bluuebunny/crossref_metadata_2025 huggingface dataset:
Topologizing Different Classes of Real Functions
Authors: Ciesielski Krzysztof
Published: December 2010

The purpose of this paper is to examine which classesof functions fromcan be topologized in a sense that there exist topologies τ1and τ2onandrespectively, such thatis equal to the class C(τ1, τ2) of all continuous functions. We will show that the Generalized Continuum Hypothesis GCH implies the positive answer for this question for a large number of classes of functionsfor which the sets {x : f(x) = g(x)} are small in some sense for all f, g ∈f ≠ g. The topologies will be Hausdorff and connected. It will be also shown that in some model of set theory ZFC with GCH these topologies could be completely regular and Baire. One of the corollaries of this theorem is that GCH implies the existence of a connected Hausdorff topology T onsuch that the class L of all linear functions g(x) = ax + b coincides with. This gives an affirmative answer to a question of Sam Nadler. The above corollary remains true for the classof all polynomials, the classof all analytic functions and the class of all harmonic functions.

We will also prove that several other classes of real functions cannot be topologized. This includes the classes of C∞functions, differentiable functions, Darboux functions and derivatives.
On Dihedral Galois Coverings
Authors: Tokunaga Hiro-o
Published: December 2010

In this paper, we shall give a method in constructing dihedral Galois
covering with prescribed branch locus. As an application, we shall look into
dihedral Galois covering of P2, where torsion elements of the
Mordell-Weil group of an elliptic surface play key roles in constructing
coverings
Asymptotic Monotonicity of the Relative Extrema of Jacobi Polynomials
Authors: Wong R. , Zhang J.-M.
Published: December 2010

If μk,n
(α,β) denotes the relative extrema of the
Jacobi polynomial P(α,β)
n(x), ordered so that
μ

k+1,n
(α,β) lies to the left of μ
k,n
(α,β), then R. A. Askey has conjectured
twenty years ago that for

for k = 1,…,
n — 1 and n = 1,2,=. In
this paper, we give an asymptotic expansion for μ

k,n
(α,β) when k is
fixed and n → ∞, which corrects an earlier result of R.
Cooper (1950). Furthermore, we show that Askey's conjecture is true at least in
the asymptotic sense.
Factorization of Positive Invertible Operators in af Algebras
Authors: Huang Houben , Hudson Timothy D.
Published: December 2010

We examine the problem of factoring a positive invertible operator in an AF C*-algebra as T*T for some invertible operator T with both T and T-1 in a triangular AF subalgebra. A factorization theorem for a certain class of positive invertible operators in AF algebras is proven. However, we explicitly construct a positive invertible operator in the CAR algebra which cannot be factored with respect to the 2∞ refinement algebra. Our main result generalizes this example, showing that in any AF algebra, there exist positive invertible operators which fail to factor with respect to a given triangular AF subalgebra. We also show that in the context of AF algebras, the notions of having a factorization and having a weak factorization are the same.
A Dilation and Norm in Several Variable Operator Theory
Authors: Binding Paul , Farenick D. R. , Li Chi-Kwong
Published: December 2010

For every m-tuple of operators acting on a Hilbert space, it is shown that there exists a common dilation of these operators to mcommuting normal operators on some larger Hilbert space. We then introduce a norm on the m-fold cartesian product of ℬ(ℋ) that is defined to be, for a given w-tuple, the infimum of the joint spectral radii of all joint normal dilations of the m operators. This norm has several good features, one of which is that it is invariant under the passage to adjoints.
Generalized Stirling Numbers, Convolution Formulae and p, q-Analogues
Authors: Médicis Anne de , Leroux Pierre
Published: December 2010

In this paper, we study two generalizations of the Stirling numbers of the first and second kinds, inspired from their combinatorial interpretation in terms of 0-1 tableaux. They are the 𝔄-Stirling numbers and the partial Stirling numbers. In particular, we give a q and a p, q-analogue of convolution formulae for Stirling numbers of the second kind, due to Chen and Verde-Star, and we extend these formulae to Stirling numbers of the first kind. Included in this study are the a, d-progressive Stirlingnumbers, corresponding to 0-1 tableaux with column lengths from an arithmetic progression ﹛a + id﹜i≥0.
Free Extensions of Chiral Polytopes
Authors: Schulte Egon , Weiss Asia Ivić
Published: December 2010

Abstract polytopes are discrete geometric structures which generalize the classical notion of a convex polytope. Chiral polytopes are those abstract polytopes which have maximal symmetry by rotation, in contrast to the abstract regular polytopes which have maximal symmetry by reflection. Chirality is a fascinating phenomenon which does not occur in the classical theory. The paper proves the following general extension result for chiral polytopes. If 𝒦 is a chiral polytope with regular facets 𝓕 then among all chiral polytopes with facets 𝒦 there is a universal such polytope 𝓟, whose group is a certain amalgamated product of the groups of 𝒦 and 𝓕. Finite extensions are also discussed.
Free E0-Semigroups
Authors: Fowler Neal J.
Published: December 2010

Given a strongly continuous semigroup of isometries ∪ acting on a Hilbert space ℋ, we construct an E0-semigroup α∪, the free E0-semigroup over ∪, acting on the algebra of all bounded linear operators on full Fock space over ℋ. We show how the semigroup αU⊗V can be regarded as the free product of α∪ and αV. In the case where U is pure of multiplicity n, the semigroup au, called the Free flow of rank n, is shown to be completely spatial with Arveson index +∞. We conclude that each of the free flows is cocycle conjugate to the CAR/CCR flow of rank +∞.
Closed Ideals in a Convolution Algebra of Holomorphic Functions
Authors: Brück Rainer , Müller Jürgen
Published: December 2010

We consider the usual topological vector space H(G) of all functions holomorphic in a region G ⊂ ℂ. If G satisfies certain conditions, it is possible to introduce the Hadamard product as multiplication in H(G), and then H(G) turns out to be a commutative topological algebra. In [5] we characterized the invertible elements in H(G), and the aim of this paper is to study the closed ideals and some further questions.
Extreme Measures with Given Moments or Marginals
Authors: Girardin Valerie
Published: December 2010

We study the generalized moment problem and the marginal constraints problem. We connect them when the measures have a finite support.

