpolating polynomials [9].

The determination of the abelian groups in which every neat subgroup is pure is a relatively routine exercise (see [6]). There are numerous problems of this type; for example, the determination of the groups in which every pure subgroup is isotype or the groups in which every subgroup is isotype. These are all special cases of the general problem of determining the abelian groups in which every α-pure subgroup is β-pure for arbitrary ordinal numbers α and β. The solution of this general problem is the object of this paper.

The dual of Hp of the unit disk for 0 < p < 1 has been characterized by Duren, Romberg and Shields (see [3]). The present paper is concerned with the analogous result for Hp(R+n+1) in the sense of Stein and Weiss (see [11]). In this connection it may be recalled that the dual of H1 has been characterized by Fefferman (see [4]).

We let , where the xi are positive integers and i ∈ N, the set of all integers. We define , where where . We let = [0; x1, x2, … ] where

We let

and define

The range of L(ξ) is known as the Lagrange spectrum and the range of M(ξ) as the Markov spectrum. It is known that both are closed and that the Markov spectrum includes the Lagrange spectrum.

We begin with some definitions and a formulation of the problem treated in subsequent sections. Also included in this section is a brief indication of some of the known results dealing with the n-omino enumeration problem. Some of what follows together with more details may be found in [3] or [4].

Erdös and Hajnal [1] have introduced an edge partition relation for graphs

(1)

which means that whenever the edges of G are separated into two sets, E1 and E2, there exists a subgraph G’ of G such that G’ is isomorphic to Hi and the edges of G’ are all in Ei. for i = 1 or 2. A class of graphs has the G-R (Galvin-Ramsey) property [2] if for each H in there exists a G in which satisfies G→(H,H).

Meier [8, Hauptsatz] proved a remarkable theorem concerning the boundary behavior of functions meromorphic in the upper half plane; but his techniques are very complicated. So Noshiro [10, p. 72-73] proved an analogous (but somewhat weaker) result to Meier's by a simple method using the theorem of Gross and Iversen.

In this paper, we sharpen and generalize Noshiro's theorem in some directions by making use of the notion “porosity”, and we state some applications.

If A is a real normal matrix At (the transpose of A) is a real polynomial in A. We study here those normal (0, 1)-matrices A with constant row sums which have At a polynomial of degree two in A.

An f-ring R with zero right annihilator is called a qf-ring if its Utumi maximal left quotient ring Q = Q(R) can be made into and f-ring extension of R. F. W. Anderson [2, Theorem 3.1] has characterized unital qf-rings with the following conditions: For each q ∈ Q and for each pair d1, d2 ∈ R+ such that diq ∈ R

(i) (d1q)+ Λ (d2q)- = 0, and

(ii) d1 Λ d2 = 0 implies (d1q)+ Λ d2 = 0.

We remark that this characterization holds even when R does not have an identity element.