bluuebunny/crossref_metadata_2025_split huggingface dataset:
An Application of Separate Convergence for Continued Fractions to Orthogonal Polynomials
Authors: Jones William B. , Thron W. J. , Wyshinski Nancy J. 
Published: December 2010

AbstractIt is known that the n-th denominators Qn (α, β, z) of a real J-fractionwhereform an orthogonal polynomial sequence (OPS) with respect to a distribution function ψ(t) on ℝ. We use separate convergence results for continued fractions to prove the asymptotic formulathe convergence being uniform on compact subsets of
On the Residual Finiteness of Polygonal Products of Nilpotent Groups
Authors: Kim Goansu , Tang C. Y. 
Published: December 2010

AbstractIn general polygonal products of finitely generated torsion-free nilpotent groups amalgamating cyclic subgroups need not be residually finite. In this paper we prove that polygonal products of finitely generated torsion-free nilpotent groups amalgamating maximal cyclic subgroups such that the amalgamated cycles generate an isolated subgroup in the vertex group containing them, are residually finite. We also prove that, for finitely generated torsion-free nilpotent groups, if the subgroups generated by the amalgamated cycles have the same nilpotency classes as their respective vertex groups, then their polygonal product is residually finite.
Weakness of the Topology of a JB*-Algebra
Authors: Bensebah Ali 
Published: December 2010

AbstractThe main purpose of this paper is to prove, that the topology of any (non-complete) algebra norm on a JB* -algebra is stronger than the topology of the usual norm. The proof of this theorem consists of an adaptation of the recent Rodriguez proof [8] that every homomorphism from a complex normed (associative) Q-algebra onto a B*-algebra is continuous.
Conorme et Inverse Généralisé Dans Les C*-Algèbres
Authors: Mbekhta Mostafa 
Published: December 2010

RésuméDans ce travail, on étudie les propriétés de la conorme, c(a) d'un élément a d'une C*-algèbre A. Nous montrons que c(a) est aussi douée de la condition de B*- algèbre, c'est-à-dire qu'elle vérifie l'égalité: c(a)2 = c(a*a) = c(aa*) = c(a*)2. Nous remarquons que la conorme est invariante par restriction à toute sous-C*-algèbre de A, propriété connue pour le spectre.Soit {an} une suite d'éléments réguliers telle que an → a régulier. Nous donnons des conditions nécessaires et suffisantes pour que où a† désigne l'inverse de Moore-Penrose de a.
Nörlund Operators On lp
Authors: Borwein David 
Published: December 2010

AbstractThe Nörlund matrix Na is the triangular matrix {an-k /An}, where an ≥ 0 and An := a0 + a1 + • • • + an > 0. It is proved that, subject to the existence of α := lim nan/An, Na ∊ B(lp) for 1 < p < ∞ if and only if α < ∞. It is also proved that it is possible to have Na ∊ B(lp) for 1 < p < ∞ when sup nan/An = ∞.
Descriptions of the Characteristic Sequence of an Irrational
Authors: Brown Tom C. 
Published: December 2010

AbstractLet α be a positive irrational real number. (Without loss of generality assume 0 < α < 1.) The characteristic sequence of α isf(α) =f1f2 ···, where fn = [(n + 1)α] - [nα].We make some observations on the various descriptions of the characteristic sequence of α which have appeared in the literature. We then refine one of these descriptions in order to obtain a very simple derivation of an arithmetic expression for [nα] which appears in A. S. Fraenkel, J. Levitt, and M. Shimshoni [17]. Some concluding remarks give conditions on n which are equivalent to fn = 1.
Weighted Restriction for Curves
Authors: Lakey Joseph D. 
Published: December 2010

AbstractWe prove weighted norm inequalities for the Fourier transform of the formwhere v is a nonnegative weight function on ℝd and ψ: [— 1,1 ] —> ℝd is a nondegenerate curve. Our results generalize unweighted (i.e. v = 1) restriction theorems of M. Christ, and two-dimensional weighted restriction theorems of C. Carton-Lebrun and H. Heinig.
A Sequence of Results on Class Number Congruences
Authors: Costa Antone 
Published: December 2010

AbstractLet p ≡ 1 mod 8 be a rational prime and let h(—p) be the class number of . In [1], Barrucand and Cohn show that h(-p) = 0 mod 8 iff p = x2 + 32y2 for some x,y € Z. In this article, we generalize their result to a family of relative quadratic extensions K/F, where Fk is the maximum totally real subfield of Q(ζ2k+2 ), and a power of a prime of Fk from a family of positive density.
On Maximal Residue Difference Sets Modulo p
Authors: Fabrykowski J. 
Published: December 2010

