bluuebunny/crossref_metadata_2025 huggingface dataset:
Toeplitz Operators on Bergman Spaces
Authors: Axler Sheldon , Conway John B. , McDonald Gerard
Published: December 2010

Let G be a bounded, open, connected, non-empty subset of the complex plane C. We put the usual two dimensional (Lebesgue) area measure on G and consider the Hilbert space L2(G) that consists of the complex-valued, measurable functions defined on G that are square integrable. The inner product on L2(G) is given by the norm ‖h‖2 of a function h in L2(G) is given by ‖h‖2 = (∫G|h|2)1/2.

The Bergman space of G, denoted La2(G), is the set of functions in L2(G) that are analytic on G. The Bergman space La2(G) is actually a closed subspace of L2(G) (see [12 , Section 1.4]) and thus it is a Hilbert space.

Let G denote the closure of G and let C(G) denote the set of continuous, complex-valued functions defined on G.
Products of Positive Reflections in the Orthogonal Group
Authors: Malzan J.
Published: December 2010

ForGa group,Sa subset ofGwhich generatesG,the length problem inGwith respect toSis to find, forg∈ G, the least integerrsuch thatgcan be written as the product ofrelements ofS.ForGan orthogonal groupOf(F)(hereFis a field, and the elements ofOf(F)preserve the quadratic formf) andSthe set of reflections inOf(F)the length problem has been studied by E. Cartan [2], J. Dieudonné [4, 5], E. Ellers [7], P. Scherk [8], and others. In all of these investigations, however, the problem posed by requiring thatSbe a single conjugacy class of reflections inOf(F)has been ignored. And it is generally the case that the reflections inOf(F)fall into several conjugacy classes.
Three Topological Properties from Noetherian Rings
Authors: Johnson Jon L.
Published: December 2010

The purpose of this paper is to study three concepts that deal with the topologies on ideals of commutative integral domains. We call a domain R prime-injective if for each torsion free R-module M, and all non-zero prime ideals

commutes implies that M is injective. From [6, Theorem 1 and the technique of Example 6] this is equivalent to all non-zero ideals of R being open in the topology defined by finite products of non-zero prime ideals as a base of neighborhoods around zero.

A domain is strongly prime-injective if for each (torsion theory) topology and for ϕ the set of primes in , ϕ-injective implies -injective for torsion free modules (see [6, 8] for notation). As in the prime-injective case, this is equivalent to being the topology generated by ϕ for all topologies .
Half-Turns and Infinite Chains of Clifford Configurations
Authors: Rigby J. F.
Published: December 2010

In a recent paper [7] Longuet-Higgins and Parry prove that, given a general Clifford configuration of degree 5 (abbreviated to CL5), C0 say, there exist points P and Q such that the inverses of P in the circles of C0 form the points of another CL5C1, whilst the inverses of Q in the circles of C1 are the points of C0; also the inverses of Q in the circles of C0 form the points of a CL5 C–1, whilst the inverses of P in the circles of C–1 are the points of C0. This leads to an infinite chain …, C–2, C–1, C0, C1, C2, … of CL5s, each connected to the next by means of the same two points P and Q, called the poles of the chain.
Operateur de Stokes Dans des Espaces de Sobolev a Poids sur des Domaines Anguleux
Authors: Dauge Monique
Published: December 2010

Rappelons que l'opérateur de Stokes associe au couple vitesse-pression (, p) le couple force-divergence (, g) par:

Nous nous plaçons ici en dimension 2. . Voici l'écriture matricielle de l'opérateur:

ce que nous noterons: .

Ce système est elliptique au sens de [1] sur un domaine Ω avec les conditions complémentaires: (Dirichlet); c'est donc ce probléme que nous étudions ici.
Property kα,n on Spaces with Strictly Positive Measure
Authors: Argyros S. , Kalamidas N.
Published: December 2010

In this paper we study intersection properties of measurable sets with positive measure in a probability measure space, or equivalently, intersection properties of open subsets on a compact space with a strictly positive measure.

The first result in this direction is due to Erdös and it is a negative solution to the problem of calibers on such spaces. In particular, under C.H., Erdös proved that Stone's space of Lebesque measurable sets of [0, 1] modulo null sets, does not have ℵ1-caliber.
Locally Compact Normal Spaces in the Constructible Universe
Authors: Watson W. Stephen
Published: December 2010

Arhangel'skiĭ proved around 1959 [1] that, for the class of perfectly normal locally compact spaces, metacompactness and paracompactness are equivalent. It is shown to be consistent that this equivalence holds for the (larger) class of normal locally compact spaces (answering a question of Tall [8], [9]).

The consistency of the existence of locally compact normal noncollectionwise Hausdorff spaces has been known since 1967. It is shown that the existence of such spaces is independent of the axioms of set theory, thus establishing that Bing's example G cannot be modified under ZFC to be locally compact.

All topological spaces are assumed to be Hausdorff.

First, a definition and three standard lemmata are needed.
Special Function Potentials for the Laplacian
Authors: Fegan H. D.
Published: December 2010

The purpose of this paper is to study the operator Δ + q. Here Δ is the Laplace–Beltrami operator on a compact Lie group G and q is a matrix coefficient of a representation of G. We are able to calculate the powers of Δ + q acting on the function qku. This is done in Section 2 and the reader is refered there for definitions of the special functions q and u.

The interest in the operator Δ + q comes originally from physics and in particular from the Schrödinger equation. This is described in [4]. Here we are restricting ourselves to mathematical questions and shall not consider any applications to physics.