The extreme points of the convex set of solutions with a finite support are determined in both problems.

For the moment problem, they are shown to span in the weak topology the set of all the solutions.
A Bernstein-Schoenberg Type Operator: Shape Preserving and Limiting Behaviour
Authors: Goodman T. N. T. , Sharma A.
Published: December 2010

Using a new B-spline basis due to Dahmen, Micchelli and Seidel, we construct a univariate spline approximation operator of Bernstein-Schoenberg type. We show that it shares all the shape preserving properties of the usual Bernstein-Schoenberg operator and we derive a Voronovskaya type asymptotic error estimate.
On the Fundamental Lemma for Standard Endoscopy: Reduction to Unit Elements
Authors: Hales Thomas C.
Published: December 2010

The fundamental lemma for standard endoscopy follows from the matching of unit elements in Hecke algebras. A simple form of the stable trace formula, based on the matching of unit elements, shows the fundamental lemma to be equivalent to a collection of character identities. These character identities are established by comparing them to a compact-character expansion of orbital integrals.
Rational Hauptmoduls are Replicable
Authors: Cummins C. J. , Norton S. P.
Published: December 2010

It is shown that if ƒ is a Hauptmodul with rational integer coefficients for a group G < PGL2(ℚ)+, of genus zero, containing a with finite index and z ⟼ z+k precisely when k is an integer, then ƒ is replicable. Examples of such functions are given by the Moonshine functions described by Conway and Norton [CN].
Analytic Properties of Power Product Expansions
Authors: Gingold H. , Knopfmacher A.
Published: December 2010

Letƒ(z) be a complex function analytic in some neighbourhood of the origin withƒ(0) = 1. It is known thatƒ(z) admits a unique "power product" expansion of the formconvergent near zero. We derive a simple direct bound for the radius of convergence of this product expansion in terms of the coefficients ofƒ(z). In addition we show that the same bound holds in the case of "inverse power product" expansionsExamples are given for which these bounds are sharp. We show also that products with nonnegative coefficients have the same radius of convergence as their corresponding series.
The Topological Nature of Two Noguchi Theorems on Sequences of Holomorphic Mappings Between Complex Spaces
Authors: Joseph James E. , Kwack Myung H.
Published: December 2010

Let C,D,D* be, respectively, the complex plane, {z ∈ C : |z| < 1}, and D — {0}. If P1(C) is the Riemann sphere, the Big Picard theorem states that if ƒ:D* → P1(C) is holomorphic and P1(C) → ƒ(D*) n a s more than two elements, then ƒ has a holomorphic extension . Under certain assumptions on M, A and X ⊂ Y, combined efforts of Kiernan, Kobayashi and Kwack extended the theorem to all holomorphic ƒ: M → A → X. Relying on these results, measure theoretic theorems of Lelong and Wirtinger, and other properties of complex spaces, Noguchi proved in this context that if ƒ: M → A → X and ƒn: M → A → X are holomorphic for each n and ƒn → ƒ, then . In this paper we show that all of these theorems may be significantly generalized and improved by purely topological methods. We also apply our results to present a topological generalization of a classical theorem of Vitali from one variable complex function theory.
ImbeddingC1intoH1
Authors: Tie Jingzhi
Published: December 2010

This article gives a direct proof of Theorem 7.58 of Greiner [4]. This result implies that the classical Mikhlin-Calderón-Zygmund calculus for the principal value convolution operators on ℂ is, in a natural way, the limit of the Laguerre calculus for principal value convolution operators on ℍ1= ℂ x ℝ.
Notes on Extensions of Hopf Algebras
Authors: Andruskiewitsch Nicolás , Witsch Ruskie
Published: December 2010

This article contains examples and applications of the notion of exact sequences of Hopf algebras.
Moore Cohomology and Central Twisted Crossed Product C*-Algebras
Authors: Packer Judith A.
Published: December 2010

Let G be a locally compact second countable group, let X be a locally compact second countable Hausdorff space, and view C(X, T) as a trivial G-module. For G countable discrete abelian, we construct an isomorphism between the Moore cohomology group Hn(G, C(X, T)) and the direct sum Ext(Hn-1(G), Ȟl(βX, Ζ)) ⊕ C(X, Hn(G, T)); here Ȟ1 (βX, Ζ) denotes the first Čech cohomology group of the Stone-Čech compactification of X, βX, with integer coefficients. For more general locally compact second countable groups G, we discuss the relationship between the Moore group H2(G, C(X, T)), the set of exterior equivalence classes of element-wise inner actions of G on the stable continuous trace C*-algebra C0(X) ⊗ 𝒦, and the equivariant Brauer group BrG(X) of Crocker, Kumjian, Raeburn, and Williams. For countable discrete abelian G acting trivially on X, we construct an isomorphism is the group of equivalence classes of principal Ĝ bundles over X first considered by Raeburn and Williams.
C*-Algebras from Smale Spaces
Authors: Putnam Ian F.
Published: December 2010

We consider the C*-algebras constructed from certain hyperbolic dynamical systems. The construction, due to Ruelle, generalizes the C*-algebras of Cuntz and Krieger. We discuss relations between the C*-algebras, show the existence of natural asymptotically abelian systems and investigate the K-theory and E-theory of these C*-algebras.
The Addition of Primes and Power
Authors: Brüdern Jörg , Perelli Alberto
Published: December 2010