AbstractA residue difference set modulo p is a set A = {a1,a2,...,ak} of integers 1 ≤ ai ≤ p — 1 such that for all i and j with i ≠ j, where is the Legendre symbol. We give a lower and an upper bound for mp—the P maximal cardinality of such set A in the case of p ≡ 1 (mod 4).
Separators in Continuous Images of Ordered Continua and Hereditarily Locally Connected Continua
Authors: Grispolakis J. , Nikiel J. , Simone J. N. , Tymchatyn E. D. 
Published: December 2010

AbstractLet X be a Hausdorff space which is the continuous image of an ordered continuum. We prove that every irreducible separator of X is metrizable. This is a far reaching extension of the 1967 theorem of S. Mardešić which asserts that X has a basis of open sets with metrizable boundaries. Our first result is then used to show that, in particular, if Y is an hereditarily locally connected continuum, then for subsets of Y quasi-components coincide with components, and that the boundary of each connected open subset of Y is accessible by ordered continua. These results answer open problems in the literature due to the fourth and third authors, respectively.
Orlicz Spaces Without Strongly Extreme Points and Without H-Points
Authors: Hudzik Henryk 
Published: December 2010

AbstractW. Kurc [5] has proved that in the unit sphere of Orlicz space LΦ(μ) generated by an Orlicz function Φ satisfying the suitable Δ2-condition and equipped with the Luxemburg norm every extreme point is strongly extreme. In this paper it is proved in the case of a nonatomic measure μ that the unit sphere of the Orlicz space LΦ(μ) generated by an Orlicz function Φ which does not satisfy the suitable Δ2-condition and equipped with the Luxemburg norm has no strongly extreme point and no H-point.
On PP-Endomorphism Rings
Authors: Nicholson W. K. 
Published: December 2010

AbstractA characterization is given of when all kernels (respectively images) of endomorphisms of a module are direct summands, a necessary condition being that the endomorphism ring itself is a left (respectively right) PP-ring. This result generalizes theorems of Small, Lenzing and Colby-Rutter and shows that R is left hereditary if and only if the endomorphism ring of every injective left module is a right PP-ring.
Barnes' First Lemma and its Finite Analogue
Authors: Helversen-Pasotto Anna , Solé Patrick 
Published: December 2010

AbstractWe give a parallel proof of Barnes' first lemma and of its finite analogue. In both cases we use the Mellin transform. In the classical case, the proof avoids the residue theorem. In the finite case the Gamma function is replaced by the Gaussian sum function and the beta function by the Jacobi sum function.
Representations of Compact Right Topological Groups
Authors: Milnes Paul 
Published: December 2010

AbstractCompact right topological groups arise naturally as the enveloping semigroups of distal flows. Recently, John Pym and the author established the existence of Haar measure μ on such groups, which invites the consideration of the regular representations. We start here by characterizing the continuous representations of a compact right topological group G, and are led to the conclusion that the right regular representation r is not continuous (unless G is topological). The domain of the left regular representation l is generally taken to be the topological centreor a tractable subgroup of it, furnished with a topology stronger than the relative topology from G (the goals being to have l both defined and continuous). An analysis of l and r on H = L2(G) for some non-topological compact right topological groups G shows, among other things, that:
(i)for the simplest (perhaps) G generated by ℤ, (l, H) decomposes into one copy of each irreducible representation of ℤ and c copies of the regular representation.(ii)for the simplest (perhaps) G generated by the euclidean group of the plane , (l, H) decomposes into one copy of each of the continuous one-dimensional representations of and c copies of each continuous irreducible representation Ua,a > 0.(iii)when Λ(G) is not dense in G, it can seem very reasonable to regard r as a continuous representation of a related compact topological group, and also, G can be almost completely "lost" in the measure space (G, μ).
On Ideals Annihilating the Toral Class of BP*((BZ/PK)N)
Authors: Nakos George 
Published: December 2010

AbstractA sequence of ideals Ik,n ⊆ BP* is introduced, with the property: Ik,n ⊆ Ann(γk,n), where γk,n is the toral class of the Brown-Peterson homology of the n-fold product BZ/pk × ··· × BZ/pk. These ideals seem to play an interesting and yet unclear role in understanding Ann(γk,n). They are defined by using the formal group law of the Brown-Peterson spectrum BP, and some of their elementary properties are established. By using classical theorems of Landweber and of Ravenel-Wilson, the author computes the radicals of Ik,n and Ann(γk,n), and discusses a few examples.
The Collineation Groups of Figueroa Planes
Authors: Batten Lynn M. , Johnson Peter M. 
Published: December 2010