In this paper we take the heat equation with potential as

(1.1)

with , the upper half plane, and initial data f(x, 0) = qk(x)u(x).
Ovoids and Translation Planes
Authors: Kantor William M.
Published: December 2010

An ovoid in an orthogonal vector space V of type Ω+(2n, q) or Ω(2n – 1, q) is a set Ω of qn–1 + 1 pairwise non-perpendicular singular points. Ovoids probably do not exist when n > 4 (cf. [12], [6]) and seem to be rare when n = 4. On the other hand, when n = 3 they correspond to affine translation planes of order q2, via the Klein correspondence between PG(3, q) and the Ω+(6, q) quadric.

In this paper we will describe examples having n = 3 or 4. Those with n = 4 arise from PG(2, q3), AG(2, q3), or the Ree groups. Since each example with n = 4 produces at least one with n = 3, we are led to new translation planes of order q2.
Commutative Coherent Rings
Authors: Matlis Eben
Published: December 2010

Throughout this paper R will be a commutative ring with 1. The purpose of this paper is to provide two new characterizations of coherent rings. The first of these characterizations shows that the class of coherent rings is precisely the class of rings for which certain duality homomorphisms are isomorphisms. And the second of these characterizations shows that the class of coherent rings is precisely the class of rings for which the endomorphism ring of any infective module is a flat module. We can show as a consequence that the endomorphism ring of a universal infective R-module is a faithfully flat R-module whenever R is a coherent ring.
Topological Extension Properties and Projective Covers
Authors: Ohta Haruto
Published: December 2010

Introduction. All spaces considered in this paper are assumed to be (Hausdorff) completely regular, and all maps are continuous. Let be a topological property of spaces. We shall identify with the class of spaces having . A space having is called a -space, and a subspace of a -space is called a -regular space. The class of -regular spaces is denoted by R(). Following [37], we call a closed hereditary, productive, topological property such that each -regular space has a -regular compactification a topological extension property, or simply, an extension property. In this paper, we restrict our attention to extension properties satisfying the following axioms:

(A1) The two-point discrete space has .

(A2) If each -regular space of nonmeasurable cardinal has , then = R().
Complex Numbers with Three Radix Expansions
Authors: Gilbert William J.
Published: December 2010

1. Introduction. This paper deals with the lack of uniqueness of the representations of the complex numbers in positional notation using Gaussian integers as bases.

Kátai and Szabó [3] proved that all the complex numbers can be written in radix form using the base –n + i with the natural numbers 0, 1, 2, …, n2 as digits. They remarked that they did not assert the uniqueness of these representations but gave no further indications of any multiple expansions. The geometry of these complex bases [2] indicates that some numbers have two expansions in a given base, while a few numbers even have three different expansions.
Semidirect Product Compactifications
Authors: Dangello F. , Lindahl R.
Published: December 2010

1. Introduction. K. Deleeuw and I. Glicksberg [4] proved that if S and T are commutative topological semigroups with identity, then the Bochner almost periodic compactification of S × T is the direct product of the Bochner almost periodic compactifications of S and T. In Section 3 we consider the semidirect product of two semi topological semigroups with identity and two unital C*-subalgebras and of W(S) and W(T) respectively, where W(S) is the weakly almost periodic functions on S. We obtain necessary and sufficient conditions and for a semidirect product compactification of to exist such that this compactification is a semi topological semigroup and such that this compactification is a topological semigroup. Moreover, we obtain the largest such compactifications.
Any Spine of the Cube is 2-Collapsible
Authors: Edwards Robert , Gillman David
Published: December 2010

1. Introduction. M. Cohen [1] denned a polyhedron K to be n-collapsible if K × In PL collapses. He proved that any spine of the cube B3 is 3-collapsible. This was a step directed toward the Zeeman Conjecture [4], which asserts that every compact contractible 2-polyhedron is 1-collapsible. In this paper we improve the result of Cohen by one dimension (Theorem 3): Any spine of the cube is 2-collapsible. The central question of 1-collapsibility remains unanswered.

Gillman and Rolfsen [3] have shown that any standard spine of the cube is 1-collapsible. Conjecture: If K is any spine of the cube, then K × I collapses to a standard spine of the cube. This would imply our main theorem. Lacking a proof of this conjecture, we must resort to an argument independent of [3].

THEOREM 1. Let A1, A2, …, Anbe a finite collection of pairwise disjoint contractible PL subsets of the cube. Then the decomposition obtained by shrinking each Ai to a point is 1-collapsible.
Simplicial Quadratic Forms
Authors: Monson Barry
Published: December 2010

0. Introduction. Simplicial quadratic forms (cf. Definition 1.4), and various equivalent forms, have occasionally been studied in geometry [8], and in number theory [9], [10], in connection with the extremal properties of integral quadratic forms. Our investigations, which employ simple techniques from graph theory and geometry, partly continue both those of Coxeter [5], who introduced the graphs described in Section 1, and Vinberg [20], [21], who described an algorithm for determining a fundamental region for a discrete group acting on spherical, Euclidean, or hyperbolic space. After a preliminary discussion of reflexible forms and the Caley-Klein model for (n − 1)-space (1.2), we define a simplicial form and its graph. Having enumerated them completely, we turn in Section 2 to their equivalence, which is related to a geometric dissection. The unit group for each simplicial form can then be determined from Theorem 3.7.

I wish to thank Professor H. S. M. Coxeter for many helpful ideas, and Professor G. Maxwell and the referee for suggesting numerous improvements.
New Lattice Packings of Spheres
Authors: Barnes E. S. , Sloane N. J. A.
Published: December 2010

1. Introduction. In this paper we give several general constructions for lattice packings of spheres in real n-dimensional space Rn and complex space Cn. These lead to denser lattice packings than any previously known in R36, R64, R80, …, R128, …. A sequence of lattices is constructed in Rn for n = 24m ≦ 98328 (where m is an integer) for which the density Δ satisfies log2 Δ ≈ – (1.25 …)n, and another sequence in Rn for n = 2m (m any integer) with

The latter appear to be the densest lattices known in very high dimensional space. (See, however, the Remark at the end of this paper.) In dimensions around 216 the best lattices found are about 2131000 times as dense as any previously known.

