bluuebunny/crossref_metadata_2025 huggingface dataset:
Hermite and Hermite-Fejer Interpolation and Associated Product Integration Rules on the Real Line: The L1 Theory
Authors: Lubinsky D. S. , P. Rabinowitz
Published: December 2010

We investigate convergence in a weighted L1 -norm of Hermite-Fejér and Hermite interpolation at the zeros of orthogonal polynomials associated with weights on the real line. The results are then applied to convergences of product integration rules. From the point of view of orthogonal polynomials, the new feature is that Freud and Erdös weights are treated simultaneously and that relatively few assumptions are placed on the weight. From the point of view of product integration, the rules exhibit convergence for highly oscillatory kernels (for example) and for functions of rapid growth at infinity.
Sk2 and K3 Of Dihedral Groups
Authors: Laubenbacher Reinhard C. , Magurn Bruce A.
Published: December 2010

New computations of birelative K2 groups and recent results on K3 of rings of algebraic integers are combined in generalized Mayer-Vietoris sequences for algebraic k-theory. Upper and lower bounds for SK2(ℤ G) and lower bounds for K3(ℤ G) are deduced for G a dihedral group of square-free order, and for some other closely related groups G.
Fixed Point Theorems for Measurable Semigroups of Operations
Authors: Wong James C. S.
Published: December 2010

Let Sbe a topological semigroup, K a compact convex subset of a separated convex space Eand T: S x K → K an affine action (denoted by (s, x) → Ts(x),s ∈ S, x ∈ K) of S as continuous affine maps on K. It is shown in A. Lau and J. Wong [22] that the weakly left uniformly measurable functions WLUM(S) on S has a left invariant mean iff Shas the fixed point property for weakly measurable affine actions, i.e. affine actions such that the scalar function s → x*Ts(x) is measurable for each x ∈ K and x*∈ E* (the dual of E) with respect to the Borel sets in S. It is natural to ask for a “strongly” measurable analogue of this result. There are a number of ways to define such actions and the corresponding functions on S. In this paper, we obtained a neat analogue of this fixed point theorem by a suitable choice of strong measurability which naturally leads to another new fixed point theorem for separable actions. Also, we shall unify these and many known fixed point theorems and extend and generalise them to anti-actions of S as bounded linear operators on Banach spaces
The Structure of Schur Algebras Sk(n, p) for n ≥ p
Authors: XI Changchang
Published: December 2010

By exploiting the known quasi-heredity of Schur algebras, the structure of basic algebras of the Schur algebras Sk(n, p) for n ≥ p over an algebraically closed field k is completely determined.
Differential Forms and Resolutions on Certain Analytic Spaces II. Flat Resolutions
Authors: Ancona Vincenzo , Gaveau Bernard
Published: December 2010

This paper gives another construction of (0, p)-forms on a complex analytic space and of the operator. This construction is independent of the one in [1] and apart from the general result of Section 1 of [1], it can be read independently. As in [1], the hypotheses on S are the following: S has normal singularities, its singular locus X is smooth, the exceptional divisor in a desingularization of S is irreducible.
Continuous Hahn Polynomials of Differential Operator Argument and Analysis on Riemannian Symmetric Spaces of Constant Curvature
Authors: Badertscher Erich , Koornwinder Tom H.
Published: December 2010

For the three types of simply connected Riemannian spaces of constant curvature it is shown that the associated spherical functions can be obtained from the corresponding (zonal) spherical functions by application of a differential operator of the form p(i d/dt), where p belongs to a system of orthogonal polynomials: Gegenbauer polynomials, Hahn polynomials or continuous symmetric Hahn polynomials. We give a group theoretic explanation of this phenomenon and relate the properties of the polynomials p to the properties of the corresponding representation. The method is extended to the case of intertwining functions.
Bourgain Algebras of Douglas Algebras
Authors: Gorkin Pamela , Izuchi Keiji , Mortini Raymond
Published: December 2010

