bluuebunny/crossref_metadata_2025_split huggingface dataset:
Chern Characters of Fourier Modules
Authors: Walters Samuel G. 
Published: December 2010

AbstractLet 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

AbstractExplicit 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

AbstractLet 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

AbstractIn 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

AbstractThere 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.
Well Ramified Extensions of Complete Discrete Valuation Fields with Applications to the Kato Conductor
Authors: Spriano Luca 
Published: December 2010

AbstractWe study extensions L/K of complete discrete valuation fields K with residue field of characteristic p > 0, which we do not assume to be perfect. Our work concerns ramification theory for such extensions, in particular we show that all classical properties which are true under the hypothesis “the residue field extensionis separable” are still valid under the more general hypothesis that the valuation ring extension is monogenic. We also show that conversely, if classical ramification properties hold true for an extension L/K, then the extension of valuation rings is monogenic. These are the “well ramified” extensions. We show that there are only three possible types of well ramified extensions and we give examples. In the last part of the paper we consider, for the three types, Kato’s generalization of the conductor, which we show how to bound in certain cases.
On the Tempered Spectrum of Quasi-Split Classical Groups II
Authors: Goldberg David , Shahidi Freydoon 
Published: December 2010

AbstractWe determine the poles of the standard intertwining operators for a maximal parabolic subgroup of the quasi-split unitary group defined by a quadratic extension E/F of p-adic fields of characteristic zero. We study the case where the Levi component M ≃ GLn(E) × Um(F), with n ≡ m (mod 2). This, along with earlier work, determines the poles of the local Rankin-Selberg product L-function L(s, t′ × τ), with t′ an irreducible unitary supercuspidal representation of GLn(E) and τ a generic irreducible unitary supercuspidal representation of Um(F). The results are interpreted using the theory of twisted endoscopy.
Inequivalent Transitive Factorizations into Transpositions
Authors: Goulden I. P. , Jackson D. M. , Latour F. G. 
Published: December 2010

AbstractThe question of counting minimal factorizations of permutations into transpositions that act transitively on a set has been studied extensively in the geometrical setting of ramified coverings of the sphere and in the algebraic setting of symmetric functions.It is natural, however, from a combinatorial point of view to ask how such results are affected by counting up to equivalence of factorizations, where two factorizations are equivalent if they differ only by the interchange of adjacent factors that commute. We obtain an explicit and elegant result for the number of such factorizations of permutations with precisely two factors. The approach used is a combinatorial one that rests on two constructions.We believe that this approach, and the combinatorial primitives that have been developed for the “cut and join” analysis, will also assist with the general case.
The Symplectic Geometry of Polygons in the 3-Sphere
Authors: Treloar Thomas 
Published: December 2010

AbstractWe study the symplectic geometry of the moduli spaces Mr = Mr() of closed n-gons with fixed side-lengths in the 3-sphere. We prove that these moduli spaces have symplectic structures obtained by reduction of the fusion product of n conjugacy classes in SU(2) by the diagonal conjugation action of SU(2). Here the fusion product of n conjugacy classes is a Hamiltonian quasi-Poisson SU(2)-manifold in the sense of [AKSM]. An integrable Hamiltonian system is constructed on Mr in which the Hamiltonian flows are given by bending polygons along a maximal collection of nonintersecting diagonals. Finally, we show the symplectic structure on Mr relates to the symplectic structure obtained from gauge-theoretic description of Mr. The results of this paper are analogues for the 3-sphere of results obtained for Mr(), the moduli space of n-gons with fixed side-lengths in hyperbolic 3-space [KMT], and for Mr(), the moduli space of n-gons with fixed side-lengths in [KM1].
On the Classification of Simple Stably Projectionless C*-Algebras
Authors: Razak Shaloub 
Published: December 2010

AbstractIt is shown that simple stably projectionless C*-algebras which are inductive limits of certain specified building blocks with trivial K-theory are classified by their cone of positive traces with distinguished subset. This is the first example of an isomorphism theorem verifying the conjecture of Elliott for a subclass of the stably projectionless algebras.
Lie Algebras of Pro-Affine Algebraic Groups
Authors: Nahlus Nazih 
Published: December 2010