Minkowski proved in 1905 (see [20] and Eq. (23) below) that lattices exist with log2 Δ > –n as n → ∞, but no infinite family of lattices with this density has yet been constructed.
Rings with Enough Invertible Ideals
Authors: Smith P. F.
Published: December 2010

All rings are associative with identity element 1 and all modules are unital. A ring has enough invertible ideals if every ideal containing a regular element contains an invertible ideal. Lenagan [8, Theorem 3.3] has shown that right bounded hereditary Noetherian prime rings have enough invertible ideals. The proof is quite ingenious and involves the theory of cycles developed by Eisenbud and Robson in [5] and a theorem which shows that any ring S such that R ⊆ S ⊆ Q satisfies the right restricted minimum condition, where Q is the classical quotient ring of R. In Section 1 we give an elementary proof of Lenagan's theorem based on another result of Eisenbud and Robson, namely every ideal of a hereditary Noetherian prime ring can be expressed as the product of an invertible ideal and an eventually idempotent ideal (see [5, Theorem 4.2]). We also take the opportunity to weaken the conditions on the ring R.
Derivations with Invertible Values
Authors: Bergen Jeffrey , Herstein I. N. , Lanski Charles
Published: December 2010

In this paper we study a question which, although somewhat special, has the virtue that its answer can be given in a very precise, definitive, and succinct way. It shows that the structure of a ring is very tightly determined by the imposition of a special behavior on one of its derivations.

The problem which we shall examine is: Suppose that R is a ring with unit element, 1, and that d ≠ 0 is a derivation of R such that for every x ∊ R, d(x) = 0 or d(x) is invertible in R; must R then have a very special structure?

As we shall see, the answer to this question is yes, in particular we show that except for a special case which occurs when 2R = 0, R must be a division ring D or the ring D2 of 2 × 2 matrices over a division ring.
Mixing on Sequences
Authors: Friedman Nathaniel A.
Published: December 2010

Our aim is to study the mixing sequences of a weak mixing transformation. An ergodic measure preserving transformation is weak mixing if and only if for each pair of sets there exists a sequence of density one on which the transformation mixes the sets [9]. An unpublished result of S. Kakutani implies there actually exists a single sequence of density one on which the transformation is mixing for all sets (see Section 3). This result motivated the general définition of a transformation being mixing on a sequence, as well as mixing of higher order on a sequence. Given a weak mixing transformation, there exist sequences along which it is mixing of all degrees. In particular, this is the case for an eventually independent sequence [7].

In Section 3 it will be shown that if T is weak mixing but not mixing, then a sequence on which T is two-mixing must have upper density zero.
Central Double Centralizers on Quasi-Central Banach Algebras with Bounded Approximate Identity
Authors: Takahasi Sin-Ei
Published: December 2010

We assume throughout this paper that A is a semi-simple, quasi-central, complex Banach algebra with a bounded approximate identity {eα}. The author [6] has shown that every central double centralizer T on A can be, under suitable conditions, represented as a bounded continuous complex-valued function ΦT on Prim A, the structure space of A with the hull-kernel topology, such that

Here x + P for P ∊ Prim A denotes the canonical image of x in A/P. This map Φ is called Dixmier's representation of Z(M(A)), the central double centralizer algebra of A. We denote by τ the canonical isomorphism of A into the Banach algebra D(A) with the restricted Arens product as defined in [6]. Also denote by μ Davenport's representation of Z(M(A)). In fact, this map μ is given by

for each T ∊ Z(M(A)).
Generalized Euler Number Sequences: Asymptotic Estimates and Congruences
Authors: Leeming D. J. , Macleod R. A.
Published: December 2010

We define (as in [7]) integer sequences one for each positive integer k ≧ 2, by

1.1

where are the kth roots of unity and (E(k))n is replaced by after multiplying out. We note that (1.1) implies , n ≠ 0 (mod k).

In [7], we considered some special properties of these number sequences, proved several congruences and conjectured several others. This paper is a continuation of the work presented in [7].

In Section 2 we demonstrate the asymptotic rate of growth of the numbers by showing that

In Section 3 we present a large number of congruences (modulo 2048), some of which are proved or can be proved by the techniques presented herein, and other congruences which appear to be true on the basis of numerical evidence.
On Difference Operators and their Factorization
Authors: Browne Patrick J. , Nillsen R. V.
Published: December 2010

Throughout this paper A will be used to denote a given set and g a permutation of it. We shall assume that there is a subset C ⊆ A so that

1

Here Z denotes the set of integers. For x ∈ A it now follows that there is an unique α(x) ∈ Z so that

2

and then also

In general we shall be concerned with solving the following equation for u

3

where pi, n ≤ i ≤ r, and v are given real valued functions on A and pnpr does not vanish on A. For B ⊆ A, F(B) will denote the set of all real valued functions defined on B.
On Large Inductive Dimension of Proximity Spaces
Authors: Kandil A.
Published: December 2010

The notion of proximity spaces was introduced by Efremovic in [2, 3]. An analysis of proximity spaces was carried out by Smirnov in [5].

The study of covering dimension of proximity spaces was originated by Smirnov in [6].

In this paper we introduce the concept of δ-large inductive dimension of proximity spaces and study some of its properties.