AbstractWe describe the structure of the collineation groups of Figueroa planes, giving examples and explanations that show why the description in Dempwolff [3] is not completely accurate. We also give criteria for when Figueroa planes are isomorphic, and show that certain subplanes are Figueroa or Pappian planes.
Oscillations of Second Order Neutral Differential Equations
Authors: Ruan Shigui 
Published: December 2010

AbstractIn this paper, we consider the oscillatory behavior of the second order neutral delay differential equationwheret ≥ t0,Tandσare positive constants,a,p, q € C(t0, ∞), R),f ∊ C[R, R]. Some sufficient conditions are established such that the above equation is oscillatory. The obtained oscillation criteria generalize and improve a number of known results about both neutral and delay differential equations.
Blow Analytic Mappings and Functions
Authors: Yoshinaga Etsuo 
Published: December 2010

AbstractLet π: M —> Rn be the blowing-up of Rn at the origin. Then a continuous map-germ f: (Rn — 0,0) —> Rm is called blow analytic if there exists an analytic map-germ such that Then an inverse mapping theorem for blow analytic mappings as a generalization of classical theorem is shown. And the following is shown. Theorem: The analytic family of blow analytic functions with isolated singularities admits an analytic trivialization after blowing-up.
A Note on the Analogue of the Bogomolov Type Theorem on Deformations of CR-Structures
Authors: Akahori Takao , Miyajima Kimio 
Published: December 2010

AbstractLet (M, °T″) be a compact strongly pseudo-convex CR-manifold with trivial canonical line bundle. Then, in [A-M2], a weak version of the Bogomolov type theorem for deformations of CR-structures was shown by an analogy of the Tian- Todorov method. In this paper, we show that: in the very strict sense, there is a counterexample.
Small Sets of k-th Powers
Authors: Ding Ping , Freedman A. R. 
Published: December 2010

AbstractLet k ≥ 2 and q = g(k) — G(k), where g(k) is the smallest possible value of r such that every natural number is the sum of at most r k-th powers and G(k) is the minimal value of r such that every sufficiently large integer is the sum of r k-th powers. For each positive integer r ≥ q, let Then for every ε > 0 and N ≥ N(r, ε), we construct a set A of k-th powers such that |A| ≤ (r(2 + ε)r + l)N1/(k+r) and every nonnegative integer n ≤ N is the sum of k-th powers in A. Some related results are also obtained.
On a Property of Nilpotent Groups
Authors: Dokuchaev Michael 
Published: December 2010

AbstractLet g be an element of a group G and [g, G] = 〈g-1a-1ga | a ∊ G〉. We prove that if G is locally nilpotent then for each g,t ∊ G either g[g, G] = t[t, G] or g[g, G] ∩ t[t, G] = Ø. The converse is true if G is finite.
On The Tails of the Exponential Series
Authors: Yalçin Yildirim C. 
Published: December 2010

AbstractA relation between the zeros of the partial sums and the zeros of the corresponding tails of the Maclaurin series for ez is established. This allows an asymptotic estimation of a quantity which came up in the theory of the Riemann zeta-function. Some new properties of the tails of ez are also provided.
A Note on Epi-Convergence
Authors: Beer Gerald 
Published: December 2010

AbstractLet LSC(X) denote the set of extended real valued lower semicontinuous functions on a metrizable space X. If f, f1, f2, f3,... is a sequence in LSC(X), we say 〈fn〉 is epi-convergent to f provided the sequence of epigraphs 〈epi fn〉 is Kuratowski- Painlevé convergent to epi f. In this note we address the following question: what conditions on f and/or on X are necessary and sufficient for this mode of convergence to force epigraphical convergence with respect to the stronger Hausdorff metric and Vietoris topologies?
Global Hypoellipticity of a Class of Second Order Operators
Authors: Bergamasco Adalberto P. , Zani Sérgio Luís 
Published: December 2010

AbstractWe show that almost all perturbations P — λ, λ € C, of an arbitrary constant coefficient partial differential operator P are globally hypoelliptic on the torus. We also give a characterization of the values λ € C for which the operator is globally hypoelliptic; in particular, we show that the addition of a term of order zero may destroy the property of global hypoellipticity of operators of principal type, contrary to that happens with the usual (local) hypoellipticity.
Parareductive Operators on Banach Spaces
Authors: Drnovšek Roman 
Published: December 2010