Let k ≥ 2 be an integer. Let Ek(N) be the number of natural numbers not exceeding N which are not the sum of a prime and a k-th power of a natural number. Assuming the Riemann Hypothesis for all Dirichlet L-functions it is shown that Ek(N) ≪ N1-1/25k.
On Weighted Sobolev Spaces
Authors: Chua Seng-Kee
Published: December 2010

We study density and extension problems for weighted Sobolev spaces on bounded (ε, δ) domains𝓓when a doubling weight w satisfies the weighted Poincaré inequality on cubes near the boundary of 𝓓 and when it is in the MuckenhouptApclass locally in 𝓓. Moreover, when the weightswi(x) are of the form dist(x,Mi)αi,αi∈ ℝ,Mi⊂ 𝓓that are doubling, we are able to obtain some extension theorems on (ε, ∞) domains.
Maps in Locally Orientable Surfaces, the Double Coset Algebra, and Zonal Polynomials
Authors: Goulden I. P. , Jackson D. M.
Published: December 2010

Thegenusseries is the generating series for the number of maps (inequivalent two-cell embeddings of graphs), in locally orientable surfaces, closed and without boundary, with respect to vertex- and face-degrees, number of edges and genus. Ahypermapis a face two-colourable map. An expression for the genus series for (rooted) hypermaps is derived in terms of zonal polynomials by using a double coset algebra in conjunction with an encoding of a map as a triple of matchings. The expression is analogous to the one obtained for orientable surfaces in terms of Schur functions.
Structural Properties of Weak Cotype 2 Spaces
Authors: Mankiewicz Piotr , Tomczak-Jaegermann Nicole
Published: December 2010

Several characterizations of weak cotype 2 and weak Hilbert spaces are given in terms of basis constants and other structural invariants of Banach spaces. For finite-dimensional spaces, characterizations depending on subspaces of fixed proportional dimension are proved.
Diffusion on Lie Groups (III)
Authors: Varopoulos N. TH.
Published: December 2010

For amenable Lie groups of NC-type the heat kernel satisfies pt ~ t-a. We find the exact value of a ≥ 0.
Fiber Completions, Contact Singularities and Single Valued Solutions for C∞-Second Order Ode
Authors: Kossowski Marek
Published: December 2010

An implicitly defined second order ODE is said to be singular if the second derivative cannot be smoothly written in terms of lower order variables. The standard existence and uniqueness theory cannot be applied to such ODE and the graphs of solutions may fail to be regular curves (i.e., the solutions may have isolated C0-points or may fail to be single valued). In this paper we describe a local analysis for a large class of implicit second order ODE whose singular points satisfy a regularity condition. Within this class of ODE there is a secondary notion of (contact) singularity which is analogous to rest points for regular ODE. Theorems 5, 6, 7 and 8 produce invariants for these singularities which control the existence, uniqueness and the level of regularity in solutions.
The 3x+ 1 Conjugacy Map
Authors: Bernstein Daniel J. , Lagarias Jeffrey C.
Published: December 2010

The 3x+1 mapTand the shift mapSare defined byT(x)= (3x+ 1)/2 forxodd,T(x) = x/2forxeven, whileS(x)= (x− 1)/2 forxodd,S(x) = x/2forxeven. The 3x+ 1 conjugacy map Φ on the 2-adic integersZ2conjugatesStoT, i.e.,Φ oSo Φ-1=T.The map Φ mod2ninduces a permutation ΦnonZ/2nZ. We study the cycle structure of Φn. In particular we show that it has order2n− 4forn ≥6. We also count 1-cycles of Φnfornup to 1000; the results suggest that Φ has exactly two odd fixed points. The results generalize to theax+ bmap, whereabis odd.
Finite Subgroups in Integral Group Rings
Authors: Dokuchaev Michael A. , Juriaans Stanley O.
Published: December 2010

A p-subgroup version of the conjecture of Zassenhaus is proved for some finite solvable groups including solvable groups in which any Sylow p-subgroup is either abelian or generalized quaternion, solvable Frobenius groups, nilpotent-by-nilpotent groups and solvable groups whose orders are not divisible by the fourth power of any prime.
Induction and Restriction of π-Partial Characters and their Lifts
Authors: Isaacs I. M.
Published: December 2010

Let G be a finite π-separable group, where π is a set of primes. The π-partial characters of G are the restrictions of the ordinary characters to the set of π-elements of G. Such an object is said to be irreducible if it is not the sum of two nonzero partial characters and the set of irreducible π- partial characters of G is denoted Iπ(G). (If p is a prime and π = p′, then Iπ(G) is exactly the set of irreducible Brauer characters at p.)

From their definition, it is obvious that each partial character φ ∊ Iπ(G) can be “lifted” to an ordinary character χ ∊ Irr(G). (This means that φ is the restriction of χ to the π-elements of G.) In fact, there is a known set of canonical lifts Bπ(G) ⊆ Irr(G) for the irreducible π-partial characters. In this paper, it is proved that if 2 ∉ π, then there is an alternative set of canonical lifts (denoted Dπ(G)) that behaves better with respect to character induction.

