bluuebunny/crossref_metadata_2025_split huggingface dataset:
On the Zeros of Some Genus Polynomials
Authors: Stahl Saul 
Published: December 2010

AbstractIn the genus polynomial of the graph G, the coefficient of xk is the number of distinct embeddings of the graph G on the oriented surface of genus k. It is shown that for several infinite families of graphs all the zeros of the genus polynomial are real and negative. This implies that their coefficients, which constitute the genus distribution of the graph, are log concave and therefore also unimodal. The geometric distribution of the zeros of some of these polynomials is also investigated and some new genus polynomials are presented.
Dilations of one Parameter Semigroups of Positive Contractions on Lp Spaces
Authors: Fendler Gero 
Published: December 2010

AbstractIt is proved in this note, that a strongly continuous semigroup of (sub)positive contractions acting on an Lp-space, for 1 < p < ∞ p ≠ 2, can be dilated by a strongly continuous group of (sub)positive isometries in a manner analogous to the dilation M. A. Akçoglu and L. Sucheston constructed for a discrete semigroup of (sub)positive contractions. From this an improvement of a von Neumann type estimation, due to R. R.Coifman and G.Weiss, on the transfer map belonging to the semigroup is deduced.
Trace Functions in the Ring of Fractions of Polycyclic Group Rings, II
Authors: Lichtman A. I. 
Published: December 2010

AbstractWe prove the existence of trace functions in the rings of fractions of polycyclic-by-finite group rings or their homomorphic images. In particular a trace function exists in the ring of fractions of KH, where H is a polycyclic-by-finite group and char K > N, where N is a constant depending on H.
Approximation by Multiple Refinable Functions
Authors: Jia R. Q. , Riemenschneider S. D. , Zhou D. X. 
Published: December 2010

AbstractWe consider the shift-invariant space, 𝕊(Φ), generated by a set Φ = {Φ1,..., Φr} of compactly supported distributions on R when the vector of distributions ϕ:= {Φ1,..., Φr} T satisfies a system of refinement equations expressed in matrix form aswhere a is a finitely supported sequence of r x r matrices of complex numbers. Such multiple refinable functions occur naturally in the study of multiple wavelets.The purpose of the present paper is to characterize the accuracy of Φ, the order of the polynomial space contained in 𝕊(Φ), strictly in terms of the refinement mask a. The accuracy determines the Lp-approximation order of 𝕊(Φ) when the functions in (Φ) belong to Lp(ℝ) (see Jia [10]). The characterization is achieved in terms of the eigenvalues and eigenvectors of the subdivision operator associated with the mask a. In particular, they extend and improve the results of Heil, Strang and Strela [7], and of Plonka [16]. In addition, a counterexample is given to the statement of Strang and Strela [20] that the eigenvalues of the subdivision operator determine the accuracy. The results do not require the linear independence of the shifts of Φ.
Majorations Effectives Pour L’ Équation de Fermat Généralisée
Authors: Kraus Alain 
Published: December 2010

RésuméSoient A, B et C trois entiers non nuls premiers entre eux deux à deux, et p un nombre premier. Comme conséquence des travaux de A. Wiles et F. Diamond sur la conjecture de Taniyama-Weil, on explicite une constante f(A, B, C) telle que, sous certaines conditions portant sur A, B et C, l’équation Axp+ Byp+ Czp= 0 n’a aucune solution non triviale dans ℤ, si p est > f(A, B, C). On démontre par ailleurs, sans condition supplémentaire portant sur A, B et C, que cette équation n’a aucune solution non triviale dans ℤ, si p divise xyz, et si p est > f(A, B,C).
1-Complemented Subspaces of Spaces With 1-Unconditional Bases
Authors: Randrianantoanina Beata 
Published: December 2010

AbstractWe prove that if X is a complex strictly monotone sequence space with 1-unconditional basis, Y ⊆ X has no bands isometric to ℓ22 and Y is the range of norm-one projection from X, then Y is a closed linear span a family of mutually disjoint vectors in X.We completely characterize 1-complemented subspaces and norm-one projections in complex spaces ℓp(ℓq) for 1 ≤ p,q > ∞.Finally we give a full description of the subspaces that are spanned by a family of disjointly supported vectors and which are 1-complemented in (real or complex) Orlicz or Lorentz sequence spaces. In particular if an Orlicz or Lorentz space X is not isomorphic to ℓp for some 1 ≤ p,q > ∞ then the only subspaces of X which are 1-complemented and disjointly supported are the closed linear spans of block bases with constant coefficients.
Hecke Algebras and Class-Group Invariants
Authors: Snaith V. P. 
Published: December 2010

