bluuebunny/crossref_metadata_2025_split huggingface dataset:
Finite Extensions of Valued Fields
Authors: Warner Seth 
Published: December 2010

AbstractA corollary of the main result is that if L is a finite-dimensional Galois extension of a field K and if w is a valuation of L extending a valuation v of K, then K is closed in L if and only if all valuations of L extending v are dependent. A further consequence is a generalization of Ostrowski's criterion for a real-valued valuation to be henselian.
One-Sided L1-Approximation
Authors: Pinkus A. , Totik V. 
Published: December 2010

AbstractLet Un be an n-dimensional subspace of C[0, 1]. We prove that if n ≥ 2, and Un contains a function which is strictly positive on (0, 1), then there exists an f ∈ C[0, 1] which has more than one best one-sided L '-approximation from Un. We also characterize those Un with the property that each f ∈ C[0, 1] has a unique best one-sided L1(w)-approximation from Un with respect to every strictly positive continuous weight function w.
Asymptotic Approximation of an Integral Involving the Normal Distribution*
Authors: McClure J. P. , Wong R. 
Published: December 2010

AbstractAn asymptotic approximation is obtained, as k → ∞, for the integralwhere Φ is the cumulative distribution function for a standard normal random variable, and L is a positive constant. The problem is motivated by a question in statistics, and an outline of'the application is given. Similar methods may be used to approximate other integrals involving the normal distribution.
A Characterization of Projective Metric Spaces
Authors: Frank Rolfdieter 
Published: December 2010

AbstractA projective metric space is a pappian projective space together with a quadric and a certain equivalence relation on the pairs of those points which do not belong to the quadric. This equivalence relation is defined by means of the corresponding quadratic form and satisfies a condition which is a projective version of Miquel's theorem. We characterize the projective metric spaces of dimension at least two over fields of order at least 13.
Cup Products in Sheaf Cohomology
Authors: Jardine J. F. 
Published: December 2010

AbstractLet k be an algebraically closed field, and let l be a prime number not equal to char(k). Let X be a locally fibrant simplicial sheaf on the big étale site for k, and let Y be a k scheme which is cohomologically proper. Then there is a Künneth-type isomorphismwhich is induced by an external cup-product pairing. Reductive algebraic groups G over k are cohomologically proper, by a result of Friedlander and Parshall. The resulting Hopf algebra structure on may be used together with the Lang isomorphism to give a new proof of the theorem of Friedlander-Mislin which avoids characteristic 0 theory. A vanishing criterion is established for the Friedlander-Quillen conjecture.
Dickson Polynomials Over Finite Fields and Complete Mappings
Authors: Mullen Gary L. , Niederreiter Harald 
Published: December 2010

AbstractDickson polynomials over finite fields are familiar examples of permutation polynomials, i.e. of polynomials for which the corresponding polynomial mapping is a permutation of the finite field. We prove that a Dickson polynomial can be a complete mapping polynomial only in some special cases. Complete mapping polynomials are of interest in combinatorics and are defined as polynomials f(x) over a finite field for which both f(x) and f(x) + x are permutation polynomials. Our result also verifies a special case of a conjecture of Chowla and Zassenhaus on permutation polynomials.
Rectangularity Versus Piecewise Rectangularity of Product Spaces
Authors: Tsuda Kôichi 
Published: December 2010

AbstractWe shall discuss relations between rectangularity and piecewise rectangularity of product spaces. In particular, we show that for each positive integer n there exists an n-dimensional, collectionwise normal, non-piecewise rectangular product X × Y which satisfies the inequality dim (X × Y) ≤ dim X + dim Y.
Continuous Images of Compact Semilattices
Authors: Bell Murray , Pelant Jan 
Published: December 2010

