bluuebunny/crossref_metadata_2025 huggingface dataset:
Espace des États Normaux Dun Facteur de Type IIIλ 0 < λ < 1 et D'Un Facteur de Type III0
Authors: Bion-Nadal Jocelyne
Published: December 2010

Soit M un facteur de type IIIλ 0 ≦ λ< 1, agissant sur un espace hilbertien à base dénombrable. Le propos de ce travail est l'étude des états normaux d'un tel facteur à équivalence unitaire près. L'espace quotient n'est pas séparé; l'espace séparé associé est obtenu comme quotient de l'espace des états normaux par la relation d'équivalence R dont les classes sont les fermetures des orbites précédentes.

Pour étudier cet espace, on définit un calcul fonctionnel sur M+* (espace des formes linéaires positives normales sur M) à valeurs dans M. Ce calcul fonctionnel est déterminé par la donnée d'une C* algèbre d'applications de M+ * dans M “continues” en un certain sens, notée C*(M).
Universal Pettis Integrability
Authors: Andrews Kevin T.
Published: December 2010

Since the invention of the Pettis integral over forty years ago [11], the problem of recognizing the Pettis integrability of a function against an individual measure has been much studied [5, 6, 7, 8, 9, 20]. More recently, Riddle-Saab-Uhl [14] and Riddle-Saab [13] have considered the problem of when a function is integrable against every Radon measure on a fixed compact Hausdorff space. These papers give various sufficient conditions on a function that ensure this universal Pettis integrability. In this paper, we see how far these various conditions go toward characterizing universal Pettis integrability. We base our work on a w*-analogue of the core of a vector-valued function [8].

We also give some sufficient conditions that ensure that a Banach space has the so-called universal Pettis integral property (UPIP) and consider some particular examples of spaces with this property. It is interesting that in these examples some of the special set theoretic axioms that play an important role in the study of the stronger Pettis integral property [6, 7] make an appearance.
Criteria for Biquadratic Residuacity Modulo a Prime p involving Quaternary Representations of p
Authors: Williams Kenneth S. , Friesen Christian , Howe Lawrence J.
Published: December 2010

In 1958, Hasse [10, p. 236], in connection with his work on the 2n-th power character of 2 in the cyclotomic field Q(exp(2πi/2n)), proved that for every prime p ≡ 1 (mod 16) the pair of equations

is always solvable in integers x, u, v, w. Later in 1972 Giudici, Muskat, and Robinson [7, p. 388] showed in their work on Brewer's character sums that Hasse's system is also solvable for primes p ≡ 7 (mod 16). Moreover they also showed [7, p. 345] that for primes p ≡ 1 (mod 5) the pair of equations

is solvable in integers x, u, v, w. In this paper we consider a pair of diophantine equations (involving a prime p and an integer m) which includes, the above two systems as the special cases when m = 2 and m = 5. The system is then used to give criteria for m to be a biquadratic residue modulo p.
Opérations En K-Théorie Algébrique
Authors: Soulé Christophe
Published: December 2010

C'est pour étendre le théorème de Riemann-Roch à un morphisme projectif arbitraire que Grothendieck a introduit le groupe K(X) (noté aujourd'hui K0(X)), construit à l'aide des -modules localement libres sur un schéma X[14]. La somme directe et le produit tensoriel de modules font de K0(X) un anneau, et les opérations de puissances extérieures lui fournissent une structure supplémentaire, que Grothendieck appelle λ-anneau. Un λ-anneau est muni d'une filtration décroissante, la γ-filtration, et un des principaux résultats de Grothendieck est que, si X est lisse sur un corps, le groupe

est isomorphe, à la torsion près, au groupe de Chow CH1(X) des cycles de codimension i sur X, modulo l'équivalence linéaire.
A Uniform Asymptotic Expansion of the Jacobi Polynomials with Error Bounds
Authors: Frenzen C. L. , Wong R.
Published: December 2010

In a recent investigation of the asymptotic behavior of the Lebesgue constants for Jacobi polynomials, we encountered the problem of obtaining an asymptotic expansion for the Jacobi polynomials , as n → ∞, which is uniformly valid for θ in . The leading term of such an expansion is provided by the following well-known formula of “Hilb's type” [13, p. 197]:

(1.1)

where α > – 1, β real and ; c and are fixed positive numbers. Note that the remainder in (1.1) is always θ1/2O(n–3/2).
Banach Envelopes of Non-Locally Convex Spaces
Authors: Kalton N. J.
Published: December 2010

Let X be a quasi-Banach space whose dual X* separates the points of X. Then X* is a Banach space under the norm

From X we can construct the Banach envelope Xc of X by defining for x ∊ X, the norm

Then Xc is the completion of (X, ‖ ‖c). Alternatively ‖ ‖c is the Minkowski functional of the convex hull of the unit ball. Xc has the property that any bounded linear operator L:X → Z into a Banach space extends with preservation of norm to an operator .
Antichains and Finite Sets that Meet all Maximal Chains
Authors: Ginsburg J. , Rival I. , Sands B.
Published: December 2010

This paper is inspired by two apparently different ideas. Let P be an ordered set and let M(P) stand for the set of all of its maximal chains. The collection of all sets of the form

and

where x ∊ P, is a subbase for the open sets of a topology on M(P). (Actually, it is easy to check that the B(x) sets themselves form a subbase.) In other words, as M(P) is a subset of the power set 2|p| of P, we can regard M(P) as a subspace of 2|p| with the usual product topology. M. Bell and J. Ginsburg [1] have shown that the topological space M(P) is compact if and only if, for each x ∊ P, there is a finite subset C(x) of P all of whose elements are noncomparable to x and such that {x} ∪ C(x) meets each maximal chain.
Paracompactness in Locally Lindelöf Spaces
Authors: Balogh Zoltán
Published: December 2010

This paper contains a set of results concerning paracompactness of locally nice spaces which can be proved by (variations on) the technique of “stationary sets and chaining” combined with other techniques available at the present stage of knowledge in the field. The material covered by the paper is arranged in three sections, each containing, in essence, one main result.

