bluuebunny/crossref_metadata_2025_split huggingface dataset:
Localization of Right Noetherian Rings at Semiprime Ideals
Authors: Lambek J. , Michler G. 
Published: December 2010

In [11] and [12] we investigated the process of localization of right Noetherian rings R at prime ideals. We shall now extend these investigations to semiprime ideals N of R.In Section 2 we show that localizing at the injective right R-module E(R/N) is the same as localizing with respect to the multiplicative set
A Local Ergodic Theorem on Lp
Authors: Baxter J. R. , Chacon R. V. 
Published: December 2010

Two general types of pointwise ergodic theorems have been studied: those as t approaches infinity, and those as t approaches zero. This paper deals with the latter case, which is referred to as the local case.Let (X, , μ) be a complete, σ-finite measure space. Let {Tt} be a strongly continuous one-parameter semi-group of contractions on , defined for t ≧ 0. For Tt positive, it was shown independently in [2] and [5] that1.1almost everywhere on X, for any f ∊ L1. The same result was obtained in [1], with the continuity assumption weakened to having it hold for t > 0.
Coefficients of Symmetric Functions of Bounded Boundary Rotation
Authors: Leach Ronald J. 
Published: December 2010

Let denote the family of all functions of the formthat are analytic in the unit disc U, f′(z) ≠ 0 in U and f maps U onto a domain of boundary rotation at most . Recently Brannan, Clunie and Kirwan [2] and Aharonov and Friedland [1] have solved the problem of estimating |amp+1| for all , provided m = 1.
Growth Conditions and Decomposable Operators
Authors: Radjabalipour Mehdi 
Published: December 2010

Throughout this paper T will denote a bounded linear operator which is defined on a Banach space and whose spectrum lies on a rectifiable Jordan curve J .The operators having some growth conditions on their resolvents have been the subject of discussion for a long time. Many sufficient conditions have been found to ensure that such operators have invariant subspaces [2 ; 3 ; 7 ; 8 ; 12 ; 13; 14; 21; 27; 28; 29], are S-operators [14], are quasidecomposable [9], are decomposable [4 ; 11], are spectral [7 ; 10 ; 15 ; 17], are similar to normal operators [16 ; 23 ; 25 ; 26], or are normal [15 ; 18 ; 22]. In this line we are going to show that many such operators are decomposable.
Ranges of Products of Operators
Authors: Grabiner Sandy 
Published: December 2010

Suppose that T and A are bounded linear operators. In this paper we examine the relation between the ranges of A and TA, under various additional hypotheses on T and A. We also consider the dual problem of the relation between the null-spaces of T and AT; and we consider some cases where T or A are only closed operators. Our major results about ranges of bounded operators are summarized in the following theorem.Theorem 1. Suppose that T is a bounded operator on a Banach space E and that A is a non-zero bounded operator from some Banach space to E.
On Some Results in Morse Theory
Authors: Kalmbach Gudrun 
Published: December 2010

The /z-cobordism theorem in [8], the generalized Poincaré conjecture in higher dimensions in [20] and several other results in differential topology are proved by using the following theorems of Morse theory:(1) the elimination of critical points;(2) the existence of nondegenerate functions for which the descending and ascending bowls have normal intersection;(3) the alteration of function values at critical points. (For the details see below.)We shall give short and elementary pr∞fs of these theorems together with some stronger statements than the ones given in [8-13] or [19].The theorems are proved for noncompact manifolds rather than for compact manifolds since, by a trivial modification of the manifold (deleting the boundary or one point) the case of compact manifolds is included.
Strongly Oscillatory and Nonoscillatory Subspaces of Linear Equations
Authors: Michael Dolan J. , Klaasen Gene A. 
Published: December 2010

Consider the nth order linear equationand particularly the third order equationA nontrivial solution of (1)n is said to be oscillatory or nonoscillatory depending on whether it has infinitely many or finitely many zeros on [a, ∞). Let denote respectively the set of all solutions, oscillatory solutions, nonoscillatory solutions of (1)n. is an n-dimensional linear space. A subspace is said to be nonoscillatory or strongly oscillatory respectively if every nontrivial solution of is nonoscillatory or oscillatory. If contains both oscillatory and nonoscillatory solutions then is said to be weakly oscillatory.
The Characterization of a Lattice Homomorphism
Authors: Kim Jongsik 
Published: December 2010

We shall give a simple characterization of a lattice homomorphism from a linear lattice E to a linear lattice F. This paper is motivated by the following two theorems in Kaplan [2] :If ϕ is a lattice homomorphism, then ϕt(Fb) is an ideal in Eb.(2) If ϕ is a lattice homomorphism, then ϕtt is a lattice homomorphism from ϕbb into ϕbb.The main theorem is stated and proved in section 3. In section 1, we shall give notations and in section 2, we shall prove a main lemma. For details, we refer to Vulikh [3].
Multivalent and Meromorphic Functions of Bounded Boundary Rotation
Authors: Leach Ronald J. 
Published: December 2010