AbstractLet G be a finite group. To a set of subgroups of order two we associate a mod 2 Hecke algebra and construct a homomorphism, ψ, from its units to the class-group of Z[G]. We show that this homomorphism takes values in the subgroup, D(Z[G]). Alternative constructions of Chinburg invariants arising fromthe Galois module structure of higher-dimensional algebraic K-groups of rings of algebraic integers often differ by elements in the image of ψ. As an application we show that two such constructions coincide.
The Explicit Solution of the -Neumann Problem in a Non-Isotropic Siegel Domain
Authors: Tie Jingzhi 
Published: December 2010

AbstractIn this paper, we solve the-Neumann problem on (0, q) forms, 0 ≤ q ≤ n, in the strictly pseudoconvex non-isotropic Siegel domain:where aj> 0 for j = 1,2, . . . , n. The metric we use is invariant under the action of the Heisenberg group on the domain. The fundamental solution of the related differential equation is derived via the Laguerre calculus. We obtain an explicit formula for the kernel of the Neumann operator. We also construct the solution of the corresponding heat equation and the fundamental solution of the Laplacian operator on the Heisenberg group.
Intégration Du Sous-Différentiel Proximal: Un Contre Exemple
Authors: Benoist Joël 
Published: December 2010

RésuméEtant donnée une partie D dénombrable et dense de ℝ, nous construisons une infinité de fonctions Lipschitziennes définies sur ℝ, s’annulant en zéro, dont le sous-différentiel proximal est égal à ]–1, 1[ en tout point de D et est vide en tout point du complémentaire de D. Nous déduisons que deux fonctions dont la différence n’est pas constante peuvent avoir les mêmes sous-différentiels.
Some Norms on Universal Enveloping Algebras
Authors: Gross Leonard 
Published: December 2010

AbstractThe universal enveloping algebra,U(𝔤), of a Lie algebra 𝔤 supports some norms and seminorms that have arisen naturally in the context of heat kernel analysis on Lie groups. These norms and seminorms are investigated here from an algebraic viewpoint. It is shown that the norms corresponding to heat kernels on the associated Lie groups decompose as product norms under the natural isomorphism. The seminorms corresponding to Green's functions are examined at a purely Lie algebra level for sl (2, ℂ). It is also shown that the algebraic dual spaceU′ is spanned by its finite rank elements if and only if 𝔤 is nilpotent.
Unbounded Fredholm Modules and Spectral Flow
Authors: Carey Alan , Phillips John 
Published: December 2010

AbstractAn odd unbounded (respectively, p-summable) Fredholm module for a unital Banach *-algebra, A, is a pair (H,D) where A is represented on the Hilbert space, H, and D is an unbounded self-adjoint operator on H satisfying:(1) (1 + D2)-1 is compact (respectively, Trace_(1 + D2)-(p/2)_∞), and(2) ﹛a ∈ A | [D, a] is bounded﹜ is a dense *- subalgebra of A.If u is a unitary in the dense *-subalgebra mentioned in (2) thenuDu* = D + u[D, u*] = D + Bwhere B is a bounded self-adjoint operator. The pathis a “continuous” path of unbounded self-adjoint “Fredholm” operators. More precisely, we show thatis a norm-continuous path of (bounded) self-adjoint Fredholm operators. The spectral flow of this path is roughly speaking the net number of eigenvalues that pass through 0 in the positive direction as t runs from 0 to 1. This integer,recovers the pairing of the K-homology class [D] with the K-theory class [u].We use I.M. Singer's idea (as did E. Getzler in the θ-summable case) to consider the operator B as a parameter in the Banach manifold, Bsa(H), so that spectral flow can be exhibited as the integral of a closed 1-formon this manifold. Now, for B in ourmanifold, any X ∈ TB_Bsa(H)_ is given by an X in Bsa(H) as the derivative at B along the curve t→ B + tX in the manifold. Then we show that for m a sufficiently large half-integer:is a closed 1-form. For any piecewise smooth path {Dt = D + Bt} with D0 and D1 unitarily equivalent we show thatthe integral of the 1-form ã. If D0 and D1 are not unitarily equivalent, wemust add a pair of correction terms to the right-hand side. We also prove a bounded finitely summable version of the form:for an integer. The unbounded case is proved by reducing to the bounded case via the map . We prove simultaneously a type II version of our results.
Trace Class Elements and Cross-Sections in Kac-Moody Groups
Authors: Brüchert Gerd 
Published: December 2010