The main result of Section 1 says that a locally Lindelöf, submeta-Lindelöf ( = δθ-refinable) space is paracompact if and only if it is strongly collectionwise Hausdorff. Two consequences of this theorem, respectively, answer a question raised by Tall [7], and strengthen a result of Watson [9]. In the last two sections, connected spaces are dealt with. The main result of the second section can be best understood from one of its consequences which says that under 2ωl > 2ω, connected, locally Lindelöf, normal Moore spaces are metrizable.
Homomorphisms of Distributive Lattices as Restrictions of Congruences
Authors: Grätzer George , Lakser Harry
Published: December 2010

Given a lattice L and a convex sublattice K of L, it is well-known that the map Con L → Con K from the congruence lattice of L to that of K determined by restriction is a lattice homomorphism preserving 0 and 1. It is a classical result (first discovered by R. P. Dilworth, unpublished, then by G. Grätzer and E. T. Schmidt [2], see also [1], Theorem II.3.17, p. 81) that any finite distributive lattice is isomorphic to the congruence lattice of some finite lattice. Although it has been conjectured that any algebraic distributive lattice is the congruence lattice of some lattice, this has not yet been proved in its full generality. The best result is in [4]. The conjecture is true for ideal lattices of lattices with 0; see also [3].
A Lower Bound for the Volume of Hyperbolic 3-Manifolds
Authors: Meyerhoff Robert
Published: December 2010

The motivation for this paper was the work of Thurston and Jørgensen on volumes of hyperbolic 3-manifolds. They prove, among other things, that the set of all volumes of complete hyperbolic 3-manifolds is well-ordered. In particular, there is a hyperbolic 3-manifold which has minimum volume among all complete hyperbolic 3-manifolds. Further, there is a minimum volume member in the collection of complete hyperbolic 3-manifolds with one cusp; and similarly for n cusps. Computer studies to date show that the manifold obtained by performing (5,1) Dehn surgery on the figure-eight knot in the 3-sphere is the leading candidate for the minimum volume hyperbolic 3-manifold. Its volume is about 0.98. The leading one-cusp minimum volume candidate is the figure-eight knot complement in the 3-sphere. Its volume is about 2.03.
Estimating the Size of Context-Free Tiling Languages
Authors: Holladay Kenneth
Published: December 2010

The problem of counting polyominoes motivates this paper. We will develop a general question for study that has counting polyominoes as a special case. We generalize in two ways. Polyominoes are shapes on the tiling made of square tiles. We will consider shapes on other tilings. The set of all polyominoes can be generated by a context-free array grammar, but the size of this set is estimated by counting the words of certain subsets and supersets that are generated by more convenient grammars. Our general question is the problem of counting the words of a context-free array language on a periodic tiling.

Counting polyominoes is a difficult problem that has not been completely solved yet. There are various techniques for roughly estimating the number of polyominoes of a given size. We will extend some of these techniques to our general question.
Higher Derivations and Distinguished Subfields
Authors: Deveney James K. , Heerema Nickolas
Published: December 2010

Let L be a finitely generated extension of a field K having characteristic p ≠ 0. A rank t higher derivation on L over K is a sequence

of additive maps of K into K such that

d0 is the identity map and dt(x) = 0, i > 0, x ∊ K. [6] contains the relevant background material on higher derivations. By Zorn's Lemma, there are maximal separable extensions of K in L. A maximal separable extension D of K in L is called distinguished if

Dieudonné [4] established that any finitely generated extension always has distinguished subfields. L has the same dimension over any distinguished subfield [5], and this dimension is called the order of inseparability of L/K. The least n such that K(LP)n is separable over K is called the inseparable exponent of L/K, inex(L/K).
Projective Modules over Higher-Dimensional Non-Commutative Tori
Authors: Rieffel Marc A.
Published: December 2010

The non-commutative tori provide probably the most accessible interesting examples of non-commutative differentiable manifolds. We can identify an ordinary n-torus Tn with its algebra, C(Tn), of continuous complex-valued functions under pointwise multiplication. But C(Tn) is the universal C*-algebra generated by n commuting unitary operators. By definition, [15, 16, 50], a non-commutative n-torus is the universal C*-algebra generated by n unitary operators which, while they need not commute, have as multiplicative commutators various fixed scalar multiples of the identity operator. As Connes has shown [8, 10], these algebras have a natural differentiable structure, defined by a natural ergodic action of Tn as a group of automorphisms. The non-commutative tori behave in inany ways like ordinary tori. For instance, it is an almost immediate consequence of the work of Pimsner and Voiculescu [37] that the K-groups of a non-commutative torus are the same as those of an ordinary torus of the same dimension. (In particular, non-commutative tori are KK-equivalent to ordinary tori by Corollary 7.5 of [52].) Furthermore, the structure constants of non-commutative tori can be continuously deformed into those for ordinary tori. (This is exploited in [17].)
The Additive Characters of the Witt Ring of an Algebraic Number Field
Authors: Conner P. E. , Yui Noriko
Published: December 2010

