bluuebunny/crossref_metadata_2025_split huggingface dataset:
On the Pontrjagin Algebra of a Certain Class of Flags of Foliations
Authors: Carreras F. J. , Naveira A. M. 
Published: December 2010

AbstractLet (𝓜,g) be a Riemannian manifold and let 1, 2, 3 be mutually orthogonal distributions on 𝓜 of dimensions p1, p2,P3 such that p1 + p2 + p3 = dim 𝓜. We assume that , and 1, ⊕ 2 are integrable and that all the geodesies of 𝓜 with initial tangent vector in 2 remain tangent to 2. Then, we prove that Pontk(2, ⊕ 3) = 0 for k > p2 + 2p3, where Pontk(2, ⊕ 3) is the subspace of the Pontrjagin algebra of 2 ⊕ 3 generated by forms of degree k.
Groups Preserving a Class of Bilinear Functions
Authors: Greub W. H. , Malzan J. , Vanstone J. R. 
Published: December 2010

AbstractGiven a finite dimensional Euclidean vector space V, ( , ) and an involution τ of V, one can form the bilinear function ( , )τ defined by (x, y)τ = (τ(x), y), x,y ∊ V.Let O(τ) = {ϕ ∊ GL(V)|(ϕx, ϕy)τ = (x, y)τ}.If t is self-adjoint the structure of O(t) is well known. The purpose of this paper is to detemine the structure of O(t) in the general case. This structure is also determined in the complex and quaternionic case, as well as the case when the condition on t is replaced by τ2 = ∊ι, ∊ ∈ ℝ.
The L-Functions L(s, Symm(r), π)
Authors: Moreno C. J. , Shahidi F. 
Published: December 2010

AbstractThe exact form for the gamma factor for the L-function corresponding to the m-th symmetric power of a cuspidal automorphic representation of PGL(2) is given. This information is used to obtain, via a theorem of Landau, bounds for the eigenvalues of Hecke operators.
Some Classes of θ-Compactness
Authors: Broverman S. 
Published: December 2010

AbstractLet A and A denote the classes of ordinal spaces with the order topology and Σ-product spaces of the two point discrete space respectively. Characterizations are given in terms of ultrafiIters of clopen sets of those O-dimensional Hausdorff topological spaces that can be embedded homeomorphically as a closed subspace of a topological product of either spaces from the class Λ or the class Δ. Both classes consist of spaces that are ω0-bounded. An example is given of a O-dimensional Hausdorff ω0-bounded space that cannot be homeomorphically embedded as a closed subset of a product of spaces from either Λ or Δ, answering a question of R. G. Woods.
On Characterization of Hypersurfaces of Degrees 2 and 3 in the Complex Projective Space
Authors: Szurek Michal 
Published: December 2010

RésuméLe but de cette note est de proposer une caractérisation des espaces projectifs complexes, des hyperquadriques et des hypersurfaces du troisième degré dans Pnc à l'aide de leurs points d'intersection avec l'ensemble des zéros d'une section d'un fibre positif donné sur la variété ambiante. Ceci généralise et complète ainsi certains résultats présentés par Badescu et Itoh.
Semi-Groups in L∞ And Local Ergodic Theorem
Authors: R. Emilion  
Published: December 2010

AbstractWe show that any W*-continuous semi-group in L∞ is L1-norm continuous. As an application we prove the n-dimensional local ergodic theorem in L∞. We also note that any bounded additive process in L∞ is absolutely continuous.For n = 1 this local theorem improves those of R. Sato [14] and D. Feyel [6] and for n ≥ 1 it generalizes M. Lin's ones which hold for positive operators [12].
Even Covering Properties and Somewhat Normal Spaces
Authors: Künzi Hans-Peter , Fletcher Peter 
Published: December 2010

