bluuebunny/crossref_metadata_2025_split huggingface dataset:
On Minimal Sets of Generators for Primitive Roots
Authors: Pappalardi Francesco 
Published: December 2010

AbstractA conjecture of Brown and Zassenhaus (see [2]) states that the first log/? primes generate a primitive root (mod p) for almost all primes p. As a consequence of a Theorem of Burgess and Elliott (see [3]) it is easy to see that the first log2p log log4+∊p primes generate a primitive root (mod p) for almost all primes p. We improve this showing that the first log2p/ log log p primes generate a primitive root (mod p) for almost all primes p.
A Quantitative Estimate on Fixed-Points of Composite Meromorphic Functions
Authors: Zheng Jian-Hua 
Published: December 2010

AbstractLet ƒ(z) be a transcendental meromorphic function of finite order, g(z) a transcendental entire function of finite lower order and let α(z) be a non-constant meromorphic function with T(r, α) = S(r,g). As an extension of the main result of [7], we prove thatwhere J has a positive lower logarithmic density.
Nonexistence of Maxima for Perturbations of Some Inequalities with Critical Growth
Authors: Pruss Alexander R. 
Published: December 2010

AbstractWe study the question of nonexistence of extremal functions for perturbations of some sharp inequalities such as those of Moser-Trudinger (1971) and Chang- Marshall (1985). We shall show that for each critically sharp (in a sense that will be precisely defined) inequality of the formwhere is a collection of measurable functions on a finite measure space (I, μ) and O a nonnegative continuous function on [0, ∞), we have a continuous Ψ on [0, ∞) with 0 ≤ Ψ ≤ Φ, but withnot being attained even if the supremum in (1) is attained. We then apply our results to the Moser-Trudinger and Chang-Marshall inequalities. Our result is to be contrasted with the fact shown by Matheson and Pruss (1994) that if Ψ(t) = o(Φ(t) as t —> ∞ then the supremum in (2) is attained. In the present paper, we also give a converse to that fact.
Nonnegative Linearization and Quadratic Transformation of Askey-Wilson Polynomials
Authors: Szwarc Ryszard 
Published: December 2010

AbstractNonnegative product linearization of the Askey-Wilson polynomials is shown for a wide range of parameters. As a corollary we obtain Rahman's result on the continuous q-Jacobi polynomials with α ≥ β > — 1 and α + β + 1 ≥ 0.
Nearrings of Continuous Functions From Topological Spaces into Topological Nearrings
Authors: Magill K. D. 
Published: December 2010

AbstractLet λ be a map from the additive Euclideann-groupRninto the spaceRof real numbers and define a multiplication * onRnbyv * w = (λ(w))v. Then (Rn, + , *) is a topological nearring if and only if λ is continuous and λ(av) =aλ(v) for everyv€Rnand every a in the range ofλ. For any such mapλand any topological spaceXwe denote byNλ(X, Rn) the nearring of all continuous functions fromXinto (Rn, +, *) where the operations are pointwise. The ideals ofNλ(X, Rn) are investigated in some detail for certain λ and the results obtained are used to prove that two compact Hausdorff spacesXandYare homeomorphic if and only if the nearringsNλ(X, Rn) andNλ(Y, Rn) are isomorphic.
C* -Algebras of Real Rank Zero Whose K0's are not Riesz Groups
Authors: Goodearl K. R. 
Published: December 2010

AbstractExamples are constructed of stably finite, imitai, separable C* -algebras A of real rank zero such that the partially ordered abelian groups K0(A) do not satisfy the Riesz decomposition property. This contrasts with the result of Zhang that projections in C* -algebras of real rank zero satisfy Riesz decomposition. The construction method also produces a stably finite, unital, separable C* -algebra of real rank zero which has the same K-theory as an approximately finite dimensional C*-algebra, but is not itself approximately finite dimensional.
Convex functions on Banach spaces not containing ℓ1
Authors: Borwein Jon , Vanderwerff Jon 
Published: December 2010