For an algebraic number field K there is a similarity between the additive characters defined on the Witt ring W(K), [20], [11], [17], [14, p. 131], and the local root numbers associated to a real orthogonal representation of the absolute Galois group of K, [18], [5]. Using results of Deligne and of Serre, [16], we shall derive in (5.3) a formula expressing the value, at a prime in K, of the additive character on a Witt class in terms of the rank modulo 2, the stable Hasse-Witt invariant and the local root number associated to the real quadratic character defined by the square class of the discriminant. Thus we are able to separate out the contributions made to the value of the additive character by each of the standard Witt class invariants.
An Addition Theorem and Some Product Formulas for q-Bessel Functions
Authors: Rahman Mizan
Published: December 2010

The most familiar series representation of the Bessel function is

1.1

Jackson [12] gave the following q-analogues:

1.2

1.3

where 0 < q < 1, the q-shifted factorials are defined by

1.4

and the q-gamma function is given by

1.5
The Poset of Perfect Irreducible Images of a Space
Authors: Porter Jack R. , Woods R. Grant
Published: December 2010

We begin by briefly summarizing the contents of this paper; details, and some definitions of terminology, appear in subsequent sections. All hypothesized topological spaces are assumed to be Hausdorff. The reader is referred to [13] for undefined notation and terminology.

A perfect irreducible continuous surjection is called a covering map. Let X be a space, let f and g be two such functions with domain X, and let Rf denote the range of (i.e., the set f [Z]). Then f and g are said to be equivalent (denoted f≈ g) if there is a homeomorphism h : Rf —” Rg such that h of = g. We identify equivalent covering maps with domain X, and then denote by IP(X) the set of such covering maps.
Orbital Integrals on Forms of SL(3), II
Authors: Langlands R. P. , Shelstad D.
Published: December 2010

In the paper [6] we described in a precise fashion the notion of transfer of orbital integrals from a reductive group over a local field to an endoscopic group. We did not, however, prove the existence of the transfer. This remains, indeed, an unsolved problem, although in [7] we have reduced it to a local problem at the identity.

In the present paper we solve this local problem for two special cases, the group SL(3), which is not so interesting, and the group SU(3), and then conclude that transfer exists for any group of type A2.The methods are those of [4], and are based on techniques of Igusa for the study of the asymptotic behavior of integrals on p-adic manifolds. (As observed in [7], the existence of the transfer over archimedean fields is a result of earlier work by Shelstad.)
The 4-Rank of K2(0)
Authors: Conner P. E. , Hurrelbrink Jurgen
Published: December 2010

Let 0F) denote the integers of an algebraic number field F. Classically the Dirichlet Units Theorem gives us the structure of the K-group K1(0F). Then recently the structure of the K-group K3(0F) was found by Merkurjev and Suslin, [11]. But as of now we have only limited information about the structure of the tame kernel K2(0F).
C*-Algebras With Real Rank Zero and The Internal Structure of Their Corona and Multiplier Algebras Part III
Authors: Zhang Shuang
Published: December 2010

In this part, we shall be concerned with the structure of projections in a simple σ-unital C*-algebra with the FS property, and in the associated multiplier and corona algebras. We shall also consider the closed ideal structure of the corona algebra. Most of results appear to be new even for separable simple AF algebras, and are technically independent of the previous parts I and II ([37] and [38]). The whole work develops after finding a new property of a σ-unital (nonunital) simple C*-algebra with FS, which was not known even for a separable simple AF algebra. We relate this new property to the structure of the multiplier and corona algebras from vairous points of view.
Prime Producing Quadratic Polynomials and Class-Numbers of Real Quadratic Fields
Authors: Louboutin Stéphane
Published: December 2010

Frobenius-Rabinowitsch's theorem provides us with a necessary and sufficient condition for the class-number of a complex quadratic field with negative discriminant D to be one in terms of the primality of the values taken by the quadratic polynomial with discriminant Don consecutive integers (See [1], [7]). M. D. Hendy extended Frobenius-Rabinowitsch's result to a necessary and sufficient condition for the class-number of a complex quadratic field with discriminant D to be two in terms of the primality of the values taken by the quadratic polynomials and with discriminant D (see [2], [7]).
Generalized Amalgams, With Applications to Fourier Transform
Authors: Feichtinger Hans G.
Published: December 2010

A recent survey article by J. Fournier and J. Stewart (Bull.AMS 13 (1985), 1-21) explains how amalgams of Lp with lq (as function spaces over any locally compact abelian group G) can be used as an effective tool for the treatment of various problems in harmonic analysis. The present article may be seen as a complement to this survey, indicating further advantages that arise if one works with generalized amalgams (introduced in 1980 under the name of Wiener-type spaces by the author [10]). The main difference between amalgams and these more general spaces is the fact that they allow a more precise description of the local behavior of functions (or distributions) by rather arbitrary norms and that the conditions on the global behavior (of the quantity obtained using that chosen local norm) is described in a way that includes both growth and integrability conditions (not only lq-summability).
Exact Values for Degree Sums Over Strips of Young Diagrams
Authors: Goulden I. P.
Published: December 2010

If λ = (λ1,…, λm) where λ1,…,λm are nonnegative integers with λ1 ≥…≥ λm, then λ is a partition of |λ| = λ1 + …+λm, and we write λ⊢ |λ|. The non-zero λi's are the parts of λ, so λ1 is the largest part, and ℓ(λ) is the number of parts of λ. Two partitions with the same parts, so they differ only in number of zeros, are the same. The set of all partitions, including the partition of 0 (with 0 parts) is denoted by The conjugate of λ, denoted by , is the partition (μ1,…, μk), in which μi is the number of λ's that are ≥i , for i = 1,…, k, where k=λ1.
On Functional Properties of Incomplete Gaussian Sums
Authors: Oskolkov K. I.
Published: December 2010