AbstractHyadic spaces are the continuous images of a hyperspace of a compact space. We prove that every non-isolated point in a hyadic space is the endpoint of some infinite cardinal subspace. We isolate a more general order-theoretic property of hyerspaces of compact spaces which is also enjoyed by compact semilattices from which the theorem follows.
Hypersurfaces Framées et L'Élément β1, de Toda
Authors: Baker A. , Ray N. , Schwartz L. 
Published: December 2010

RésuméL'objet de cet article est de construire un modèle pour l'élément β1, de Toda (premier élément non nul de la composante p - primaire de l'homotopie stable des sphères qui n'est pas dans l'image du J-homomorphisme, p ≠ 2). Le modèle construit possède en outre la propriété de se plonger, comme variété différentiable, en codimension 1.La construction, basée sur la J-théorie et la chirurgie, exhibe en outre des complexes cellulaires satisfaisant à certaines conditions de plongement, répondant partiellement à un problème posé par le 2e et le 3e auteur.
On Darboux and Mean Value Properties
Authors: Bullen P. S. , Sarkhel D. N. 
Published: December 2010

AbstractIn this paper we extend and greatly generalize, with some new information, the well known results that an approximately continuous function is Darboux, and that a finite approximate derivative has the mean value property and is Darboux. Our theorems on Darboux and mean value properties of derivatives include also those of selective derivatives and I-approximate derivatives.
On Incomplete Character Sums to a Prime-Power Modulus
Authors: Chalk J. H. H. 
Published: December 2010

AbstractLet x denote a primitive character to a prime-power modulus k = pα. The expected estimatefor the incomplete character sum has been established for r = 1 and 2 by D. A. Burgess and recently, he settled the case r = 3 for all primes p < 3, (cf. [2] for the proof and for references). Here, a short proof of the main inequality (Theorem 2) which leads to this result is presented; the argument being based upon my characterization in [3] of the solution-set of a related congruence.
Un Théorème de Transfert Pour la Propriété des Boules
Authors: Deville Robert 
Published: December 2010

AbstractWe show that, if X and Y are Banach spaces such that X has the Mazur's intersection property and such that there exists T, an operator from Y into X so that T* and T** are injective, then there exists on Y an equivalent norm which has the Mazur's intersection property.We deduce from this result and from a result of M. Talagrand that there exists on the long James space J(η) an equivalent norm which has the Mazur's intersection property.
Local Complements to the Hausdorff-Young Theorem for Amalgams
Authors: Torres de Squire Maria L. 
Published: December 2010

AbstractLet G be a locally compact abelian group. An amalgam space (Lp ℓq)(G) (1 ≦ p,q ≦ ∞) is a Banach space of functions which belong locally to LP(G) and globally to ℓq. In this paper we present noninclusion results related to the Hausdorff-Young theorem for amalgams.
Non-Isomorphic Equivalent Azumaya Algebras
Authors: Childs Lindsay N. 
Published: December 2010

AbstractWe explicitly describe an infinite collection of pairs of Azumaya algebras over the ring of integers of real quadratic number fields K which are maximal orders in the usual quaternion algebra over K, hence Brauer equivalent, but are not isomorphic. The result follows from an identification of the groups of norm one units, using the classification of Coxeter.
Oppenheim's Inequality for the Second Immanant
Authors: Merris Russell 
Published: December 2010

AbstractDenote by d2 the immanant afforded by Sn and the character corresponding to the partition (2, 1n-2). If n ≥ 4, the following analog of Oppenheim's inequality is proved:for all n-by-n positive semidefinite hermitian A and B.
On The Number of Groups of Squarefree Order
Authors: Ram Murty M. , Srinivasan S. 
Published: December 2010

AbstractLet G(n) denote the number of non-isomorphic groups of order n. We prove that for squarefree integers n, there is a constant A such thatwhere denotes the Euler function. This upper bound is essentially best possible, apart from the constant A.
Anneaux de Bezout, Hermite et Kaplansky "Universels"
Authors: Carbonne Philippe 
Published: December 2010

