bluuebunny/crossref_metadata_2025_split huggingface dataset:
Chinburg's Third Invariant in the Factorisability Defect Class Group
Authors: Holland D. 
Published: December 2010

AbstractChinburg's third invariant Ω(N/K, 3) ∊ C1(Z[Γ]) of a Galois extensionN/Kof number fields with group Γ is closely related to the Galois structure of unit groups and ideal class groups, and deep unsolved problems such as Stark's conjecture.We give a formula for Ω(N/K, 3) modulo D(ZΓ) in the factorisability defect class group, reminiscent of analytic class number formulas. Specialising to the case of an absolutely abelian, real fieldN, we give a natural conjecture in terms of Hecke factorisations which implies the vanishing of the invariant in the defect class group.We prove this conjecture whenNhas prime-power conductor using Euler systems of cyclotomic units, Ramachandra units and Hecke factorisation. This supports a general conjecture of Chinburg, which in our situation specialises to the statement that Ω(N/K, 3) = 0 for such extensions.We also develop a slightly extended version of Euler systems of units for general abelian extensions, which will be applied to abelian extensions of imaginary quadratic fields elsewhere
On the Canonical Module of A 0-Dimensional Scheme
Authors: Kreuzer Martin 
Published: December 2010

AbstractThe main topic of this paper is to give characterizations of geometric properties of O-dimensional subschemes in terms of the algebraic structure of the canonical module of their projective coordinate ring. We characterize Cayley- Bacharach, (higher order) uniform position, linearly and higher order general position properties, and derive inequalities for the Hilbert functions of such schemes. Finally we relate the structure of the canonical module to properties of the minimal free resolution of X.
Two Contrasting Properties of Solutions for One-Dimensional Stochastic Partial Differential Equations
Authors: Shiga Tokuzo 
Published: December 2010

AbstractThe paper is concerned with the comparison of two solutions for a one-dimensional stochastic partial differential equation. Noting that support compactness of solutions propagates with passage of time, we define the SCP property and show that the SCP property and the strong positivity are two contrasting properties of solutions for one-dimensional SPDEs, which are due to degeneracy of the noise-term coefficient
Degree of Approximation by Rational Functions with Prescribed Numerator Degree
Authors: Leviatan D. , Lubinsky D. S. 
Published: December 2010

AbstractWe prove a Jackson type theorem for rational functions with prescribed numerator degree: For continuous functions f: [—1,1] —> ℝ with ℓ sign changes in (—1,1), there exists a real rational function Rℓ,n(x) with numerator degree ℓ and denominator degree at most n, that changes sign exactly where f does, and such thatHere C is independent of f, n and ℓ, and ωφ is the Ditzian-Totik modulus of continuity. For special functions such as f(x) = sign(x)|x|α we consider improvements of the Jackson rate.
On Direct Sums of Injective Modules and Chain Conditions
Authors: Page Stanley S. , Zhou Yiqiang 
Published: December 2010

AbstractLet R be a ring and M a right R-module. Let σ[M] be the full subcategory of Mod-R subgenerated by M. An M-natural class 𝒦 is a subclass of σ[M] closed under submodules, direct sums, isomorphic copies, and M-injective hulls. We present some equivalent conditions each of which describes when σ has the property that direct sums of (M-)injective modules in σ are (M-)injective. Specializing to particular M, and/or special subclasses we obtain many new results and known results as corollaries.
The Extensions of an Invariant Mean and the Set LIM ∽ TLIM
Authors: Miao Tianxuan 
Published: December 2010