The following special function of two real variables x2 and x1 is considered: and its connections with the incomplete Gaussian sums where ω are intervals of length |ω| ≤1. In particular, it is proved that for each fixed x2 and uniformly in X2 the function H(x2, x1) is of weakly bounded 2-variation in the variable x1 over the period [0, 1]. In terms of the sums W this means that for collections Ω = {ωk}, consisting of nonoverlapping intervals ωk ∪ [0,1) the following estimate is valid: where card denotes the number of elements, and c is an absolute positive constant. The exact value of the best absolute constant к in the estimate (which is due to G. H. Hardy and J. E. Littlewood) is discussed.
On the Points of Inflection of Bessel Functions of Positive Order, II
Authors: Wong R. , Lang T.
Published: December 2010

Let jν, 1, jν,2, … denote the positive zeros of the Bessel function Jν(x), and similarly, let j'v,1, j'v,2, … denote the positive zeros of J'v(x), which are the positive critical points of Jv(x). It is well-known that when v is positive, both jν ,k. it and j'ν k are increasing functions of ν; see, e.g., [12, pp. 246 and 248]. Recently, Lorch and Szego [6] have attempted to show that the same is true for the positive zeros j″v,1, j″v,2, … of j″v(x), which are the positive inflection points of Jv(x).
Navier Stokes Derivative Estimates in Three Dimensions with Boundary Values and Body Forces
Authors: Duff G. F. D.
Published: December 2010

For a vector solution u(x, t) with finite energy of the Navier Stokes equations with body forces and boundary values on a region Ω ⊆ R3 for t > 0, conditions are established on the L6/5(Ω) and L2(Ω) norms of derivatives of the data that ensure the estimates and max , up to any given integer value of the weighted order 2r+s, where r or s = s1 + s2 + s3 > 0 and 0 < T < ∞.
Positive Polynomials and Time Dependent Integer-Valued Random Variables
Authors: Baker B. M. , Handelman D. E.
Published: December 2010

Let {Pi} be a sequence of real (Laurent) polynomials each of which has no negative coefficients, and suppose that f is a real polynomial. Consider the problem of deciding whether

for all integers k, there exists Nsuch that the product of polynomials

(*) Pk+1. Pk+2.....Pk+N·ƒ has no negative coefficients.
A Characterization of Universal Loeb Measurability for Completely Regular Hausdorff Spaces
Authors: Aldaz J. M.
Published: December 2010

In this paper it is shown that the construction of measures on standard spaces via Loeb measures and the standard part map does not depend on the full structure of the internal algebra being used. A characterization of universal Loeb measurability is given for completely regular Hausdorff spaces, and the behavior of this property under various topological operations is investigated.
Analysis on Sparse Parts in the Maximal Ideal Space of H∞
Authors: izuchi Keiji
Published: December 2010

Analysis on sparse parts of the Banach algebra of bounded analytic functions is given. It is proved that Sarason's theorem for QC-level sets cannot be generalized to general Douglas algebras.
A Lower Estimate for Central Probabilities on Polycyclic Groups
Authors: Alexopoulos G.
Published: December 2010

We give a lower estimate for the central value μ*n(e) of the nth convolution power μ*···*μ of a symmetric probability measure μ on a polycyclic group G of exponential growth whose support is finite and generates G. We also give a similar large time diagonal estimate for the fundamendal solution of the equation (∂/∂t + L)u = 0, where L is a left invariant sub-Laplacian on a unimodular amenable Lie group G of exponential growth.
Minorations de Combinaisons Linéaires de Logarithmes de Nombres Algébriques
Authors: Waldschmidt Michel
Published: December 2010

Resume

On sait que la méthode classique de Schneider (en une variable) permet de minorer des combinaisons linéaires de deux logarithmes de nombres algébriques avec des coefficients algébriques. Nous généralisons cette méthode en plusieurs variables pour minorer des combinaisons linéaires de plusieurs logarithmes.
Non-Symmetric Ornstein-Uhlenbeck Processes in Banach Space Via Dirichlet Forms
Authors: Schmuland Byron
Published: December 2010

We use recent advances in the theory of non-symmetric Dirichlet forms to study a class of Banach space valued Ornstein-Uhlenbeck processes. As an example, we look at Walsh's stochastic model of neural response and show that it is a continuous process in any Sobolev space Hα(α < ½), and that it takes values only among functions with unbounded variation.
Co-H-Structures on Moore Spaces of Type (G, 2)
Authors: Arkowitz Martin , Golasinski Marek
Published: December 2010

We consider the set (of homotopy classes) of co-H-structures on a Moore space M(G,n), where G is an abelian group and n is an integer ≥ 2. It is shown that for n > 2 the set has one element and for n = 2 the set is in one-one correspondence with Ext(G, G ⊗ G). We make a detailed investigation of the co-H-structures on M(G, 2) in the case G = ℤm, the integers mod m. We give a specific indexing of the co-H-structures on M(ℤm, 2) and of the homotopy classes of maps from M(ℤm, 2) to M(ℤn, 2) by means of certain standard homotopy elements. In terms of this indexing we completely determine the co-H-maps from M{ℤm, 2) to M(ℤn, 2) for each co-H-structure on M(ℤm, 2) and on M(ℤn, 2). This enables us to describe the action of the group of homotopy equivalences of M(ℤn, 2) on the set of co-H-structures of M(ℤm, 2). We prove that the action is transitive. From this it follows that if m is odd, all co-H-structures on M(ℤm, 2) are associative and commutative, and if m is even, all co-H-structures on M(ℤm, 2) are associative and non-commutative.
Separating Points of βℕ By Minimal Flows
Authors: Hindman Neil , Lawson Jimmie , Lisan Amha
Published: December 2010

