bluuebunny/crossref_metadata_2025_split huggingface dataset:
Isometric Dilations of Non-Commuting Finite Rank n-Tuples
Authors: Davidson Kenneth R. , Kribs David W. , Shpigel Miron E. 
Published: December 2010

AbstractA contractive n-tuple A = (A1,…,An) has a minimal joint isometric dilation S = (S1,…,Sn) where the Si’s are isometries with pairwise orthogonal ranges. This determines a representation of the Cuntz-Toeplitz algebra. When A acts on a finite dimensional space, the wot-closed nonself-adjoint algebra generated by S is completely described in terms of the properties of A. This provides complete unitary invariants for the corresponding representations. In addition, we show that the algebra is always hyper-reflexive. In the last section, we describe similarity invariants. In particular, an n-tuple B of d × d matrices is similar to an irreducible n-tuple A if and only if a certain finite set of polynomials vanish on B.
Multi-Sided Braid Type Subfactors
Authors: Erlijman Juliana 
Published: December 2010

AbstractWe generalise the two-sided construction of examples of pairs of subfactors of the hyperfinite II1factorRin [E1]—which arise by considering unitary braid representations with certain properties—to multisided pairs. We show that the index for the multi-sided pair can be expressed as a power of that for the two-sided pair. This construction can be applied to the natural examples—where the braid representations are obtained in connection with the representation theory of Lie algebras of typesA,B,C,D. We also compute the (first) relative commutants.
On Some Exponential Equations of S. S. Pillai
Authors: Bennett Michael A. 
Published: December 2010

AbstractIn this paper, we establish a number of theorems on the classic Diophantine equation of S. S. Pillai, ax – by = c, where a, b and c are given nonzero integers with a, b ≥ 2. In particular, we obtain the sharp result that there are at most two solutions in positive integers x and y and deduce a variety of explicit conditions under which there exists at most a single such solution. These improve or generalize prior work of Le, Leveque, Pillai, Scott and Terai. The main tools used include lower bounds for linear forms in the logarithms of (two) algebraic numbers and various elementary arguments.
Représentations irréductibles bornées des groupes de Lie exponentiels
Authors: Ludwig J. , Molitor-Braun C. 
Published: December 2010

AbstractLet G be a solvable exponential Lie group. We characterize all the continuous topologically irreducible bounded representations (T, ) of G on a Banach space by giving a G-orbit in n* (n being the nilradical of g), a topologically irreducible representation of L1(ℝn, ω), for a certain weight ω and a certain n ∈ ℕ, and a topologically simple extension norm. If G is not symmetric, i.e., if the weight ω is exponential, we get a new type of representations which are fundamentally different from the induced representations.
The Complete (Lp, Lp) Mapping Properties of Some Oscillatory Integrals in Several Dimensions
Authors: Sampson G. , Szeptycki P. 
Published: December 2010

AbstractWe prove that the operators map Lp(ℝ2) into itself for p ∈ J = if al , bl ≥ 1 and φ(x, y) = |x – y|–r, 0 ≤ r < 2, the result is sharp. Generalizations to dimensions d > 2 are indicated.
Monotone Paths on Zonotopes and Oriented Matroids
Authors: Athanasiadis Christos A. , Santos Francisco 
Published: December 2010

AbstractMonotone paths on zonotopes and the natural generalization to maximal chains in the poset of topes of an oriented matroid or arrangement of pseudo-hyperplanes are studied with respect to a kind of local move, called polygon move or flip. It is proved that any monotone path on a $d$-dimensional zonotope with $n$ generators admits at least $\left\lceil 2n/\left( n-d+2 \right) \right\rceil -1$ flips for all $n\ge d+2\ge 4$ and that for any fixed value of $n-d$, this lower bound is sharp for infinitely many values of $n$. In particular, monotone paths on zonotopes which admit only three flips are constructed in each dimension $d\ge 3$. Furthermore, the previously known 2-connectivity of the graph of monotone paths on a polytope is extended to the 2-connectivity of the graph of maximal chains of topes of an oriented matroid. An application in the context of Coxeter groups of a result known to be valid for monotone paths on simple zonotopes is included.
On the Milnor Fiber of a Quasi-ordinary Surface Singularity
Authors: Ban Chunsheng , McEwan Lee J. , Némethi András 
Published: December 2010

