bluuebunny/crossref_metadata_2025 huggingface dataset:
Relatively Finitely Determined Implies Relatively Very Weak Bernoulli
Authors: Rahe M.
Published: December 2010

In the isomorphism theory of Bernoulli shifts, the or Hamming
distance plays an important role. Two finite state stationary processes are close
in the metric if, on the
average, strings from one process can be matched with strings from the other
process so that their outputs agree with high frequency. Since such agreement must
hold in the arbitrarily distant future, it might at first seem difficult to
control the pairing.
Thick Groups and Essentially Finitely Indecomposable Groups
Authors: Benabdallah Khalid , Wilson Robert
Published: December 2010

In this article, we examine the relationship between the notions of thick
groups and that of essentially finitely indecomposable (e.f.i.) groups. These
groups are indecomposable objects in the quotient category of the category of
abelian groups induced by the Serre-class of bounded groups.
On Almost-Fixed-Point Theory
Authors: Hazewinkel Michiel , Van De Vel Marcel
Published: December 2010

Let X be a topological space, a finite covering of X (the words ‘covering’ and ‘cover’ are used interchangeably). We say that has the almost fixed point property for a class of continuous maps f : X → X if for all there is an x ∈ X and such that x ∈ U and f(x) ∈ U, or, equivalently, if there is a such that .
Coverings of Groups by Abelian Subgroups
Authors: Faber V. , Laver R. , McKenzie R.
Published: December 2010

Paul Erdôs has suggested an investigation of infinite groups from the point of view of the partition relations of set theory. In particular, he suggested that given a group G, one considers the graph T with vertex set G whose edges are the pairs ﹛g, h﹜ which do not commute.
On Linear Functionals and Summability Factors for Strong Summability
Authors: Balser W. , Jurkat W. B. , Peyerimhoff A.
Published: December 2010

Let be an infinite matrix. We call a sequence A-limitable (denoted by s ∈ (A)) if the sequence anksk exists and converges.
Representations and Divisibility of Operator Polynomials
Authors: Gohberg I. , Lancaster P. , Rodman L.
Published: December 2010

Let be a complex Banach space and the algebra of bounded linear operators on . In this paper we study functions from the complex numbers to of the form
Poincaré Transversality for Double Covers
Authors: Hambleton I. , Milgram R. J.
Published: December 2010

Let π: X’ —” X be a double cover of 2n-dimensional Poincaré duality (PD) spaces. The double cover is a fibering so it is classified by a map f: X → RP1+1(l ≫ n). If the homotopy class of f contains a representative which is Poincaré transverse [5] to RPl ⊂ RPl+1, we say that w is Poincarésplit-table.
The Maximal Ideal Space of H∞ + C on the ball in Cn
Authors: Mcdonald Gerard
Published: December 2010

Let S denote the unit sphere in Cn, B the (open) unit ball in Cn and H∞(B) the collection of all bounded holomorphic functions on B. For f ∈ H∞(B) the limits

exist for almost every ζ in S, and the map ƒ → ƒ* defines an isometric isomorphism from H∞(B) onto a closed subalgebra of L∞(S), denoted H∞(S). (The only measure on S we will refer to in this paper is the Lebesgue measure, dσ, generated by Euclidean surface area.) Rudin has shown in [4] that the spaces H∞(B) + C(B) and H∞(S) + C(S) are Banach algebras in the sup norm. In this paper we will show that the maximal ideal space of H∞(B) + C(B), Σ (H∞(B) + C(B)), is naturally homeomorphic to Σ (H∞(B)) and that Z (H∞(S) + C(S)) is naturally homeomorphic to Σ (H∞(S))\B.
Coinitial Grapfis and Whitehead Automorphisms
Authors: Hoare A. H. M.
Published: December 2010

Coinitial graphs were used in [2; 3 ; 4] as a combinatorial tool in the Reidemeister- Schreier process in order to prove subgroup theorems for Fuchsian groups. Whitehead had previously introduced such graphs but used topological methods for his proofs [8; 9]. Subsequently Rapaport [7] and Iliggins and Lyndon [1] gave algebraic proofs of the results in [9], and AIcCool [5; 6] has further developed these methods so that presentations of automorphism groups could be found.

In this paper it is shown that Whitehead automorphisms can be described by a “cutting and pasting” operation on coinitial graphs. Section 1 defines and gives some combinatorial properties of these operations, based on [1].
Quelques Propriétés Sur Le Normalisateur D'un Pseudogroupe De Lie Transitif
Authors: Abib Odinete Renée
Published: December 2010

Etant donné une variété différaitiable M, deux pseudogroupes ℒ1 et ℒ2 sur M sont dits appartenir au même type, s'il existe un difféomorphisme local de M transformant ℒ1 en ℒ1

Le problème général de la recherche des pseudogroupes sur M peut être énoncé de manière suivante:

(1) Déterminer tous les types des pseudogroupes sur M, et pour chaque type un représentant particulier.

(2) Pour chaque pseudogroupe ainsi obtenu, déterminer le plus grand pseudogroupe sur M dans lequel il est invariant.

Dans [5], E. Cartan a utilisé cette méthode pour classifier les pseudogroupes sur R2; pour une démonstration plus récente voir [6]. Ceci montre ce plus l'intérêt d'étudier le normalisateur d'un pseudogroupe de Lie ℒ sur M.
On a Class of Analytic Functions of Smirnov
Authors: Schiff J. L.
Published: December 2010

The class S of functions under study in this paper was introduced by V. I. Smirnov in 1932. This class was subsequently investigated by various authors, a pertinent paper to the present wrork being that of Tumarkin and Havinson [2], who showed that a plane compact set of logarithmic capacity zero is 5-removable. Another important development, due to Yamashita [3], wras that the class 5 could be characterized as those analytic functions ƒ for which log+ |ƒ| has a quasi-bounded harmonic majorant.