Let A be a Banach algebra and let B be a linear subspace of A. Recall that A has the Dunford Pettis property if whenever ƒn→ 0 weakly in A* and φn → 0 weakly in A* then φn(ƒn) → 0. Bourgain showed that H∞ has the Dunford Pettis property using the theory of ultraproducts. The Dunford Pettis property is related to the notion of Bourgain algebra, denoted Bb, introduced by [6] Cima and Timoney. The algebra Bb is the set of ƒ in A such that if ƒn → 0 weakly in B then dist(ƒƒn, B) —> 0. Bourgain showed [2] that a closed subspace X of C(L)y where L is a compact Hausdorff space, has the Dunford Pettis property if Xb — C(L). Cima and Timoney proved that Bb is a closed subalgebra of A and that if B is an algebra then B⊂Bb. In this paper we study the Bourgain algebra associated with various algebras of functions on the unit circle T.
Approximation by (Pluri) Subharmonic Functions: Fusion and Localization
Authors: Gauthier P.M.
Published: December 2010

Let u1 and u2 be subharmonic (plurisubharmonic) on overlapping sets K1 and K2 respectively. We seek to approximate u1 and u2 simultaneously by a single subharmonic (plurisubharmonic) function u.
A Topological Transversality Theorem For Multi-Valued Maps In Locally Convex Spaces With Applications To Neutral Equations
Authors: Kaczynski Tomasz , Wu Jianhong
Published: December 2010

The concept of essential map and topological transversality due to A. Granas is extended to multi-valued maps in locally convex spaces and it is next applied to prove the solvability of boundary value problems for certain neutral functional differential equations. In order to achieve a required compactness property, the weak topology in a Sobolev space is considered. The topological tool established in the first part of the paper allows to avoid some obstacles which are encountered when trying to use standard degree-theoretical arguments.
Some Conjectures for Immanants
Authors: Stembridge J. R.
Published: December 2010

We present a series of conjectures for immanants, together with the supporting evidence we possess for them. The conjectures are loosely organized into three families. The first concerns inequalities involving the immanants of totally positive matrices (Le.,real matrices with nonnegative minors). This includes, for example, the conjecture that immanants of totally positive matrices are nonnegative. The second family involves the immanants of Jacobi-Trudi matrices. These conjectures were suggested by a previous conjecture of Goulden and Jackson (recently proved by C. Greene) that the immanants of Jacobi-Trudi matrices are polynomials with nonnegative coefficients. The third family involves geometric and combinatorial structures associated with total positivity and paths in acyclic digraphs.
A Tauberian Theorem for the General Euler-Borel Summability Method
Authors: Tam Laying
Published: December 2010

Our main result is a Tauberian theorem for the general Euler-Borel summability method. Examples of the method include the discrete Borel, Euler, Meyer- Kônig, Taylor and Karamata methods. Every function/ analytic on the closed unit disk and satisfying some general conditions generates such a method, denoted by (£,ƒ). For instance the function ƒ(z) = exp(z — 1) generates the discrete Borel method. To each such function ƒ corresponds an even positive integer p = p(f).We show that if a sequence (sn)is summable (E,f)and as n→ ∞ m > n, (m— n)n-p(f)→0, then (sn)is convergent. If the Maclaurin coefficients of/ are nonnegative, then p(f) =2. In this case we may replace the condition . This generalizes the Tauberian theorems for Borel summability due to Hardy and Littlewood, and R. Schmidt. We have also found new examples of the method and proved that the exponent —p(f)in the Tauberian condition (*) is the best possible.
On the Normal Growth of Prime Factors of Integers
Authors: De Koninck J. M. , Kátai I. , Mercier A.
Published: December 2010

Let h: [0,1] → R be such that and define .In 1966, Erdős [8] proved that holds for almost all n, which by using a simple argument implies that in the case h(u) = u, for almost all n, He further obtained that, for every z > 0 and almost all n, and that where ϕ, ψ, are continuous distribution functions. Several other results concerning the normal growth of prime factors of integers were obtained by Galambos [10], [11] and by De Koninck and Galambos [6].