AbstractWe verify a generalization of (3.3) from [Lê73] proving that the homotopy type of the Milnor fiber of a reduced hypersurface singularity depends only on the embedded topological type of the singularity. In particular, using [Zariski68, Lipman83, Oh93, Gau88] for irreducible quasi-ordinary germs, it depends only on the normalized distinguished pairs of the singularity. The main result of the paper provides an explicit formula for the Euler-characteristic of the Milnor fiber in the surface case.
Convergence Factors and Compactness in Weighted Convolution Algebras
Authors: Ghahramani Fereidoun , Grabiner Sandy 
Published: December 2010

AbstractWe study convergence in weighted convolution algebras L1(ω) on R+, with the weights chosen such that the corresponding weighted space M(ω) of measures is also a Banach algebra and is the dual space of a natural related space of continuous functions. We determine convergence factor ɳ for which weak*-convergence of {λn} to λ in M(ω) implies norm convergence of λn * f to λ * f in L1(ωɳ). We find necessary and sufficent conditions which depend on ω and f and also find necessary and sufficent conditions for ɳ to be a convergence factor for all L1(ω) and all f in L1(ω). We also give some applications to the structure of weighted convolution algebras. As a preliminary result we observe that ɳ is a convergence factor for ω and f if and only if convolution by f is a compact operator from M(ω) (or L1(ω)) to L1(ωɳ).
Equivariant Embeddings into Smooth Toric Varieties
Authors: Hausen Jürgen 
Published: December 2010

AbstractWe characterize embeddability of algebraic varieties into smooth toric varieties and prevarieties. Our embedding results hold also in an equivariant context and thus generalize a well-known embedding theorem of Sumihiro on quasiprojectiveG-varieties. The main idea is to reduce the embedding problem to the affine case. This is done by constructing equivariant affine conoids, a tool which extends the concept of an equivariant affine cone over a projectiveG-variety to a more general framework.
Frames and Single Wavelets for Unitary Groups
Authors: Weber Eric 
Published: December 2010

AbstractWe consider a unitary representation of a discrete countable abelian group on a separable Hilbert space which is associated to a cyclic generalized frame multiresolution analysis. We extend Robertson’s theorem to apply to frames generated by the action of the group. Within this setup we use Stone’s theorem and the theory of projection valued measures to analyze wandering frame collections. This yields a functional analytic method of constructing a wavelet from a generalized frame multiresolution analysis in terms of the frame scaling vectors. We then explicitly apply our results to the action of the integers given by translations on L2(ℝ).
The Valuative Theory of Foliations
Authors: Fortuny Ayuso Pedro 
Published: December 2010

AbstractThis paper gives a characterization of valuations that follow the singular infinitely near points of plane vector fields, using the notion of L'Hôpital valuation, which generalizes a well known classical condition. With that tool, we give a valuative description of vector fields with infinite solutions, singularities with rational quotient of eigenvalues in its linear part, and polynomial vector fields with transcendental solutions, among other results.
Combinatorics of the Heat Trace on Spheres
Authors: Polterovich Iosif 
Published: December 2010

AbstractWe present a concise explicit expression for the heat trace coefficients of spheres. Our formulas yield certain combinatorial identities which are proved following ideas of D. Zeilberger. In particular, these identities allow to recover in a surprising way some known formulas for the heat trace asymptotics. Our approach is based on a method for computation of heat invariants developed in [P].
Multipliers on Vector Valued Bergman Spaces
Authors: Blasco Oscar , Arregui José Luis 
Published: December 2010

AbstractLet X be a complex Banach space and let Bp(X) denote the vector-valued Bergman space on the unit disc for 1 ≤ p < ∞. A sequence (Tn)n of bounded operators between two Banach spaces X and Y defines a multiplier between Bp(X) and Bq(Y) (resp. Bp(X) and lq(Y)) if for any function we have that belongs to Bq(Y) (resp. (Tn(xn))n ∈ lq(Y)). Several results on these multipliers are obtained, some of them depending upon the Fourier or Rademacher type of the spaces X and Y. New properties defined by the vector-valued version of certain inequalities for Taylor coefficients of functions in Bp(X) are introduced.
Zariski Hyperplane Section Theorem for Grassmannian Varieties
Authors: Shimada Ichiro 
Published: December 2010

AbstractLet ϕ: X → M be a morphism from a smooth irreducible complex quasi-projective variety X to a Grassmannian variety M such that the image is of dimension ≥ 2. Let D be a reduced hypersurface in M, and γ a general linear automorphism of M. We show that, under a certain differentialgeometric condition on ϕ(X) and D, the fundamental group π1((γ ○ ϕ)−1 (M \ D)) is isomorphic to a central extension of π1(M \ D) × π1(X) by the cokernel of π2(ϕ) : π2(X) → π2(M).
A Generalized Torelli Theorem
Authors: Dhillon Ajneet 
Published: December 2010