We consider minimal left ideals L of the universal semigroup compactification of a topological semigroup S. We show that the enveloping semigroup of L is homeomorphically isomorphic to if and only if given q ≠ r in , there is some p in the smallest ideal of with qp ≠ rp. We derive several conditions, some involving minimal flows, which are equivalent to the ability to separate q and r in this fashion, and then specialize to the case that S = , and the compactification is . Included is the statement that some set A whose characteristic function is uniformly recurrent has .
Extra-Special Groups of Order 32 as Galois Groups
Authors: Smith Tara L.
Published: December 2010

In this article we examine conditions for the appearance or nonappearance of the twoextra-special 2-groups of order 32 as Galois groups over a fieldFof characteristic not 2. The groups in question are the central productsDDof two dihedral groups of order 8, andDQof a dihedral group with the quaternion group, obtained by identifying the central elements of order 2 in each factor group. It is shown that the realizability of each of these groups as Galois groups overFimplies the realizability of other 2-groups (which are not their quotient groups), and in turn that realizability of certain other 2-groups implies the realizability ofDDandDQ. We conclude by providing an explicit construction of field extensions with Galois groupDD.
Classes D'homotopie de Surfaces Avec Rebroussements et Queues D'aronde dans ℝ3
Authors: Langevin Rémi , Levitt Gilbert , Rosenberg Harold
Published: December 2010

We consider surfaces in ℝ3 with generic wave front singularities, called A-mersions (A for Arnold who classified these singularities), we classify A-mersions up to generic homotopy. For the sphere they are classified by the degree of the Gauss map, and for higher genus surfaces the degree of the Gauss map and the number of zig-zags classify the A-mersion.
Moving Ergodic Theorems for Superadditive Processes
Authors: Ferrando S. E.
Published: December 2010

Letbe a semigroup of measure preserving transformations on a measure space (Ω, ℱ, μ). The main result of the paper is the proof of a.e. convergence for the moving averageswhere {FIn} is a superadditive process and {In} is a sequence of cubes insatisfying the "cone-condition". The identification of the limit is given. A moving local theorem is also proved.
Rational Interpolation of the Exponential Function
Authors: Baratchart L. , Saff E. B. , Wielonsky F.
Published: December 2010

Let m, n be nonnegative integers and B(m+n) be a set of m + n + 1 real interpolation points (not necessarily distinct). Let Rm,n = Pm,n/Qm.n be the unique rational function with deg Pm,n ≤ m, deg Qm,n ≤ n, that interpolates ex in the points of B(m+n). If m = mv, n = nv with mv + nv → ∞, and mv / nv → λ as v → ∞, and the sets B(m+n) are uniformly bounded, we show that locally uniformly in the complex plane C, where the normalization Qm,n(0) = 1 has been imposed. Moreover, for any compact set K ⊂ C we obtain sharp estimates for the error |ez — Rm,n(z)| when z ∈ K. These results generalize properties of the classical Padé approximants. Our convergence theorems also apply to best (real) Lp rational approximants to ex on a finite real interval.
On the Distribution of Supersingular Primes
Authors: Fouvry Etienne , Murty M. Ram
Published: December 2010

Let E be a fixed elliptic curve defined over the rational numbers. We prove that the number of primes p ≤ x such that E has supersingular reduction mod p is greater than for any positive δ and x sufficiently large. Here logkx is defined recursively as log(logk-1 x) and log1x = logx. We also establish several results related to the Lang-Trotter conjecture.
Superresolution Rates in Prokhorov Metric
Authors: Doukhan P. , Gamboa F.
Published: December 2010

Consider the problem of recovering a probability measure supported by a compact subsetUof ℝmwhen the available measurements concern only some of its Ф-moments (Ф being an ℝkvalued continuous function onU). When thetrueФ-momentclies on the boundary of the convex hull of Ф(U), generalizing the results of [10], we construct asmallsetRα,δ(∊)such that any probability measureμsatisfyingisalmostconcentrated onRα,δ(∊). When Ф is a pointwiseT-system (extension ofT-systems), the study of the setRα,δ(∊)leads to the evaluation of the Prokhorov radius of the set.
Density of Resonances for Strictly Convex Analytic Obstacles
Authors: Sjöstrand Johannes
Published: December 2010

We estimate the density of resonances close to a critical curve, for strictly convex obstacles with analytic boundary. Contrary to the C∞-case, already treated with Zworski, the estimates are in terms of dynamical quantities. A new feature in the proof is a certain averaging procedure.
Subspaces of Rearrangement-Invariant Spaces
Authors: Hernandez Francisco L. , Kalton Nigel J.
Published: December 2010

We prove a number of results concerning the embedding of a Banach lattice X into an r. i. space Y. For example we show that if Y is an r. i. space on [0, ∞) which is p-convex for some p > 2 and has nontrivial concavity then any Banach lattice X which is r-convex for some r > 2 and embeds into Y must embed as a sublattice. Similar conclusions can be drawn under a variety of hypotheses on Y; if X is an r. i. space on [0, 1] one can replace the hypotheses of r-convexity for some r > 2 by X ≠ L2.