AbstractThis note gives a Banach space extension of the Hilbert space result due to P. A. Fillmore (see [3]). In particular, it is shown that the adjoint T* = A — iB of an operator T = A + iB (with A and B hermitian) is a polynomial in T if and only if T* leaves invariant every linear subspace invariant under T, and this is equivalent to the assertion that T* leaves invariant every paraclosed subspace invariant under T.
On Infinite Locally Finite Groups
Authors: Rhemtulla Akbar , Smith Howard 
Published: December 2010

AbstractIf G is a group such that every infinite subset of G contains a commuting pair of elements then G is centre-by-finite. This result is due to B. H. Neumann. From this it can be shown that if G is infinite and such that for every pair X, Y of infinite subsets of G there is some x in X and some y in Y that commute, then G is abelian. It is natural to ask if results of this type would hold with other properties replacing commutativity. It may well be that group axioms are restrictive enough to provide meaningful affirmative results for most of the properties. We prove the following result which is of similar nature.If G is a group such that for each positive integer n and for every n infinite subset X1,...,Xn of G there exist elements xi of Xii = 1,... ,n, such that the subgroup generated by {x1,... ,xn} is finite, then G is locally finite.
Hopf's Ergodic Theorem for Particles with Different Velocities and the "Strong Sweeping out Property"
Authors: Bellow A. , Calderón A. P. , Krengel U. 
Published: December 2010

AbstractIn an earlier paper we provided a counterexample to an old conjecture of Hopf. In this note we show that the "strong sweeping out property" obtains for the Hopf operators (Tt) both when t —> +∞ and when t —> 0+, that is a.e. convergence fails in the worst possible way.
The Class Number Formula of a Real Quadratic Field and an Estimate of the Value of a Unit
Authors: Mitsuhiro T. , Nakahara T. , Uehara T. 
Published: December 2010

AbstractOur aim is to give an arithmetical expression of the class number formula of real quadratic fields. Starting from the classical Dirichlet class number formula, our proof goes along arithmetical lines not depending on any analytical method such as an estimate for
On Traces of Separable Simple Sub Algebras in Matrix Rings
Authors: Nagahara Takasi , Yokota Seiya 
Published: December 2010

AbstractFor the trace map on an irreducible semigroup of n × n matrices over a field, I. N. Herstein presented a theorem in [3] which enables us to limit the nature of matrix groups of a certain kind. However, this is incorrect in general. For the theorem, we shall present a counter example, a revision, and some generalizations to non-irreducible semigroups.
Positive Linear Mappings Between C*-Algebras
Authors: Zhong Yong 
Published: December 2010

AbstractWe prove that a positive unital linear mapping from a von Neumann algebra to a unital C*-algebra is a Jordan homomorphism if it maps invertible selfadjoint elements to invertible elements, and that for any compact Hausdorff space X, all positive unital linear mappings from C(X) into a unital C*-algebra that preserve the invertibility for self-adjoint elements are *-homomorphisms if and only if X is totally disconnected.
An Extension Theorem Concerning Frechet Measures
Authors: Blei Ron C. 
Published: December 2010

AbstractAn F-measure on a Cartesian product of algebras of sets is a scalar-valued function which is a scalar measure independently in each coordinate. It is demonstrated that an F-measure on a product of algebras determines an F-measure on the product of the corresponding σ-algebras if and only if its Fréchet variation is finite. An analogous statement is obtained in a framework of fractional Cartesian products of algebras, and a measurement of p-variation of F-measures, based on Littlewood-type inequalities, is discussed.
Homéomorphismes Uniformes Entre les Sphères Unité des Espaces D'Interpolation
Authors: Daher Mohamad 
Published: December 2010

RésuméSi (A0,A1) est un couple d'interpolation et si A0 est uniformément convexe on montre que pour tous θ1, θ2 ∊ ]0,1 [ il existe un homéomorphisme uniforme entre la sphère unité de (A0,A1)θ1 et la sphère unité de (A0, A1)θ2.
Finite-Dimensional Subspaces of the p-Adic Space ℓ∞
Authors: Perez-Garcia C. , Schikhof Wim H. 
Published: December 2010

AbstractFor finite-dimensional subspaces of ℓ∞ over a non-archimedean valued base field K we study orthocomplementation as related to the Hahn-Banach property and strictness. As a corollary we obtain that, if K is not spherically complete, a closed hyperplane in c0 having the Hahn-Banach property is orthocomplemented (Theorem 2.1, Remark 2).
Semiprime Rings with Hypercentral Derivations
Authors: Lee Tsiu-Kwen 
Published: December 2010

AbstractLetRbe a semiprime ring with a derivationd, λ a left ideal ofRandk, ntwo positive integers. Suppose that[d(xn),xn]k= 0 for allx∊ λ. Then [λ,R]d(R)= 0. That is, there exists a central idempotente∊U, the left Utumi quotient ring ofR, such thatdvanishes identically oneUand λ(l —e) is central in (1 —e)U
Divisor Sums of Generalised Exponential Polynomials
Authors: Everest G. R. , Shparlinski I. E. 
Published: December 2010