AbstractThere is a sizeable class of results precisely relating boundedness, convergence and differentiability properties of continuous convex functions on Banach spaces to whether or not the space contains an isomorphic copy of ℓ1. In this note, we provide constructions showing that the main such results do not extend to natural broader classes of functions.
A Universal Coefficient Decomposition for Subgroups Induced by Submodules of Group Algebras
Authors: Hartl Manfred 
Published: December 2010

AbstractDimension subgroups and Lie dimension subgroups are known to satisfy a ‘universal coefficient decomposition’, i.e. their value with respect to an arbitrary coefficient ring can be described in terms of their values with respect to the ‘universal’ coefficient rings given by the cyclic groups of infinite and prime power order. Here this fact is generalized to much more general types of induced subgroups, notably covering Fox subgroups and relative dimension subgroups with respect to group algebra filtrations induced by arbitrary N-series, as well as certain common generalisations of these which occur in the study of the former. This result relies on an extension of the principal universal coefficient decomposition theorem on polynomial ideals (due to Passi, Parmenter and Seghal), to all additive subgroups of group rings. This is possible by using homological instead of ring theoretical methods.
Monochromatic Homothetic Copies of {1, 1 + s, 1 + s + t}
Authors: Brown Tom C. , Landman Bruce M. , Mishna Marni 
Published: December 2010

AbstractFor positive integers s and t, let f(s, t) denote the smallest positive integer N such that every 2-colouring of [1, N] = {1, 2,...,N} has a monochromatic homothetic copy of {1, 1 + s, 1 + s + t}.We show that f (s, t) = 4(s + t) + 1 whenever s/g and t/g are not congruent to 0 (modulo 4), where g = gcd(s, t). This can be viewed as a generalization of part of van der Waerden’s theorem on arithmetic progressions, since the 3-term arithmetic progressions are the homothetic copies of {1, 1 + 1, 1 + 1 + t}. We also show that f (s, t) = 4(s + t) + 1 in many other cases (for example, whenever s > 2t > 2 and t does not divide s), and that f (s, t) ≤ 4 (s + t) + 1 for all s, t.Thus the set of homothetic copies of {1, 1 + s, 1 + s + t} is a set of triples with a particularly simple Ramsey function (at least for the case of two colours), and one wonders what other “natural” sets of triples, quadruples, etc., have simple (or easily estimated) Ramsey functions.
Theη-Invariants of Cusped Hyperbolic 3-Manifolds
Authors: Meyerhoff Robert , Ouyang Mingqing 
Published: December 2010

AbstractIn this paper, we define theη-invariant for a cusped hyperbolic 3-manifold and discuss some of its applications. Such an invariant detects the chirality of a hyperbolic knot or link and can be used to distinguish many links with homeomorphic complements.
D-Spaces and Resolution
Authors: Boudhraa Zineddine 
Published: December 2010

AbstractA space X is a D-space if, for every neighborhood assignment f there is a closed discrete set D such that f(D) = X. In this paper we give some necessary conditions and some sufficient conditions for a resolution of a topological space to be a D-space. In particular, if a space X is resolved at each x ∊ X into a D-space Yx by continuous mappings fx: X − {x} → Yx, then the resolution is a D-space if and only if {x} × Bd(Yx) is a D-space.
A Uniform L∞ Estimate of the Smoothing Operators Related to Plane Curves
Authors: Guo Kanghui 
Published: December 2010

AbstractIn dealing with the spectral synthesis property for a plane curve with nonzero curvature, a key step is to have a uniform L∞ estimate for some smoothing operators related to the curve. In this paper, we will show that the same L∞ estimate holds true for a plane curve that may have zero curvature.
Approximation of Smooth Maps by Real Algebraic Morphisms
Authors: Kucharz Wojciech , Rusek Kamil 
Published: December 2010

