bluuebunny/crossref_metadata_2025_split huggingface dataset:
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 idealscommutes 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 .
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.
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.
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) withThe 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.
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 thatHere 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 byfor 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, by1.1where 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 thatIn 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 that1Here Z denotes the set of integers. For x ∈ A it now follows that there is an unique α(x) ∈ Z so that2and then alsoIn general we shall be concerned with solving the following equation for u3where 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 ∊ 2X3. 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 letLet 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) of1where 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 harmoniqueet d'une partie singulièreavec 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 formeet newtonienne ou logarithmique si elle s'écrit
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 diagonalof 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:1We 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.
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).
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 beWhat 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 hasSince 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.