RésuméLes anneaux de Kaplansky sont aussi connus sous le nom d'anneaux à diviseurs élémentaires.On construit pour un cardinal donné un anneau de Bezout (resp. Hermite, resp. Kaplansky) tel que tout anneau de même cardinal de la même classe soit un quotient de l'anneau construit.Comme application on montre que l'on a ainsi des contreexemples nouveaux à deux problèmes classiques. On réduit aussi un troisième problème, posé par Kaplansky, sans arriver à le résoudre.
Groupe de Brauer d'une Courbe de Tate
Authors: Touibi C. 
Published: December 2010

RésuméSoient k un corps de séries formelles à corps résiduel fini et X une courbe elliptique définie sur k dont l'invariant modulaire j n'est pas un entier de k. On détermine le groupe de Brauer Br(X) de X, ainsi que le groupe Br(X(q) ) où X(q) est la courbe de Tate définie sur k et associée à un élément q de k* et on établit une dualité entre Br(X) et Pic(X). On examine ensuite le cas où le corps résiduel est quasi-fini.
Some New Product Theorems in Summability
Authors: Parameswaran Mangalam R. 
Published: December 2010

AbstractLet A, B denote sequence-to-sequence matrix methods of summability and A · B the “dot” or iteration product defined by (A · B)x = A(Bx) for all sequences x for which this exists. Some inclusion relations are given involving the methods A, B, A · B, B · A and the method defined by the matrix product AB. We take A, B to be of certain types whose products have not been studied extensively before, e.g. H* · Ck or Ck · H* where H* is quasi-Hausdorff (and hence upper triangular) and Ck is a Cesàro matrix (which is lower triangular). The investigations show also a link between the “Product Property” A ⊂ A · B and the translativity properties of A and B.
Isomorphisms and Automorphisms of Witt Rings
Authors: Leep David , Marshall Murray 
Published: December 2010

AbstractFor a field F, char(F) ≠ 2, let WF denote the Witt ring of quadratic forms of F and let denote the multiplicative group of 1-dimensional forms It follows from a construction of D. K. Harrison that if E, F are fields (both of characteristic ≠ 2) and ρ.WE → WF is a ring isomorphism, then there exists a ring isomorphism which “preserves dimension” in the sense that In this paper, the relationship between ρ and is clarified.
A Remark on Maps Between Classifying Spaces of Compact Lie Groups
Authors: Wojtkowiak Zdzisław 
Published: December 2010

AbstractWe show that two maps between classifying spaces of compact, connected Lie groups are homotopic after inverting the order of the Weyl group of the source if and only if they induce the same maps on rational cohomology. We shall also give some results on maps from classifying spaces of finite groups to classifying spaces of compact Lie groups. Among other things we construct a map from B(Z/2 + Z/2 4- Z/3) into BSO(3) which is not induced by a homomorphism.
Semiderivations and Commutativity in Prime Rings
Authors: Bell H. E. , Martindale W. S. 
Published: December 2010

AbstractA semiderivation of a ring R is an additive mapping f:R → R together with a function g:R → R such that f(xy) = f(x)g(y) + xf(y) = f(x)y + g(x)f(y) and f(g(x) ) = g(f(x)) for all x, y ∊ R. Motivating examples are derivations and mappings of the form x → x — g(x), g a ring endomorphism. A semiderivation f of R is centralizing on an ideal U if [f(u), u] is central for all u ∊ U. For R prime of char. ≠2, U a nonzero ideal of R, and 0 ≠ f a semiderivation of R we prove: (1) if f is centralizing on U then either R is commutative or f is essentially one of the motivating examples, (2) if [f(U), f(U) ] is central then R is commutative.
Asymptotic Properties of Semilinear Equations
Authors: Edelson Allan L. 
Published: December 2010