The classVk(p). We generalize the class Vk of analytic functions of bounded boundary rotation [8] by allowing critical points in the unit disc U.Definition. Let f(z) = aqzq + . . . (q 1) be analytic in U. Then f(z) belongs to the class Vk(p) if for r sufficiently close to 1,andWe note that (1.1) implies that / has precisely p — 1 critical points in U.
Non-Free Groups Generated by Two 2 X 2 Matrices
Authors: Brenner J. L. , Macleod R. A. , Olesky D. D. 
Published: December 2010

Let m be any real or complex number, and let Gm be the group generated by the 2 X 2 matrices A = (1, m\ 0, 1) and B = (1, 0; m, 1), where we use the notation (C11, C12; c21, C22) to denote (by rows) the elements of a 2 X 2 matrix C. Thus, Gm is the set of all finite products (or words) of the form… Ah(3)Bh(2)Ah(1)where the h(i) are nonzero integers with h﹛\) possibly zero. If a non-trivial word of this form equals the identity / = (1, 0; 0, 1), then Gm is non-free; otherwise, Gm is free.
Free Decompositions of a Lattice
Authors: Grätzer G. , Sichler J. 
Published: December 2010

Two basic questions have been raised for free products of lattices:1. Do any two free products have a common refinement?2. Can every lattice be decomposed into a free product of freely indecomposable lattices?Both questions have been around for some time and attempts at solving them were made especially after the Structure Theorem for Free Products was discovered (see G. Grâtzer, H. Lasker, and C. R. Piatt [3]). Partial answer to question one was supplied in A. Kostinsky [7].In this paper we answer both questions. Our basic observation is that the proper framework for these results is the theory of free K-products, that is, free products in an arbitrary equational class K of lattices.
Ultrafunctor
Authors: Magid Andy R. 
Published: December 2010

Let G be a functor from commutative rings to abelian groups and let ﹛Rt : i ∈ S﹜ be a family of commutative rings indexed by the set S. Let be an ultrafilter on S, and let denote the ultraproduct of the Rt with respect to . This paper studies the problem of computing from the G(Rj) via the mapThe functors studied are Pic = Picard group, Br = Brauer group, U = units, and the functors K0, K1, SK1, K2 of Algebraic K-Theory. For G = Pic, U, K1 and SK1, (*) is always a monomorphism. An example is given to show that even if all the Rt are finite fields the map (*) has a kernel for G = K2.
Solution Space Decompositions for nth Order Linear Differential Equations
Authors: Gustafson G. B. , Sedziwy S. 
Published: December 2010

Consider the wth order scalar ordinary differential equationwith pr ∈ C([0, ∞) → R ) . The purpose of this paper is to establish the following:DECOMPOSITION THEOREM. The solution space X of (1.1) has a direct sum Decompositionwhere M1 and M2 are subspaces of X such that(1) each solution in M1\﹛0﹜ is nonzero for sufficiently large t ﹛nono sdilatory) ;(2) each solution in M2 has infinitely many zeros ﹛oscillatory).
Criteria for Groups with Representations of the Second Kind and for Simple Phase Groups
Authors: Van Zanten A. J. , De Vries E. 
Published: December 2010

In this paper we consider matrix representations of compact groups over the field of the complex numbers. We shall deal mainly with finite groups.The Kronecker product of two irreducible representations σ1and σ2of a groupis in general a reducible representation of. The explicit reduction of such a product to irreducible representations σ3can be performed by means of a unitary matrix, the elements of which are called Wigner coefficients or Clebsch-Gordan coefficients [1; 25; 27].
Immersions with Semi-Definite Second Fundamental Forms
Authors: Jonker Leo B. 
Published: December 2010

Let M be a. complete connected Riemannian manifold of dimension n and let £:M → Rn+k be an isometric immersion into the Euclidean space Rn+k. Let ∇ be the connection on Mn and let be the Euclidean connection on Rn+k. Also letdenote the second fundamental form B(X, Y) = (xY)→. Here TP(M) denotes the tangent space at p, NP(M) the normal space and (…)→ the normal component.
Equidistribution Des Valeurs Dune Application Holomorphe Generique a Valeurs Dans L'Espace Projectif
Authors: Gauthier P. M. 
Published: December 2010