1. Definitions and basic concepts.

Definition 1. [5]A proximity space or (δ-space) is a pair (X, δ) where X is a set and δ is a mapping from 2X × 2X into the set {0, 1} satisfying the following axioms:

1. δ(A, B) = δ(B, A)∀ A, B ∊ 2X.

2. δ(A, B ∪ C) = δ(A, B) δ(A, C) ∀ A, B, C ∊ 2X

3. δ({x}, {y}) = 0 ⇔ x = y.

4. δ(X, ∅) = 1.

5. δ(A, B) = 1 ⇒ ∃ C, D ∊ 2X ∋ C ∪ D = X and δ(A, C) · δ(B, C) = 1.
On the Structure and Tensor Products of JC-Algebras
Authors: Hanche-Olsen Harald
Published: December 2010

Norm closed (or weakly closed) Jordan algebras of self-adjoint operators on a Hilbert space were initially studied by Topping, Effros, and Stormer [15], [4], [12], [13]. These works are very “spatial”, in that the algebras are considered in one given representation. The introduction of their abstract counterparts, the JB- and JBW-algebras, has led to an increased interest in this subject. The author hopes this paper will support the view that a more “space-free” approach is fruitful, even if only the “concrete” algebras are under study. In accordance with this view, a “JC-algebra” in this paper will mean a normed Jordan algebra over the reals, which is isometrically isomorphic to a norm closed Jordan algebra of self-adjoint operators.

Some of the results in this paper are closely related to, or rewordings of, results in the above-mentioned papers. However, I feel that the present approach is sufficiently different to be of interest in itself. In particular, many of the technical difficulties associated with earlier approaches are avoided.
Some Results on L-Indistinguishability for SL(r)
Authors: Shahidi Freydoon
Published: December 2010

Fix a positive integer r. Let AF be the ring of adeles of a number field F. For a parabolic subgroup P of SLr, we fix a Levi decomposition P = MN, and we let

Let be the Weyl group of . It follows from a recent work of James Arthur [1,2] (also cf. [3]) that, among the terms appearing in the trace formula for SLr(AF), coming from the Eisenstein series, are those which are a constant multiple (depending only on M and w) of

1

where σ is a cusp form on M(AF) satisfying wσ ≅ σ,

and

in the notation of [2, 3]).
Approximation Harmonique Sur Les Surfaces de Riemann
Authors: Boivin A. , Gauthier P. M.
Published: December 2010

Dans le présent article, surface de Riemann ou plus simplement surface désignera une variété analytique complexe R, connexe, sans bord et de dimension 1. En terme d'une variable locale, une fonction harmonique h, définie sur R, possédant une singularité isolée au point z0, peut s'écrire comme la somme d'une fonction harmonique

et d'une partie singulière

avec αn, βn ∈ C, γ ∈ R; les deux séries sont supposées convergentes, la première pour |z – z0| suffisamment petit, la seconde pour tout z ≠ z0. Alors h(z) = u(z) + s(z). Nous dirons que la singularité de h est non-essentielle si s(z) est de la forme

et newtonienne ou logarithmique si elle s'écrit
Deformations G-Verselles Et G-Stables
Authors: Gervais Jean-Jacques
Published: December 2010

Soitℰnl'anneau des germes en 0 des fonctions numériques de classe C∞dansRn. On écrira aussiℰxpourℰnoùxest la variable dansRn. Désignons par Diff(n)le groupe des germes en 0 des difféomorphismes locaux τ de classe C∞d'un voisinage de 0 dansRnsur un voisinage de 0 tels que τ(0) = 0. SoientGun sous-groupe de Lie deGlp(R) et C∞0(Rn,G) l'ensemble des germes en 0 des applications de classe C∞deRndansG.
Serial Right Noetherian Rings
Authors: Singh Surjeet
Published: December 2010

A module M is called a serial module if the family of its submodules is linearly ordered under inclusion. A ring R is said to be serial if RR as well as RR are finite direct sums of serial modules. Nakayama [8] started the study of artinian serial rings, and he called them generalized uniserial rings. Murase [5, 6, 7] proved a number of structure theorems on generalized uniserial rings, and he described most of them in terms of quasi-matrix rings over division rings. Warfield [12] studied serial both sided noetherian rings, and showed that any such indecomposable ring is either artinian or prime. He further showed that a both sided noetherian prime serial ring is an (R:J)-block upper triangular matrix ring, where R is a discrete valuation ring with Jacobson radical J. In this paper we determine the structure of serial right noetherian rings (Theorem 2.11).
The Character of Certain Closed Sets
Authors: Swardson Mary Anne
Published: December 2010

Let X be a topological space and let A ⊂ X. The character of A in X is the minimal cardinal of a base for the neighborhoods of A in X. Previous studies have shown that the character of certain subsets of X (or of X2) is related to compactness conditions on X. For example, in [12], Ginsburg proved that if the diagonal

of a space X has countable character in X2, then X is metrizable and the set of nonisolated points of X is compact. In [2], Aull showed that if every closed subset of X has countable character, then the set of nonisolated points of X is countably compact. In [18], we noted that if every closed subset of X has countable character, then MA + ┐ CH (Martin's axiom with the negation of the continuum hypothesis) implies that X is paracompact.
Nonnegative Solutions for Weakly Nonlinear Elliptic Equations
Authors: Allegretto Walter
Published: December 2010

Let x = (x1, … xn) denote a point of Euclidean n space En and set Di = ∂/∂xi for i = 1, … n. Let Ω denote an exterior domain in En with smooth boundary and consider in Ω the formal elliptic problem:

1

We first consider the problem of finding nonnegative generalized solutions of (1) when τ ≧ 0, τ ≢ 0, and r(x) ≡ 0. Under more stringent conditions on the coefficients and for suitable r(x), we then show the existence of a locally bounded solution. Next, we show that, under stronger assumptions, our main criterion is also necessary. The final arguments are devoted to the consideration of illustrative examples.
Directionally Lipschitzian Mappings on Baire Spaces
Authors: Borwein J. M. , Stròjwas H. M.
Published: December 2010

Studies of optimization problems have led in recent years to definitions of several types of generalized directional derivatives. Those derivatives of primary interest in this paper were introduced and investigated by F. M. Clarke ([5], [6], [7], [8]), J. B. Hiriart-Urruty ([12]), Lebourg ([16], [17]), R. T. Rockafellar ([23], [24], [26], [27]), Penot ([21], [22]) among others.