In what follows, we discuss the Smirnov class in the context of planar surfaces, exploiting some ideas in the work of Hejhal [1] to establish that a closed, bounded, totally disconnected set is S-removable if and only if its complement belongs to the null class Os.
Indicator Sets in an Affine Space of any Dimension
Authors: Sherk F. A.
Published: December 2010

It is well known that a translation plane can be represented in a vector space over a field F where F is a subfield of the kernel of a quasifield which coordinatizes the plane [1; 2; 4, p.220; 10]. If II is a finite translation plane of order qr (q = pn, p any prime), then II may be represented in V2r(q), the vector space of dimension 2r over GF(q), as follows:

(i) The points of II are the vectors in V = V2r(q)

(ii) The lines of II are

(a) A set of qr + 1 mutually disjoint r-dimensional subspaces of V.

(b) All translates of in V.

(iii) Incidence is inclusion.
On Counting Types of Symmetries in Finite Unitary Reflection Groups
Authors: Morgan C. L.
Published: December 2010

Let K be a field of characteristic zero. Let V be an n-dimensional vector space over K. A linear automorphism of V is said to be of type i if it leaves fixed a subspace of dimension i. A reflection is a linear automorphism of type n − 1 which has finite order. A finite reflection group is a finite group of linear automorphisms which is generated by reflections. These groups are especially interesting because the full group of symmetries of a regular poly tope is always a finite reflection group. There is also a strong connection between these groups and Lie groups.
Classification of Finite Spaces of Orderings
Authors: Marshall Murray
Published: December 2010

1. Introduction. A space of orderings will refer to what was called a “set of quasi-orderings” in [5]. That is, a space of orderings is a pair (X, G) where G is an elementary 2-group (i.e. x2 = 1 for all x ∈ G) with a distinguished element – 1 ∈ G, and X is a subset of the character group x(G) = Horn (G, {1, –1};) satisfying the following properties:

01: X is a closed subset of χ(G).

02: σ(−l) = −1 holds for all σ ∊ X.

03: X⊥ = {a ∊ G|χa = 1 for all a ∊ X} = 1.

04: If f and g are forms over G and if x ∊ Df⊗g, then there exist y ∊ Df and z ∊ Dg such that x ∊ D(y, z).
The Unrestricted Section Properties of Sequences
Authors: Sember John , Raphael Marc
Published: December 2010

1. Introduction. An unrestricted section of a sequence x is any sequence of the form Σk∈Fxkδk, where F is some finite subset of the natural numbers. The notion of boundedness of the set of unrestricted sections of a sequence in a K-space was studied in [10], and called unconditional section boundedness (UAB). It was shown in [10] (Theorem 7) that the class of FK-spaces in which every element has UAB consists of those FK-spaces that are invariant under coordinatewise multiplication by the convergent sequences.
L'isolateur D'Un Homomorphisme de Groupes
Authors: Cassidy C. , Hilton P. J.
Published: December 2010

Dans ce travail, nous désignons par la catégorie des groupes localement nilpotents. Si P est un ensemble de premiers, nous disons que n est un P-nombre et nous écrivons n ∈ P si tous les facteurs premiers de n appartiennent à P; on convient toujours que 1 ∈ P. Dans tout ce qui suit, il est souvent commode de ne pas faire explicitement la distinction dans la notation entre un ensemble P de premiers et l'ensemble de tous les entiers naturels ayant tous leurs facteurs premiers dans P; par exemple, n ∈ P signifiera toujours que n est un P-nombre mais pas nécessairement un premier. L'ensemble de tous les premiers n'appartenant pas à P est désigné par P′; on convient que 1 appartient à la fois à P et à P′.
Representable Dualities between Finitely Closed Subcategories of Modules
Authors: MacDonald Roderick N. S.
Published: December 2010

This paper studies dualities (or contravariant category equivalences) between two categories of R-right and S-left modules which are finitely closed) that is, closed under submodules, factor modules and finite direct sums. Omitting the requirement that the categories contain all finitely generated modules from the classical Morita situation provides a generalization which substantially increases the number of such dualities.

We prove that a duality between two finitely closed categories A and B of modules is representable if and only if A and B consist of linearly compact modules. This encompasses work of Mueller ([7], [8]) for Morita dualities and of Goblot ([5], [6]).
Colorful Partitions of Cardinal Numbers
Authors: Baumgartner J. , Erdös P. , Galvin F. , Larson J.
Published: December 2010

Use the two element subsets of κ, denoted by [κ]2, as the edge set for the complete graph on κ points. Write CP(κ, µ, v) if there is an edge coloring R: [κ]2 → µ with µ colors so that for every proper v element set X ⊊ κ, there is a point x ∈ κ ∼ X so that the edges between x and X receive at least the minimum of µ and v colors. Write CP⧣(K, µ, v) if the coloring is oneto- one on the edges between x and elements of X.

Peter W. Harley III [5] introduced CP and proved that for κ ≧ ω, CP(κ+, κ, κ) holds to solve a topological problem, since the fact that CP(ℵ1, ℵ0, ℵ0) holds implies the existence of a symmetrizable space on ℵ1 points in which no point is a Gδ.
Periodic Algorithms and their Application
Authors: Bernstein Leon
Published: December 2010

In two previous papers [1, 2] we investigated the zeros of certain arithmetic functions. Using units of cubic fields, we also succeeded to construct, almost by accident, and as a by-product so to speak, entirely new and comparatively complicated combinatorial identities. In an interesting paper combinatorialist L. Carlitz [10] proved those identities in an elementary way. In a/m, we had to prove that the units used were fundamental ones.