AbstractLet with . If G is a nondiscrete locally compact group which is amenable as a discrete group and m ∈ LIM(CB(G)), then we can embed into the set of all extensions of m to left invariant means on L∞(G) which are mutually singular to every element of TLIM(L∞(G)), where LIM(S) and TLIM(S) are the sets of left invariant means and topologically left invariant means on S with S = CB(G) or L∞(G). It follows that the cardinalities of LIM(L∞(G)) ̴ TLIM(L∞(G)) and LIM(L∞(G)) are equal. Note that which contains is a very big set. We also embed into the set of all left invariant means on CB(G) which are mutually singular to every element of TLIM(CB(G)) for G = G1 ⨯ G2, where G1 is nondiscrete, non–compact, σ–compact and amenable as a discrete group and G2 is any amenable locally compact group. The extension of any left invariant mean on UCB(G) to CB(G) is discussed. We also provide an answer to a problem raised by Rosenblatt.
Reduction of Exponential Rank in Direct Limits of C*-Algebras
Authors: Christopher Phillips N. 
Published: December 2010

AbstractWe prove the following result. Let A be a direct limit of direct sums of
C*-algebras of the form C(X) ⊗ Mn, with the spaces X being compact metric. Suppose that there is a finite upper bound on the dimensions of the spaces involved, and suppose that A is simple. Then the C* exponential rank of A is at most 1 + ε, that is, every element of the identity component of the unitary group of A is a limit of exponentials. This is true regardless of whether the real rank of A is 0 or 1.
On Complex Homogeneous Spaces with Top Homology in Codimension Two
Authors: Akhiezer D. N. , Gilligan B. 
Published: December 2010

AbstractDefine dx to be the codimension of the top nonvanishing homology
group of the manifold X with coefficients in 2. We investigate homogeneous spaces X := G/H, where G is a connected complex Lie group and H is a closed complex subgroup for which dx = 1,2 and O(X) ≠ ℂ. There exists a fibration π: G/H → G/U such that G/U is holomorphically separable and π*(O(G/U)) = O(G/H), see [11]. We prove the following. If dx = 1, then F := U/H is compact and connected and Y :=G/U is an affine cone with its vertex removed. If dx = 2, then either F is connected with dF = 1 and Y is an affine cone with its vertex removed, or F is compact and connected and dy = 2, where Y is ℂ, the affine quadric Q2, ℙ2 — Q (with Q a quadric curve) or a homogeneous holomorphic * -bundle over an affine cone minus its vertex which is itself an algebraic principal bundle or which admits a two-to-one covering that is.
On the Attracting Orbit of a Non-Linear Transformation Arising From Renormalization Of Hierarchically Interacting Diffusions Part I: The Compact Case
Authors: Baillon J. B. , Clément PH. , Greven A. , Hollander F. Den 
Published: December 2010

AbstractThis paper analyzes the n-fold composition of a certain non-linear integral operator acting on a class of functions on [0,1 ]. The attracting orbit is identified and various properties of convergence to this orbit are derived. The results imply that the space-time scaling limit of a certain infinite system of interacting diffusions has universal behavior independent of model parameters.
Densities of Ultraproducts of Boolean Algebras
Authors: Koppelberg Sabine , Shelah Saharon 
Published: December 2010

AbstractWe answer three problems by J. D. Monk on cardinal invariants of Boolean algebras. Two of these are whether taking the algebraic density πA resp. the topological density cL4 of a Boolean algebra A commutes with formation of ultraproducts; the third one compares the number of endomorphisms and of ideals of a Boolean algebra.
Addition Theorems and Binary Expansions
Authors: Borwein Jonathan M. , Girgensohn Roland 
Published: December 2010

AbstractLet an interval I ⊂ ℝ and subsets D0, D1 ⊂ I with D0 ∪ D1 = I and D0 ∩ D1 = Ø be given, as well as functions r0: D0 → I, r1: D1 → I. We investigate the system (S) of two functional equations for an unknown function f: I → [0, 1]: We derive conditions for the existence, continuity and monotonicity of a solution. It turns out that the binary expansion of a solution can be computed in a simple recursive way. This recursion is algebraic for, e.g., inverse trigonometric functions, but also for the elliptic integral of the first kind. Moreover, we use (S) to construct two kinds of peculiar functions: surjective functions whose intervals of constancy are residual in I, and strictly increasing functions whose derivative is 0 almost everywhere.
Elementary Chains of Invariant Subspaces of a Banach Space
Authors: Clauss Jon M. 
Published: December 2010