We also show that if Y is an order-continuous Banach lattice which contains no complemented sublattice lattice-isomorphic to ℓ2X is an order-continuous Banach lattice so that ℓ2 is not complementary lattice finitely representable in X and X is isomorphic to a complemented subspace of Y then X is isomorphic to a complemented sublattice of YN for some integer N.
Extensions Of Subdifferential Calculus Rules in Banach Spaces
Authors: Jourani A. , Thibault L.
Published: December 2010

This paper is devoted to extending formulas for the geometric approximate subdifferential and the Clarke subdifferential of extended-real-valued functions on Banach spaces. The results are strong enough to include completely the finite dimensional setting.
Simple Stably Projectionless C*-Algebras Arising as Crossed Products
Authors: Kishimoto Akitaka , Kumjian Alex
Published: December 2010

large class of simple stably projectionless C*-algebras are shown to arise as crossed products of simple purely infinite C*-algebras by trace scaling one-parameter automorphism groups. The Elliott invariant is computed for this class.
The Hopf Ring for P(n)
Authors: Ravenel Douglas C. , Wilson W. Stephen
Published: December 2010

We show that , the E-homology of the Ω-spectrum for P(n), is an E* free Hopf ring for E a complex oriented theory with In sent to 0. This covers the cases and . The generators of the Hopf ring are those necessary for the stable result. The motivation for this paper is to show that P(n) satisfies all of the conditions for the machinery of unstable cohomology operations set up in [BJW95]. This can then be used to produce splittings analogous to those for BP done in [Wil75]
Local Bifurcations of Critical Periods in the Reduced Kukles System
Authors: Rousseau C. , Toni B.
Published: December 2010

In this paper, we study the local bifurcations of critical periods in the neighborhood of a nondegenerate centre of the reduced Kukles system. We find at the same time the isochronous systems. We show that at most three local critical periods bifurcate from the Christopher-Lloyd centres of finite order, at most two from the linear isochrone and at most one critical period from the nonlinear isochrone. Moreover, in all cases, there exist perturbations which lead to the maximum number of critical periods. We determine the isochrones, using the method of Darboux: the linearizing transformation of an isochrone is derived from the expression of the first integral. Our approach is a combination of computational algebraic techniques (Gröbner bases, theory of the resultant, Sturm’s algorithm), the theory of ideals of noetherian rings and the transversality theory of algebraic curves.
Galois Module Structure of the Integers in Wildly Ramified Cp × Cp Extensions
Authors: Elder G. Griffith , Madan Manohar L.
Published: December 2010

Let L/K be a finite Galois extension of local fields which are finite extensions of ℚp, the field of p-adic numbers. Let Gal(L/K) = G, and 𝔒L and ℤp be the rings of integers in L and ℚp, respectively. And let 𝔓L denote the maximal ideal of 𝔒L. We determine, explicitly in terms of specific indecomposable ℤp[G]-modules, the ℤp[G]-module structure of 𝔒L and 𝔓L, for L, a composite of two arithmetically disjoint, ramified cyclic extensions of K, one of which is only weakly ramified in the sense of Erez [6].
Ray Sequences of Best Rational Approximants For |x|α
Authors: Saff E. B. , Stahl H.
Published: December 2010

The convergence behavior of best uniform rational approximations with numerator degree m and denominator degree n to the function |x|α, α > 0, on [-1, 1] is investigated. It is assumed that the indices (m, n) progress along a ray sequence in the lower triangle of the Walsh table, i.e. the sequence of indices {(m, n)} satisfies

In addition to the convergence behavior, the asymptotic distribution of poles and zeros of the approximants and the distribution of the extreme points of the error function on [-1, 1] will be studied. The results will be compared with those for paradiagonal sequences (m = n + 2[α/2]) and for sequences of best polynomial approximants.
Sets on which Measurable Functions are Determined by their Range
Authors: Burke Maxim R. , Ciesielski Krzysztof
Published: December 2010

We study sets on which measurable real-valued functions on a measurable space with negligibles are determined by their range.
Factorization in the Invertible Group of a C*-Algebra
Authors: Leen Michael J.
Published: December 2010

In this paper we consider the following problem: Given a unital C*- algebra A and a collection of elements S in the identity component of the invertible group of A, denoted inv0(A), characterize the group of finite products of elements of S. The particular C*-algebras studied in this paper are either unital purely infinite simple or of the form (A ⊗ K)+, where A is any C*-algebra and K is the compact operators on an infinite dimensional separable Hilbert space. The types of elements used in the factorizations are unipotents (1+ nilpotent), positive invertibles and symmetries (s2 = 1). First we determine the groups of finite products for each collection of elements in (A ⊗ K)+. Then we give upper bounds on the number of factors needed in these cases. The main result, which uses results for (A ⊗ K)+, is that for A unital purely infinite and simple, inv0(A) is generated by each of these collections of elements.
Subgroups of the Adjoint Group of a Radical Ring
Authors: Amberg B. , Dickenschied O. , Sysak YA. P.
Published: December 2010

It is shown that the adjoint group R° of an arbitrary radical ring R has a series with abelian factors and that its finite subgroups are nilpotent. Moreover, some criteria for subgroups of R° to be locally nilpotent are given.
Six Primes and an Almost Prime in Four Linear Equations
Authors: Balog Antal
Published: December 2010

