bluuebunny/crossref_metadata_2025_split huggingface dataset:
The Addition of Primes and Power
Authors: Brüdern Jörg , Perelli Alberto 
Published: December 2010

AbstractLet 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

AbstractWe 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

AbstractThegenusseries 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

AbstractSeveral 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.
Fiber Completions, Contact Singularities and Single Valued Solutions for C∞-Second Order Ode
Authors: Kossowski Marek 
Published: December 2010

AbstractAn 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

AbstractThe 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

AbstractA 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

AbstractLet 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

AbstractWe 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

AbstractWe 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.
Classifying Pl 5-Manifolds by Regular Genus: The Boundary Case
Authors: Casali Maria Rita 
Published: December 2010

AbstractIn 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

AbstractWe 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

AbstractWe 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

AbstractUsing 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

AbstractThe 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.
Stable Parallelizability of Partially Oriented Flag Manifolds II
Authors: Sankaran Parameswaran , Zvengrowski Peter 
Published: December 2010

AbstractIn 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

AbstractWe 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

AbstractCentral 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

RésuméWe 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

AbstractExamples 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

AbstractConsider 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

AbstractWe 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

AbstractLet 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

AbstractWe 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

AbstractFor 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

AbstractA 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

RésuméSoit 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

AbstractA 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

AbstractLet 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

AbstractIn 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

AbstractWe 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

AbstractA 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

AbstractIn 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.