AbstractWe will generalize Ringrose's notion of a simple chain of closed invariant subspaces of a compact operator acting on a Banach space, to that of an elementary chain of invariant subspaces of a subalgebra of compact operators. With this we expand the notion of diagonal coefficients to that of diagonal representations and subsequently generalize Ringrose's theorem equating the spectrum of an operator to the collection of diagonal coefficients. This in turn, in conjunction with some results from the theory of Polynomial Identity algebras, allows us to generalize Murphy's theorem which states that a closed subalgebra of compact operators is simultaneously triangularizable if and only if / rad () is commutative. Let be an algebra of compact operators acting on a Banach space with a norm ‖ · ‖ which dominates the operator norm, and under which 𝒜 is complete. Then has an elementary chain of invariant subspaces of bound n if and only if / rad () satisfies the standard polynomial .
Lattice Paths and a Sergeev-Pragacz Formula for Skew Supersymmetric Functions
Authors: Hamel A. M. , Goulden I. P. 
Published: December 2010

AbstractWe obtain a new version of the Sergeev–Pragacz formula for supersymmetric functions of standard shape–one applicable to arbitrary skew shape. The result involves an antisymmetrized sum of determinants that are themselves flagged supersymmetric functions. The proof is combinatorial, and follows by means of lattice path transformations.
Addition Formula For Big q-Legendre Polynomials From The Quantum Su(2) Group
Authors: Koelink H. T. 
Published: December 2010

AbstractFrom Koornwinder's interpretation of big q-Legendre polynomials as spherical elements on the quantum SU(2) group an addition formula is derived for the big g-Legendre polynomial. The formula involves Al-Salam-Carlitz polynomials, little q-Jacobi polynomials and dual q-Krawtchouk polynomials. For the little q-ultraspherical polynomials a product formula in terms of a big q-Legendre polynomial follows by q-integration. The addition and product formula for the Legendre polynomials are obtained when q tends to 1.
A Family of RealPn-Tic Fields
Authors: Shen Yuan-Yuan , Washington Lawrence C. 
Published: December 2010

AbstractLetq=pifpis an odd prime,q= 4 ifp= 2. Let ζqbe any primitiveq-th root of unity, and let. We study the family of polynomialswhere Rn(X) and Sn(X) are the polynomials in the expansionWe show that for fixedn,Pn(X;a) is irreducible for all but finitely many a ∈ O, and forp= 3, we show that it is irreducible for all a ∈ O. The roots are all real and are permuted cyclically by a linear fractional transformation defined over the real pn-th cyclotomic field. From the roots we obtain a non-maximal set of independent units for the splitting field. In the last section we briefly treat extensions of our methods to compositep.
On the Tensor Products of JW-Algebras
Authors: Jamjoom Fatmah B. 
Published: December 2010

AbstractIn this article we introduce and develop a theory of tensor products of JW-algebras. Since JW-algebras are so close to W*-algebras, one can expect that the W*-algebra tensor product theory will be actively involved. It is shown that if Mand N are JW-algebras with centres Z1 and Z2 respectively, then Z1 ⊗ Z2 is not the centre of the JW-tensor product JW() (see below for notation) ofMand N, in general. Also, the type decomposition of JW() has been determined in terms of the type decomposition of the JW-algebras M and N which, essentially, rely on the relationship between the types of the JW-algebra and the types of its universal enveloping Von Neumann algebra.
Prime Segments of Skew Fields
Authors: Brungs H. H. , Schröder M. 
Published: December 2010