AbstractA topological space X is said to be somewhat normal provided that for each open cover is a normal cover of X. We show that a completely regular somewhat normal space need not be normal, thereby answering a question of W. M. Fleischman. We note that a collectionwise normal somewhat normal space need not be almost 2-fully normal, as had previously been asserted, and that neither the perfect image nor the perfect preimage of a somewhat normal space has to be somewhat normal.
Uniqueness of Subfields
Authors: Deveney James K. , Mordeson John N. 
Published: December 2010

AbstractLet L be a finitely generated field extension of a field K. The order of inseparability of L/K is the minimum of {n|[L:S] = pn where S is a separable extension of K}. If V is a subfield of L/K, then its order of inseparability is less than or equal to that of L/K. This paper examines the question of when there are unique minimal subfields of order of inseparability n — j, 0 ≤ j ≤ n.
On the Distance Between Consecutive Divisors of an Integer
Authors: Koninck Jean-Marie de , Ivić Aleksandar 
Published: December 2010

AbstractLet ω(n) denote the number of distinct prime divisors of a positive integer n. Then we define and where are primes and r ≥ 2. Similarly denote by the number of divisors of n and let be defined by where are the divisors of n. We prove that there exists constants A and B such that and
Algebras with Transitive Automorphism Groups
Authors: Sweet L. G. , MacDougall J. A. 
Published: December 2010

AbstractLet A be a finite dimensional algebra (not necessarily associative) over a field, whose automorphism group acts transitively. It is shown that K = GF(2) and A is a Kostrikin algebra. The automorphism group is determined to be a semi-direct product of two cyclic groups. The number of such algebras is also calculated.
On Rank One Commutators and Triangular Representations
Authors: Ma Tsoy-Wo 
Published: December 2010

AbstractStarting with the extension of Lomonosov's Lemma by Tychonoff fixed point theorem, a result of Daughtry and Kim — Pearcy-Shields on rank-one commutators is extended to the context of locally convex spaces. Non-zero diagonal coefficients, eigenvalues and simultaneous triangular representations of compact operators on locally convex spaces are studied.
Goldie Dimension and Chain Conditions for Modular Lattices with Finite Group Actions
Authors: Grzeszczuk Piotr , Puczyłowski Edmund R. 
Published: December 2010

AbstractA relation between Goldie dimensions of a modular lattice L and its sublattice LG of fixed points under a finite group G of automorphisms of L is obtained. The method used also gives a relation between ACC (DCC) for L and for LG. The results obtained are applied to rings and modules.
Free Subgroups and the Residual Nilpotence of the Group of Units of Modular and p-Adic Group Rings
Authors: Gonçalves Jairo Zacarias 
Published: December 2010

AbstractLet G be a group, let RG be the group ring of the group G over the unital commutative ring R and let U(RG) be its group of units. Conditions which imply that U(RG) contains no free noncyclic group are studied, when R is a field of characteristic p ≠ 0, not algebraic over its prime field, and G is a solvable-by-finite group without p-elements. We also consider the case R = ℤp, the ring of p-adic integers and G torsionby- nilpotent torsion free group. Finally, the residual nilpotence of U(ℤpG) is investigated.
The Herzog-Schönheim Conjecture for Finite Nilpotent Groups
Authors: Berger Marc A. , Felzenbaum Alexander , Fraenkel Aviezri 
Published: December 2010

AbstractThe purpose of this note is to prove the Herzog-Schônheim [3] conjecture for finite nilpotent groups. This conjecture states that any nontrivial partition of a group into cosets must contain two cosets of the same index (Corollary IV below). See Porubský [4, Section 8] for a perspective on coset partitions.
The Integration of Exact Peano Derivatives
Authors: Cross G. E. 
Published: December 2010

AbstractIt is well known that the Riemann-complete integral (or equivalently the Perron integral) integrates an everywhere finite ordinary first derivative (which may be thought of as a Peano derivative of order one). It is also known that the Cesàro-Perron integral of order(n- 1) integrates an everywhere finite Peano derivative of ordern.The present work concerns itself with necessary and sufficient conditions for the Riemann-complete integrability of an exact Peano derivative of ordern.It is shown that when the integral exists, it can be expressed as the ‘Henstock' limit of the sum of a particular kind of interval function. All functions considered will be real valued.
Note on Continuous and Purely Finitely Additive Set Functions
Authors: Siebe Wilfried 
Published: December 2010