AbstractWe study the asymptotic properties of positive solutions to the semilinear equation — Δu = f(x, u). Existence and asymptotic estimates are obtained for solutions in exterior domains, as well as entire solutions, for n ≧ 2. The study uses integral operator equations in Rn, and convergence theorems for solutions of Poisson's equation in bounded domains. A consequence of the method is that more precise estimates can be obtained for the growth of solutions at infinity, than have been obtained by other methods. As a special case the results are applied to the generalized Emden-Fowler equation — Δu = p(x)uγ, for γ > 0
On Condensed Noetherian Domains Whose Integral Closures are Discrete Valuation Rings
Authors: Gottlieb Christian 
Published: December 2010

AbstractA condensed domain is an integral domain such that IJ = {xy : x ∊ I, y ∊ J } holds for each pair I, J of ideals. We prove that, under suitable conditions, a subring of a discrete valuation ring is condensed if and only if it contains an element of value 2. We also define the concept strongly condensed.
On Strong Matrix Summability with Respect to a Modulus and Statistical Convergence
Authors: Connor Jeff 
Published: December 2010

AbstractThe definition of strong Cesaro summability with respect to a modulus is extended to a definition of strong A -summability with respect to a modulus when A is a nonnegative regular matrix summability method. It is shown that if a sequence is strongly A-summable with respect to an arbitrary modulus then it is A-statistically convergent and that Astatistical convergence and strong A-summability with respect to a modulus are equivalent on the bounded sequences.
Absolute Retracts and Amalgamation in Certain Congruence Distributive Varieties
Authors: Jipsen Peter , Rose Henry 
Published: December 2010

AbstractIt is shown that if V is a congruence distributive variety whose members have one element subalgebras, then the class of absolute retracts of V is closed under direct products. If V is residually small, then a characterisation of the amalgamation class of V is given.
Approximation of Lp-Contractions by Isometries
Authors: Akcoglu M. A. , Boivin D. 
Published: December 2010

AbstractWe construct a positive linear contraction T of all LP(X, μ)- spaces, 1 ≦ p ≦ ∞, μ(X) = 1 such that T1 = 1, T* 1 = 1 and also Tf > 0 a.e. for all f ≧ 0 a.e., f ≢ 0 but for which there is an f ∊ L∞ such that (Tnf — ∫ fdμ) does not converge in L1-norm. We also show that if T is a contraction of a Hilbert space H, there exists an isometry Q and a contraction R such that ∥Tnx - QnRx∥ —> 0 as n —» ∞ for all x in H
A Note on M-Ideals of Compact operators
Authors: Cho Chong-Man 
Published: December 2010

AbstractSuppose X and Y are closed subspaces of (ΣXn)p and (ΣYn)q (1 < p ≦ q < ∞, dim Xn < ∞, dimYn < ∞), respectively. If K(X, Y), the space of the compact linear operators from X to Y, is dense in L(X, Y), the space of the bounded linear operators from X to Y, in the strong operator topology, then K(X, Y) is an M-ideal in L(X, Y).
Généralisation d'un Lemme de Kummer
Authors: Hoechsmann Klaus 
Published: December 2010

AbstractIf A is a finite abelian group and ZAits integral group ring, consider unitsu∊ ZAwhich have coefficient sum = 1 and are fixed under the involution a —> a-1, a ∊A. For an odd regular primepand ap-groupA, it is shown thatu≡ 1 mod p if only ifu = π(v)v-p, where v is the same kind of unit, and π is the ring endomorphism given bya —> ap, a∊A.
On Coefficients of Artin L Functions as Dirichlet Series
Authors: Funakura Takeo 
Published: December 2010

AbstractThe paper is motivated by a result of Ankeny [1] above Dirichlet L functions in 1952. We generalize this from Dirichlet L functions to Artin L functions of relative abelian extensions, by complementing the ingenious proof of Ankeny's theorem given by Iwasaki [4]. Moreover, we characterize Dirichlet L functions in the class of all Artin L functions in terms of coefficients as Dirichlet series.
Limit Cycles Close to Infinity of Certain Non-Linear Differential Equations
Authors: Guíñez Víctor , Sáez Eduardo , Szántó Iván 
Published: December 2010