An application of this theory to M-groups is presented. If G is an M-group and S ⊆ G is a subnormal subgroup, consider a primitive character θ ⊆ Irr(S). It was known previously that if |G : S| is odd, then θ must be linear. It is proved here without restriction on the index of S that θ(1) is a power of 2.
The Representation Ring of the Twisted Quantum Double of a Finite Group
Authors: Witherspoon S. J.
Published: December 2010

We provide an isomorphism between the Grothendieck ring of modules of the twisted quantum double of a finite group, and a product of centres of twisted group algebras of centralizer subgroups. It follows that this Grothendieck ring is semisimple. Another consequence is a formula for the characters of this ring in terms of representations of twisted group algebras of centralizer subgroups.
Spatial Branching Processes and Subordination
Authors: Bertoin Jean , Le Gall Jean-François , Le Jan Yves
Published: December 2010

We present a subordination theory for spatial branching processes. This theory is developed in three different settings, first for branching Markov processes, then for superprocesses and finally for the path-valued process called the Brownian snake. As a common feature of these three situations, subordination can be used to generate new branching mechanisms. As an application, we investigate the compact support property for superprocesses with a general branching mechanism.
The Classical Limit of Dynamics for Spaces Quantized by an Action of ℝd
Authors: Rieffel Marc A.
Published: December 2010

We have previously shown how to construct a deformation quantization of any locally compact space on which a vector group acts. Within this framework we show here that, for a natural class of Hamiltonians, the quantum evolutions will have the classical evolution as their classical limit.
Classifying Pl 5-Manifolds by Regular Genus: The Boundary Case
Authors: Casali Maria Rita
Published: December 2010

In the present paper, we face the problem of classifying classes of orientable PL 5-manifolds M5 with h ≥ 1 boundary components, by making use of a combinatorial invariant called regular genusG(M5). In particular, a complete classification up to regular genus five is obtained: where denotes the regular genus of the boundary ∂M5 and denotes the connected sumof h ≥ 1 orientable 5-dimensional handlebodies 𝕐αi of genus αi ≥ 0 (i = 1, . . . ,h), so that .

Moreover, we give the following characterizations of orientable PL 5-manifolds M5 with boundary satisfying particular conditions related to the “gap” between G(M5) and either G(∂M5) or the rank of their fundamental group rk(π1(M5)): Further, the paper explains how the above results (together with other known properties of regular genus of PL manifolds) may lead to a combinatorial approach to 3-dimensional Poincaré Conjecture.
On Some Alternative Characterizations of Riordan Arrays
Authors: Merlini Donatella , Rogers Douglas G. , Sprugnoli Renzo , Verri M. Cecilia
Published: December 2010

We give several new characterizations of Riordan Arrays, the most important of which is: if {dn,k}n,k∈N is a lower triangular arraywhose generic element dn,k linearly depends on the elements in a well-defined though large area of the array, then {dn,k}n,k∈N is Riordan. We also provide some applications of these characterizations to the lattice path theory.
Characteristic Cycles in Hermitian Symmetric Spaces
Authors: Boe Brian D. , Fu Joseph H. G.
Published: December 2010

We give explicit combinatorial expresssions for the characteristic cycles associated to certain canonical sheaves on Schubert varieties X in the classical Hermitian symmetric spaces: namely the intersection homology sheaves IHX and the constant sheaves ℂX. The three main cases of interest are the Hermitian symmetric spaces for groups of type An (the standard Grassmannian), Cn (the Lagrangian Grassmannian) and Dn. In particular we find that CC(IHX) is irreducible for all Schubert varieties X if and only if the associated Dynkin diagramis simply laced. The result for Schubert varieties in the standard Grassmannian had been established earlier by Bressler, Finkelberg and Lunts, while the computations in the Cn and Dn cases are new.

Our approach is to compute CC(ℂX) by a direct geometric method, then to use the combinatorics of the Kazhdan-Lusztig polynomials (simplified for Hermitian symmetric spaces) to compute CC(IHX). The geometric method is based on the fundamental formula where the Xr ↓ X constitute a family of tubes around the variety X. This formula leads at once to an expression for the coefficients of CC(ℂX) as the degrees of certain singular maps between spheres.
Fine Spectra and Limit Laws I. First-Order Laws
Authors: Burris Stanley , Sárközy András
Published: December 2010

Using Feferman-Vaught techniques we show a certain property of the fine spectrumof an admissible class of structures leads to a first-order law. The condition presented is best possible in the sense that if it is violated then one can find an admissible class with the same fine spectrum which does not have a first-order law. We present three conditions for verifying that the above property actually holds.

The first condition is that the count function of an admissible class has regular variation with a certain uniformity of convergence. This applies to a wide range of admissible classes, including those satisfying Knopfmacher's Axiom A, and those satisfying Bateman and Diamond's condition.

The second condition is similar to the first condition, but designed to handle the discrete case, i.e., when the sizes of the structures in an admissible class K are all powers of a single integer. It applies when either the class of indecomposables or the whole class satisfies Knopfmacher's Axiom A#.

The third condition is also for the discrete case, when there is a uniform bound on the number of K-indecomposables of any given size.
Maps in Locally Orientable Surfaces and Integrals Over Real Symmetric Surfaces
Authors: Goulden I. P. , Jackson D. M.
Published: December 2010

The genus series for maps is the generating series for the number of rooted maps with a given number of vertices and faces of each degree, and a given number of edges. It captures topological information about surfaces, and appears in questions arising in statistical mechanics, topology, group rings, and certain aspects of free probability theory. An expression has been given previously for the genus series for maps in locally orientable surfaces in terms of zonal polynomials. The purpose of this paper is to derive an integral representation for the genus series. We then show how this can be used in conjunction with integration techniques to determine the genus series for monopoles in locally orientable surfaces. This complements the analogous result for monopoles in orientable surfaces previously obtained by Harer and Zagier. A conjecture, subsequently proved by Okounkov, is given for the evaluation of an expectation operator acting on the Jack symmetric function. It specialises to known results for Schur functions and zonal polynomials.
Tensor Products of Analytic Continuations of Holomorphic Discrete Series
Authors: Ørsted Bent , Zhang Genkai
Published: December 2010