Encouraged by these results, we took a closer look at this method that had led to the construction of combinatorial identities. Since the latter are such an important tool in mathematics, we thought it would be “einer Messe wert“ to generalize these results and lay the theoretical foundations of a new method for the construction of highly sophisticated combinatorial identities.
A Generalization of Uniformly Rotund Banach Spaces
Authors: Sullivan Francis
Published: December 2010

Let X be a real Banach space. According to von Neumann's famous geometrical characterization X is a Hilbert space if and only if for all x, y ∈ X

Thus Hilbert space is distinguished among all real Banach spaces by a certain uniform behavior of the set of all two dimensional subspaces. A related characterization of real Lp spaces can be given in terms of uniform behavior of all two dimensional subspaces and a Boolean algebra of norm-1 projections [16]. For an arbitrary space X, one way of measuring the “uniformity” of the set of two dimensional subspaces is in terms of the real valued modulus of rotundity, i.e. for

The space is said to be uniformly rotund if for each 0 we have .
On the Number of Conjugates of N-Ary Ouasigroups
Authors: McLeish Mary
Published: December 2010

Higher dimensional quasigroups (a set Q with a cancellative, n-ary operation 〈 〉, ([2]) have been studied by T. Evans ([3], [4]), A. Cruse [1], C. C. Lindner ([10], [11]) and also by many others under the guise of magic cubes, Graeco-latin cubes, etc. Conjugates or parastrophes have been discussed by S. K. Stein [18], A. Sade [17] and more recently by C. C. Lindner and D. Steedley in [14], where it is shown that ordinary quasigroups exist of every order ≧ 4 with a prescribed number of distinct conjugates. It is suggested that the problem be extended to n-ary quasigroups.
Baire Category And Laurent Extensions
Authors: Farkas Daniel R.
Published: December 2010

Based on a strategy of Kaplansky ([3]), Dixmier proved that a prime, separable C*-algebra is primitive ([1]). As a consequence, when the C*-closure of a countable discrete group is prime, it is primitive. The argument may be regarded as a clever application of the Baire Category Theorem to the spectrum of irreducible representations.

The present note is the first step in adapting this technique to abstract group algebras. For which groups G is the primitive ideal space of k[G] a Baire space? One corollary of our main result is that the space is Baire when k is an uncountable field and G is a polycyclic-by-finite group. This gives an alternate proof of a special case of Passman's theorem that such a k[G] will be primitive when its center is k ([4], p. 379).
On the Operator Identity ∑ AkXBk ≡ 0
Authors: Fong C. K. , Sourour A. R.
Published: December 2010

Let Aj and Bj (1 ≦ j ≦ m) be bounded operators on a Banach space ᚕ and let Φ be the mapping on , the algebra of bounded operators on ᚕ, defined by

(1)

We give necessary and sufficient conditions for Φ to be identically zero or to be a compact map or (in the Hilbert space case) for the induced mapping on the Calkin algebra to be identically zero. These results are then used to obtain some results about inner derivations and, more generally, about mappings of the form

For example, it is shown that the commutant of the range of C(S, T) is “small” unless S and T are scalars.
Block-Finite Orthomodular Lattices
Authors: Bruns Günter
Published: December 2010

Introduction. Every orthomodular lattice (abbreviated : OML) is the union of its maximal Boolean subalgebras (blocks). The question thus arises how conversely Boolean algebras can be amalgamated in order to obtain an OML of which the given Boolean algebras are the blocks. This question we deal with in the present paper.

The problem was first investigated by Greechie [6, 7, 8, 9]. His technique of pasting [6] will also play an important role in this paper. A case solved completely by Greechie [9] is the case that any two blocks intersect either in the bounds only or have the bounds, an atom and its complement in common. This is, of course, a very special situation. The more surprising it is that Greechie's methods, if skillfully applied, yield considerable insight into the structure of OMLs and provide a seemingly unexhaustible source for counter-examples.
Characterizations of Vitali Conditions with Overlap in Terms of Convergence of Classes of Amarts
Authors: Millet Annie , Sucheston Louis
Published: December 2010

In a series of fundamental papers [20], [21], [22], [23], K. Krickeberg introduced 'Vitali’ conditions on σ-algebras and showed that they are sufficient for convergence of properly bounded martingales, and supermartingales. It is now known that the conditions V∞ (= V), and V′ are both sufficient and necessary for convergence of L1-bounded amarts, and ordered amarts (Astbury [1]; [24], [25]); an amart (ordered amart) is a process (Xt) such that the net (EXτ)τ∈T* converges, where T* is the net of simple (ordered) stopping times. We undertake here to similarly characterize the Vitali conditions Vp, 1 ≦ p < ∞, in terms of convergence of properly defined classes of amarts. (In terms of convergence of L∞-bounded martingales, Krickeberg himself [22] was able to characterize V1.)
On the Zeta-Functions of Some Simple Shimura Varieties
Authors: Langlands R. P.
Published: December 2010

In an earlier paper [14] I have adumbrated a method for establishing that the zeta-function of a Shimura variety associated to a quaternion algebra over a totally real field can be expressed as a product of L-functions associated to automorphic forms. Now I want to add some body to that sketch. The representation-theoretic and combinatorial aspects of the proof will be given in detail, but it will simply be assumed that the set of geometric points has the structure suggested in [13]. This is so at least when the algebra is totally indefinite, but it is proved by algebraic-geometric methods that are somewhat provisional in the context of Shimura varieties. However, contrary to the suggestion in [13] the general moduli problem has yet to be treated fully. There are unresolved difficulties, but they do not arise for the problem attached to a totally indefinite quaternion algebra, which is discussed in detail in [17].
Groups in which every Finitely Generated Subgroup is almost a Free Factor
Authors: Brunner A. M. , Burns R. G.
Published: December 2010