AbstractThrough successive radial perturbations of a certain planar Hamiltonian polynomial vector field of degree 2K + 1, we obtain a least K limit cycles containing (2K + 1)2 singularities.
Image Area and the Weighted Subspaces of Hardy Spaces
Authors: Kwon E. G. 
Published: December 2010

AbstractLet Hp,ϕ be the subspace of Hardy space Hp consisting of those f ∊ Hp(Bn) satisfying where ϕ is a positive decreasing differentiable function on [0, 1) with ϕ(1—) = 0. Concerning image area growth, criteria for f to be of Hp,ϕ are considered extending known results for Hp.
The Integrability of Riemann Summable Trigonometric Series
Authors: Bullen P. S. , Mukhopadhyay S. N. 
Published: December 2010

AbstractIt is shown that if a trigonometric series is (R, 3), respectively (R, 4), summable then its (R, 3) sum, respectively (R, 4) sum, is James P3—, respectively P4—, integrable and that such series are Fourier series with respect to these integrals.
A Decomposition Theorem for Positive Superharmonic Functions
Authors: Eriksson-Bique Sirkka-Liisa 
Published: December 2010

AbstractLet X be a harmonic space in the sense of C. Constantinescu and A. Cornea. We show that, for any subset E of X, a positive superharmonic function u on X has a representation u = p + h, where p is the greatest specific minorant of u satisfying . This result is a generalization of a theorem of M. Brelot. We also state some characterizations of extremal superharmonic functions.
Indecomposable Positive Quadratic Forms
Authors: Krüskemper Martin 
Published: December 2010

AbstractLet F be a formally real field. A quadratic form q is called positive if sgnp ≧ 0 for all orderings P of F. A positive q is called decomposable if there exist positive forms q1, q2 such that q = q1⊥q2. Otherwise it is called indecomposable. In a first part we ask for which F there exist indecomposable three dimensional forms over F. We show that such forms exist iff F does not satisfy the property (A) defined in (J. K. Arason, A. Pfister: Zur Théorie der quadratischen Formen über formal reellen Körpern, Math Z. 153, 289-296 (1977)). We use an indecomposable three dimensional form defined by Arason and Pfister to construct indecomposable forms of arbitrary dimension. Then we examine the question for which fields F every positive form over F represents a nonzero sum of squares.
Fuglede's Commutativity Theorem and ∩ R(T - λ)
Authors: Whitley Robert 
Published: December 2010

AbstractFuglede's commutativity theorem for normal operators is an easy consequence of the result that: For T normal, denoting the range of T - λ by R(T - λ), ∩ {R(T - λ) : all λ} = {0}:
Unstable Neutral Fuctional Differential Equations
Authors: Feldstein Alan , Jackiewicz Zdzislaw 
Published: December 2010

AbstractLet y be the solution of the equationwhere A, B, C, λ and η aie complex numbers and It is shown that y has exponential order equal to one if A ≠ 0 and if y is not a polynomial; otherwise, y has exponential order equal to zero. In the latter case, y and all of its derivatives are unbounded on any ray.
A Characterization of the Minkowski Norms
Authors: Anderson C. L. 
Published: December 2010

AbstractIf n > 2 and M(m1,..., xn) is a symmetric norm of the form m(x1, m(x2, m{...)...), where m is a symmetric norm on ℝ2, then m(x, y) = (|x|p + |y|p)1/p for some p ≥ 1 or else m(x, y) = max{|x|,|y|}.
A Characterization of the Quadratic Irrationals
Authors: Brown Tom C. 
Published: December 2010

AbstractLet α be a positive irrational real number, and let fα (n) = [(n + l)α] — [nα] — [α],n > 1, where [x] denotes the greatest integer not exceeding x. It is shown that the sequence fα has a certain 'substitution property' if and only if α is the root of a quadratic equation over the rationals.
Two Consequences of Brunel's Theorem
Authors: Olsen James H. 
Published: December 2010