AbstractAn additive subgroupPof a skew fieldFis called aprimeofFifPdoes not contain the identity, but if the productxyof two elementsxandyinFis contained inP, thenxoryis inP. A prime segment ofFis given by two neighbouring primesP1⊃P2; such a segment is invariant, simple, or exceptional depending on whetherA(P1) = {a∈P1|P1aP1⊂P1} equalsP1,P2or lies properly betweenP1andP2. The setT(F) of all primes ofFtogether with the containment relation is a tree if |T(F)| is finite, and 1 < |T(F)| < ∞ is possible if F is not commutative. In this paper we construct skew fields with prescribed types of sequences of prime segments as skew fieldsFof fractions of group rings of certain right ordered groups. In particular, groupsGof affine transformations on ordered vector spacesVare considered, and the relationship between properties of Dedekind cuts ofV, certain right orders onG, and chains of prime segments ofFis investigated. A general result in Section 4 describing the possible orders on vector spaces over ordered fields may be of independent interest.
On 2-Groups as Galois Groups
Authors: Ledet Arne 
Published: December 2010

AbstractLetL/Kbe a finite Galois extension in characteristic ≠ 2, and consider a non-split Galois theoretical embedding problem overL/Kwith cyclic kernel of order 2. In this paper, we prove that if the Galois group ofL/Kis the direct product of two subgroups, the obstruction to solving the embedding problem can be expressed as the product of the obstructions to related embedding problems over the corresponding subextensions ofL/Kand certain quaternion algebra factors in the Brauer group ofK. In connection with this, the obstructions to realising non-abelian groups of order 8 and 16 as Galois groups over fields of characteristic ≠ 2 are calculated, and these obstructions are used to consider automatic realisations between groups of order 4, 8 and 16.
The Topology of Quasibundles
Authors: Movahedi-Lankarani H. , Wells R. 
Published: December 2010

AbstractLet ℳ(N, N) be the space of all N × N real matrices and let 𝒢(N) be the set of all linear subspaces of ℝN. The maps ker and coker from ℳ(N, N) onto 𝒢(N) induce two quotient topologies, the right and left respectively. A quasibundle over a space X is defined as a continuous map from X into 𝒢(N)\ it is a right quasibundle if 𝒢(N) = ℳ(N,N)/ ker and a left quasibundle if 𝒢(N) = ℳ(N,N)/ coker. The following is established. Theorem: Let ξ be a left quasibundle over a closed subset of some Euclidean space. Then the following statements are equivalent: (i) ξ has enough sections pointwise. (ii) Sections zero at infinity over closed subsets may be extended globally, (iii) A vector subbundle over a closed subset extends to a vector subbundle over a neighborhood, (iv) ξ is a fibrewise sum of local vector subbundles. (v) There exist finitely many global sections spanning ξ. (vi) ξ is an image quasibundle. (vii) ξ results from a Swan construction. These results are used to prove a version of the Hirsch-Smale immersion theorem for locally compact subsets of Euclidean space.
On a Generalization of a Result of Waldspurger
Authors: Guo Jiandong 
Published: December 2010

AbstractWe consider a generalization of a trace formula identity of Jacquet, in the context of the symmetric spaces GL(2n)/GL(/n) × GL(n) and G′/H′. Here G′ is an inner form of GL(2n) over F with a subgroup H′ isomorphic to GL(n, E) where E/F is a quadratic extension of number field attached to a quadratic idele class character η of F. A consequence of this identity would be the following conjecture: Let π be an automorphic cuspidal representation of GL(2n). If there exists an automorphic representation π′ of G′ which is related to π by the Jacquet-Langlands correspondence, and a vector ø in the space of π′ whose integral over H′ is nonzero, then both L(1/2, π) and L(1/2,π ⊗ η) are nonvanishing. Moreover, we have L(1/2, π)L(1/2, π ⊗ η) > 0. Here the nonvanishing part of the conjecture is a generalization of a result of Waldspurger for GL(2) and the nonnegativity of the product is predicted from the generalized Riemann Hypothesis. In this article, we study the corresponding local orbital integrals for the symmetric spaces. We prove the "fundamental lemma for the unit Hecke functions" which says that unit Hecke functions have "matching" orbital integrals. This serves as the first step toward establishing the trace formula identity and in the same time it provides strong evidence for what we proposed.
Positive Powers of Positive Positive Definite Matrices
Authors: Rosen Lon 
Published: December 2010