In [5] M. Hall Jr. proved, without stating it explicitly, that every finitely generated subgroup of a free group is a free factor of a subgroup of finite index. This result was made explicit, and used to give simpler proofs of known results, in [1] and [7]. The standard generalization to free products was given in [2]: If, following [13], we call a group in which every finitely generated subgroup is a free factor of a subgroup of finite index an M. Hall group, then a free product of M. Hall groups is again an M. Hall group. The recent appearance of [13], in which this result is reproved, and the rather restrictive nature of the property of being an M. Hall group, led us to attempt to determine the structure of such groups. In this paper we go a considerable way towards achieving this for those M. Hall groups which are both finitely generated and accessible.
On the Extreme Rays of the Metric Cone
Authors: Avis David
Published: December 2010

A classical result in the theory of convex polyhedra is that every bounded polyhedral convex set can be expressed either as the intersection of half-spaces or as a convex combination of extreme points. It is becoming increasingly apparent that a full understanding of a class of convex polyhedra requires the knowledge of both of these characterizations. Perhaps the earliest and neatest example of this is the class of doubly stochastic matrices. This polyhedron can be defined by the system of equations

Birkhoff [2] and Von Neuman have shown that the extreme points of this bounded polyhedron are just the n × n permutation matrices. The importance of this result for mathematical programming is that it tells us that the maximum of any linear form over P will occur for a permutation matrix X.
Sylvester's Problem for Spreads of Curves
Authors: Watson Kym S.
Published: December 2010

Spreads of curves were introduced by Grunbaum in [1]. A spread of curves is a continuous family of simple arcs in the real plane, every two of which intersect in exactly one point. A spread is the continuous analogue of a finite arrangement of pseudolines in the plane. Sylvester's problem for finite arrangements of pseudolines asks if every non-trivial arrangement has a simple vertex, that is a point contained in exactly two pseudolines of the arrangement. This question was answered in the affirmative by Kelly and Rottenberg [5]. One interesting feature of this result is that it does not depend on the pseudolines being straight lines.

Here we settle Sylvester's problem for spreads. We show that every nontrivial spread of line segments has uncountably many simple vertices. But we also give examples of non-trivial spreads with no simple vertices.
Invariant Factors Under Rank One Perturbations
Authors: Thompson Robert C.
Published: December 2010

Let R be a principal ideal domain, i.e., a commutative ring without zero divisors in which every ideal is principal. The invariant factors of a matrix A with entries in R are the diagonal elements when A is converted to a diagonal form D = UAV, where U, V have entries in R and are unimodular (invertible over R), and the diagonal entries d1 …, dn of D form a divisibility chain: d1|d2| … |dn. Very little has been proved about how invariant factors may change when matrices are added. This is in contrast to the corresponding question for matrix multiplication, where much information is now available [6].
Topological Reflection Groups
Authors: Djoković Dragomir Ž.
Published: December 2010

Let G be a closed subgroup of one of the classical compact groups 0(n), U(n), Sp(n). By a reflection we mean a matrix in one of these groups which is conjugate to the diagonal matrix diag (–1, 1, …, 1). We say that G is a topological reflection group (t.r.g.) if the subgroup of G generated by all reflections in G is dense in G.

It was shown recently by Eaton and Perlman [5] that, in case of 0(n), the whole group 0(n) is the unique infinite irreducible t.r.g. In this paper we solve the analogous problem for U(n) and Spin). Our method of proof is quite different from the one used in [5]. We treat simultaneously all the three cases.
The Inductive Step of the Second Brauer-Thrall Conjecture
Authors: Smalø Sverre O.
Published: December 2010

In this paper we are going to use a result of H. Harada and Y. Sai concerning composition of nonisomorphisms between indecomposable modules and the theory of almost split sequences introduced in the representation theory of Artin algebras by M. Auslander and I. Reiten to obtain the inductive step in the second Brauer-Thrall conjecture.

Section 1 is devoted to giving the necessary background in the theory of almost split sequences.

As an application we get the first Brauer-Thrall conjecture for Artin algebras. This conjecture says that there is no bound on the length of the finitely generated indecomposable modules over an Artin algebra of infinite type, i.e., an Artin algebra such that there are infinitely many nonisomorphic indecomposable finitely generated modules. This result was first proved by A. V. Roiter [8] and later in general for Artin rings by M. Auslander [2] using categorical methods.
An Inclusion Relation for Abel, Borel, and Lambert Summability
Authors: Gawronski W. , Siebert H. , Trautner R.
Published: December 2010

In this paper a new type of inclusion theorem concerning Abel, Borel and Lambert summability is established. To state our results we need some definitions and notations. With a formal series ∑k=0∞ak, ak∈ C, and its partial sums snwe associate the series

Then ∑k=0∞ ak is said to be summable to the value s

(a) by Abel's method, if (1.1) is convergent for |v| > 1 and limv→1+A(v)= s,

(b) by Lambert's method, if (1.2) is convergent for |v| > 1 and limv→1+L(v)= s,

(c) by Borel's method, if (1.3) is convergent for all x ∈ R and limx→+∞B(x)= s,
A Hahn-Banach Theorem in Subbase Convexity Theory
Authors: van de Vel M.
Published: December 2010