We give the irreducible decomposition of the tensor product of an analytic continuation of the holomorphic discrete series of SU(2, 2) with its conjugate.
Stable Parallelizability of Partially Oriented Flag Manifolds II
Authors: Sankaran Parameswaran , Zvengrowski Peter
Published: December 2010

In the first paper with the same title the authors were able to determine all partially oriented flag manifolds that are stably parallelizable or parallelizable, apart from four infinite families that were undecided. Here, using more delicate techniques (mainly K-theory),we settle these previously undecided families and show that none of the manifolds in them is stably parallelizable, apart from one 30-dimensional manifold which still remains undecided.
On Critical Level Sets of Some two Degrees of Freedom Integrable Hamiltonian Systems
Authors: Médan Christine
Published: December 2010

We prove that all Liouville's tori generic bifurcations of a large class of two degrees of freedom integrable Hamiltonian systems (the so called Jacobi–Moser– Mumford systems) are nondegenerate in the sense of Bott. Thus, for such systems, Fomenko's theory [4] can be applied (we give the example of Gel'fand–Dikii's system). We also check the Bott property for two interesting systems: the Lagrange top and the geodesic flow on an ellipsoid.
The Torsion Free Pieri Formula
Authors: Britten D. J. , Lemire F. W.
Published: December 2010

Central to the study of simple infinite dimensional g𝓵(n, C)-modules having finite dimensional weight spaces are the torsion free modules. All degree 1 torsion free modules are known. Torsion free modules of arbitrary degree can be constructed by tensoring torsion free modules of degree 1 with finite dimensional simple modules. In this paper, the central characters of such a tensor product module are shown to be given by a Pieri-like formula, complete reducibility is established when these central characters are distinct and an example is presented illustrating the existence of a nonsimple indecomposable submodule when these characters are not distinct.
Noncommutative Disc Algebras for Semigroups
Authors: Davidson Kenneth R. , Popescu Gelu
Published: December 2010

We study noncommutative disc algebras associated to the free product of discrete subsemigroups of ℝ+. These algebras are associated to generalized Cuntz algebras, which are shown to be simple and purely infinite. The nonself-adjoint subalgebras determine the semigroup up to isomorphism. Moreover, we establish a dilation theorem for contractive representations of these semigroups which yields a variant of the von Neumann inequality. These methods are applied to establish a solution to the truncated moment problem in this context.
Purely Infinite, Simple C*-Algebras Arising From Free Product Constructions
Authors: Dykema Kenneth J. , Rørdam Mikael
Published: December 2010

Examples of simple, separable, unital, purely infinite C*-algebras are
constructed, including:

(1)

some that are not approximately divisible;

(2)

those that arise as crossed products of any of a certain class of C*-algebras by any of a certain class of non–unital endomorphisms;

(3)

those that arise as reduced free products of pairs of C*-algebras with respect
to any from a certain class of states.
Primes in Short Segments of Arithmetic Progressions
Authors: Goldston D. A. , Yildirim C. Y.
Published: December 2010

Consider the variance for the number of primes that are both in the interval [y,y + h] for y ∈ [x,2x] and in an arithmetic progression of modulus q. We study the total variance obtained by adding these variances over all the reduced residue classes modulo q. Assuming a strong form of the twin prime conjecture and the Riemann Hypothesis one can obtain an asymptotic formula for the total variance in the range when 1 ≤ h/q ≤ x1/2-∈ , for any ∈ > 0. We show that one can still obtain some weaker asymptotic results assuming the Generalized Riemann Hypothesis (GRH) in place of the twin prime conjecture. In their simplest form, our results are that on GRH the same asymptotic formula obtained with the twin prime conjecture is true for “almost all” q in the range 1 ≤ h/q ≤ x1/4-∈, that on averaging over q one obtains an asymptotic formula in the extended range 1 ≤ h/q ≤ x1/2-∈, and that there are lower bounds with the correct order of magnitude for all q in the range 1 ≤ h/q ≤ x1/3-∈.
Estimates on Renormalization Group Transformations
Authors: Brydges D. , Dimock J. , Hurd T. R.
Published: December 2010

We consider a specific realization of the renormalization group (RG) transformation acting on functional measures for scalar quantum fields which are expressible as a polymer expansion times an ultra-violet cutoff Gaussian measure. The new and improved definitions and estimates we present are sufficiently general and powerful to allow iteration of the transformation, hence the analysis of complete renormalization group flows, and hence the construction of a variety of scalar quantum field theories.
Galois Module Structure of Ambiguous Ideals in Biquadratic Extensions
Authors: Elder G. Griffith
Published: December 2010

Let N/K be a biquadratic extension of algebraic number fields, and G = Gal(N/K). Under a weak restriction on the ramification filtration associated with each prime of K above 2, we explicitly describe the ℤ[G]-module structure of each ambiguous ideal of N. We find under this restriction that in the representation of each ambiguous ideal as a ℤ[G]-module, the exponent (or multiplicity) of each indecomposable module is determined by the invariants of ramification, alone.