AbstractGiven a smooth projective curve C of positive genus g, Torelli's theorem asserts that the pair (J(C), Wg−1) determines C. We show that the theorem is true with Wg−1 replaced by Wd for each d in the range 1 ≤ d ≤ g − 1.
Weak Explicit Matching for Level Zero Discrete Series of Unit Groups of 𝔭-Adic Simple Algebras
Authors: Silberger Allan J. , Zink Ernst-Wilhelm 
Published: December 2010

AbstractLet F be a p-adic local field and let be the unit group of a central simple F-algebra Ai of reduced degree n > 1 (i = 1, 2). Let ℛ2() denote the set of irreducible discrete series representations of . The “Abstract Matching Theorem” asserts the existence of a bijection, the “Jacquet- Langlands” map, which, up to known sign, preserves character values for regular elliptic elements. This paper addresses the question of explicitly describing the map 𝒥ℒ, but only for “level zero” representations. We prove that the restriction is a bijection of level zero discrete series (Proposition 3.2) and we give a parameterization of the set of unramified twist classes of level zero discrete series which does not depend upon the algebra Ai and is invariant under 𝒥ℒA2,A1 (Theorem 4.1).
Automorphic Orthogonal and Extremal Polynomials
Authors: Lukashov A. L. , Peherstorfer F. 
Published: December 2010

AbstractIt is well known that many polynomials which solve extremal problems on a single interval as the Chebyshev or the Bernstein-Szegö polynomials can be represented by trigonometric functions and their inverses. On two intervals one has elliptic instead of trigonometric functions. In this paper we show that the counterparts of the Chebyshev and Bernstein-Szegö polynomials for several intervals can be represented with the help of automorphic functions, so-called Schottky-Burnside functions. Based on this representation and using the Schottky-Burnside automorphic functions as a tool several extremal properties of such polynomials as orthogonality properties, extremal properties with respect to the maximum norm, behaviour of zeros and recurrence coefficients etc. are derived.
Quaternions and Some Global Properties of Hyperbolic 5-Manifolds
Authors: Kellerhals Ruth 
Published: December 2010

AbstractWe provide an explicit thick and thin decomposition for oriented hyperbolic manifolds M of dimension 5. The result implies improved universal lower bounds for the volume vol5(M) and, for M compact, new estimates relating the injectivity radius and the diameter of M with vol5(M). The quantification of the thin part is based upon the identification of the isometry group of the universal space by the matrix group PSΔ L(2, ℍ) of quaternionic 2 × 2-matrices with Dieudonné determinant Δ equal to 1 and isolation properties of PSΔ L(2, ℍ).
Selmer Groups of Elliptic Curves with Complex Multiplication
Authors: Saikia A. 
Published: December 2010

AbstractSuppose K is an imaginary quadratic field and E is an elliptic curve over a number field F with complex multiplication by the ring of integers in K. Let p be a rational prime that splits as in K. Let Epn denote the pn-division points on E. Assume that F(Epn) is abelian over K for all n ≥ 0. This paper proves that the Pontrjagin dual of the -Selmer group of E over F(Ep∞) is a finitely generated free Λ-module, where Λ is the Iwasawa algebra of . It also gives a simple formula for the rank of the Pontrjagin dual as a Λ-module.
Asymptotics for Minimal Discrete Riesz Energy on Curves in ℝd
Authors: Martínez-Finkelshtein A. , Maymeskul V. , Rakhmanov E. A. , Saff E. B. 
Published: December 2010

AbstractWe consider the s-energy for point sets 𝒵 = {𝒵k,n: k = 0, …, n} on certain compact sets Γ in ℝd having finite one-dimensional Hausdorff measure,is the Riesz kernel. Asymptotics for the minimum s-energy and the distribution of minimizing sequences of points is studied. In particular, we prove that, for s ≥ 1, the minimizing nodes for a rectifiable Jordan curve Γ distribute asymptotically uniformly with respect to arclength as n → ∞.
Solvable Points on Projective Algebraic Curves
Authors: Pál Ambrus 
Published: December 2010

AbstractWe examine the problem of finding rational points defined over solvable extensions on algebraic curves defined over general fields. We construct non-singular, geometrically irreducible projective curves without solvable points of genus g, when g is at least 40, over fields of arbitrary characteristic. We prove that every smooth, geometrically irreducible projective curve of genus 0, 2, 3 or 4 defined over any field has a solvable point. Finally we prove that every genus 1 curve defined over a local field of characteristic zero with residue field of characteristic p has a divisor of degree prime to 6p defined over a solvable extension.
Lie Elements and Knuth Relations
Authors: Schocker Manfred 
Published: December 2010