Let χ = ﹛xm : w ∈ N﹜ be a sequence of real numbers such that limm→∞ xm = +∞. For each x ∈ χ let be a set of primes p ≤x. Denote by p(n) the smallest prime factor of n. In this paper, we investigate the number of prime divisors p of n, belonging to for which Th(n,p) > z. Given Δ < 1, we study the behaviour of the function We also investigate the two functions , where, in each case, h belongs to a large class of functions.
Symmetries and Variation of Spectra
Authors: Bhatia R. , Elsner L.
Published: December 2010

An interesting class of matrices is shown to have the property that the spectrum of each of its elements is invariant under multiplication by p-th. roots of unity. For this class and for a class of Hamiltonian matrices improved spectral variation bounds are obtained.
Compactness of the Fluctuations Associated with some Generalized Nonlinear Boltzmann Equations
Authors: Ferland René , Fernique Xavier , Giroux Gaston
Published: December 2010

In this paper, we develop a new approach to obtain the compactness of the fluctuation processes for Boltzmann dynamics. Our method is applicable to Kac's model, already studied by Uchiyama, but it covers many other cases. A novelty worth mentioning is the use of the weak topology of a Hilbert space.
Rational Homotopy Types with the Rational Cohomology Algebra of Stunted Complex Projective Space
Authors: Lupton Gregory , Umble Ronald
Published: December 2010

We consider the number of spaces, up to rational homotopy equivalence, which have rational cohomology algebra isomorphic to that of stunted complex projective space . Using a classification theory due to Schlessinger and Stasheff, we determine the number of rational homotopy types with rational comology algebra isomorphic to , for any given n and k. The necessary computations make use of a spectral sequence introduced by the second named author.
A Class of Generalized Hypergeometric Functions in Several Variables
Authors: Yan Zhimin
Published: December 2010

We study a class of generalized hypergeometric functions in several variables introduced by A. Korânyi. It is shown that the generalized Gaussian hypergeometric function is the unique solution of a system partial differential equations. Analogues of some classical results such as Kummer relations and Euler integral representations are established. Asymptotic behavior of generalized hypergeometric functions is obtained which includes some known estimates.
Non-Local Lie Primitive Subgroups of Lie Groups
Authors: Cohen Arjeh M. , Griess Robert L.
Published: December 2010

Borovik found a Lie primitive subgroup of E8(ℂ) isomorphic to (Alt5 × Sym6) : 2. In this note, we provide a short proof of existence and his result that the conjugacy class of this subgroup is the only one among those of non-local Lie primitive subgroups of finite dimensional simple complex Lie groups having a socle with more than one simple factor.
On the Law of the Iterated Logarithm for Infinite Dimensional Ornstein-Uhlenbeck Processes
Authors: Shao QI-Man
Published: December 2010

Let be independent Ornstein-Uhlenbeck processes and In this paper the law of iterated logarithm for X(t, n)is considered. The results obtained improve those of Csorgő and Lin(1988) and Schmuland(1987).
Random Dirichlet Functions: Multipliers and Smoothness
Authors: Cochran W. George , Shapiro Joel H. , Ullrich David C.
Published: December 2010

We show that ifis a holomorphic function in the Dirichlet space of the unit disk, then almost all of its randomizationsare multipliers of that space. This parallels a known result for lacunary power series, which also has a version for smoothness classes: every lacunary Dirichlet series lies in the Lipschitz class Lip1/2of functions obeying a Lipschitz condition with exponent 1/2. However, unlike the lacunary situation, no corresponding “almost sure” Lipschitz result is possible for random series: we exhibit a Dirichlet function withnorandomization in Lip1/2. We complement this result with a “best possible” sufficient condition for randomizations to belong almost surely to Lip1/2. Versions of our results hold for weighted Dirichlet spaces, and much of our work is carried out in this more general setting.
On the Asphericity of Knot Complements
Authors: Liem Vo Thanh , Venema Gerard A.
Published: December 2010

Two examples of topological embeddings ofS2inS4are constructed. The first has the unusual property that the fundamental group of the complement is isomorphic to the integers while the second homotopy group of the complement is nontrivial. The second example is a non-locally flat embedding whose complement exhibits this property locally.