AbstractLet C be an n x n positive definite matrix. If C ≥ 0 in the sense that Cij ≥ 0 and if p > n — 2, then Cp ≥ 0. This implies the following "positive minorant property" for the norms ‖A‖p = [tr(A*A)p/2]1/P. Let 2 < p ≠ 4, 6, … . Then 0 ≤ A ≤ B => ‖A‖p ≥ ‖B‖P if and only if n < p/2 + 1.
Compact Almost Discrete Hypergroups
Authors: Voit Michael 
Published: December 2010

AbstractA compact hypergroup is called almost discrete if it is homeomorphic to the one-point-compactification of a countably infinite discrete set. If the group Up of all p-adic units acts multiplicatively on the p-adic integers, then the associated compact orbit hypergroup has this property. In this paper we start with an exact projective sequence of finite hypergroups and use successive substitution to construct a new surjective projective system of finite hypergroups whose limit is almost discrete. We prove that all compact almost discrete hypergroups appear in this way—up to isomorphism and up to a technical restriction. We also determine the duals of these hypergroups, and we present some examples coming from partitions of compact totally disconnected groups.
Explicit Forms of Local Lifting for GL2
Authors: Kim Donggyun 
Published: December 2010

AbstractLet F be a local non-Archimedean field and let Ꮪ(GL2(F)) be the set of equivalence classes of irreducible admissible representations of GL(F). When K/F be a Galois field extension, there is a map, called lifting, from Ꮪ(GL2(F)) to Ꮪ(GL2(K)). We give an explicit form of lifting when K/F is a quadratic wildly ramified extension and the given representations are Weil supercuspidal. We also provide a comparison between Weil representations and induced representations of GL2(F).
Hardy-Littlewood-Sobolev Theorems of Fractional Integration on Herz-Type Spaces and its Applications
Authors: Lu Shanzhen , Yang Dachun 
Published: December 2010

AbstractIn this paper, the authors first establish the Hardy-Littlewood-Sobolev theorems of fractional integration on the Herz spaces and Herz-type Hardy spaces. Then the authors give some applications of these theorems to the Laplacian and wave equations.
On Finite Essential Extensions of Torsion Free Abelian Groups
Authors: Benabdallah K. , Ouldbeddi M. A. 
Published: December 2010

AbstractLet A be a torsion free abelian group. We say that a group K is a finite essential extension of A if K contains an essential subgroup of finite index which is isomorphic to A. Such K admits a representation as (A ℤ xkx)/ℤky where y = Nx + a for some k x k matrix N over Z and α ∈ Ak satisfying certain conditions of relative primeness and ℤk = {(α1,..., αk) : αi, ∈ ℤ}. The concept of absolute width of an f.e.e. K of A is defined and it is shown to be strictly smaller than the rank of A. A kind of basis substitution with respect to Smith diagonal matrices is shown to hold for homogeneous completely decomposable groups. This result together with general properties of our representations are used to provide a self contained proof that acd groups with two critical types are direct sum of groups of rank one and two.
Riesz's Functions in Weighted Hardy and Bergman Spaces
Authors: Nakazi Takahiko , Yamada Masahiro 
Published: December 2010

AbstractLet μ be a finite positive Borel measure on the closed unit disc . For each a in , put where ƒ ranges over all analytic polynomials with f(a) = 1. This upper semicontinuous function S(a) is called a Riesz's function and studied in detail. Moreover several applications are given to weighted Bergman and Hardy spaces.
On the Principle of Duality in Lorentz Spaces
Authors: Gol'Dman M. L. , Heinig H. P. , Stepanov V. D. 
Published: December 2010