AbstractThe Sobczyk-Hammer respectively Yosida-Hewitt decomposition ([17], [19]) generates the class of continuous respectively purely finitely additive charges. In this paper, attention is limited to hereditable properties for these classes. It is proved that the property of continuity is preserved with respect to extensions and that if all extensions of a charge to a charge on a given field are continuous, then the original charge is continuous. An analogous heredity theorem for purely finite additivity holds true in the monogenic case.
Probability Density Function of the Product and Quotient of Two Correlated Exponential Random Variables
Authors: Malik Henrick J. , Roger Trudel  
Published: December 2010

AbstractThis article deals with the distributions of the product and the quotient of two correlated exponential random variables. We consider here three types of bivariate exponential distributions: Marshall-Olkin's bivariate exponential distribution, Gumbel's Type I bivariate exponential distribution, and Gumbel's Type II bivariate exponential distribution.
Sur Une Representation Explicite des Solutions Optimales D'un Programme Lineaire
Authors: Bilodeau Martin 
Published: December 2010

AbstractThis paper gives a sharper explicit representation of the set of optimal solutions for a class of linear programs than those obtained by A. Ben-Israel, A. Charnes and S. Zlobec since 1968. The representation is used to determine bounds on the coefficients of the objective function that produce the same set of optimal solutions (sensitivity analysis).
Integral Group Rings Without Proper Units
Authors: Hoechsmann K. , Sehgal S.K. 
Published: December 2010

AbstractIf A is an elementary abelian ρ-group and C one of its cyclic subgroups, the integral group rings ZA contains, of course, the ring ZC. It will be shown below, for A of rank 2 and ρ a regular prime, that every unit of ZA is a product of units of ZC, as C ranges over all cyclic subgroups.
Some Remarks on Artin's Conjecture
Authors: Ram Murty M. , Srinivasan S. 
Published: December 2010

AbstractIt is a classical conjecture of E. Artin that any integer a > 1 which is not a perfect square generates the co-prime residue classes (mod ρ) for infinitely many primes ρ. Let E be the set of a > 1, a not a perfect square, for which Artin's conjecture is false. Set E(x) = card(e ∊ E: e ≤ x). We prove that E(x) = 0(log6 x) and that the number of prime numbers in E is at most 6.
On Weighted Geodesics in Groups
Authors: Lipschutz Seymour 
Published: December 2010

AbstractA word W in a group G is a geodesic (weighted geodesic) if W has minimum length (minimum weight with respect to a generator weight function α) among all words equal to W. For finitely generated groups, the word problem is equivalent to the geodesic problem. We prove: (i) There exists a group G with solvable word problem, but unsolvable geodesic problem, (ii) There exists a group G with a solvable weighted geodesic problem with respect to one weight function α1, but unsolvable with respect to a second weight function α2. (iii) The (ordinary) geodesic problem and the free-product geodesic problem are independent.
On the Semigroup of Probability Measures of a Locally Compact Semigroup
Authors: Wong James C.S. 
Published: December 2010

AbstractWe show that a locally compact semigroup S is topological left amenable iff a certain space of left uniformly continuous functions on the convolution semigroup of probability measures M0(S) on S is left amenable or equivalently iff the convolution semigroup M0(S) has the fixed point property for uniformly continuous affine actions on compact convex sets.
Separating Splitting Tilting Modules and Hereditary Algebras
Authors: Assem Ibrahim 
Published: December 2010