AbstractWe extend the basic theory of Lie algebras of affine algebraic groups to the case of pro-affine algebraic groups over an algebraically closed fieldKof characteristic 0. However, some modifications are needed in some extensions. So we introduce the pro-discrete topology on the Lie algebra ℒ(G) of the pro-affine algebraic groupGoverK, which is discrete in the finite-dimensional case and linearly compact in general. As an example, ifLis any sub Lie algebra of ℒ(G), we show that the closure of [L,L] in ℒ(G) is algebraic in ℒ(G).We also discuss the Hopf algebra of representative functions H(L) of a residually finite dimensional Lie algebraL. As an example, we show that ifLis a sub Lie algebra of ℒ(G) andGis connected, then the canonical Hopf algebra morphism fromK[G] intoH(L) is injective if and only ifLis algebraically dense in ℒ(G).
q-Integral and Moment Representations for q-Orthogonal Polynomials
Authors: Ismail Mourad E. H. , Stanton Dennis 
Published: December 2010

AbstractWe develop a method for deriving integral representations of certain orthogonal polynomials as moments. These moment representations are applied to find linear and multilinear generating functions for q-orthogonal polynomials. As a byproduct we establish new transformation formulas for combinations of basic hypergeometric functions, including a new representation of the q-exponential function εq.
Admissible Majorants for Model Subspaces of H2, Part I: Slow Winding of the Generating Inner Function
Authors: Havin Victor , Mashreghi Javad 
Published: December 2010

AbstractA model subspace Kϴ of the Hardy space H2 = H2(ℂ+) for the upper half plane ℂ+ is H2(ℂ+) ϴ ϴH2(ℂ+) where ϴ is an inner function in ℂ+. A function ω: ⟼ [0,∞) is called an admissible majorant for Kϴ if there exists an f ∈ Kϴ, f ≢ 0, |f(x)| ≤ ω(x) almost everywhere on ℝ. For some (mainly meromorphic) ϴ's some parts of Adm ϴ (the set of all admissible majorants for Kϴ) are explicitly described. These descriptions depend on the rate of growth of argϴ along ℝ. This paper is about slowly growing arguments (slower than x). Our results exhibit the dependence of Adm B on the geometry of the zeros of the Blaschke product B. A complete description of Adm B is obtained for B's with purely imaginary (“vertical”) zeros. We show that in this case a unique minimal admissible majorant exists.
Ternary Diophantine Equations via Galois Representations and Modular Forms
Authors: Bennett Michael A. , Skinner Chris M. 
Published: December 2010

AbstractIn this paper, we develop techniques for solving ternary Diophantine equations of the shape Axn + Byn = Cz2, based upon the theory of Galois representations and modular forms. We subsequently utilize these methods to completely solve such equations for various choices of the parameters A, B andC. We conclude with an application of our results to certain classical polynomial-exponential equations, such as those of Ramanujan–Nagell type.
Éléments unipotents réguliers des sous-groupes de Levi
Authors: Bonnafé Cédric 
Published: December 2010

RésuméNous étudions la structure du centralisateur d'un élément unipotent régulier d'un sousgroupe de Levi d'un groupe réductif, ainsi que la structure du groupe des composantes de ce centralisateur en relation avec la notion de système local cuspidal définie par Lusztig. Nous déterminons son radical unipotent, montrons l'existence d'un complément de Levi et étudions la structure de son groupe de Weyl. Comme application, nous démontrons des résultats qui étaient annoncés dans un précédent article de l'auteur sur les éléments unipotents réguliers.
Non-Abelian Generalizations of the Erdős-Kac Theorem
Authors: Murty M. Ram , Saidak Filip 
Published: December 2010

AbstractLet a be a natural number greater than 1. Let fa(n) be the order of a mod n. Denote by ω(n) the number of distinct prime factors of n. Assuming a weak form of the generalised Riemann hypothesis, we prove the following conjecture of Erdös and Pomerance:The number of n ≤ x coprime to a satisfyingis asymptotic to as x tends to infinity.
On the Neumann Problem for the Schrödinger Equations with Singular Potentials in Lipschitz Domains
Authors: Tao Xiangxing , Wang Henggeng 
Published: December 2010

AbstractWe consider the Neumann problem for the Schrödinger equations –Δu + Vu = 0, with singular nonnegative potentials V belonging to the reverse Hölder class ℬn, in a connected Lipschitz domain Ω Rn. Given boundary data g in Hp or Lp for 1 – ɛ < p ≤ 2, where 0 < ɛ < , it is shown that there is a unique solution, u, that solves the Neumann problem for the given data and such that the nontangential maximal function of ▽u is in Lp(∂Ω). Moreover, the uniform estimates are found.
Variations of Mixed Hodge Structures of Multiple Polylogarithms
Authors: Zhao Jianqiang 
Published: December 2010