AbstractIn this note we observe two consequences of Brunei's recent theorem. If T1,..., Tn are majorized by positive power-bounded operators S1,..., Sn of Lp, 1 < p < ∞, for which the ergodic theorem holds, then a multiple sequence ergodic theorem holds for T1,....,Tn. Further, the individual convergence for each Tk can be taken along uniform sequences.
Komlos Limits and Fatou's Lemma in Several Dimensions
Authors: Page Frank H. 
Published: December 2010

AbstractUsing Komlos' Theorem, a sequence decomposition result due to Gaposhkin, and two results due to Artstein, we prove a result concerning the properties of Komlos limits. We then show that a stronger version of Fatou's Lemma in several dimensions can be deduced from Artstein's version of the Lemma. The version of Fatou's Lemma proved here subsumes the most recent version of the Lemma in several dimensions given by Balder.
Conditional Local Nondeterminism and Hausdorff Measure of Level Sets
Authors: Shieh Narn-Rueih 
Published: December 2010

AbstractLet X be a real stochastic process. We localize S. M. Berman's formulation on the local nondeterminism of X to a fixed level. With this localized idea, we prove that, for large classes of Gaussian and Markov X, at each x the level set X(t, w) = x has infinite Hausdorff ϕ - measure (ϕ is certain measure function) for w in a set of positive probability.
K-Uniform Rotundity of Sequence Orlicz Spaces
Authors: Tingfu Wang , Shutao Chen 
Published: December 2010

AbstractThis paper presents a criterion of KUR for sequence Orlicź spaces with Luxemburg's norm. The result also indicates that for any integer k ≥ 1, there exists a k + 1-uniformly rotund Banach space not being k-uniformly rotund.
Approximation Holomorphe Globale Sur L'union de Deux Sous-Espaces Totalement Réels Maximaux de Cn
Authors: Frih El Mostapha 
Published: December 2010

AbstractLet E and F be real subspaces of Cn which contain no non trivial complex subspace of Cn and intersecting only at the origin. We prove in a special case that every continuous function on E ∪ F can be asymptotically approximated on E ∪ F by an entire function.
A New Approach to Operator Spaces
Authors: Effros Edward G. , Ruan Zhong-Jin 
Published: December 2010

AbstractThe authors previously observed that the space of completely bounded maps between two operator spaces can be realized as an operator space. In particular, with the appropriate matricial norms the dual of an operator space V is completely isometric to a linear space of operators. This approach to duality enables one to formulate new analogues of Banach space concepts and results. In particular, there is an operator space version ⊗μ of the Banach space projective tensor product , which satisfies the expected functorial properties. As is the case for Banach spaces, given an operator space V, the functor W |—> V ⊗μ W preserves inclusions if and only if is an injective operator space.
A Note on Minimal Usco Maps
Authors: Verona Andrei , Verona Maria Elena 
Published: December 2010

AbstractWe prove that the composition of a minimal usco map, defined on a Baire space, with a lower semicontinuous function is single valued and usco at each point of a dense G$ subset of its domain. This extends earlier results of Kenderov and Fitzpatrick. As a first consequence, we prove that a Banach space, with the property that there exists a strictly convex, weak* lower semicontinuous function on its dual, is a weak Asplund space. As a second consequence, we present a short proof of the fact that a Banach space with separable dual is an Asplund space.
On an Estimate of the Partial Sums of Vilenkin-Fourier
Authors: Young Wo-Sang 
Published: December 2010

AbstractWe show that the partial sums Snf of the Vilenkin-Fourier series of f ∊ L1 are of exponential type off any set where the Hardy-Littlewood maximal function of f is bounded. It then follows that Snkf(x) = o(log log nk) a.e. for any lacunary sequence {nk}. Our results are Vilenkin-Fourier series analogues of those of R. A. Hunt [1].