AbstractLet A be a finite-dimensional algebra over an algebraically closed field. By module is meant a finitely generated right module. A module T^ is called a tilting module if and there exists an exact sequence 0 → A^ → T' → T" → 0 with T'. T" direct sums of summands of T. Let B = End T^·T^ is called separating (respectively, splitting) if every indecomposable A-module M (respectively, B-module N) is such that either Hom^(T,M) = 0 or (respectively, N ⊗ T = 0 or . We prove that A is hereditary provided the quiver of A has no oriented cycles and every separating tilting module is splitting.
On the Ergodic Hilbert Transform for Operators In Lp, 1 < p < ∞
Authors: Sato Ryotaro 
Published: December 2010

AbstractIn this paper the ergodic Hilbert transform is investigated at the operator theoretic level. Let T be an invertible positive operator on Lp = Lp(X, , μ) for some fixed p, 1 < p < ∞, such that sup{||Tn||p: — ∞ < n < ∞} < ∞. It is proved that the limitexists almost everywhere and in the strong operator topology, where the prime denotes that the term with zero denominator is omitted. Related results are also proved.
Units in Integral Group Rings of Some Metacyclic Groups
Authors: Allen P. J. , Hobby C. 
Published: December 2010

AbstractLet p be odd prime and suppose that G = 〈a, b〉 where ap-1 = bp = 1, a-1 ba = br, and r is a generator of the multiplicative group of integers mod p. An explicit characterization of the group of normalized units V of the group ring ZG is given in terms of a subgroup of GL(p - 1, Z). This characterization is used to exhibit a normal complement for G in V.
Mixed Groups of Finite Nilstufe
Authors: Wilson George V. 
Published: December 2010

AbstractThis paper constructs a class of examples to show that for torsion-free groups H with finite nilstufe v(H) = n < ∞ there can be divisible torsion groups D with v(H ⊕ D) - n + k for all k ≤ n + 1. This answers a question of Feigelstock. The construction is based on a proposition which bounds v(H ⊕ D) in terms of v(H) and rank (D).
On Knopp's Inequality for Convex Functions
Authors: Pečarić J. E. , Beesack P. R. 
Published: December 2010

AbstractKnopp's inequality for convex functions ϕ on an interval I = [m,M] states thatfor an explicit functional H, and all integrable g: [0, 1] → I. In this paper we give results of this kind in which the integral operator, ∫, is replaced by a general isotonic linear functional.
Weierstrass Points on Rational Nodal Curves of Genus 3
Authors: Lax R. F. , Widland Carl 
Published: December 2010

AbstractWe determine, except for one unsettled case, which combinations of Weierstrass weights can occur on irreducible rational nodal curves of arithmetic genus three. It is shown that the number of nonsingular Weierstrass points on such curves can be any integer between 0 and 6, except 1.
Sums of Squares Formulae With Integer Coefficients
Authors: Yiu Paul Y. H. 
Published: December 2010

AbstractHidden behind a sums of squares formula are other such formulae not obtainable by restriction. This drastically simplifies the combinatorics involved in the existence problem of sums of squares formulae, and leads to a proof that the product of two sums of 16 squares cannot be rewritten as a sum of 28 squares, if only integer coefficients are permitted. We also construct all [10, 10, 16] formulae.
A Decomposition Theorem for Complex Nilmanifolds
Authors: Loeb Jean-Jacques , Oeljeklaus Karl , Richthofer Wolfgang 
Published: December 2010

AbstractA complex nilmanifold X is isomorphic to a product X ⋍ ℂp x N/┌, where N is a simply connected nilpotent complex Lie group and ┌ is a discrete subgroup of N not contained in a proper connected complex subgroup of N. The pair (N, ┌) is uniquely determined up to holomorphic group isomorphisms.
The Spectrum of Weighted Mean Operators
Authors: Rhoades B. E. 
Published: December 2010

AbstractRecently J. B. Reade determined the spectrum of C, the Cesaro matrix of order 1, considered as an operator on c0, the space of null sequences. Previously F. P. A. Cass and the author had determined the spectra for a large class of weighted mean operators on c, the space of convergent sequences. Subsequently the author determined the fine spectra of these operators over c. This paper examines the spectra and fine spectra of weighted mean operators on c0, obtaining the result of Reade as a special case.
Uniform Mazur's Intersection Property of Balls
Authors: Whitfield J. H. M. , Zizler V. 
Published: December 2010