There are infinitely many triplets of primes p, q, r such that the arithmetic means of any two of them, are also primes. We give an asymptotic formula for the number of such triplets up to a limit. The more involved problem of asking that in addition to the above the arithmetic mean of all three of them, is also prime seems to be out of reach. We show by combining the Hardy-Littlewood method with the sieve method that there are quite a few triplets for which six of the seven entries are primes and the last is almost prime.
On the Liouville Property for Divergence Form Operators
Authors: Barlow Martin T.
Published: December 2010

In this paper we construct a bounded strictly positive function σ such that the Liouville property fails for the divergence form operator L= ▽ (σ2▽). Since in addition Δσ/σ is bounded, this example also gives a negative answer to a problem of Berestycki, Caffarelli and Nirenberg concerning linear Schrödinger operators.
Eigenpolytopes of Distance Regular Graphs
Authors: Godsil C. D.
Published: December 2010

Let X be a graph with vertex set V and let A be its adjacency matrix. If E is the matrix representing orthogonal projection onto an eigenspace of A with dimension m, then E is positive semi-definite. Hence it is the Gram matrix of a set of |V| vectors in Rm. We call the convex hull of a such a set of vectors an eigenpolytope of X. The connection between the properties of this polytope and the graph is strongest when X is distance regular and, in this case, it is most natural to consider the eigenpolytope associated to the second largest eigenvalue of A. The main result of this paper is the characterisation of those distance regular graphs X for which the 1-skeleton of this eigenpolytope is isomorphic to X.
Fourier Multipliers For Local Hardy Spaces On Chébli-Trimèche Hypergroups
Authors: Bloom Walter R. , Xu Zengfu
Published: December 2010

In this paper we consider Fourier multipliers on local Hardy spaces hp (0 < p ≤ 1) for Chébli-Trimèche hypergroups. The molecular characterization is investigated which allows us to prove a version of Hörmander’s multiplier theorem.
Mean Convergence of Lagrange Interpolation for Exponential weights on [-1, 1]
Authors: Lubinsky D. S.
Published: December 2010

We obtain necessary and sufficient conditions for mean convergence of Lagrange interpolation at zeros of orthogonal polynomials for weights on [-1, 1], such as

w(x) = exp(-(1 - x2)-α), α > 0

or

w(x) = exp(-expk(1 - x2)-α), k≥1, α > 0,

where expk = exp(exp(. . . exp( ) . . .)) denotes the k-th iterated exponential.
Separable Reduction and Supporting Properties of Fréchet-Like Normals in Banach Spaces
Authors: Fabian Marián , Mordukhovich Boris S.
Published: December 2010

We develop a method of separable reduction for Fréchet-like normals and ε-normals to arbitrary sets in general Banach spaces. This method allows us to reduce certain problems involving such normals in nonseparable spaces to the separable case. It is particularly helpful in Asplund spaces where every separable subspace admits a Fréchet smooth renorm. As an applicaton of the separable reduction method in Asplund spaces, we provide a new direct proof of a nonconvex extension of the celebrated Bishop-Phelps density theorem. Moreover, in this way we establish new characterizations of Asplund spaces in terms of ε-normals.
Tensor Products and Transferability of Semilattices
Authors: Grätzer G. , Wehrung F.
Published: December 2010

In general, the tensor product, A ⊗ B, of the lattices A and B with zero is not a lattice (it is only a join-semilattice with zero). If A ⊗ B is a capped tensor product, then A ⊗ B is a lattice (the converse is not known). In this paper, we investigate lattices A with zero enjoying the property that A ⊗ B is a capped tensor product, for every lattice B with zero; we shall call such lattices amenable.

The first author introduced in 1966 the concept of a sharply transferable lattice. In 1972, H. Gaskill defined, similarly, sharply transferable semilattices, and characterized them by a very effective condition (T).

We prove that a finite lattice A is amenable iff it is sharply transferable as a join-semilattice.

For a general lattice A with zero, we obtain the result: A is amenable iff A is locally finite and every finite sublattice of A is transferable as a join-semilattice.

This yields, for example, that a finite lattice A is amenable iff A ⊗ F(3) is a lattice iff A satisfies (T), with respect to join. In particular, M3 ⊗ F(3) is not a lattice. This solves a problem raised by R. W. Quackenbush in 1985 whether the tensor product of lattices with zero is always a lattice.
The Representation Ring and the Centre of a Hopf Algebra
Authors: Witherspoon Sarah J.
Published: December 2010

When H is a finite dimensional, semisimple, almost cocommutative Hopf algebra, we examine a table of characters which extends the notion of the character table for a finite group. We obtain a formula for the structure constants of the representation ring in terms of values in the character table, and give the example of the quantum double of a finite group. We give a basis of the centre of H which generalizes the conjugacy class sums of a finite group, and express the class equation of H in terms of this basis. We show that the representation ring and the centre of H are dual character algebras (or signed hypergroups).
Cohomology of Complex Projective Stiefel Manifolds
Authors: Astey L. , Gitler S. , Micha E. , Pastor G.
Published: December 2010

The cohomology algebra mod p of the complex projective Stiefel manifolds is determined for all primes p. When p = 2 we also determine the action of the Steenrod algebra and apply this to the problem of existence of trivial subbundles of multiples of the canonical line bundle over a lens space with 2-torsion, obtaining optimal results in many cases.
Semi-Affine Coxeter-Dynkin Graphs and G ⊆ SU2(C)
Authors: McKay John
Published: December 2010