AbstractIt is well known that multiple polylogarithms give rise to good unipotent variations of mixed Hodge-Tate structures. In this paper we shall explicitly determine these structures related to multiple logarithms and some other multiple polylogarithms of lower weights. The purpose of this explicit construction is to give some important applications. First we study the limit of mixed Hodge-Tate structures and make a conjecture relating the variations of mixed Hodge-Tate structures of multiple logarithms to those of general multiple polylogarithms. Then following Deligne and Beilinson we describe an approach to defining the single-valued real analytic version of the multiple polylogarithms which generalizes the well-known result of Zagier on classical polylogarithms. In the process we find some interesting identities relating single-valued multiple polylogarithms of the same weight k when k = 2 and 3. At the end of this paper, motivated by Zagier's conjecture we pose a problem which relates the special values of multiple Dedekind zeta functions of a number field to the single-valued version of multiple polylogarithms.
Extensions by Simple C*-Algebras: Quasidiagonal Extensions
Authors: Lin Huaxin 
Published: December 2010

AbstractLet A be an amenable separable C*-algebra and B be a non-unital but σ-unital simple C*- algebra with continuous scale. We show that two essential extensions τ1 and τ2 of A by B are approximately unitarily equivalent if and only ifIf A is assumed to satisfy the Universal Coefficient Theorem, there is a bijection fromapproximate unitary equivalence classes of the abovementioned extensions to KL(A,M(B)/B). Using KL(A,M(B)/B), we compute exactly when an essential extension is quasidiagonal. We show that quasidiagonal extensions may not be approximately trivial. We also study the approximately trivial extensions.
Convex Polynomial Approximation in the Uniform Norm: Conclusion
Authors: Kopotun K. A. , Leviatan D. , Shevchuk I. A. 
Published: December 2010

AbstractEstimating the degree of approximation in the uniform norm, of a convex function on a finite interval, by convex algebraic polynomials, has received wide attention over the last twenty years. However, while much progress has been made especially in recent years by, among others, the authors of this article, separately and jointly, there have been left some interesting open questions. In this paper we give final answers to all those open problems. We are able to say, for each r-th differentiable convex function, whether or not its degree of convex polynomial approximation in the uniform norm may be estimated by a Jackson-type estimate involving the weighted Ditzian–Totik kth modulus of smoothness, and how the constants in this estimate behave. It turns out that for some pairs (k, r) we have such estimate with constants depending only on these parameters. For other pairs the estimate is valid, but only with constants that depend on the function being approximated, while there are pairs for which the Jackson-type estimate is, in general, invalid.
Extremal Metric for the First Eigenvalue on a Klein Bottle
Authors: Jakobson Dmitry , Nadirashvili Nikolai , Polterovich Iosif 
Published: December 2010

AbstractThe first eigenvalue of the Laplacian on a surface can be viewed as a functional on the space of Riemannian metrics of a given area. Critical points of this functional are called extremal metrics. The only known extremal metrics are a round sphere, a standard projective plane, a Clifford torus and an equilateral torus. We construct an extremal metric on a Klein bottle. It is a metric of revolution, admitting a minimal isometric embedding into a sphere by the first eigenfunctions. Also, this Klein bottle is a bipolar surface for Lawson's -torus. We conjecture that an extremal metric for the first eigenvalue on a Klein bottle is unique, and hence it provides a sharp upper bound for λ1 on a Klein bottle of a given area. We present numerical evidence and prove the first results towards this conjecture.
Smooth Values of the Iterates of the Euler Phi-Function
Authors: Lamzouri Youness 
Published: December 2010

AbstractLet ϕ(n) be the Euler phi-function, define ϕ0(n) = n and ϕk+1(n) = ϕ(ϕk(n)) for all k ≥ 0. We will determine an asymptotic formula for the set of integers n less than x for which ϕk(n) is y-smooth, conditionally on a weak form of the Elliott–Halberstam conjecture.
Eigenvalues,K-theory and Minimal Flows
Authors: Itzá-Ortiz Benjamín A. 
Published: December 2010

AbstractLet (Y,T) be a minimal suspension flow built over a dynamical system (X,S) and with (strictly positive, continuous) ceiling functionf:X→ ℝ. We show that the eigenvalues of (Y,T) are contained in the range of a trace on theK0-group of (X,S). Moreover, a trace gives an order isomorphism of a subgroup ofK0(C(X) ⋊Sℤ) with the group of eigenvalues of (Y,T). Using this result, we relate the values oftfor which the time-tmap on the minimal suspension flow is minimal with theK-theory of the base of this suspension.
Hecke L-Functions and the Distribution of Totally Positive Integers
Authors: Ash Avner , Friedberg Solomon 
Published: December 2010