In the last fifteen years, topology has shown up with an increasing interest in the use of closed subbases. Starting from Frink's internal characterization of complete regularity (Frink [6]), DeGroot and Aarts used closed subbases to obtain Hausdorff compactifications of completely regular spaces, thus giving a characterization of the latter in terms of their subbases [1]. The main tool of that paper is the notion of a linked system, which naturally leads to the notions of supercompactness and superextensions [7]. After 1970, these two topics developed to indepedennt theories, with several deep results available at this moment. Most results up to 1976 are summarized in [12].
Non-Extendability of Bounded Continuous Functions
Authors: Levy Ronnie
Published: December 2010

If X is a dense subspace of Y, much is known about the question of when every bounded continuous real-valued function on X extends to a continuous function on Y. Indeed, this is one of the central topics of [5]. In this paper we are interested in the opposite question: When are there continuous bounded real-valued functions on X which extend to no point of Y – X? (Of course, we cannot hope that every function on X fails to extend since the restrictions to X of continuous functions on Y extend to Y.) In this paper, we show that if Y is a compact metric space and if X is a dense subset of Y, then X admits a bounded continuous function which extends to no point of Y – X if and only if X is completely metrizable. We also show that for certain spaces Y and dense subsets X, the set of bounded functions on X which extend to a point of Y – X form a first category subset of C*(X).
On Extensions of Weakly Primitive Rings
Authors: Nicholson W. K. , Waiters J. F. , Zelmanowitz J. M.
Published: December 2010

If R is a ring an R-module M is called compressible when it can be embedded in each of its non-zero submodules; and M is called monoform if each partial endomorphism N → M, N ⊆ M, is either zero or monic. The ring R is called (left) weakly primitive if it has a faithful monoform compressible left module. It is known that a version of the Jacobson density theorem holds for weakly primitive rings [4], and that weak primitivity is a Mori ta invariant and is inherited by a variety of subrings and matrix rings. The purpose of this paper is to show that weak primitivity is preserved under formation of polynomials, rings of quotients, and group rings of torsion-free abelian groups. The key result is that R[x] is weakly primitive when R is (Theorem 1).
Absolute C-Embedding of Spaces with Countable Character and Pseudocharacter Conditions
Authors: Dow Alan
Published: December 2010

Absolute C-embeddings have been studied extensively by C. E. Aull. We will use his notation P = C[Q] to mean that a space satisfying property Q is C-embedded in every space having property Q that it is embedded in if (and only if) it has property P. The first result of this type is due to Hewitt [5] where he proves that if Q is “Tychonoff” then P is almost compactness. Aull [2] proves that if Q is “T4 and countable pseudocharacter” or “T4 and first countable” then P is “countably compact”. In this paper we show that P is almost compactness if Q is “Tychonoff” and any of countable pseudocharacter, perfect, or first countability. Unfortunately for the last case we require the assumption that . Finally we show that P is countable compactness if Q is Tychonoff and “closed sets have a countable neighborhood base”. In each of the above results C-embedding may be replaced by C*-embeddings and the results hold if restricted to closed embeddings.
The Bergman Projection on Weighted Norm Spaces
Authors: Burbea Jacob
Published: December 2010

Quite recently Bekollé and Bonami [1] have characterized the weighted measures λ on the unit disk Δ for which the Bergman projection is bounded on Lp(Δ : λ), 1 < p < ∞. Our methods in [4] can be applied to even extend their result by replacing the unit disk with multiply connected domains. This is done via a rather interesting identity between the Bergman kernel and its “adjoint” [2]. As a corollary of our result we obtain a generalization of a result due to Shikhvatov [7].

Let D be a bounded plane domain and let λ be a positive locally integrate function in D. λ is said to belong to Mp(D) (1 < p < ∞) if it satisfies the Muckenhoupt condition:

where the supremum is taken over all sectors V ⊂ D, dσ is the area Lebesgue measure and |V| = σ(V).
Divisible Properties and the Stone-Čech Compactification
Authors: Glasner S.
Published: December 2010

Let T be an abelian infinite countable group. We say that a property of subsets of T is divisible if it satisfies the following requirements. (We identify with the set of all subsets of T which satisfy .)

(i) ∅ ∉ and T ∈

(ii) A ∈ and B ⊃ A implies B ∈

(iii) A ∈ and A = B1 ∪ B2 implies that either B1 or B2 is in
On the and Transformations
Authors: Rooney P. G.
Published: December 2010

Denote by C0 the collection of complex-valued functions which are continuous and compactly supported on (0, ∞). The transformations of the title are defined on C0 by

1.1

and

1.2

respectively, where Yv(x) is the Bessel function of the second kind, and Hv(x) is the Struve function; see [1; 7.5.4(55)]. The two transformations are studied briefly in [6; §8.4]; tables of transform pairs are given in [2; Chapters IX and XI], where it is also stated that, for – , each of the transformations is the inverse of the other.
The Two-Sided Factorization of Ordinary Differential Operators
Authors: Browne Patrick J. , Nillsen Rodney
Published: December 2010

Throughout this paper we shall use I to denote a given interval, not necessarily bounded, of real numbers and Cn to denote the real valued n times continuously differentiable functions on I and C0 will be abbreviated to C. By a differential operator of order n we shall mean a linear function L:Cn → C of the form

1.1

where pn(x) ≠ 0 for x ∊ I and pi ∊ Cj 0 ≦ j ≦ n. The function pn is called the leading coefficient of L.