The semi-affine Coxeter-Dynkin graph is introduced, generalizing both the affine and the finite types.
On Russell-Type Modular Equations
Authors: Chan Heng Huat , Liaw Wen-Chin
Published: December 2010

In this paper, we revisit Russell-type modular equations, a collection of modular equations first studied systematically by R. Russell in 1887. We give a proof of Russell’s main theorem and indicate the relations between such equations and the constructions of Hilbert class fields of imaginary quadratic fields. Motivated by Russell’s theorem, we state and prove its cubic analogue which allows us to construct Russell-type modular equations in the theory of signature 3.
Localization in Categories of Complexes and Unbounded Resolutions
Authors: Alonso Tarrío Leovigildo , Jeremías López Ana , Souto Salorio María José
Published: December 2010

In this paper we show that for a Grothendieck category and a complex E in C() there is an associated localization endofunctor ℓ in D(). This means that ℓ is idempotent (in a natural way) and that the objects that go to 0 by ℓ are those of the smallest localizing (= triangulated and stable for coproducts) subcategory of D() that contains E. As applications, we construct K-injective resolutions for complexes of objects of and derive Brown representability for D() from the known result for D(R-mod), where R is a ring with unit.
Chern Characters of Fourier Modules
Authors: Walters Samuel G.
Published: December 2010

Let Aθ denote the rotation algebra—the universal C*-algebra generated by unitaries U, V satisfying VU = e2πiθUV, where θ is a fixed real number. Let σ denote the Fourier automorphism of Aθ defined by U ↦ V, V ↦ U-1, and let denote the associated C*-crossed product. It is shown that there is a canonical inclusion for each θ given by nine canonical modules. The unbounded trace functionals of Bθ (yielding the Chern characters here) are calculated to obtain the cyclic cohomology group of order zero HC0(Bθ) when θ is irrational. The Chern characters of the nine modules—and more importantly, the Fourier module—are computed and shown to involve techniques from the theory of Jacobi’s theta functions. Also derived are explicit equations connecting unbounded traces across strongMorita equivalence, which turn out to be non-commutative extensions of certain theta function equations. These results provide the basis for showing that for a dense Gδ set of values of θ one has and is generated by the nine classes constructed here.
Algebraic Evaluations of Some Euler Integrals, Duplication Formulae for Appell's Hypergeometric Function F1, and Brownian Variations
Authors: Ismail Mourad E. H. , Pitman Jim
Published: December 2010

Explicit evaluations of the symmetric Euler integral are obtained for some particular functions f. These evaluations are related to duplication formulae for Appell’s hypergeometric function F1 which give reductions of F1(α, β, β, 2α, y, z) in terms of more elementary functions for arbitrary β with z = y/(y − 1) and for β = α + 1/2 with arbitrary y, z. These duplication formulae generalize the evaluations of some symmetric Euler integrals implied by the following result: if a standard Brownian bridge is sampled at time 0, time 1, and at n independent randomtimes with uniformdistribution on [0, 1], then the broken line approximation to the bridge obtained from these n + 2 values has a total variation whose mean square is n(n + 1)/(2n + 1).
Holomorphic Functions of Slow Growth on Nested Covering Spaces of Compact Manifolds
Authors: Lárusson Finnur
Published: December 2010

Let Y be an infinite covering space of a projective manifold M in N of dimension n ≥ 2. Let C be the intersection with M of at most n − 1 generic hypersurfaces of degree d in N. The preimage X of C in Y is a connected submanifold. Let φ be the smoothed distance from a fixed point in Y in a metric pulled up from M. Let φ(X) be the Hilbert space of holomorphic functions f on X such that f2e−φ is integrable on X, and define φ(Y) similarly. Our main result is that (under more general hypotheses than described here) the restriction φ(Y) → φ(X) is an isomorphism for d large enough.

This yields new examples of Riemann surfaces and domains of holomorphy in n with corona. We consider the important special case when Y is the unit ball in n, and show that for d large enough, every bounded holomorphic function on X extends to a unique function in the intersection of all the nontrivial weighted Bergman spaces on . Finally, assuming that the covering group is arithmetic, we establish three dichotomies concerning the extension of bounded holomorphic and harmonic functions from X to .
The Spectrum of an Infinite Graph
Authors: Urakawa Hajime
Published: December 2010

In this paper, we consider the (essential) spectrum of the discrete Laplacian of an infinite graph. We introduce a new quantity for an infinite graph, in terms of which we give new lower bound estimates of the (essential) spectrum and give also upper bound estimates when the infinite graph is bipartite. We give sharp estimates of the (essential) spectrum for several examples of infinite graphs.
Representations with Weighted Frames and Framed Parabolic Bundles
Authors: Hurtubise J. C. , Jeffrey L. C.
Published: December 2010

There is a well-known correspondence (due to Mehta and Seshadri in the unitary case, and extended by Bhosle and Ramanathan to other groups), between the symplectic variety Mh of representations of the fundamental group of a punctured Riemann surface into a compact connected Lie group G, with fixed conjugacy classes h at the punctures, and a complex variety of holomorphic bundles on the unpunctured surface with a parabolic structure at the puncture points. For G = SU(2), we build a symplectic variety P of pairs (representations of the fundamental group into G, “weighted frame” at the puncture points), and a corresponding complex variety of moduli of “framed parabolic bundles”, which encompass respectively all of the spaces Mh, , in the sense that one can obtain Mh from P by symplectic reduction, andMh from by a complex quotient. This allows us to explain certain features of the toric geometry of the SU(2) moduli spaces discussed by Jeffrey and Weitsman, by giving the actual toric variety associated with their integrable system.