For a given group, G, define SG to be the set of indecomposable ℤ[G]-modules, M, such that there is an extension, N/K, for which G ≅ Gal(N/K), and M is a ℤ[G]-module summand of an ambiguous ideal of N. Can SG ever be infinite? In this paper we answer this question of Chinburg in the affirmative.
Gradient Estimates for Harmonic Functions on Manifolds With Lipschitz Metrics
Authors: Chen Jingyi , Hsu Elton P.
Published: December 2010

We introduce a distributional Ricci curvature on complete smooth manifolds with Lipschitz continuous metrics. Under an assumption on the volume growth of geodesics balls, we obtain a gradient estimate for weakly harmonic functions if the distributional Ricci curvature is bounded below.
Integral Representation of P-Class Groups In ℤp-Extensions and the Jacobian Variety
Authors: Pedro Ricardo López-Bautista , Villa-Salvador Gabriel Daniel
Published: December 2010

For an arbitrary finite Galois p-extension L/K of ℤp-cyclotomic number fields of CM-type with Galois group G = Gal(L/K) such that the Iwasawa invariants are zero, we obtain unconditionally and explicitly the Galois module structure of CL-(p), the minus part of the p-subgroup of the class group of L. For an arbitrary finite Galois p-extension L/K of algebraic function fields of one variable over an algebraically closed field k of characteristic p as its exact field of constants with Galois group G = Gal(L/K) we obtain unconditionally and explicitly the Galois module structure of the p-torsion part of the Jacobian variety JL(p) associated to L/k.
Tractable Fields
Authors: Chacron M. , Tignol J.-P. , Wadsworth A. R.
Published: December 2010

A field F is said to be tractable when a condition described below on the simultaneous representation of quaternion algebras holds over F. It is shown that a global field F is tractable iff F has at most one dyadic place. Several other examples of tractable and nontractable fields are given.
Algèbres quasi-commutatives et carrés de Steenrod
Authors: Ndombol Bitjong , El haouari M.
Published: December 2010

Soit k un corps de caractéristique p quelconque. Nous définissons la catégorie des k-algèbres de cochaînes fortement quasi-commutatives et nous donnons une condition nécessaire et suffisante pour que l’algèbre de cohomologie à coefficients dans Z2 d’un objet de cette catégorie soit un module instable sur l’algèbre de Steenrod à coefficients dans Z2.

A tout c.w. complexe simplement connexe de type fini X on associe une k-algèbre de cochaînes fortement quasi-commutative; la structure de module sur l’algèbre de Steenrod définie sur l’algèbre de cohomologie de celle-ci coïncide avec celle de H*(X; Z2).
On a Theorem of Hermite and Joubert
Authors: Reichstein Zinovy
Published: December 2010

A classical theorem of Hermite and Joubert asserts that any field extension of degree n = 5 or 6 is generated by an element whose minimal polynomial is of the form λn + c1λn−1 + ··· + cn−1λ + cn with c1 = c3 = 0. We show that this theorem fails for n = 3m or 3m + 3l (and more generally, for n = pm or pm + pl, if 3 is replaced by another prime p), where m > l ≥ 0. We also prove a similar result for division algebras and use it to study the structure of the universal division algebra UD(n).

We also prove a similar result for division algebras and use it to study the structure of the universal division algebra UD(n).
Homeomorphic Analytic Maps into the Maximal Ideal Space of H∞
Authors: Suárez Daniel
Published: December 2010

Let m be a point of the maximal ideal space of H∞ with nontrivial Gleason part P(m). If Lm : D → P(m) is the Hoffman map, we show that H∞ ° Lm is a closed subalgebra of H∞. We characterize the points m for which Lm is a homeomorphism in terms of interpolating sequences, and we show that in this case H∞ ° Lm coincides with H∞. Also, if Im is the ideal of functions in H∞ that identically vanish on P(m), we estimate the distance of any f ϵ H∞ to Im.
A Brunn-Minkowski Type Theorem on the Minkowski Spacetime
Authors: Bahn Hyoungsick , Ehrlich Paul
Published: December 2010

In this article, we derive a Brunn-Minkowski type theorem for sets bearing some relation to the causal structure on the Minkowski spacetime. We also present an isoperimetric inequality in the Minkowski spacetimeas a consequence of this Brunn-Minkowski type theorem.
On Polynomial Invariants of Exceptional Simple Algebraic Groups
Authors: Elduque A. , Iltyakov A. V.
Published: December 2010

We study polynomial invariants of systems of vectors with respect to exceptional simple algebraic groups in their minimal linear representations. For each type we prove that the algebra of invariants is integral over the subalgebra of trace polynomials for a suitable algebraic system (cf. [27], [28], [13]).
Quotient Hereditarily Indecomposable Banach Spaces
Authors: Ferenczi V.
Published: December 2010

A Banach space X is said to be quotient hereditarily indecomposable if no infinite dimensional quotient of a subspace of X is decomposable. We provide an example of a quotient hereditarily indecomposable space, namely the space XGM constructed by W. T. Gowers and B. Maurey in [GM]. Then we provide an example of a reflexive hereditarily indecomposable space whose dual is not hereditarily indecomposable; so is not quotient hereditarily indecomposable. We also show that every operator on * is a strictly singular perturbation of an homothetic map.
Langlands-Shahidi Method and Poles of Automorphic L-Functions: Application to Exterior Square L-Functions
Authors: Kim Henry H.
Published: December 2010

In this paper we use Langlands-Shahidimethod and the result of Langlands which says that non selfconjugatemaximal parabolic subgroups do not contribute to the residual spectrum, to prove the holomorphy of several completed automorphic L-functions on the whole complex plane which appear in constant terms of the Eisenstein series. They include the exterior square L-functions of GLn, n odd, the Rankin-Selberg L-functions of GLn × GLm, n ≠ m, and L-functions L(s, σ, r), where σ is a generic cuspidal representation of SO10 and r is the half-spin representation of GSpin(10, ). The main part is proving the holomorphy and non-vanishing of the local normalized intertwining operators by reducing them to natural conjectures in harmonic analysis, such as standard module conjecture.
Galois Representations with Non-Surjective Traces
Authors: David Chantal , Kisilevsky Hershy , Pappalardi Francesco
Published: December 2010