AbstractWe give a dual characterization of the following uniformization of the Mazur's intersection property of balls in a Banach space X: for every ∊ > 0 there is a K > 0 such that whenever a closed convex set C ⊂ X and a point p ∊ X are such that diam C ≤ 1/∊ and dist(p, C) ≤ ∊, then there is a closed ball B of radius ≤ K with B ⊃ C and dist(p,B) ≥ ∊/2.
Borel Sets in Metric Spaces With Small Separable Subsets
Authors: Daniels P. , Gruenhage G. 
Published: December 2010

AbstractLet X be a metric space such that every separable subspace of X has size less than the continuum. We answer a question of D. H. Fremlin by showing that MA + ┐CH does not necessarily imply that every subset of X is analytic.
On Hloosterman Sums with Oscillating Coefficients
Authors: Hajela D. , Pollington A. , B. Smith  
Published: December 2010

AbstractAn estimate for Kloosterman sums with oscillating coefficients is presented. Precisely we show: for any ϵ > 0 and a, b positive integers with (a, b) — 1 we have, Similar techniques may be used to estimate other Kloosterman sums with oscillating coefficients which are not smooth.
Generalization of a Result of E. Lucas
Authors: Macleod R. A. 
Published: December 2010

AbstractA well-known result of E. Lucas enables one to obtain the residue modulo p of in terms of the base-p digits of M and N. Using a recent result of P. W. Haggard and J. O. Kiltenen, a proof of N. J. Fine has been adapted to yield the corresponding residue modulo pr.
Some Results in the Connective K-Theory of Lie Groups
Authors: Magalhães L. 
Published: December 2010

AbstractIn this paper we give a description of:(1) the Hopf algebra structure of k*(G; L) when G is a compact, connected Lie group and L is a ring of type Q(P) so that H*(G; L) is torsion free;(2) the algebra structure of k*(G2; L) for L = Z2 or Z.
Comparaison de la Méthode des Constantes de Lyapunov et de la Bifurcation de Hopf*
Authors: Bonin Guy , Josée Legault  
Published: December 2010

RésuméDans cet article, nous démontrons l'équivalence théorique de la méthode des constantes de Lyapunov et de la bifurcation de Hopf, pour l'étude de l'apparition ou de la disparition de cycles limites dans un système d'équations différentielles ordinaires.
A Partial Generalization of Mann's Theorem Concerning Orthogonal Latin Squares
Authors: Parker E. T. , Somer Lawrence 
Published: December 2010

AbstractLetn = 4t+- 2, where the integert ≧ 2. A necessary condition is given for a particular Latin squareLof ordernto have a complete set ofn — 2mutually orthogonal Latin squares, each orthogonal toL.This condition extends constraints due to Mann concerning the existence of a Latin square orthogonal to a given Latin square.
Strong Morita equivalence for the Denjoy C*-Algebras
Authors: Putnam Ian F. 
Published: December 2010

AbstractThe C*-algebras associated with irrational rotations of the circle were classified up to strong Morita equivalence by M. A. Rieffel. As a corollary, he gave a complete classification of the C*-algebras arising from irrational or Kronecker flows on the 2-torus up to *-isomorphism. Here, we extend the result to the socalled Denjoy homeomorphisms. Specifically, we give a necessary and sufficient condition for the strong Morita equivalence of two C*-algebras arising from homeomorphisms of the circle without periodic points. As a corollary, we show that two C*-algebras arising from flows on the 2-torus obtained from such homeomorphisms by the “flow under constant function” construction are *-isomorphic if and only if the flows themselves are topologically conjugate.
A Note on the Dubois-Efroymson Dimension Theorem
Authors: Kucharz Wojciech 
Published: December 2010