AbstractLet G be an affine Kac-Moody group, π0, … ,πr, πδ its fundamental irreducible representations and χ0, … , χr, χδ their characters. We determine the set of all group elements x such that all πi(x) act as trace class operators, i.e., such that χi(x) exists, then prove that the χ i are class functions. Thus, χ := (χ0, … , χr, χδ) factors to an adjoint quotient χ for G. In a second part, following Steinberg, we define a cross-section C for the potential regular classes in G. We prove that the restriction χ|C behaves well algebraically. Moreover, we obtain an action of C ℂ✗ on C, which leads to a functional identity for χ|C which shows that χ|C is quasi-homogeneous.
Localization Theories for Simplicial Presheaves
Authors: Goerss P. G. , Jardine J. F. 
Published: December 2010

AbstractMost extant localization theories for spaces, spectra and diagrams of such can be derived from a simple list of axioms which are verified in broad generality. Several new theories are introduced, including localizations for simplicial presheaves and presheaves of spectra at homology theories represented by presheaves of spectra, and a theory of localization along a geometric topos morphism. The ƒ-localization concept has an analog for simplicial presheaves, and specializes to the 𝔸1-local theory of Morel-Voevodsky. This theory answers a question of Soulé concerning integral homology localizations for diagrams of spaces.
Sur les Transformées de Riesz sur les Groupes de Lie Moyennables et sur Certains Espaces Homogènes
Authors: Noël Lohoué  , Mustapha Sami 
Published: December 2010

RésuméLet Δ be a left invariant sub-Laplacian on a Lie group G and let ▽ be the associated gradient. In this paper we investigate the boundness of the Riesz transform ▽Δ-1/2 on Lie groups G which are amenable and with exponential volume growth and on certain homogenous spaces.
Tempered Representations and the Theta Correspondence
Authors: Roberts Brooks 
Published: December 2010

AbstractLet V be an even dimensional nondegenerate symmetric bilinear space over a nonarchimedean local field F of characteristic zero, and let n be a nonnegative integer. Suppose that σ ∈ Irr (O(V)) and π ∈ Irr (Sp(n, F)) correspond under the theta correspondence. Assuming that õ is tempered, we investigate the problem of determining the Langlands quotient data for π.
Isomorphism Problem for Metacirculant Graphs of Order a Product of Distinct Primes
Authors: Dobson Edward 
Published: December 2010

AbstractIn this paper, we solve the isomorphism problem for metacirculant graphs of order pq that are not circulant. To solve this problem, we first extend Babai’s characterization of the CI-property to non-Cayley vertex-transitive hypergraphs. Additionally, we find a simple characterization of metacirculant Cayley graphs of order pq, and exactly determine the full isomorphism classes of circulant graphs of order pq.
The Behaviour of Legendre And Ultraspherical Polynomials in Lp-Spaces
Authors: Kalton N. J. , Tzafriri L. 
Published: December 2010

AbstractWe consider the analogue of the λ(p)problem for subsets of the Legendre polynomials or more general ultraspherical polynomials. We obtain the “best possible” result that if 2 < p < 4 then a random subset of N Legendre polynomials of size N4/p-1 spans an Hilbertian subspace. We also answer a question of König concerning the structure of the space of polynomials of degree n in various weighted Lp-spaces.
Imprimitively Generated Lie-Algebraic Hamiltonians and Separation of Variables
Authors: Milson Robert 
Published: December 2010

AbstractTurbiner’s conjecture posits that a Lie-algebraic Hamiltonian operator whose domain is a subset of the Euclidean plane admits a separation of variables. A proof of this conjecture is given in those cases where the generating Lie-algebra acts imprimitively. The general form of the conjecture is false. A counter-example is given based on the trigonometric Olshanetsky-Perelomov potential corresponding to the A2 root system.
Convergence of Subdifferentials of Convexly Composite Functions
Authors: Combari C. , Poliquin R. , Thibault L. 
Published: December 2010