AbstractLet𝔾p,q(𝔽) be the Grassmann space of allq-dimensional𝔽-vector subspaces of𝔽p, where𝔽stands forℝ,ℂorℍ(the quaternions). Here𝔾p,q(𝔽) is regarded as a real algebraic variety. The paper investigates which C∞maps from a nonsingular real algebraic varietyXinto𝔾p,q(𝔽) can be approximated, in theC∞compact-open topology, by real algebraic morphisms.
On the Solvability of a Neumann Boundary Value Problem at Resonance
Authors: Kuo Chung-Cheng 
Published: December 2010

AbstractWe study the existence of solutions of the semilinear equations (1) in which the non-linearity g may grow superlinearly in u in one of directions u → ∞ and u → −∞, and (2) −Δu + g(x, u) = h, in which the nonlinear term g may grow superlinearly in u as |u| → ∞. The purpose of this paper is to obtain solvability theorems for (1) and (2) when the Landesman-Lazer condition does not hold. More precisely, we require that h may satisfy are arbitrarily nonnegative constants, . The proofs are based upon degree theoretic arguments.
Caractérisations Spectrales du Radical et du Socle d’Une Paire de Jordan-Banach
Authors: Maouche Abdelaziz 
Published: December 2010

RésuméIf f and g are two analytic functions from a domain D of the complex plane into respectively the Banach spaces V+ and V−, we prove that is an analytic multivalued function. From this derives the subharmonicity of the functions where ρ denotes the spectral radius. We apply these results to obtain nice caracterizations of the radical and the socle of a Banach Jordan pair, and finally we get an algebraic structural theorem.
Sequences with Translates Containing Many Primes
Authors: Brown Tom , Shiue Peter Jau-Shyong , Yu X.Y. 
Published: December 2010

AbstractGarrison [3], Forman [2], and Abel and Siebert [1] showed that for all positive integers k and N, there exists a positive integer λ such that nk + λ is prime for at least N positive integers n. In other words, there exists λ such that nk + λ represents at least N primes.We give a quantitative version of this result.We show that there exists λ ≤ xk such that nk + λ, 1 ≤ n ≤ x, represents at least primes, as x → ∞. We also give some related results.
Subordinacy Analysis and Absolutely Continuous Spectra for Sturm-Liouville Equations with Two Singular Endpoints
Authors: Clemence Dominic P. 
Published: December 2010

AbstractThe Gilbert-Pearson characterization of the spectrum is established for a generalized Sturm-Liouville equation with two singular endpoints. It is also shown that strong absolute continuity for the one singular endpoint problem guarantees absolute continuity for the two singular endpoint problem. As a consequence, we obtain the result that strong nonsubordinacy, at one singular endpoint, of a particular solution guarantees the nonexistence of subordinate solutions at both singular endpoints.
On Generalized Third Dimension Subgroups
Authors: Tahara Ken-Ichi , Vermani L.R. , Razdan Atul 
Published: December 2010

AbstractLet G be any group, and H be a normal subgroup of G. Then M. Hartl identified the subgroup of G. In this note we give an independent proof of the result of Hartl, and we identify two subgroups of G for some subgroup K of G containing [H, G].
Minimal Pencil Realizations of Rational Matrix Functions with Symmetries
Authors: Krupnik Ilya , Lancaster Peter 
Published: December 2010

AbstractA theory of minimal realizations of rational matrix functionsW(λ) in the “pencil” formW(λ) =C(λA1−A2)−1Bis developed. In particular, properties of the pencil λA1−A2are discussed whenW(λ) is hermitian on the real line, and whenW(λ) is hermitian on the unit circle.
Mazur Intersection Properties for Compact and Weakly Compact Convex Sets
Authors: Vanderwerff Jon 
Published: December 2010