AbstractLet X ⊂ Rnn be an irreducible nonsingular algebraic set and let Z be an algebraic subset of X with dim Z ≦ dim X — 2. In this paper it is shown that there exists an irreducible algebraic subset Y of X satisfying the following conditions: dim Y = dim X — 1, Z ⊂ Y and that the ideal of regular functions on X vanishing on Y is principal.
Norm Inequalities for Generators of Analytic Semigroups and Cosine Operator Functions
Authors: Siddiqi Jamil A. , Elkoutri Abdelkader 
Published: December 2010

AbstractWe prove that if A is the infinitesimal generator of a bounded analytic semigroup in a sector {z ∊ C : |arg z| ≦ (απ)/2} of bounded linear operators on a Banach space, then the following inequalities hold:for any x ∊ D(An) and for any 0 < β < α. This result helps us to answer in affirmative a question raised by M. W. Certain and T. G. Kurtz [3]. Similar inequalities are proved for cosine operator funtions.
On the Deterministic and Asymptotic σ-Algebras of a Markov Operator
Authors: Krengel Ulrich , Lin Michael 
Published: December 2010

AbstractLet P be a Markov operator on L∞(X, Σ, m) which does
not disappear (i.e., P1A ≡ 0 => 1A ≡ 0 ) . We study the relationship
between the σ-algebras(the deterministicσ-algebra), and the asymptoticσ-algebraWhen m is a σ-finite invariant measure, measurable iff p*npnf = f, and also iff Pnf has the same distribution as f . The case of a convolution operator on a locally compact group is considered.
A Note on the Rn,k Property for L1 (μ E)
Authors: Rao T. S. S. R. K. 
Published: December 2010

AbstractIn this paper we show that for a Banach space X having the Rn,k property and such that X is constrained in a dual space having the Radon-Nikodým property, the space of X-valued Bochner integrable functions has the Rn,k property.
Isomorphic Group Rings Over Domains
Authors: Adjaero Isabelle , Spiegel Eugene 
Published: December 2010

AbstractLet R and S be rings, G and H abelian groups, and RG and SH the goup rings of G and H over R and S respectively. In this note we consider what relations must hold between G and H or between R and S if the group rings RG and SH are isomorphic. For example, it is shown that if R and S are integral domains of characteristic zero, G and H torsion abelian groups such that if G has an element of order p then p is not invertible in R, and RG and SH are isomorphic, then the rings R and 5 are isomorphic and the groups G and H are isomorphic.
Fixed Point Theorems for Lipspchitzian Semigroups
Authors: ishihara Hajime 
Published: December 2010

AbstractLet U be a nonempty subset of a Banach space, S a left reversible semitopological semigroup, a continuous representation of S as lipschitzian mappings on U into itself, that is for each s ∊ S, there exists ks > 0 such that for x, y ∊ U. We first show that if there exists a closed subset C of U such that then S with lim sups has a common fixed point in a Hilbert space. Next, we prove that the theorem is valid in a Banach space E if lim sups
On the Distribution of the Sequence {nd*(n)}
Authors: Abbott H. L. , Subbarao M. V. 
Published: December 2010

AbstractLet d*(n) denote the number of unitary divisors of the positive integer n. For x > 1, let B(x) denote the number of integers n for which nd*(n) ≦ x. Balasubramanian and Ramachandra proved that there exists a positive constant β such that . In this note we give an explicit expression for β as an infinite product, namely where the product is over all primes p.
The Conjugate Function on the Finite Dimensional Torus
Authors: Asmar Nakhle 
Published: December 2010

AbstractWe consider the group Ta, its group of characters Za, and an arbitrary order P on Za. For x ∊ Za, let sgnpx be 1, - 1 , or 0 according as x € P\{0}, x € (-P)\{0}, or X = 0. For f in Lp(Ta), 1 < p < ∞, it is known that there is a function in Lp(Ta) such that for all X in Za. Summability methods for are also available. In this paper, we obtain summability methods for that apply for in L1(Ta), and we show how various properties of can be derived from our construction.