Two theorems are proved. The first answers the question of just when goodπ1implies the vanishing of the higher homotopy groups for knot complements inS4. The second theorem characterizes local flatness for 2-spheres inS4in terms of a localπ1condition.
Hopf Algebras of Combinatorial Structures
Authors: Schmitt William R.
Published: December 2010

A generalization of the definition of combinatorial species is given by considering functors whose domains are categories of finite sets, with various classes of relations as moronisms. Two cases in particular correspond to species for which one has notions of restriction and quotient of structures. Coalgebras and/or Hopf algebras can be associated to such species, the duals of which provide an algebraic framework for studying invariants of structures.
Moving Weighted Averages
Authors: Akcoglu M. A. , Déniel Y.
Published: December 2010

Let ℝ denote the real line. Let {Tt}tєℝ be a measure preserving ergodic flow on a non atomic finite measure space (X, ℱ, μ). A nonnegative function φ on ℝ is called a weight function if ∫ℝ φ(t)dt = 1. Consider the weighted ergodic averages

of a function f X —> ℝ, where {θk} is a sequence of weight functions. Some sufficient and some necessary and sufficient conditions are given for the a.e. convergence of Akf, in particular for a special case in which

where φ is a fixed weight function and {(ak, rk)} is a sequence of pairs of real numbers such that rk > 0 for all k. These conditions are obtained by a combination of the methods of Bellow-Jones-Rosenblatt, developed to deal with moving ergodic averages, and the methods of Broise-Déniel-Derriennic, developed to deal with unbounded weight functions.
Mappings which Preserve Idempotents, Local Automorphisms, and Local Derivations
Authors: Brešar Matej , Šemrl Peter
Published: December 2010

It is proved that linear mappings of matrix algebras which preserve idempotents are Jordan homomorphisms. Applying this theorem we get some results concerning local derivations and local automorphisms. As an another application, the complete description of all weakly continuous linear surjective mappings on standard operator algebras which preserve projections is obtained. We also study local ring derivations on commutative semisimple Banach algebras.
Continuum-Wise Expansive Homeomorphisms
Authors: Kato Hisao
Published: December 2010

The notion of expansive homeomorphism is important in topological dynamics and continuum theory. In this paper, a new kind of homeomorphism will be introduced and studied, namely the continuum-wise expansive homeomorphism. The class of continuum-wise expansive homeomorphisms is much larger than the one of expansive homeomorphisms. In fact, the class of continuum-wise expansive homeomorphisms contains many important homeomorphisms which often appear in "chaotic" topological dynamics and continuum theory, but which are not expansive homeomorphisms. For example, the shift maps of Knaster's indecomposable chainable continua are continuum-wise expansive homeomorphisms, but they are not expansive homeomorphisms. Also, there is a continuum-wise expansive homeomorphism on the pseudoarc. We study several properties of continuum-wise expansive homeomorphisms. Many theorems concerning expansive homeomorphisms will be generalized to the case of continuum-wise expansive homeomorphisms.
On a Class of Generalized Baker's Transformations
Authors: Rahe M.
Published: December 2010

Let f define a baker's transformation (Tf, Pf). We find necessary and sufficient conditions on f for (Tf, Pf) to be an N(ω)-step random Markov chain. Using this result, we give a simplified proof of Bose's results on Holder continuous baker's transformations where f is bounded away from zero and one. We extend Bose's results to show that, for the class of baker's transformations which are random Markov chains where TV has finite expectation, a sufficient condition for weak Bernoullicity is that the Lebesgue measure λ{x f(x) = 0 or f(x) = 1} = 0. We also examine random Markov chains satisfying a strictly weaker condition, those for which the differences between the entropy of the process and the conditional entropy given the past to time n form a summable sequence; and we show that a similar result holds. A condition is given on/ which is weaker than Holder continuity, but which implies that the entropy difference sequence is summable. Finally, a particular baker's transformation is exhibited as an easy example of a weakly Bernoulli transformation on which the supremum of the measure of atoms indexed by n-strings decays only as the reciprocal of n.
On the Hermitian-Einstein Tensor of a Complex Homogenous Vector Bundle
Authors: Zelewski Piotr M.
Published: December 2010

We prove that any holomorphic, homogenous vector bundle admits a homogenous minimal metric—a metric for which the Hermitian-Einstein tensor is diagonal in a suitable sense. The concept of minimality depends on the choice of the Jordan-Holder filtration of the corresponding parabolic module. We show that the set of all admissible Hermitian-Einstein tensors of certain class of minimal metrics is a convex subset of the euclidean space. As an application, we obtain an algebraic criterion for semistability of homogenous holomorphic vector bundles.
Representations of Lie Groups by Contact Transformations, II: Non-Compact Simple Groups
Authors: Herz Carl
Published: December 2010