In an attempt to explore in more detail relationships between various types of generalized directional derivatives we discovered some unexpected results which were not observed by the above mentioned authors. We are able to give simple conditions which characterize directionally Lipschitzian functions defined on a Baire metrizable locally convex topological vector space.
On Central Ω-Krull Rings and their Class Groups
Authors: Jespers E. , Wauters P.
Published: December 2010

The aim of this note is to study the class group of a central Ω-Krull ring and to determine in some cases whether a twisted (semi) group ring is a central Ω-Krull ring. In [8] we defined an Ω-Krull ring as a generalization of a commutative Krull domain. In the commutative theory, the class group plays an important role. In the second and third section, we generalize some results to the noncommutative case, in particular the relation between the class group of a central Ω-Krull ring and the class group of a localization. Some results are obtained in case the ring is graded. Theorem 3.2 establishes the relation between the class group and the graded class group. In particular, in the P.I. case we obtain that the class group is equal to the graded class group. As a consequence of a result on direct limits of Ω-Krull rings, we are able to derive a necessary and sufficient condition in order that a polynomial ring R[(Xi)i∊I] (I may be infinite) is a central Ω-Krull ring.
Smooth Boundary Values Along Totally Real Submanifolds
Authors: Stout Edgar Lee
Published: December 2010

The main result of this paper is the following regularity result:

THEOREM. Let D ⊂ CNbe a bounded, strongly pseudoconvex domain with bD of class Ck, k ≧ 3. Let Σ ⊂ bD be an N-dimensional totally real submanifold, and let f ∊ A(D) satisfy |f| = 1 on Σ, |f| < 1 on. If Σ is of class Cr, 3 ≦ r < k, then the restriction fΣ = f|Σ of f to Σ is of class Cr − 0, and if Σ is of class Ck, then fΣ is of class Ck − 1.

Here, of course, A(D) denotes the usual space of functions continuous on , holomorphic on D, and we shall denote by Ak(D), k = 1, 2, …, the space of functions holomorphic on D whose derivatives or order k lie in A(D).
Towards Minimal Binding Varieties of Lattices
Authors: Koubek Václav
Published: December 2010

By classical results of Ambrust and Schmidt, every monoid is isomorphic to the endomorphism monoid of an algebra. Thus if we want to investigate in which varieties (or generally, in a concrete category) each monoid is isomorphic to the endomorphism monoid of an algebra in this variety (or an object of this category) then the important role is played by the concept of a binding category (see the definition below). Moreover, as shows the Hedrlín-Kučera Theorem [13] if the set-theoretical assumption (M) holds (i.e., there is an infinite cardinal α such that each ultrafilter closed under α intersections is trivial) every concrete category can be fully embedded into any binding category. Other properties of binding categories are in [7, 11, 13]. A list of the most important binding categories and the properties of binding categories can be found in an excellent monograph [13].
On the Symmetric Hypercenter of a Ring
Authors: Giambruno A.
Published: December 2010

The hypercenter theorem [6] asserts that in a ring with no non-zero nil ideals an element commuting with a suitable power of each element of the ring must be central. In this paper we shall be concerned with a similar problem in the setting of rings with involution. Let R be a ring with involution *, let Z denote the center of R and let S = {x ∈ R|x = x*} be the set of symmetric elements in R. We define the symmetric hypercenter of R to be

What can one hope to say about H? That H need not equal Z is clear. For instance, in the ring R = F2 of 2 X 2 matrices over a field, if * is the symplectic involution, all symmetric elements are central, hence H = R but Z ≠ R. Furthermore if R is a noncommutative ring in which every symmetric element is nilpotent then even in this case H = R and Z ≠ R follows.
Weakly Compact, Operator-Valued Derivations of Type I Von Neumann Algebras
Authors: Wright Steve
Published: December 2010

In [18], the author initiated an investigation of compact, Banach-module-valued derivations of C*-algebras. In collaboration with C. A. Akemann [3] and S.-K. Tsui [16], he determined the structure of all compact and weakly compact, A-valued derivations of a C*-algebra A, and of all compact, B(H)-valued derivations of a C*-subalgebra of B(H), the algebra of bounded linear operators on a Hilbert space H. In this paper, we begin the study of weakly compact, B(H)-valued derivations of C*-subalgebras of B(H).

Let R be a C*-subalgebra of B(H), δ:R → B(H) a weakly compact derivation, i.e., a weakly compact linear map which has

Since δ has a unique weakly compact extension to a derivation of the closure of R in the weak operator topology (WOT) on B(H) (consult the proof of Theorem 3.1 of [16]), we may assume with no loss of generality that R is a von Neumann subalgebra of B(H). In this paper, we determine in Lemma 4.1 and Theorems 4.3 and 4.10 the structure of δ when R is type I, using I. E. Segal's multiplicity theory [14] for type I von Neumann algebras and results of E. Christensen [6], [7] on B(H)-valued derivations of von Neumann algebras.
On Special Group-Automorphisms and Their Composition
Authors: Hilton Peter
Published: December 2010

Let G be a group and φ an automorphism of G. We say that φ is a pseudo-identity (pi) if, for each x ∈ G, there exists a finitely generated (fg) subgroup K = Kx(φ) of G such that x ∈ K and φ|K is an automorphism of K. It has been shown [1, 3] that such special automorphisms of abelian or nilpotent groups play an important role in homotopy theory; and it was indicated in [2] that their purely algebraic properties might well repay study.