AbstractIn this paper we establish conditions that guarantee, in the setting of a general Banach space, the Painlevé-Kuratowski convergence of the graphs of the subdifferentials of convexly composite functions. We also provide applications to the convergence of multipliers of families of constrained optimization problems and to the generalized second-order derivability of convexly composite functions.
Symmetric sequence subspaces of C(α), II
Authors: Leung Denny H. , Tang Wee-Kee 
Published: December 2010

AbstractIf α is an ordinal, then the space of all ordinals less than or equal to α is a compact Hausdorff space when endowed with the order topology. Let C(α) be the space of all continuous real-valued functions defined on the ordinal interval [0; α]. We characterize the symmetric sequence spaces which embed into C(α) for some countable ordinal α. A hierarchy (Eα) of symmetric sequence spaces is constructed so that, for each countable ordinal α, Eα embeds into C(ωωα), but does not embed into C(ωωβ) for any β < α.
Representations of Virasoro-Heisenberg Algebras and Virasoro-Toroidal Algebras
Authors: Fabbri Marc A. , Okoh Frank 
Published: December 2010

AbstractVirasoro-toroidal algebras, , are semi-direct products of toroidal algebras and the Virasoro algebra. The toroidal algebras are, in turn, multi-loop versions of affine Kac-Moody algebras. Let Γ be an extension of a simply laced lattice by a hyperbolic lattice of rank two. There is a Fock space V(Γ) corresponding to Γ with a decomposition as a complex vector space: V(Γ) = . Fabbri and Moody have shown that when m ≠ 0, K(m) is an irreducible representation of . In this paper we produce a filtration of -submodules of K(0). When L is an arbitrary geometric lattice and n is a positive integer, we construct a Virasoro-Heisenberg algebra . Let Q be an extension of by a degenerate rank one lattice. We determine the components of V(Γ) that are irreducible -modules and we show that the reducible components have a filtration of -submodules with completely reducible quotients. Analogous results are obtained for . These results complement and extend results of Fabbri and Moody.
Nilpotency of Some Lie Algebras Associated with p-Groups
Authors: Shumyatsky Pavel 
Published: December 2010

AbstractLet L = L0 + L1 be a 2-graded Lie algebra over a commutative ring with unity in which 2 is invertible. Suppose that L0 is abelian and L is generated by finitely many homogeneous elements a1,...,ak such that every commutator in a1,...,ak is ad-nilpotent. We prove that L is nilpotent. This implies that any periodic residually finite 2ʹ-group G admitting an involutory automorphism ϕ with CG(ϕ) abelian is locally finite.
Brownian Motion and Harmonic Analysis on Sierpinski Carpets
Authors: Barlow Martin T. , Bass Richard F. 
Published: December 2010

AbstractWe consider a class of fractal subsets ofdformed in a manner analogous to the construction of the Sierpinski carpet. We prove a uniform Harnack inequality for positive harmonic functions; study the heat equation, and obtain upper and lower bounds on the heat kernel which are, up to constants, the best possible; construct a locally isotropic diffusionXand determine its basic properties; and extend some classical Sobolev and Poincaré inequalities to this setting.
A New Form of the Segal-Bargmann Transform for Lie Groups of Compact Type
Authors: Hall Brian C. 
Published: December 2010

AbstractI consider a two-parameter familyBs,tof unitary transforms mapping anL2-space over a Lie group of compact type onto a holomorphicL2-space over the complexified group. These were studied using infinite-dimensional analysis in joint work with B. Driver, but are treated here by finite-dimensional means. These transforms interpolate between two previously known transforms, and all should be thought of as generalizations of the classical Segal-Bargmann transform. I consider also the limiting casess→ ∞ ands→t/2.
Quasiconformal Contactomorphisms and Polynomial Hulls with Convex Fibers
Authors: Balogh Zoltán M. , Leuenberger Christoph 
Published: December 2010

AbstractConsider the polynomial hull of a smoothly varying family of strictly convex smooth domains fibered over the unit circle. It is well-known that the boundary of the hull is foliated by graphs of analytic discs. We prove that this foliation is smooth, and we show that it induces a complex flow of contactomorphisms. These mappings are quasiconformal in the sense of Korányi and Reimann. A similar bound on their quasiconformal distortion holds as in the one-dimensional case of holomorphic motions. The special case when the fibers are rotations of a fixed domain in C2 is studied in details.
On Limit Multiplicities for Spaces of Automorphic Forms
Authors: Deitmar Anton , Hoffmann Werner 
Published: December 2010