If a Lie group acts faithfully as a transitive group of contact transformations
of a compact manifold it is either compact with centre of dimension at most 1
or non-compact simple. The latter case is described
Asymptotic Behavior of Skew Conditional Heat Kernels on Graph Networks
Authors: Okada Tatsuya
Published: December 2010

In this note, we will consider the heat propagation on locally finite graph networks which satisfy a skew condition on vertices (See Definition of Section 2). For several periodic models, we will construct the heat kernels Pt with the skew condition explicitly, and derive the decay order of Pt as time goes to infinity.
Orthogonal Polynomials and Rational Modifications of Measures
Authors: Godoy E. , Marcellan F.
Published: December 2010

Given a finite positive measure on the Borel subsets of the complex plane with compact support containing infinitely many points, we deduce some formulas for the sequence of monic orthogonal polynomials associated to a rational modification of the measure. These expressions depend on so called functions of the second kind. Some examples for particular Jordan curves are given
Isomorphisms Between Linear Groups Over Division Rings
Authors: Petechuk Vasilij M.
Published: December 2010

In the present paper we completely describe the isomorphisms between projective elementary groups PSLn and PSLm (n ≥ 2, m ≥ 2) over division rings. It was found that such groups can be isomorphic only if n = m; the division rings are isomorphic or anti-isomorphic, except for the following groups:

PSL(2,F7) and PSL(3,F2); PSL(2, F4) and PSL(2,F5).

The idea is based on a deepening of the classical Hua's approach. This problem has been solved independently by H. Ren, Z. Wan and X. Wu using a different way
Dixmier-Douady Classes of Dynamical Systems and Crossed Products
Authors: Raeburn Iain , Williams Dana P.
Published: December 2010

Continuous-trace C*-algebras A with spectrum T can be characterized as those algebras which are locally Monta equivalent to C0(T). The Dixmier-Douady class δ(A) is an element of the Čech cohomology group Ȟ3(T, ℤ) and is the obstruction to building a global equivalence from the local equivalences. Here we shall be concerned with systems (A, G, α) which are locally Monta equivalent to their spectral system (C0(T),G, τ), in which G acts on the spectrum T of A via the action induced by α. Such systems include locally unitary actions as well as N-principal systems. Our new Dixmier-Douady class δ (A, G, α) will be the obstruction to piecing the local equivalences together to form a Monta equivalence of (A, G, α) with its spectral system. Our first main theorem is that two systems (A, G, α) and (B, G, β) are Monta equivalent if and only if δ (A, G, α) = δ (B, G, β). In our second main theorem, we give a detailed formula for δ (A ⋊α G) when (A, G, α) is N-principal.
Essentially Commuting Toeplitz Operators With Harmonic Symbols
Authors: Stroethoff Karel
Published: December 2010

In this paper we characterize the bounded harmonic functions ƒ and g on the unit disk for which the Toeplitz operators Tƒ and Tg defined on the Bergman space of the unit disk are essentially commuting.
Boundedness of Some Integral Operators
Authors: Carro María J. , Soria Javier
Published: December 2010

We apply the expression for the norm of a function in the weighted Lorentz space, with respect to the distribution function, to obtain as a simple consequence some weighted inequalities for integral operators.
On the Equivariant Formality of Kähler Manifolds With Finite Group Action
Authors: Fine Benjamin L. , Triantafillou Georgia
Published: December 2010

An appropriate definition of equivariant formality for spaces equipped with the action of a finite group G, and for equivariant maps between such spaces, is given. Kahler manifolds with holomorphic G-actions, and equivariant holomorphic maps between such Kàhler manifolds, are proven to be equivariantly formal, generalizing results of Deligne, Griffiths, Morgan, and Sullivan
Relative Kloosterman Integrals For Gl(3): III
Authors: Mao Zhengyu
Published: December 2010

Let E be a quadratic extension of a number field F with Galois conjugation σ, G’ the quasi-split unitary group in three variables, G the group GL(3, E). We let S be the space of the matrices s in G such that σ(s)s = e. One conjectures a comparison identity between the relative Kuznietsov trace formula for the symmetric space S and the ordinary Kuznietsov trace formula for the group G’ (See [10]). We prove the corresponding “fundamental lemmas”.
Measure-Valued Branching Diffusions with Singular Interactions
Authors: Evans Steven N. , Perkins Edwin A.
Published: December 2010

The usual super-Brownian motion is a measure-valued process that arises as a high density limit of a system of branching Brownian particles in which the branching mechanism is critical. In this work we consider analogous processes that model the evolution of a system of two such populations in which there is inter-species competition or predation.