AbstractA study is made of sums of reciprocal norms of integral and prime ideal divisors of algebraic integer values of a generalised exponential polynomial. This includes the important special cases of linear recurrence sequences and general sums of S-units. In the case of an integral binary recurrence sequence, similar (but stronger) results were obtained by P. Erdős, P. Kiss and C. Pomerance.
The Division Algorithm in Complex Bases
Authors: Gilbert William J. 
Published: December 2010

AbstractComplex numbers can be represented in positional notation using certain Gaussian integers as bases and digit sets. We describe a long division algorithm to divide one Gaussian integer by another, so that the quotient is a periodic expansion in such a complex base. To divide by the Gaussian integer w in the complex base b, using a digit set D, the remainder must be in the set wT(b,D) ∩ ℤ[i], where T(b,D) is the set of complex numbers with zero integer part in the base. The set T(b,D) tiles the plane, and can be described geometrically as the attractor of an iterated function system of linear maps. It usually has a fractal boundary. The remainder set can be determined algebraically from the cycles in a certain directed graph.
On Self-Injective Perfect Rings
Authors: Herbera Dolors , Shamsuddin Ahmad 
Published: December 2010

AbstractLet R be a left and right perfect right self-injective ring. It is shown that if the radical of R is countably generated as a left ideal then R is quasi-Frobenius. It is also shown that the same conclusion can be drawn if r(A ∩ B) = r(A) + r(B) for all left ideals A and B of R.
Backward Continued Fractions and their Invariant Measures
Authors: Gröchenig Karlheinz , Haas Andrew 
Published: December 2010

AbstractThis paper continues our investigation of backward continued fractions, associated with the generalized Renyi maps on [0,1). We first show that the dynamics of the shift map on a specific class of shift invariant spaces of nonnegative integer sequences exactly models the maps Tu for u € (0,4). In the second part we construct a new family of explicit invariant measures for certain values of the parameter u.
Purely Infinite Simple C*-Crossed Products II
Authors: Jeong JA A. , Kodaka Kazunori , Osaka Hiroyuki 
Published: December 2010

AbstractWe study the pure infiniteness of C* -crossed products by endomorphisms and automorphisms. Let A be a purely infinité simple unital C*-algebra. At first we show that a crossed product A × p N by a corner endomorphism p is purely infinite if it is simple. From this observation we prove that any simple C*-crossed products A ×αZ by an automorphism α is purely infinite. Combining this with the result in [Je] on pure infiniteness of crossed products by finite groups, one sees that if α is an outer action by a countable abelian group G then the simple C*-algebra A ×α G is purely infinite.
Quasi-Duality, Linear Compactness and Morita Duality for Power Series Rings
Authors: Xue Weimin 
Published: December 2010

AbstractAS a generalization of Morita duality, Kraemer introduced the notion of quasi-duality and showed that each left linearly compact ring has a quasi-duality. Let R be an associative ring with identity and R[[x]] the power series ring. We prove that (1) R[[x]] has a quasi-duality if and only if R has a quasi-duality; (2) R[[x]] is left linearly compact if and only if R is left linearly compact and left noetherian; and (3) R[[x]] has a Morita duality if and only if R is left noetherian and has a Morita duality induced by a bimodule RUS such that S is right noetherian.
Uniform Kadec-Klee Lorentz Spaces Lw,1 and Uniformly Concave Functions
Authors: Dilworth S. J. , Lennard C. J. 
Published: December 2010

AbstractWe consider the notion of a uniformly concave function, using it to characterize those Lorentz spaces Lw,1 that have the weak-star uniform Kadec-Klee property as precisely those for which the antiderivative ϕ of w is uniformly concave; building on recent work of Dilworth and Hsu. We also derive a quite general sufficient condition for a twice-differentiable ϕ to be uniformly concave; and explore the extent to which this condition is necessary.
Oscillation and Global Attractivity in a Periodic Delay Equation
Authors: Graef J. R. , Qian C. , Spikes P. W. 
Published: December 2010

AbstractConsider the delay differential equationwhereα(t) andβ(t) are positive, periodic, and continuous functions with periodw> 0, andmis a nonnegative integer. We show that this equation has a positive periodic solutionx*(t) with periodw. We also establish a necessary and sufficient condition for every solution of the equation to oscillate aboutx*(t) and a sufficient condition forx*(t) to be a global attractor of all solutions of the equation.