Abstractcharacterization of the spaces dual to weighted Lorentz spaces are given by means of reverse Hölder inequalities (Theorems 2.1, 2.2). This principle of duality is then applied to characterize weight functions for which the identity operator, the Hardy-Littlewood maximal operator and the Hilbert transform are bounded on weighted Lorentz spaces.
Asymptotic Expansion of a Class of Multi-Dimensional Integrals
Authors: Sellier A. 
Published: December 2010

AbstractThe aim of this paper is to derive the expansion of the following class of multi-dimensional integralswith respect to the large parameter λ when Ω is a subset of ℝn, a > 0, w is a strictly positive and bounded function on Σ and fp means an integration in the finite part sense of Hadamard (see Section 2). This is performed for weak assumptions bearing on pseudofunction K and by extending to higher dimensional cases the tools developed in the one-dimensional context. The range of applications of the proposed results is outlined by the exhibition of several examples.
New Almost Periodic Type Functions and Solutions of Differential Equations
Authors: Basit Bolis , Zhang Chuanyi 
Published: December 2010

AbstractLet X be a Banach space and . Let Π and Π0 be two subspaces of , the Banach space of bounded continuous functions from 𝕁 to X. We seek conditions under which Π + Π0 is closed in . This led to introduce a general space, which contains many classes of almost periodic type functions as subspaces. We prove some recent results on indefinite integral for the elements of these classes. We apply certain results on harmonic analysis to investigate solutions of differential equations. As an application we study specific spaces: the spaces of asymptotic and pseudo almost automorphic functions and their solutions of some ordinary quasi-linear and a non-linear parabolic partial differential equations.
Multiplication Invariant Subspaces of Hardy Spaces
Authors: Lance T. L. , Stessin M. I. 
Published: December 2010

AbstractThis paper studies closed subspaces L of the Hardy spaces Hp which are g-invariant (i.e., g. L ⊆ L) where g is inner, g ≠ 1. If p = 2, theWold decomposition theorem implies that there is a countable “g-basis” f1, f2, . . . of L in the sense that L is a direct sum of spaces fj . H2[g] where H2[g] = {f o g | f ∈ H2}. The basis elements fj satisfy the additional property that ∫T |fj|2gk = 0, k = 1, 2, . . . . We call such functions g-2-inner. It also follows that any f ∈ H2 can be factored f = hf ,2 . (F2 o g) where hf,2 is g-2-inner and F is outer, generalizing the classical Riesz factorization. Using Lp estimates for the canonical decomposition of H2,we find a factorization f = hf ,p.(Fpog) for f ∈ Hp. If p ≤ 1 and g is a finite Blaschke product we obtain, for any g-invariant L ⊆ Hp, a finite g-basis of g-p-inner functions.
Differential Equations Defined by the Sum of two Quasi-Homogeneous Vector Fields
Authors: Coll B. , Gasull A. , Prohens R. 
Published: December 2010

AbstractIn this paper we prove, that under certain hypotheses, the planar differential equation: ˙x = X1(x, y) + X2(x, y), ˙y = Y1(x, y) + Y2(x, y), where (Xi, Yi), i = 1, 2, are quasi-homogeneous vector fields, has at most two limit cycles. The main tools used in the proof are the generalized polar coordinates, introduced by Lyapunov to study the stability of degenerate critical points, and the analysis of the derivatives of the Poincar´e return map. Our results generalize those obtained for polynomial systems with homogeneous non-linearities.
A Counterexample in Lp Approximation by Harmonic Functions
Authors: Mateu Joan 
Published: December 2010

AbstractFor we show that the conditions for all open sets G, C2,q denoting Bessel capacity, are not sufficient to characterize the compact sets X with the property that each function harmonic on and in Lp(X) is the limit in the Lp norm of a sequence of functions which are harmonic on neighbourhoods of X.