The following facts about pi's are elementary.

PROPOSITION 0.1. Let φ be an automorphism of G and let n be a non-zerointeger. Then φ is pi if and only if φn is pi.

PROPOSITION 0.2. Let φ be a pseudo-identity of G and a an automorphismof G. Then αφα-1 is a pseudo-identity.
Asymptotic Behavior of Normal Mappings of Several Complex Variables
Authors: Hahn Kyong T.
Published: December 2010

Let M and N be connected Hermitian manifolds of dimensions m and n with Hermitian metrics hM and hN, respectively. Then the space ℓ(M, N) of continuous mappings between M and N endowed with the compact-open topology is second countable so that a metric can be furnished in ℓ(M, N) which induces the compact-open topology. A sequence {fn} in ℓ(M, N) converges to a n f in ℓ(M, N) in this topology if and only if fn converges to f uniformly on compact subsets of M. It is then an easy consequence of the Cauchy integral formula to show that the space ℋ(M, N) of holomorphic mappings f:M → N is a closed subspace of ℓ(M, N).

In this paper, generalizing the classical notions of normal functions, Bloch functions, regular sequences and P-point sequences of one complex variable to the mappings in ℋ(M, N), see also [25], we obtain various relations which exist between these notions.
Some Special Classes of Cartan Matrices
Authors: Ogg A. P.
Published: December 2010

Let A = (Aij)l≦ij≦l be a Cartan matrix, i.e., Aii = 2 for all i and Aij is an integer ≦ 0 for i ≠ j, with Aij = 0 if Aji = 0. The size l of A is called its rank, for Lie-theoretic reasons, and may be larger than its matrix rank. We associate to A its Dynkin diagram, with vertices 1, 2, … , l, with AijAji lines joining i to j, and with an arrow pointing from i to j if Aij/Aji < 1, i.e., pointing toward the shorter root (see below). The Cartan matrix A is indecomposable if its diagram is connected, and symmetrizable if there exist positive rational numbers q1 … , ql with

qiAij = qjAji for all i and j.

Symmetrizability is automatic if the diagram contains no cycle.
Generalized Mellin Convolutions and their Asymptotic Expansions
Authors: Wong R. , Mcclure J. P.
Published: December 2010

A large number of important integral transforms, such as Laplace, Fourier sine and cosine, Hankel, Stieltjes, and Riemann- Liouville fractional integral transforms, can be put in the form

1.1

where f(t) and the kernel, h(t), are locally integrable functions on (0,∞), and x is a positive parameter. Recently, two important techniques have been developed to give asymptotic expansions of I(x) as x → + ∞ or x → 0+. One method relies heavily on the theory of Mellin transforms [8] and the other is based on the use of distributions [24]. Here, of course, the integral I(x) is assumed to exist in some ordinary sense.

If the above integral does not exist in any ordinary sense, then it may be regarded as an integral transform of a distribution (generalized function). There are mainly two approaches to extend the classical integral transforms to distributions.
Localisation Relative Associee a une Theorie de Torsion
Authors: Lemaire Claude
Published: December 2010

Dans [3], Peter Hilton a introduit la notion de “localisation relative” d'une extension de groupes à noyau nilpotent. Etant donné une extension de groupes

oú N est nilpotent, il s'agit de l'introduire dans un diagramme commutatif:

oú NP est la P-localisation de N.

L'idée (issue de la Topologie algébrique) est de tourner autant que possible l'absence de localisation maniable dans la catégorie des groupes. J'ai moi-même exploité cette idée dans [6], dans le cas oú une action de groupe est exercée sur G.
Compactness and Weak Compactness in Spaces of Compact-Range Vector Measures
Authors: Graves William H. , Ruess Wolfgang
Published: December 2010

This paper features strong and weak compactness in spaces of vector measures with relatively compact ranges in Banach spaces. Its tools are the measure-operator identification of [16] and [24] and the description of strong and weak compactness in spaces of compact operators in [10], [11], and [29].

Given a Banach space X and an algebra of sets, it is shown in [16] that under the usual identification via integration of X-valued bounded additive measures on with X-valued sup norm continuous linear operators on the space of -simple scalar functions, the strongly bounded, countably additive measures correspond exactly to those operators which are continuous for the coarser (locally convex) universal measure topology τ on . It is through the latter identification that the results on strong and weak compactness in [10], [11], and [29] can be applied to X-valued continuous linear operators on the generalized DF space to yield results on strong and weak compactness in spaces of vector measures.
On Explicit Decomposition for Positive Polynomials on [-1, +1] with Applications to Extremal Problems
Authors: Pierre R.
Published: December 2010

The following well known inequality was first proved by Bernstein [2].

THEOREM A. If pn(x) is a polynomial of degree n, such that |pn(x)| ≦ 1 for –1 ≦ x = +1, then

1

The dominant n(1 – x2)–;1/2 is best possible only at the zeros of the Tchebychev polynomial

but the bound is precise at every interior point as far as the exponent of n is concerned.

Theorem A was extended to the case of higher derivatives by Duffin and Schaeffer in [4]. In that paper they make extensive use of the oscillation property of the polynomial Tn(x) and of the related function
A General form of the Functional LIL for Banach-Valued Brownian Motion
Authors: Wong H. Ship-Fah
Published: December 2010

In a recent paper [12], C. Mueller proved a general version of the functional LIL which unifies Strassen's LIL and the Lévy modulus of continuity for Brownian motion W(t). His theorem also contains other known forms of the LIL.