AbstractA coplactic class in the symmetric groupconsists of all permutations inwith a given SchenstedQ-symbol, and may be described in terms of local relations introduced by Knuth. Any Lie element in the group algebra ofwhich is constant on coplactic classes is already constant on descent classes. As a consequence, the intersection of the Lie convolution algebra introduced by Patras and Reutenauer and the coplactic algebra introduced by Poirier and Reutenauer is the direct sum of all Solomon descent algebras.
K-Homology of the Rotation Algebras Aθ
Authors: Hadfield Tom 
Published: December 2010

AbstractWe study the K-homology of the rotation algebras Aθ using the six-term cyclic sequence for the K-homology of a crossed product by Z. In the case that θ is irrational, we use Pimsner and Voiculescu's work on AF-embeddings of the Aθ to search for the missing generator of the even K-homology.
Division par un polynôme hyperbolique
Authors: Chaumatet Jacques , Chollet Anne-Marie 
Published: December 2010

RésuméOn se donne un intervalle ouvert non vide ω de ℝ, un ouvert connexe non vide Ω de ℝset unpolynôme unitairede degrém> 0, dépendant du paramètre λ ∈ Ω. Un tel polynôme est dit ω-hyperbolique si, pour tout λ ∈ Ω, ses racines sont réelles et appartiennent à ω.On suppose que les fonctionsak,k= 1, … ,m, appartiennent à une classe ultradifférentiableCM(Ω). On s‘intéresse au problème suivant. Soitfappartient àCM(Ω), existe-t-il des fonctionsQfetRf, k,k= 0, … ,m–1, appartenant respectivement àCM(ω × Ω) et àCM(Ω), telles que l’on ait, pour (x, λ) ∈ ω × Ω,On donne ici une réponse positive dès que le polynôme est ω-hyperbolique, que la class untradifférentiable soit quasi-analytique ou non ; on obtient alors, des exemples d’idéaux fermés dansCM(ℝn). On complète ce travail par une généralisation d’un résultat de C. L. Childress dans le cadre quasi-analytique et quelques remarques.
Meromorphic Functions Sharing the Same Zeros and Poles
Authors: Frank Günter , Hua Xinhou , Vaillancourt Rémi 
Published: December 2010

AbstractIn this paper, Hinkkanen's problem (1984) is completely solved, i.e., it is shown that any meromorphic function f is determined by its zeros and poles and the zeros of f(j) for j = 1, 2, 3, 4.
Bending Flows for Sums of Rank One Matrices
Authors: Flaschka Hermann , Millson John 
Published: December 2010

AbstractWe study certain symplectic quotients ofn-fold products of complex projectivem-space by the unitary group acting diagonally. After studying nonemptiness and smoothness of these quotients we construct the action-angle variables, defined on an open dense subset, of an integrable Hamiltonian system. The semiclassical quantization of this system reporduces formulas from the representation theory of the unitary group.
Certain Exponential Sums and Random Walks on Elliptic Curves
Authors: Lange Tanja , Shparlinski Igor E. 
Published: December 2010

AbstractFor a given elliptic curve E, we obtain an upper bound on the discrepancy of sets of multiples zsG where zs runs through a sequence Z = (z1, … , zT) such that kz1, … , kzT is a permutation of z1, … , zT, both sequences taken modulo t, for sufficiently many distinct values of k modulo t.We apply this result to studying an analogue of the power generator over an elliptic curve. These results are elliptic curve analogues of those obtained for multiplicative groups of finite fields and residue rings.
Approximating Flats by Periodic Flats in CAT(0) Square Complexes
Authors: Wise Daniel T. 
Published: December 2010

AbstractWe investigate the problem of whether every immersed flat plane in a nonpositively curved square complex is the limit of periodic flat planes. Using a branched cover, we reduce the problem to the case of VH-complexes. We solve the problem for malnormal and cyclonormal VH-complexes. We also solve the problem for complete square complexes using a different approach. We give an application towards deciding whether the elements of fundamental groups of the spaces we study have commuting powers. We note a connection between the flat approximation problem and subgroup separability.
Some Results on Surfaces of General Type
Authors: Purnaprajna B. P. 
Published: December 2010