It is well known (see, for example, [2, pp. 73-74]) thai a differential operator L of order n uniquely determines both a differential operator L* of order n (the adjoint of L) and a bilinear form [·,·]L (the Lagrange bracket) so that if D denotes differentiation, we have for u, v ∊ Cn,

1.2
Translation Planes of Dimension Two with Odd Characteristic
Authors: Ostrom T. G.
Published: December 2010

A translation plane of dimension d over its kernel K = GF(q) can be represented by a vector space of dimension 2d over K. The lines through the zero vector form a “spread”; i.e., a class of mutually independent vector spaces of dimension d which cover the vector space.

The case where d = 2 has aroused the most interest. The more exotic translation planes tend to be of dimension two; a spread in this case can be interpreted as a class of mutually skew lines in projective three-space.

The stabilizer of the zero vector in the group of collineations is a group of semi-linear transformations and is called the translation complement. The subgroup consisting of linear transformations is the linear translation complement.
Some Generalizations of Ramanujan's Sum
Authors: Ramanathan K. G. , Subbarao M. V.
Published: December 2010

Ramanujan's well known trigonometrical sum C(m, n) denned by

where x runs through a reduced residue system (mod n), had been shown to occur in analytic problems concerning modular functions of one variable, by Poincaré [4]. Ramanujan, independently later, used these trigonometrical sums in his remarkable work on representation of integers as sums of squares [6]. There are various generalizations of C(m, n) in the literature (some also to algebraic number fields); see, for example, [9] which gives references to some of these. Perhaps the earliest generalization to algebraic number fields is due to H. Rademacher [5]. We here consider a novel generalization involving matrices.
The Poincaré Series Of Stretched Cohen-Macaulay Rings
Authors: Sally Judith D.
Published: December 2010

There are relatively few classes of local rings (R, m) for which the question of the rationality of the Poincaré series

where k = R/m, has been settled. (For an example of a local ring with non-rational Poincaré series see the recent paper by D. Anick, “Construction of loop spaces and local rings whose Poincaré—Betti series are nonrational”, C. R. Acad. Sc. Paris 290 (1980), 729-732.) In this note, we compute the Poincaré series of a certain family of local Cohen-Macaulay rings and obtain, as a corollary, the rationality of the Poincaré series of d-dimensional local Gorenstein rings (R, m) of embedding dimension at least e + d – 3, where e is the multiplicity of R. It follows that local Gorenstein rings of multiplicity at most five have rational Poincaré series.
K-Coherence is Cyclicly Extensible and Reducible
Authors: Lehman B.
Published: December 2010

K-coherence (K an integer ≧ –1), has been defined by W. R. R. Transue [3] in such a way that 0-coherence is connectedness and 1-coherence is unicoherence plus local connectedness. It is well-known (see, for instance, [5, p. 82]), that for metric spaces, unicoherence is cyclicly extensible and reducible; furthermore, this result has been generalized by Minear to locally connected spaces, [2, Theorems 4.1 and 4.3]. In this paper we show that for a (k – 1)-coherent and locally (k – 1)-coherent Hausdorff space M,k-coherence is cyclicly extensible and reducible.
Concerning σ-Connectedness of Baire Spaces
Authors: García-Máynez A.
Published: December 2010

A well known theorem of Sierpiński states that every compact connected Hausdorff space is σ-connected. Hence, if X is locally compact and Hausdorff and X is locally connected at x, then x has a σ-connected neighborhood. However, local connectedness at x is not a necessary condition for x to have a σ-connected neighborhood, because the whole space may be σ-connected without being locally connected at x. One of the purposes of the present paper is then to investigate which points of a given locally compact Hausdorff space have σ-connected neighborhoods. We find also sufficient conditions for a connected, hereditarily Baire space to be σ-connected and prove the impossibility of expressing a connected, Čech-complete, rim compact space as a countable infinite union of mutually disjoint compact sets. Finally, we introduce the concept of D-connected space and relate it to σ-connectedness.
Spline Functions on the Circle: Cardinal L-Splines Revisited
Authors: Micchelli Charles A. , Sharma A.
Published: December 2010

Although the literature on splines has grown vastly during the last decade [11], the study of polynomial splines on the circle seems to have suffered neglect. The first to study the subject in depth seem to be Ahlberg, Nilson and Walsh [1]. Almost at the same time I. J. Schoenberg [8] studied the problem of interpolation at the roots of unity by splines and its relation to quadrature on the circle. For discrete polynomial splines on the circle we refer to [5]. M. Golomb [3] also considers interpolation by a class of “spline” functions in the complex plane but his point of view is based on minimum norm properties of spline functions. Perhaps the reason for this neglect may be attributed to the fact that one can pass from the circle to the line by means of the transformation z → exp 2-πix. This changes the problem on the circle into periodic interpolation on the line with the difference that instead of interpolation by piecewise polynomial, we now consider piecewise exponential polynomials with complex exponents.
A Product Formula and a Non-Negative Poisson Kernel for Racah-Wilson Polynomials
Authors: Rahman Mizan
Published: December 2010

Physicists have long been using Racah's [7] 6-j symbols as a representation for the addition coefficients of three angular momenta. Racah himself discovered a series representation of the 6-j symbol which can be expressed as a balanced 4F3 series of argument 1, that is, a generalized hypergeometric function such that the sum of the 3 denominator parameters exceeds that of the 4 numerator parameters by 1. What Racah does not seem to have realized or, perhaps, cared to investigate, is that his 4F3 functions, with variables and parameters suitably identified, form a system of orthogonal polynomials in a discrete variable. The orthogonality of 6-j symbols as an orthogonality of 4F3 polynomials was recognized much later by Biedenharn et al. [3] in some special cases. Recently J. Wilson [13, 14] introduced a very general system of orthogonal polynomials expressible as balanced 4F3 functions of argument 1 orthogonal with respect to an absolutely continuous measure and/or a discrete weight function. Wilson's polynomials contain Racah's 6-j symbols as a special case. These polynomials might rightfully be credited to Wilson alone, but justice might be better served if we call them Racah-Wilson polynomials.
On the Tumber of Planar Maps
Authors: Wormald Nicholas C.
Published: December 2010