Let E be an elliptic curve over , and let r be an integer. According to the Lang-Trotter conjecture, the number of primes p such that ap(E) = r is either finite, or is asymptotic to CE,r√x/log x where CE,r is a non-zero constant. A typical example of the former is the case of rational ℓ-torsion, where ap(E) = r is impossible if r ≡ 1 (mod ℓ). We prove in this paper that, when E has a rational ℓ-isogeny and ℓ ≠ 11, the number of primes p such that ap(E) ≡ r (mod ℓ) is finite (for some r modulo ℓ) if and only if E has rational ℓ-torsion over the cyclotomic field (ζℓ). The case ℓ = 11 is special, and is also treated in the paper. We also classify all those occurences.
First Steps of Local Contact Algebra
Authors: Arnold V. I.
Published: December 2010

We consider germs of mappings of a line to contact space and classify the first simple singularities up to the action of contactomorphisms in the target space and diffeomorphisms of the line. Even in these first cases there arises a new interesting interaction of local commutative algebra with contact structure.
Quadratic Integers and Coxeter Groups
Authors: Johnson Norman W. , Weiss Asia Ivić
Published: December 2010

Matrices whose entries belong to certain rings of algebraic integers can be associated with discrete groups of transformations of inversiven-space or hyperbolic (n+1)-space Hn+1. For smalln, thesemay be Coxeter groups, generated by reflections, or certain subgroups whose generators include direct isometries of Hn+1. We show how linear fractional transformations over rings of rational and (real or imaginary) quadratic integers are related to the symmetry groups of regular tilings of the hyperbolic plane or 3-space. New light is shed on the properties of the rational modular group PSL2(), the Gaussian modular (Picard) group PSL2([i]), and the Eisenstein modular group PSL2([ω]).
A Stochastic Calculus Approach for the Brownian Snake
Authors: Dhersin Jean-Stéphane , Serlet Laurent
Published: December 2010

We study the “Brownian snake” introduced by Le Gall, and also studied by Dynkin, Kuznetsov, Watanabe. We prove that Itô’s formula holds for a wide class of functionals. As a consequence, we give a new proof of the connections between the Brownian snake and super-Brownian motion. We also give a new definition of the Brownian snake as the solution of a well-posed martingale problem. Finally, we construct a modified Brownian snake whose lifetime is driven by a path-dependent stochastic equation. This process gives a representation of some super-processes.
Spectral Problems for Non-Linear Sturm-Liouville Equations with Eigenparameter Dependent Boundary Conditions
Authors: Binding Paul A. , Browne Patrick J. , Watson Bruce A.
Published: December 2010

The nonlinear Sturm-Liouville equation

−(pyʹ)ʹ +qy= λ(1 −f)ryon [0, 1]

is considered subject to the boundary conditions

(ajλ +bj)y(j) = (cjλ +dj)(pyʹ)(j),j= 0, 1.

Herea0= 0 =c0andp, r> 0 andqare functions depending on the independent variablexalone, whilefdepends onx, yandyʹ. Results are given on existence and location of sets of (λ,y) bifurcating from the linearized eigenvalues, and for whichyhas prescribed oscillation count, and on completeness of theyin an appropriate sense.
Sums of Two Squares in Short Intervals
Authors: Balog Antal , Wooley Trevor D.
Published: December 2010

Letdenote the set of integers representable as a sum of two squares. Sincecan be described as the unsifted elements of a sieving process of positive dimension, it is to be expected thathasmany properties in common with the set of prime numbers. In this paper we exhibit “unexpected irregularities” in the distribution of sums of two squares in short intervals, a phenomenon analogous to that discovered by Maier, over a decade ago, in the distribution of prime numbers. To be precise, we show that there are infinitely many short intervals containing considerably more elements ofthan expected, and infinitely many intervals containing considerably fewer than expected.
Le problème de Neumann pour certaines équations du type de Monge-Ampère sur une variété riemannienne
Authors: Hanani Abdellah
Published: December 2010

Let (Mn, g) be a strictly convex riemannian manifold with C∞ boundary. We prove the existence of classical solution for the nonlinear elliptic partial differential equation of Monge-Ampère: det in M with a Neumann condition on the boundary of the form , where is an everywhere strictly positive function satisfying some assumptions, ν stands for the unit normal vector field and is a non-decreasing function in u.
The Dunford-Pettis Property for Symmetric Spaces
Authors: Kamińska Anna , Mastyło Mieczysław
Published: December 2010

A complete description of symmetric spaces on a separable measure space with the Dunford-Pettis property is given. It is shown that ℓ1, c0 and ℓ∞ are the only symmetric sequence spaces with the Dunford- Pettis property, and that in the class of symmetric spaces on (0, α), 0 < α ≤ ∞, the only spaces with the Dunford-Pettis property are L1, L∞, L1 ∩ L∞, L1 + L∞, (L∞)◦ and (L1 + L∞)◦, where X◦ denotes the norm closure of L1 ∩ L∞ in X. It is also proved that all Banach dual spaces of L1 ∩ L∞ and L1 + L∞ have the Dunford-Pettis property. New examples of Banach spaces showing that the Dunford-Pettis property is not a three-space property are also presented. As applications we obtain that the spaces (L1 + L∞)◦ and (L∞)◦ have a unique symmetric structure, and we get a characterization of the Dunford-Pettis property of some Köthe-Bochner spaces.
Complex Monge-Ampère Measures of Plurisubharmonic Functions with Bounded Values Near the Boundary
Authors: Xing Yang
Published: December 2010

We give a characterization of bounded plurisubharmonic functions by using their complex Monge-Ampère measures. This implies a both necessary and sufficient condition for a positive measure to be complex Monge-Ampère measure of some bounded plurisubharmonic function.
Ramanujan Type Buildings
Authors: Ballantine Cristina M.
Published: December 2010