AbstractLet K be a totally real number field of degree n. We show that the number of totally positive integers (or more generally the number of totally positive elements of a given fractional ideal) of given trace is evenly distributed around its expected value, which is obtained fromgeometric considerations. This result depends on unfolding an integral over a compact torus.
Large Sieve Inequalities via Subharmonic Methods and the Mahler Measure of the Fekete Polynomials
Authors: Erdélyi T. , Lubinsky D. S. 
Published: December 2010

AbstractWe investigate large sieve inequalities such as where is convex and increasing, P is a polynomial or an exponential of a potential, and the constant C depends on the degree of P, and the distribution of the points 0 ≤ Ƭ1 < Ƭ2 < … < Ƭm ≤ 2π. The method allows greater generality and is in some ways simpler than earlier ones. We apply our results to estimate the Mahler measure of Fekete polynomials.
Non-Backtracking Random Walks and Cogrowth of Graphs
Authors: Ortner Ronald , Woess Wolfgang 
Published: December 2010

AbstractLetXbe a locally finite, connected graph without vertices of degree 1. Non-backtracking random walk moves at each step with equal probability to one of the “forward” neighbours of the actual state,i.e.,it does not go back along the preceding edge to the preceding state. This is not a Markov chain, but can be turned into a Markov chain whose state space is the set of oriented edges ofX. Thus we obtain for infiniteXthat then-step non-backtracking transition probabilities tend to zero, and we can also compute their limit whenXis finite. This provides a short proof of an old result concerning cogrowth of groups, and makes the extension of that result to arbitrary regular graphs rigorous. Even whenXis non-regular, butsmall cycles are dense in X, we show that the graphXis non-amenable if and only if the non-backtrackingn-step transition probabilities decay exponentially fast. This is a partial generalization of the cogrowth criterion for regular graphs which comprises the original cogrowth criterion for finitely generated groups of Grigorchuk and Cohen.
The Geometry of L0
Authors: Kalton N. J. , Koldobsky A. , Yaskin V. , Yaskina M. 
Published: December 2010

AbstractSuppose that we have the unit Euclidean ball in ℝn and construct new bodies using three operations — linear transformations, closure in the radial metric, and multiplicative summation defined by We prove that in dimension 3 this procedure gives all origin-symmetric convex bodies, while this is no longer true in dimensions 4 and higher. We introduce the concept of embedding of a normed space in L0 that naturally extends the corresponding properties of Lp-spaces with p ≠ 0, and show that the procedure described above gives exactly the unit balls of subspaces of L0 in every dimension. We provide Fourier analytic and geometric characterizations of spaces embedding in L0, and prove several facts confirming the place of L0 in the scale of Lp-spaces.
Some Examples of Complemented Modular Lattices
Authors: Grätzer G. , Wonenburger Maria J. 
Published: December 2010

Let L be a complemented, χ-complete modular lattice. A theorem of Amemiya
and Halperin (see [l], Theorem 4.3) asserts that if the intervals [O, a] and
[O, b], a, bεL, are upper χ-continuous then [O, a∪b] is also upper
χ-continuous. Roughly speaking, in L upper χ-continuity is additive. The
following question arises naturally: is χ-completeness an additive property
of complemented modular lattices? It follows from Corollary 1 to Theorem 1
below that the answer to this question is in the negative.A complemented modular lattice is called a Von Neumann geometry or
continuous geometry if it is complete and continuous. In particular a
complete Boolean algebra is a Von Neumann geometry. In any case in a Von
Neumann geometry the set of elements which possess a unique complement form
a complete Boolean algebra. This Boolean algebra is called the centre of the
Von Neumann geometry. Theorem 2 shows that any complete Boolean algebra can
be the centre of a Von Neumann geometry with a homogeneous basis of order n
(see [3] Part II, definition 3.2 for the definition of a homogeneous basis),
n being any fixed natural integer.
The Non-Biplanar Character of the Complete 9-Graph
Authors: Tutte W. T. 
Published: December 2010

Let us define a planar partition of a graph G as a pair {H1, H2} of subgraphs of G with the following properties(i)Each of H1 and H2 includes all the vertices of G.(ii)Each edge of G belongs to just one of H1 and H2.(iii)H1 and H2 are planar graphs.It is not required that H1 and H2 are connected. Moreover either of these graphs may have isolated vertices, incident with none of its edges.We describe a graph having a planar partition as biplanar.