We first consider a competition model in which inter-species collisions may result in casualties on both sides. Using a Girsanov approach, we obtain existence and uniqueness of the appropriate martingale problem in one dimension. In two and three dimensions we establish existence only. However, we do show that, in three dimensions, any solution will not be absolutely continuous with respect to the law of two independent super-Brownian motions. Although the supports of two independent super-Brownian motions collide in dimensions four and five, we show that there is no solution to the martingale problem in these cases.

We next study a prédation model in which collisions only affect the "prey" species. Here we can show both existence and uniqueness in one, two and three dimensions. Again, there is no solution in four and five dimensions. As a tool for proving uniqueness, we obtain a representation of martingales for a super-process as stochastic integrals with respect to the related orthogonal martingale measure.

We also obtain existence and uniqueness for a related single population model in one dimension in which particles are killed at a rate proportional to the local density. This model appears as a limit of a rescaled contact process as the range of interaction goes to infinity.
Dickson Polynomials of the Second Kind that are Permutations
Authors: Cohen Stephen D.
Published: December 2010

It is known that the Dickson polynomial of the second kind permutes the elements of the finite prime field (p odd) when n + 1 = ±2 to each of the moduli and . Based on numerical evidence it has been conjectured that these congruences are necessary for the polynomial to permute . The conjecture is established here by a new method
Chinburg's Third Invariant in the Factorisability Defect Class Group
Authors: Holland D.
Published: December 2010

Chinburg'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

The 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

The 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

We 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 that

Here 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

Let 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

Let 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

We 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

Define 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.
Abstract Characterizations of Fixed Point Sub Algebras of the Rotation Algebra
Authors: Farsi Carla , Watling Neil
Published: December 2010

We determine abstract characterizations of the fixed point subalgebras of the rotation algebraunder the automorphismsand.
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

This 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

We 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

Let 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

We 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

We 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

From 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

Letq=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.
Relative Character Correspondences in Finite Groups
Authors: Felipe Maria Jose , Navarro Gabriel
Published: December 2010

In a coprime action, we study character correspondences between the invariant characters of the group and those of subgroups containing the fixed points subgroup. Some character degree consequences are obtained.
On the Tensor Products of JW-Algebras
Authors: Jamjoom Fatmah B.
Published: December 2010

In 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.
Continuation of Complex Varieties Across Rectifiable Sets
Authors: Xu Yeren
Published: December 2010

We continue our research on extension of complex varieties across closed subsets. While efforts are being made to deal with varieties of any dimensions, the paper primarily concerns 1-dimensional case, and the exceptional set is thus assumed to be connected with finite length. As applications of the main result, several corollaries are obtained with interesting features.
Prime Segments of Skew Fields
Authors: Brungs H. H. , Schröder M.
Published: December 2010

An 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

LetL/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

Let 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.
Construction of Vector Valued Modular Forms from Jacobi Forms
Authors: Yang Jae-Hyun
Published: December 2010

We give a geometrical construction of the canonical automorphic factor for the Jacobi group and construct new vector valued modular forms from Jacobi forms by differentiating them with respect to toroidal variables and then evaluating at zero.
On a Generalization of a Result of Waldspurger
Authors: Guo Jiandong
Published: December 2010

We 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

Let 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

A 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.
Polynomial Lie Subalgebras of the Infinite Matrix Lie Algebra
Authors: Chen Liang
Published: December 2010

We construct two classes of Lie subalgebras of the infinite matrix Lie algebra 𝔤𝔩∞(ℂ) and prove that they are all simple Lie algebras.
Explicit Forms of Local Lifting for GL2
Authors: Kim Donggyun
Published: December 2010

Let 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

In 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

Let 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

Let 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

characterization 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

The aim of this paper is to derive the expansion of the following class of multi-dimensional integrals

with 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.