In a survey of methods in enumerative map theory [14], W. T. Tutte pointed out that little has been done towards enumerating unrooted maps other than plane trees. A notable exception is to be found in the work of Brown, who took the initial step in this direction by enumerating non-separable maps up to sense-preserving homeomorphisms of the plane [2]. He then took a further step, allowing sense-reversing homeomorphisms, by counting triangulations and quad-rangulations of the disc [3, 4]. In all these problems, however, there is a fixed outer region of the plane. This can be considered as a certain type of rooting of a planar map, which is normally regarded as lying on the sphere or closed plane. It is our object here to find an expression for the number of unrooted planar maps in a given set, in terms of the numbers of maps in that set which have been rooted in a special way.
On The Center Of Quasi-Central Banach Algebras With bounded Approximate Identity
Authors: Takahasi Sin-Ei
Published: December 2010

Let A be a quasi-central complex Banach algebra with a bounded approximate identity and Prim A the structure space of A. In [15], we have shown that every central double centralizer T on A can be represented as a bounded continuous complex-valued function ΦT on Prim A such that Tx + P = ΦT(P)(x + P) for all x ∈ A and P ∈ Primal when the center Z(A) of A is completely regular. Here x + P for P ∈ Prim A denotes the canonical image of x in A/P. In particular, in the case of quasi-central C*-algebras, this result is equivalent to the Dixmier's representation theorem of central double centralizers on C*-algebras (see [3, Section 2] and [9, Theorem 5]).

In this paper, it is shown that if Z(A) is completely regular then the space Prim A is locally quasi-compact and for each element z of Z(A), ΦLz vanishes at infinity, where Lz for z ∊ Z(i) is the central double centralizer on A defined by Lz(x) = zx for all x ∊ A.
A Localization of R[x]
Authors: Huckaba James A. , Papick Ira J.
Published: December 2010

Throughout this paper, R will be a commutative integral domain with identity and x an indeterminate. If ƒ ∈ R[x], let CR(ƒ) denote the ideal of R generated by the coefficients of ƒ. Define SR = {ƒ ∈ R[x]: cR(ƒ) = R} and UR = {ƒ ∈ R(x): cR(ƒ)– 1 = R}. For a,b ∈ R, write . When no confusion may result, we will write c(ƒ), S, U, and (a:b). It follows that both S and U are multiplicatively closed sets in R[x] [7, Proposition 33.1], [17, Theorem F], and that R[x]s ⊆ R[x]U.

The ring R[x]s, denoted by R(x), has been the object of study of several authors (see for example [1], [2], [3], [12]). An especially interesting paper concerning R(x) is that of Arnold's [3], where he, among other things, characterizes when R(x) is a Priifer domain. We shall make special use of his results in our work.
Variational Methods for One and Several Parameter Non-Linear Eigenvalue Problems
Authors: Binding Paul
Published: December 2010

We shall consider a multiparameter eigenvalue problem of the form

(1.1)

where λ ∈ Rk while Tn and Vn(λ) are self-adjoint linear operators on a Hilbert space Hn. If λ = (λ1, …, λk) ∈ Rk and satisfy (1.1) then we call λ an eigenvalue, x an eigenvector and (λ, x) an eigenpair. While our main thrust is towTards the general case of several parameters λn, the method ultimately involves reduction to a sequence of one parameter problems. Our chief contributions are (i) to generalise the conditions under which this reduction is possible, and (ii) to develop methods for the one parameter problem particularly suited to the multiparameter application. For example, we give rather general results on the magnitude and direction of the movement of non-linear eigenvalues under perturbation.
Term by Term Dyadic Differentiation
Authors: Powell Charles H. , Wade William R.
Published: December 2010

Let ψ0, ψ1, … denote the Walsh-Paley functions and let ∔ denote the group operation which Fine [5] defined on the interval [0, 1). Thus, if k ≧ 0 is an integer and if u, t are points in the interval [0, 1) then

(where αk = 0 or 1 represents the kth coefficient of the binary expansion of t), and

A real-valued function ƒ, is said to be dyadically differentiable at a point x ∈ [0, 1) if ƒ is defined at x and at x ∔ 2–n–1, n = 0, 1, …;, and if the sequence

(1)

converges as N → ∞.
Algebraic Homotopy Theory
Authors: Jardine J. F.
Published: December 2010

Kan and Miller have shown in [9] that the homotopy type of a finite simplicial set K can be recovered from its R-algebra of 0-forms A0K, when R is a unique factorization domain. More precisely, if is the category of simplicial sets and is the category of R-algebras there is a contravariant functor

with

the simplicial set homomorphisms from X to the simplicial R-algebra ∇, where

and the faces and degeneracies of ∇ are induced by

and

respectively.
Irregularity of the Rate of Decrease of Sequences of Powers in the Volterra Algebra
Authors: Esterle J.
Published: December 2010

G. R. Allan and A. M. Sinclair proved in [1] that if a commutative radical Banach algebra possesses bounded approximate identities then for every sequence (αn) of real numbers such that limn→∞αn = 0 there exists such that

In the other direction it is shown in [6] that if is separable and if the nilpotents are dense in then for every sequence (βn) of positive reals there exists such that

(This result was given in [2] for the Volterra algebra.)
Rankings and Ranking Functions
Authors: Walker W. J.
Published: December 2010

Suppose that n competitors compete in r races and in each race they are awarded placings l, 2, 3, …, n – 1, n. After the r races each competitor has a result consisting of his r placings. Let such a result be written (αj)1≦j≦r where for convenience the positive integers αj are arranged in ascending order. For example, if n = 4 and r = 6 a typical result is (1, 2, 2, 3, 4, 4).