Un exemple de Fatou-Bieberbach [1, p. 45] montre qu'il existe des applications holomorphesh:Cn → Cnà Jacobien J(h) partout non nul, mais dont le complémentaire de l'image Cn\h(Cn) est un fermé à intérieur non vide. Néanmoins on a montré récemment [3; 5] qu'une application holomorphe générique de Cn dans Cn est surjective. Nous voulons montrer qu'il en est de même pour les applications prennant leurs valeurs dans l'espace projectif Pn.
Classification of Restricted Linear Spaces
Authors: Totte Jim 
Published: December 2010

The material in this paper is taken from the author's doctoral dissertation [2]. We will use the terminology and notation of [3]. Let us recall those terms which will be needed here.We define a restricted linear space (RLS) as a finite set of p elements, called points, of which q subsets, called lines, are distinguished so that the following axioms hold:(RLS-1) Any two distinct points u, v belong to exactly one common line uv.
Fuchsian Subgroups of the Picard Group
Authors: Fine Benjamin 
Published: December 2010

The Picard group Γ = PSL2 (Z(i)) is the group of linear transformationswith a, b, c, d Gaussian integers.Γ is of interest both as an abstract group and in automorphic function theory [10]. In [10] Waldinger constructed a subgroup H of finite index which is a generalized free product, while in [1] Fine showed that T is a semidirect product with the subgroup H, contained as a subgroup of finite index in the normal factor.
Some Fixed Point Theorems for Partially Ordered Sets
Authors: Höft Hartmut , Höft Margret 
Published: December 2010

A partially ordered set P has the fixed point property if every order-preserving map f : P → P has a fixed point, i.e. there exists x ∊ P such that f(x) = x. A. Tarski's classical result (see [4]), that every complete lattice has the fixed point property, is based on the following two properties of a complete lattice P:(A)For every order-preserving map f : P → P there exists x ∊ P such that x ≦ f(x).(B)Suprema of subsets of P exist; in particular, the supremum of the set {x|x ≦ f(x)} ⊂ P exists.
A Simple Proof of the Maximal Ergodic Theorem
Authors: La Torre Alberto De 
Published: December 2010

Let X be a σ-finite measure space and let Tk, k any integer, be a group of positive linear transformations in Lp(X) such thatwith C independent of / and k. From now on / will be a positive function in Lp(X) and we will use the following notation:
On Rational Approximation on the Positive Real Axis
Authors: Rahman Q. I. , Schmeisser G. 
Published: December 2010

In their study of the uniform approximation of the reciprocal of e2 by reciprocals of polynomials on the positive real axis, Cody, Meinardus, and Varga [3] showed that if denotes the class of all polynomials of degree at most n andthen
Compatible Tight Riesz Orders on the Group of Automorphisms of an 0-2-Homogeneous Set: Addendum
Authors: Davis Gary , Fox Colin D. 
Published: December 2010

The purpose of this note is to show that Theorem 8 of Davis and Fox [1] is sharp. That is, we show that the following result is valid.THEOREM. Let Ω be an 0-2-homogeneous ordered set. Then Tρ(respectively, Tƛ ) is a maximal compatible tight Riesz order if and only if Ω has a countable cofinal(respectively, coinitial) subset.
On the Distribution Modulo 1 of the Sequence αn2 + βn
Authors: Schmidt Wolfgang M. 
Published: December 2010

Dirichlet's Theorem says that for any real α and for N ≧ 1, there exists a natural n ≦ N withwhere || || denotes the distance to the nearest integer. Heilbronn [2], improving estimates of Vinogradov [3], showed that for α, N as above and for ϵ ≧ 0, there exists an n ≦ N with
Some Good Sequences of Interpolatory Polynomials: Addendum
Authors: Freud G. , Sharma A. 
Published: December 2010

In 1974 [2] we used the n + 2 zeros of (1 - x2)Pn(α, β)(x), α, β > — 1, where Pn(α, β)(x) denotes Jacobi polynomials, to construct a sequence of linear operators {An(α, β)(f, x)} which has the following properties:(i) An(α, β)(f, x) is a linear polynomial operator mapping C[— 1, 1] into polynomials of degree ≦ n(1 + c), (c > 0 fixed but arbitrary)
On Some Classes of Univalent Polynomials
Authors: Rahman Q. I. , Szynal J. 
Published: December 2010

It was in the year 1931 that Dieudonné [4] proved the
following necessary and sufficient condition for a polynomial to be univalent in
the unit disk.
THEOREM A (Dieudonné criterion). The polynomial

is univalent in |z| &lt; 1 if and only if for every θ in [0, π/2] the
associated polynomial

does not vanish in |z| &lt; 1. For θ = 0, ϕ(z, θ) is to be interpreted as
Pn'(z).
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 limitsexist 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 ℒ1Le 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.
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).
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 ∈ XThus 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 .
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 formFor example, it is shown that the commutant of the range of C(S, T) is “small” unless S and T are scalars.