AbstractVarious authors have studied when a Banach space can be renormed so that every weakly compact convex, or less restrictively every compact convex set is an intersection of balls. We first observe that each Banach space can be renormed so that every weakly compact convex set is an intersection of balls, and then we introduce and study properties that are slightly stronger than the preceding two properties respectively.
New Characterizations of the Reflexivity in Terms of the Set of Norm Attaining Functionals
Authors: Acosta Mariá D. , Galán Manuel Ruiz 
Published: December 2010

AbstractAs a consequence of results due to Bourgain and Stegall, on a separable Banach space whose unit ball is not dentable, the set of norm attaining functionals has empty interior (in the norm topology). First we show that any Banach space can be renormed to fail this property. Then, our main positive result can be stated as follows: if a separable Banach space X is very smooth or its bidual satisfies the w*-Mazur intersection property, then either X is reflexive or the set of norm attaining functionals has empty interior, hence the same result holds if X has the Mazur intersection property and so, if the norm of X is Fréchet differentiable. However, we prove that smoothness is not a sufficient condition for the same conclusion.
Characterizing Continua by Disconnection Properties
Authors: Tymchatyn E. D. , Yang Chang-Cheng 
Published: December 2010

AbstractWe study Hausdorff continua in which every set of certain cardinality contains a subset which disconnects the space. We show that such continua are rimfinite. We give characterizations of this class among metric continua. As an application of our methods, we show that continua in which each countably infinite set disconnects are generalized graphs. This extends a result of Nadler for metric continua.
Normal Invariants of Lens Spaces
Authors: Young Carmen M. 
Published: December 2010

AbstractWe show that normal and stable normal invariants of polarized homotopy equivalences of lens spacesandare determined by certainl-polynomials evaluated on the elementary symmetric functions. Each polynomiallkappears as the homogeneous part of degreekin the Hirzebruch multiplicativeL-sequence. Whenn= 8, the elementary symmetric functions alone determine the relevant normal invariants.
Band-Limited Wavelets with Subexponential Decay
Authors: Dziubański Jacek , Hernández Eugenio 
Published: December 2010

AbstractIt is well known that the compactly supported wavelets cannot belong to the class . This is also true for wavelets with exponential decay. We show that one can construct wavelets in the class that are “almost” of exponential decay and, moreover, they are band-limited. We do this by showing that we can adapt the construction of the Lemarié-Meyer wavelets [LM] that is found in [BSW] so that we obtain band-limited, C∞-wavelets on R that have subexponential decay, that is, for every 0 < ε < 1, there exits Cε > 0 such that . Moreover, all of its derivatives have also subexponential decay. The proof is constructive and uses the Gevrey classes of functions.
Dow’s Principle andQ-Sets
Authors: Brendle Jörg 
Published: December 2010

AbstractAQ-set is a set of reals every subset of which is a relative Gδ. We investigate the combinatorics ofQ-sets and discuss a question of Miller and Zhou on the sizeqof the smallest set of reals which is not aQ-set. We show in particular that various natural lower bounds forqare consistently strictly smaller thanq.
Embedding Coverings in Bundles
Authors: Edmonds Allan L. 
Published: December 2010

AbstractIfV→Xis a vector bundle of fiber dimensionkandY→Xis a finite sheeted covering map of degreed, the implications for the Euler class e(V) inHk(X)ofVimplied by the existence of an embeddingY→Vlifting the covering map are explored. In particular it is proved that dd′e(V) = 0 where d′ is a certain divisor of d – 1, and often d′ = 1.
On the Square of the First Zero of the Bessel Function Jv(z)
Authors: Elbert Árpád , Siafarikas Panayiotis D. 
Published: December 2010

AbstractLet Jv,1 be the smallest (first) positive zero of the Bessel function Jv(z), v > −1, which becomes zero when v approaches −1. Then can be continued analytically to −2 < v < −1, where it takes on negative values. We show that is a convex function of v in the interval −2 < v ≤ 0, as an addition to an old result [Á. Elbert and A. Laforgia, SIAM J. Math. Anal. 15(1984), 206–212], stating this convexity for v > 0. Also the monotonicity properties of the functions are determined. Our approach is based on the series expansion of Bessel function Jv(z) and it turned out to be effective, especially when −2 < v < −1.
On Analytic Functions of Bergman BMO in the Ball
Authors: Kwon E. G. 
Published: December 2010