We will construct a finite union of finite quotients of the affine building of the group GL3 over the field of p-adic numbers p. We will view this object as a hypergraph and estimate the spectrum of its underlying graph.
On the Curves Associated to Certain Rings of Automorphic Forms
Authors: Khuri-Makdisi Kamal
Published: December 2010

In a 1987 paper, Gross introduced certain curves associated to a definite quaternion algebra B over Q; he then proved an analog of his result with Zagier for these curves. In Gross’ paper, the curves were defined in a somewhat ad hoc manner. In this article, we present an interpretation of these curves as projective varieties arising from graded rings of automorphic forms on B×, analogously to the construction in the Satake compactification. To define such graded rings, one needs to introduce a “multiplication” of automorphic forms that arises from the representation ring of B×. The resulting curves are unions of projective lines equipped with a collection of Hecke correspondences. They parametrize two-dimensional complex tori with quaternionic multiplication. In general, these complex tori are not abelian varieties; they are algebraic precisely when they correspond to CM points on these curves, and are thus isogenous to a product E × E, where E is an elliptic curve with complex multiplication. For these CM points one can make a relation between the action of the p-th Hecke operator and Frobenius at p, similar to the well-known congruence relation of Eichler and Shimura.
Bivariate Polynomials of Least Deviation from Zero
Authors: Bojanov Borislav D. , Haußmann Werner , Nikolov Geno P.
Published: December 2010

Bivariate polynomials with a fixed leading term xmyn, which deviate least fromzero in the uniform or L2-norm on the unit disk D (resp. a triangle) are given explicitly. A similar problem in Lp, 1 ≤ p ≤ ∞, is studied on D in the set of products of linear polynomials.
K-Theory of Non-Commutative Spheres Arising from the Fourier Automorphism
Authors: Walters Samuel G.
Published: December 2010

For a dense Gδ set of real parameters θ in [0, 1] (containing the rationals) it is shown that the group K0(Aθ ⋊σ) is isomorphic to , where Aθ is the rotation C*-algebra generated by unitaries U, V satisfying VU = e2πiθUV and σ is the Fourier automorphism of Aθ defined by σ(U) = V, σ(V) = U−1. More precisely, an explicit basis for K0 consisting of nine canonical modules is given. (A slight generalization of this result is also obtained for certain separable continuous fields of unital C*-algebras over [0, 1].) The Connes Chern character ch: K0(Aθ ⋊σ) → Hev (Aθ ⋊σ)* is shown to be injective for a dense Gδ set of parameters θ. The main computational tool in this paper is a group homomorphism T: K0(Aθ ⋊σ) → obtained from the Connes Chern character by restricting the functionals in its codomain to a certain nine-dimensional subspace of Hev (Aθ ⋊σ). The range of T is fully determined for each θ. (We conjecture that this subspace is all of Hev.)
Jacquet Modules of Parabolically Induced Representations and Weyl Groups
Authors: Ban Dubravka
Published: December 2010

The representation parabolically induced from an irreducible supercuspidal representation is considered. Irreducible components of Jacquet modules with respect to induction in stages are given. The results are used for consideration of generalized Steinberg representations.
Inverse Problems for Partition Functions
Authors: Yang Yifan
Published: December 2010

Let pw(n) be the weighted partition function defined by the generating function , where w(m) is a non-negative arithmetic function. Let be the summatory functions for pw(n) and w(n), respectively. Generalizing results of G. A. Freiman and E. E. Kohlbecker, we show that, for a large class of functions Φ(u) and λ(u), an estimate for Pw(u) of the formlog Pw(u) = Φ(u){1 + Ou(1/λ(u))} (u→∞) implies an estimate forNw(u) of the formNw(u) = Φ*(u){1+O(1/ log ƛ(u))} (u→∞) with a suitable function Φ*(u) defined in terms of Φ(u). We apply this result and related results to obtain characterizations of the Riemann Hypothesis and the Generalized Riemann Hypothesis in terms of the asymptotic behavior of certain weighted partition functions.
Potential Theory in Lipschitz Domains
Authors: Varopoulos N. Th.
Published: December 2010

We prove comparison theorems for the probability of life in a Lipschitz domain between Brownian motion and random walks.
Sur le comportement, par torsion, des facteurs epsilon de paires
Authors: Bushnell Colin J. , Henniart Guy
Published: December 2010

Soient$F$un corps commutatif localement compact non archimédien et$\psi$un caractère additif non trivial de$F$. Soient$n$et${n}'$deux entiers distincts, supérieurs à 1. Soient$\pi$et${\pi }'$des représentations irréductibles supercuspidales de$\text{G}{{\text{L}}_{n}}\left( F \right)$,$\text{G}{{\text{L}}_{{{n}'}}}\left( F \right)$respectivement. Nous prouvons qu’il existe un élément$c=c\left( \pi ,{\pi }',\psi \right)$de${{F}^{\times }}$tel que pour tout quasicaractère modéré$\mathcal{X}$de${{F}^{\times }}$on ait$\mathcal{E}\left( \chi \pi \times {\pi }',s,\psi \right)=\chi {{\left( c \right)}^{-1}}\mathcal{E}\left( \pi \times {\pi }',s,\psi \right)$. Nous examinons aussi certains cas où$n={n}',{\pi }'={{\pi }^{\text{v}}}$. Les résultats obtenus forment une étape vers une démonstration de la conjecture de Langlands pour$F$, qui ne fasse pas appel à la géométrie des variétés modulaires, de Shimura ou de Drinfeld.
A Generalized Variational Principle
Authors: Loewen Philip D. , Wang Xianfu
Published: December 2010

We prove a strong variant of the Borwein-Preiss variational principle, and show that on Asplund spaces, Stegall's variational principle follows from it via a generalized Smulyan test. Applications are discussed.