AbstractIn this article we prove some new results on projective normality, normal presentation and higher syzygies for surfaces of general type, not necessarily smooth, embedded by adjoint linear series. Some of the corollaries of more general results include: results on property Np associated to KS ⊗B⊗n where B is base-point free and ample divisor with B⊗K* nef, results for pluricanonical linear systems and results giving effective bounds for adjoint linear series associated to ample bundles. Examples in the last section show that the results are optimal.
On the Vanishing of μ-Invariants of Elliptic Curves over ℚ
Authors: Trifković Mak 
Published: December 2010

AbstractLet E/ℚ be an elliptic curve with good ordinary reduction at a prime p > 2. It has a welldefined Iwasawa μ-invariant μ(E)p which encodes part of the information about the growth of the Selmer group ) as Kn ranges over the subfields of the cyclotomic Zp-extension K∞/ℚ. Ralph Greenberg has conjectured that any such E is isogenous to a curve E′ with μ(E′)p = 0. In this paper we prove Greenberg's conjecture for infinitely many curves E with a rational p-torsion point, p = 3 or 5, no two of our examples having isomorphic p-torsion. The core of our strategy is a partial explicit evaluation of the global duality pairing for finite flat group schemes over rings of integers.
Petrie Schemes
Authors: Williams Gordon 
Published: December 2010

AbstractPetrie polygons, especially as they arise in the study of regular polytopes and Coxeter groups, have been studied by geometers and group theorists since the early part of the twentieth century. An open question is the determination of which polyhedra possess Petrie polygons that are simple closed curves. The current work explores combinatorial structures in abstract polytopes, called Petrie schemes, that generalize the notion of a Petrie polygon. It is established that all of the regular convex polytopes and honeycombs in Euclidean spaces, as well as all of the Gr¨unbaum–Dress polyhedra, possess Petrie schemes that are not self-intersecting and thus have Petrie polygons that are simple closed curves. Partial results are obtained for several other classes of less symmetric polytopes.
The Gelfond–Schnirelman Method in Prime Number Theory
Authors: Pritsker Igor E. 
Published: December 2010

AbstractThe original Gelfond–Schnirelman method, proposed in 1936, uses polynomials with integer coefficients and small norms on [0, 1] to give a Chebyshev-type lower bound in prime number theory. We study a generalization of thismethod for polynomials inmany variables. Ourmain result is a lower bound for the integral of Chebyshev'sψ-function, expressed in terms of the weighted capacity. This extends previous work of Nair and Chudnovsky, and connects the subject to the potential theory with external fields generated by polynomial-type weights. We also solve the corresponding potential theoretic problem, by finding the extremal measure and its support.
On 𝒞ℛ-Epic Embeddings and Absolute 𝒞ℛ-Epic Spaces
Authors: Barr Michael , Raphael R. , Woods R. G. 
Published: December 2010

AbstractWe study Tychonoff spaces X with the property that, for all topological embeddings X → Y, the induced map C(Y ) → C(X) is an epimorphism of rings. Such spaces are called absolute 𝒞ℛ-epic. The simplest examples of absolute 𝒞ℛ-epic spaces are σ-compact locally compact spaces and Lindelöf P-spaces. We show that absolute CR-epic first countable spaces must be locally compact.However, a “bad” class of absolute CR-epic spaces is exhibited whose pathology settles, in the negative, a number of open questions. Spaces which are not absolute CR-epic abound, and some are presented.
Asymptotic Behavior of the Length of Local Cohomology
Authors: Cutkosky Steven Dale , Hà Huy Tài , Srinivasan Hema , Theodorescu Emanoil 
Published: December 2010

AbstractLet k be a field of characteristic 0, R = k[x1, … , xd] be a polynomial ring, and m its maximal homogeneous ideal. Let I ⊂ R be a homogeneous ideal in R. Let λ(M) denote the length of an Rmodule M. In this paper, we show thatalways exists. This limit has been shown to be e(I)/d! form-primary ideals I in a local Cohen–Macaulay ring, where e(I) denotes the multiplicity of I. But we find that this limit may not be rational in general. We give an example for which the limit is an irrational number thereby showing that the lengths of these extension modules may not have polynomial growth.
Reciprocity Law for Compatible Systems of Abelian mod p Galois Representations
Authors: Khare Chandrashekhar 
Published: December 2010

AbstractThe main result of the paper is a reciprocity law which proves that compatible systems of semisimple, abelianmod p representations (of arbitrary dimension) of absolute Galois groups of number fields, arise from Hecke characters. In the last section analogs for Galois groups of function fields of these results are explored, and a question is raised whose answer seems to require developments in transcendence theory in characteristic p.