AbstractLet B = Bn be the open unit ball of Cn with volume measure v, U = B1 and B be the Bloch space on , 1 ≤ α < 1, is defined as the set of holomorphic f : B → C for whichif 0 < α < 1 and , the Hardy space. Our objective of this note is to characterize, in terms of the Bergman distance, those holomorphic f : B → U for which the composition operator defined by , is bounded. Our result has a corollary that characterize the set of analytic functions of bounded mean oscillation with respect to the Bergman metric.
Instabilité de vecteurs propres d’opérateurs linéaires
Authors: Nikolskaia Ludmila 
Published: December 2010

AbstractWe consider some geometric properties of eigenvectors of linear operators on infinite dimensional Hilbert space. It is proved that the property of a family of vectors (xn) to be eigenvectors of a bounded operator T (admissibility property) is very instable with respect to additive and linear perturbations. For instance, (1) for the sequence to be admissible for every admissible (xn) and for a suitable choice of small numbers it is necessary and sufficient that the perturbation sequence be eventually scalar: there exist such that (Theorem 2); (2) for a bounded operator A to transform admissible families (xn) into admissible families (Axn) it is necessary and sufficient that A be left invertible (Theorem 4).
Modular Vector Invariants of Cyclic Permutation Representations
Authors: Smith Larry 
Published: December 2010

AbstractVector invariants of finite groups (see the introduction for an explanation of the terminology) have often been used to illustrate the difficulties of invariant theory in the modular case: see, e.g., [1], [2], [4], [7], [11] and [12]. It is therefore all the more surprising that the unpleasant properties of these invariants may be derived from two unexpected, and remarkable, nice properties: namely for vector permutation invariants of the cyclic group of prime order in characteristic p the image of the transfer homomorphism is a prime ideal, and the quotient algebra is a polynomial algebra on the top Chern classes of the action.
Heat Kernels of Lorentz Cones
Authors: Ding Hongming 
Published: December 2010

AbstractWe obtain an explicit formula for heat kernels of Lorentz cones, a family of classical symmetric cones. By this formula, the heat kernel of a Lorentz cone is expressed by a function of timetand two eigenvalues of an element in the cone. We obtain also upper and lower bounds for the heat kernels of Lorentz cones.
Generating Ideals in Rings of Integer-Valued Polynomials
Authors: Rush David E. 
Published: December 2010

AbstractLetRbe a one-dimensional locally analytically irreducible Noetherian domain with finite residue fields. In this note it is shown that if I is a finitely generated ideal of the ring Int(R) of integer-valued polynomials such that for eachx∈ R the idealis stronglyn-generated,n≥ 2, thenIisn-generated, and some variations of this result.
The Classification of Pin4-Bundles over a 4-Complex
Authors: Weber Christian 
Published: December 2010

AbstractIn this paper we show that the Lie-group Pin4 is isomorphic to the semidirect product (SU2 × SU2) Z/2 where Z/2 operates by flipping the factors. Using this structure theorem we prove a classification theorem for Pin4-bundles over a finite 4-complex X.
Positive Definite Distributions and Subspaces of L_p With Applications to Stable Processes
Authors: Koldobsky Alexander 
Published: December 2010