A final ranking of the n competitors will be determined in all circumstances if a strict ordering is assigned to all possible results. In the next section it is shown that the number or results is . Of course only some strict orderings of this set of results will be feasible in that there are criteria which a final ranking should satisfy. For example, (1, 1, …, 1) should clearly be ranked first in any feasible ranking.
Hermitian Configurations in Odd-Dimensional Projective Geometries
Authors: Kestenband Barbu C.
Published: December 2010

A t-cap in a geometry is a set of t points no three of which are collinear. A (t, k)-cap is a set of t points, no k + 1 of which are collinear.

It has been shown in [3] that any Desarguesian PG(2n, q2) is a disjoint union of (q2n+l – l)/(q – 1) (q2n+l – l)/(q + l)-caps. These caps were obtained as intersections of 2n Hermitian Varieties of a certain kind; the intersection of 2n + 1 such varieties was empty. Furthermore, the caps in question constituted the ‘large points” of a PG(2n, q), with the incidence relation defined in a natural way.

It seemed at the time that nothing similar could be said about odd-dimensional projective geometries, if only because |PG(2n – 1, q)| ∤ |PG(2n – l, q2)|.
The Quotient Problem for Noetherian Rings
Authors: Müller Bruno J.
Published: December 2010

Our work was motivated by attempts to find a criterion for the existence of a classical quotient ring, for a noetherian ring, in analogy with the various known criteria for the existence of an artinian classical quotient ring ([9], [10], [13], [2]).

We have restricted our attention to Krull symmetric noetherian rings R, and we make heavy use of the fact that all their Krull composition factors are non-singular (Proposition 7). The collection Kprime R of the associated primes of the Krull composition factors of R plays a central role, taking the place of the collection of the associated primes of R.
Differentiation of n-Dimensional Additive Processes
Authors: Akcoglu M. A. , Junco A. Del
Published: December 2010

Let n ≧ 1 be an integer and let Rn be the usual n-dimensional real vector space, considered together with all its usual structure. The usual n-dimensional Lebesgue measure on Rn is denoted by λn. The positive cone of Rn is Rn+ and the interior of Rn + is Pn. Hence Pn is the set of vectors with strictly positive coordinates. A subset of Rn is called an interval if it is the cartesian product of one dimensional bounded intervals. If a, b ∊ Rn then [a, b] denotes the interval {u|a ≦ u ≦ b|. The closure of any interval I is of the form [a, b]; the initial point of I will be defined as the vector a. The class of all intervals contained in Rn+ is denoted by . Also, for each u ∊ Pn, let be the set of all intervals that are contained in the interval [0, u] and that have non-empty interiors. Finally let en ∊ Pn be the vector with all coordinates equal to 1.
Dilations and Hahn Decompositions for Linear Maps
Authors: Hadwin D. W.
Published: December 2010

Suppose is a C*-algebra and H is a Hilbert space. Let denote the set of completely positive maps from into the set B(H) of (bounded linear) operators on H. This paper studies the vector space spanned by , i.e., the linear maps that are finite linear combinations of completely positive maps. From another viewpoint, a map ϕ is in precisely when it has a decomposition ϕ = (ϕ1 – ϕ2) + i(ϕ3 – ϕ4) with ϕ1, ϕ2, ϕ3, ϕ4 in CP ; this decomposition is analogous to the Hahn decomposition for measures [8, 111.4.10] (see also Theorem 20). The analogous class of maps with “completely positive” replaced by “positive” was studied by R. I. Loebl [11] and S.-K. Tsui [17], and when is commutative, this latter class coincides withi , since every positive linear map on a commutative C*-algebra is completely positive [16].
Co-Absolutes with Homeomorphic Dense Subspaces
Authors: Williams Scott W.
Published: December 2010

Recall that the absolute ∈(X) of a regular space X is the unique (up to a homeomorphism) extremally disconnected space whose image is X under a perfect irreducible map. X and Y are co-absolute whenever ∈(X) and ∈(Y) are homeomorphic. Completely regular spaces X and Y are weakly co-absolute whenever βX and βY are co-absolute. For a survey of this area we suggest [6] and [8].

In this paper we prove

THEOREM 1. Suppose, for i ∈ {0, 1};, X(i) is a compact connected linearly ordered space. Then X(0) and X(l) are co-absolute if, and only if, X(0) and X(l) have homeomorphic dense sets.

Making use of Theorem 1 and a result from [7] we give Theorem 2, a cardinal generalization of

COROLLARY 1. Suppose for each i ∈ {0, 1};, X(i) is a Čech-complete space with a Gδ-diagonal.
Unbounded Negative Definite Functions
Authors: Akemann Charles A. , Walter Martin E.
Published: December 2010

Negative definite functions (all definitions are given in § 1 below) on a locally compact, σ-compact group G have been used in several different contexts recently [2, 5, 7, 11]. In this paper we show how such functions relate to other properties such a group may have. Here are six properties which G might have. They are grouped into three pairs with one property of each pair involving negative definite functions. We show that the paired properties are equivalent and, where possible, give counter-examples to other equivalences. We assume throughout that G is not compact.

(1A) G does not have property T.

(IB) There is a continuous, negative definite function on G which is unbounded.

(2A) G has the (weak and/or strong) dual R-L property.

(2B) For every closed, non-compact set Q ⊂ G there is a continuous, negative definite function on G which is unbounded on Q.