For each t ≧ 0, let be a family of points in the first quadrant of the plane. Let r ≦ 0; to each point (s0, l0), we associate a rectangle

Define Ar(t) to be the area of the union of these rectangles up to time t under the measure . Then, Theorem 1 [12, p. 166] states that for an increasing function h such that

the set of limit points of

in C[0, 1] is the closed unit ball of the reproducing kernel Hilbert space (rkhs) associated with Wiener measure.
Representations of Foundation Semigroups and their Algebras
Authors: Bami M. Lashkarizadeh
Published: December 2010

The aim of this paper is to extend to a suitable class of topological semigroups parts of well-defined theory of representations of topological groups. In attempting to obtain these results it was soon realized that no general theory was likely to be obtainable for all locally compact semigroups. The reason for this is the absence of any analogue of the group algebra Ll(G). So the theory in this paper is restricted to a certain family of topological semigroups. In this account we shall only give the details of those parts of proofs which depart from the standard proofs of analogous theorems for groups.

On a locally compact semigroup S the algebra of all μ ∊ M(S) for which the mapping and of S to M(S) (where denotes the point mass at x) are continuous when M(S) has the weak topology was first studied in the sequence of papers [1, 2, 3] by A. C. and J. W. Baker.
Derivations Tangential to Compact Group Actions: Spectral Conditions in the Weak Closure
Authors: Bratteli Ola , Goodman Frederick M.
Published: December 2010

Let G be a compact Lie group and a an action of G on a C*-algebra as *-automorphisms. Let denote the set of G-finite elements for this action, i.e., the set of those such that the orbit {αg(x):g ∊ G} spans a finite dimensional space. is a common core for all the *-derivations generating one-parameter subgroups of the action α. Now let δ be a *-derivation with domain such that Let us pose the following two problems:

Is δ closable, and is the closure of δ the generator of a strongly continuous one-parameter group of *-automorphisms?

If is simple or prime, under what conditions does δ have a decomposition

where is the generator of a one-parameter subgroup of α(G) and is a bounded, or approximately bounded derivation?
Exact Sequences for the Kasparov Groups of Graded Algebras
Authors: Skandalis George
Published: December 2010

In [11] G. G. Kasparov defined the “operatorK-functor”KK(A, B)associated with the gradedC*-algebrasAandB. If the algebrasAandBare trivially graded andAis nuclear he proves six term exact sequence theorems. He asks whether this extends to the graded case.

Here we prove such “six-term exact sequence” results in the graded case. Our proof does not use nuclearity of the algebraA. This condition is replaced by a completely positive lifting condition (Theorem 1.1).

Using our result we may extend the results by M. Pimsner and D. Voiculescu on theKgroups of crossed products by free groups toKKgroups [15]. We give however a different way of computing these groups using the equivariantKK-theory developed by G. G. Kasparov in [12]. This method also allows us to compute the KK groups of crossed products byPSL2(Z).
An n-Vertex Theorem for Convex Space Curves
Authors: Bisztriczky Tibor
Published: December 2010

The classical four-vertex theorem states that a simple closed convex C2 curve in the Euclidean plane has at least four vertices (points of extreme curvature). This theorem has many generalizations with regard to both the curve and the topological space and for a history of the subject, we refer to [4] and [1]. The particular generalization of concern, credited to H. Mohrmann, is the following n-vertex theorem.

Let a simple closed C3 curve on a closed convex surface be intersected by a suitable plane in n points. Then the curve has at least n inflections (vertices).

The closed convex surface in the preceding is defined as having at most two points in common with any straight line. Presently, we extend this result to curves on more general convex surfaces in a real projective three-space P3.
Algebras of Analytic Operators associated with a Periodic Flow on a Von Neumann Algebra
Authors: Solel Baruch
Published: December 2010

Let M be a σ-finite von Neumann algebra and {σt}t∊T be a σ-weakly continuous representation of the unit circle, T, as *-automorphisms of M. Let H∞(σ) be the set of all x ∊ M such that

The structure of H∞(σ) was studied by several authors (see [2-13]).

The main object of this paper is to study the σ-weakly closed subalgebras of M that contain H∞(σ). In [12] this was done for the special case where H∞(σ) is a nonselfadjoint crossed product.

Let Mn, for n ∊ Z, be the set of all x ∊ M such that
q-Hypercyclic Rings
Authors: Jain S. K. , Malik D. S.
Published: December 2010

A ring R is called q-hypercyclic (hypercyclic) if each cyclic ring R-module has a cyclic quasi-injective (injective) hull. A ring R is called a qc-ring if each cyclic right R-module is quasi-injective. Hypercyclic rings have been studied by Caldwell [4], and by Osofsky [12]. A characterization of qc-rings has been given by Koehler [10]. The object of this paper is to study q-hypercyclic rings. For a commutative ring R, R can be shown to be q-hypercyclic (= qc-ring) if R is hypercyclic. (Theorems 4.2 and 4.3). Whether a hypercyclic ring (not necessarily commutative) is q-hypercyclic is considered in Theorem 3.11 by showing that a local hypercyclic ring R is q-hypercyclic if and only if the Jacobson radical of R is nil. However, we do not know if there exists a local hypercyclic ring with nonnil radical [12]. Example 3.10 shows that a q-hypercyclic ring need not be hypercyclic.
Finite Projective Planes that Admit a Strongly Irreducible Collineation Group
Authors: Ho Chat Yin
Published: December 2010

This paper studies how coding theory and group theory can be used to produce information about a finite projective plane π and a collineation group G of π.