AbstractWe define embedding of an n-dimensional normed space into L_p, 0 < p < n by extending analytically with respect to p the corresponding property of the classical Lp-spaces. The well-known connection between embeddings into Lp and positive definite functions is extended to the case of negative p by showing that a normed space embeds in L_p if and only if ‖x‖−p is a positive definite distribution. We show that the technique of embedding in L_p can be applied to stable processes in some situations where standard methods do not work. As an example, we prove inequalities of correlation type for the expectations of norms of stable vectors. In particular, for every , where X1,…,Xn and Y1,…,Yn are jointly q-stable symmetric random variables, 0 < q ≤ 2, so that, for some k ∈ ℕ, 1 ≤ k < n, the vectors (X1,…,Xk) and (Xk+1,…,Xn) have the same distributions as (Y1,…,Yk) and (Yk+1,…Yn), respectively, but Yi and Yj are independent for every choice of 1 ≤ i ≤ k, k + 1 ≤ j ≤ n.
Multilinear Proofs for Convolution Estimates for Degenerate Plane Curves
Authors: Bak Jong-Guk 
Published: December 2010

AbstractSuppose that γ ∈ C2 ([0, ∞)) is a real-valued function such that γ(0) = γ′(0) = 0, and γ″(t) ≈ tm−2, for some integer m ≥ 2. Let Γ(t) = (t, γ(t)), t > 0, be a curve in the plane, and let dλ = dt be a measure on this curve. For a function ƒ on R2, letAn elementary proof is given for the optimal Lp-Lq mapping properties of T.
Subdifferential Regularity of Directionally Lipschitzian Functions
Authors: Bounkhel M. , Thibault L. 
Published: December 2010

AbstractFormulas for the Clarke subdifferential are always expressed in the form of inclusion. The equality form in these formulas generally requires the functions to be directionally regular. This paper studies the directional regularity of the general class of extended-real-valued functions that are directionally Lipschitzian. Connections with the concept of subdifferential regularity are also established.
On the Entire Coloring Conjecture
Authors: Sanders Daniel P. , Zhao Yue 
Published: December 2010

AbstractThe Four Color Theorem says that the faces (or vertices) of a plane graph may be colored with four colors. Vizing’s Theorem says that the edges of a graph with maximum degree Δ may be colored with Δ + 1 colors. In 1972, Kronk and Mitchem conjectured that the vertices, edges, and faces of a plane graph may be simultaneously colored with Δ + 4 colors. In this article, we give a simple proof that the conjecture is true if Δ ≥ 6.
Sur l’annulation de certains modules de cohomologie d’André-Quillen
Authors: Soto José J. M. 
Published: December 2010

AbstractSoient A un anneau noethérien, B un anneau régulier essentiellement de type fini sur A. Si la cohomologie d’André-Quillen Hq(A, B, B) = 0 pour tout q ≥ 2 alors A est un anneau régulier.
Maximal Subbundles of Rank 2 Vector Bundles on Projective Curves
Authors: Ballico E. 
Published: December 2010

AbstractLet E be a stable rank 2 vector bundle on a smooth projective curve X and V(E) be the set of all rank 1 subbundles of E with maximal degree. Here we study the varieties (non-emptyness, irreducibility and dimension) of all rank 2 stable vector bundles, E, on X with fixed deg(E) and deg(L), L ∈ V(E) and such that .
Courbes hyperelliptiques à multiplications réelles et une construction de Shih
Authors: Darmon Henri , Mestre Jean-François 
Published: December 2010

RésuméSoient r et p deux nombres premiers distincts, soit , et soit 𝔽 le corps résiduel de K en une place au-dessus de p. Lorsque l’image de dans 𝔽 n’est pas un carré, nous donnons une construction géométrique d’une extension réguliere de K(t) de groupe de Galois PSL2(𝔽). Cette extension correspond à un revêtement de de « signature (r, p, p) » au sens de [3, sec. 6.3], et son existence est prédite par le critère de rigidité de Belyi, Fried, Thompson et Matzat. Sa construction s’obtient en tordant la representation galoisienne associée aux points d’ordre p d’une famille de variétés abéliennes à multiplications réelles par K découverte par Tautz, Top et Verberkmoes [6]. Ces variétés abéliennes sont définies sur un corps quadratique, et sont isogènes à leur conjugué galoisien. Notre construction généralise une méthode de Shih [4], [5], que l’on retrouve quand r = 2 et r = 3.