A new proof for Hering's bound on |G| is given in 2.5. Using the idea of coding theory developed in [9], a relation between two rows of the incidence matrix of π with respect to a tactical decomposition is obtained in 2.1. This result yields, among other things, some techniques in calculating |G|, and generalizes a result of Roth [16], [see 2.4 and 2.5].

Hering [7] introduced the notion of strong irreducibility of G, that is, G does not leave invariant any point, line, triangle or proper subplane. He showed that if in addition G contains a non-trivial perspectivity, then there is a unique minimal normal subgroup of G. This subgroup is either non-abelian simple or isomorphic to the elementary abelian group Z3 × Z3 of order 9.
An Independent System of Units in Certain Algebraic Number Fields
Authors: Levesque Claude
Published: December 2010

For Kn = Q(ω) a real algebraic number field of degree n over Q such that

with D ∊ N, d ∊ Z, d|D2, and D2 + 4d > 0, we proved in [5] (by using the approach of Halter-Koch and Stender [6]) that if

with

then

is an independent system of units of Kn.
Singularity of Monomial Curves in A3 and Gorenstein Monomial Curves in A4
Authors: Kraft Jürgen
Published: December 2010

Let 2 ≦ s ∊ N and {n1, …, ns) ⊆ N*. In 1884, J. Sylvester [13] published the following well-known result on the singularity degree S of the monomial curve whose corresponding semigroup is S: = 〈n1, …, ns): If s = 2, then

Let K: = –Z\S and

for all 1 ≦ i ≦ s. We introduce the invariant

of S involving a correction term to the Milnor number 2δ [4] of S. As a modified version and extension of Sylvester's result to all monomial space curves, we prove the following theorem: If s = 3, then

We prove similar formulas for s = 4 if S is symmetric.
Nilpotent by Supersolvable M-Groups
Authors: Parks Alan E.
Published: December 2010

A character of a finite group G is monomial if it is induced from a linear (degree one) character of a subgroup of G. A group G is an M-group if all its complex irreducible characters (the set Irr(G)) are monomial.

In [1], Dade gave an example of an M-group with a normal subgroup which is itself not an M-group. In his group G, the supersolvable residual N is an extra special 2-group and G/N is supersolvable of even order. Moreover, the prime 2 is used in such a way that no analogous construction is possible in the case that |N| or |G:N| is odd. This led Isaacs in [8] and Dade in [2] to consider the effect of certain “oddness“ hypotheses in the study of monomial characters.

Our main results are in the same spirit. Although our techniques seem to require a restrictive assumption on the supersolvable residual of the groups we consider, our theorems provide more evidence that under fairly general circumstances normal subgroups of M-groups should be M-groups.
Euler's Criterion for Quintic Nonresidues
Authors: Katre S. A. , Rajwade A. R.
Published: December 2010

Let e be an integer ≧ 2, and p a prime = 1 (mod e). Euler's criterion states that for D ∊ Z,

(1.1)

if and only if D is an e-th power residue (mod p). If D is not an e-th power (mod p), one has

(1.2)

for some e-th root α(≠1) of unity (mod p). Sometimes expressions for roots of unity (mod p) can be given in terms of quadratic partitions of p. For example,

(1.3)

are the four distinct fourth roots of unity (mod p) for a prime p ≡ 1 (mod 4) in terms of a solution (a, b) of the diophantine system

(a, b unique), whereas for p ≡ 1 (mod 3), a solution (L, M) of the system

gives

(1.4)

as the three distinct cuberoots of unity (mod p).
Approximation by Λ-Splines on the Circle
Authors: Goodman T. N. T. , Lee S. L. , Sharma A.
Published: December 2010

Let Λ = {λ0,…, λn} denote a set of distinct integers and let Π(Λ) denote the set of all generalized polynomials of the form

For any given ζ on the unit circle U with

we consider the set Zk of points 1, ζ, ζ2, …, ζk−1 where

We shall denote by or the class of Λ-splines S(z) which satisfy the following conditions:

(i) S(z) ∊ Cn−1(U)

(ii) S(z)|Av ∊ Π(Λ) where
Generalized Spectral Theory in Complex Banach Algebras
Authors: Hile G. N. , Pfaffenberger W. E.
Published: December 2010

Let A be an element of a complex Banach algebra with identitI. The ordinary spectrum of A, sp(A), consists of those points z in the complex plane such that A — zI has no inverse in . If Q is any other element of , we define spQ(A), the spectrum of A relative to Q, or Q-spectrum of A, as those points z such that has no inverse in . Thus if Q = 0 the Q-spectrum of A is the same as the ordinary spectrum of A.

The generalized notion of spectrum, spQ(A), retains many of the properties of the ordinary spectrum, particularly when A and Q commute and the ordinary spectrum of Q does not meet the unit circle. Under these conditions the Q-spectrum of A is a nonempty compact subset of the plane, and if both sp(A) and sp(Q) are finite (or countable), so is spQ(A).
A measure on the Unipotent Variety
Authors: Arthur James
Published: December 2010

Suppose that G is a reductive algebraic group defined over Q. There occurs in the trace formula a remarkable distribution on G(A)1 which is supported on the unipotent set. It is defined quite concretely in terms of a certain integral over G(Q)\G(A)1. Despite its explicit description, however, this distribution is not easily expressed locally, in terms of integrals on the groups G(QV). For many applications of the trace formula, it will be essential to do this. In the present paper we shall solve the problem up to some undetermined constants.

The distribution, which we shall denote by Junip, was defined in [1] and [3] as one of a family {Jo} of distributions. It is the value at T = T0 of a certain polynomial . We shall recall the precise definition in Section 1.