AbstractLet Γ be a rank-one arithmetic subgroup of a semisimple Lie group G. For fixed K-Type, the spectral side of the Selberg trace formula defines a distribution on the space of infinitesimal characters of G, whose discrete part encodes the dimensions of the spaces of square-integrable Γ-automorphic forms. It is shown that this distribution converges to the Plancherel measure of G when Γ shrinks to the trivial group in a certain restricted way. The analogous assertion for cocompact lattices Γ follows from results of DeGeorge-Wallach and Delorme.
Extreme Pick-Nevanlinna Interpolants
Authors: Fisher Stephen D. , Khavinson Dmitry 
Published: December 2010

AbstractFollowing the investigations of B. Abrahamse [1], F. Forelli [11], M. Heins [14] and others, we continue the study of the Pick-Nevanlinna interpolation problem inmultiply-connected planar domains. One major focus is on the problem of characterizing the extreme points of the convex set of interpolants of a fixed data set. Several other related problems are discussed.
Linear Groups Generated by Reflection Tori
Authors: Cohen A. M. , Cuypers H. , Sterk H. 
Published: December 2010

AbstractA reflection is an invertible linear transformation of a vector space fixing a given hyperplane, its axis, vectorwise and a given complement to this hyperplane, its center, setwise. A reflection torus is a one-dimensional group generated by all reflections with fixed axis and center.In this paper we classify subgroups of general linear groups (in arbitrary dimension and defined over arbitrary fields) generated by reflection tori.
Symmetric Tessellations on Euclidean Space-Forms
Authors: Hartley Michael I. , McMullen Peter , Schulte Egon 
Published: December 2010

AbstractIt is shown here that, for n ⩾ 2, the n-torus is the only n-dimensional compact euclidean space-form which can admit a regular or chiral tessellation. Further, such a tessellation can only be chiral if n = 2.
Similarity Submodules and Root Systems in Four Dimensions
Authors: Baake Michael , Moody Robert V. 
Published: December 2010

AbstractLattices and -modules in Euclidean space possess an infinitude of subsets that are images of the original set under similarity transformation. We classify such self-similar images according to their indices for certain 4D examples that are related to 4D root systems, both crystallographic and non-crystallographic. We encapsulate their statistics in terms of Dirichlet series generating functions and derive some of their asymptotic properties.
On the Existence of Similar Sublattices
Authors: Conway J. H. , Rains E. M. , Sloane N. J. A. 
Published: December 2010

AbstractPartial answers are given to two questions. When does a lattice Λ contain a sublattice Λʹ of index N that is geometrically similar to Λ? When is the sublattice “clean”, in the sense that the boundaries of the Voronoi cells for Λʹ do not intersect Λ?
On Small Complete Sets of Functions
Authors: Aizenberg Lev , Vidras Alekos 
Published: December 2010

AbstractUsing Local Residues and the Duality Principle a multidimensional variation of the completeness theorems by T. Carleman and A. F. Leontiev is proven for the space of holomorphic functions defined on a suitable open strip Tα ⊂ C2. The completeness theorem is a direct consequence of the Cauchy Residue Theorem in a torus. With suitable modifications the same result holds in Cn.
An Algorithm for Fat Points on P2
Authors: Harbourne Brian 
Published: December 2010

AbstractLet F be a divisor on the blow-up X of P2 at r general points p1, . . . , pr and let L be the total transform of a line on P2. An approach is presented for reducing the computation of the dimension of the cokernel of the natural map to the case that F is ample. As an application, a formula for the dimension of the cokernel of μF is obtained when r = 7, completely solving the problem of determining the modules in minimal free resolutions of fat point subschemes m1p1 + · · · + m7p7 ⊂ P2. All results hold for an arbitrary algebraically closed ground field k.
Floer Homology for Knots and SU(2)-Representations for Knot Complements and Cyclic Branched Covers
Authors: Collin Olivier 
Published: December 2010

AbstractIn this article, using 3-orbifolds singular along a knot with underlying space a homology sphere Y3, the question of existence of non-trivial and non-abelian SU(2)-representations of the fundamental group of cyclic branched covers of Y3 along a knot is studied. We first use Floer Homology for knots to derive an existence result of non-abelian SU(2)-representations of the fundamental group of knot complements, for knots with a non-vanishing equivariant signature. This provides information on the existence of non-trivial and non-abelian SU(2)-representations of the fundamental group of cyclic branched covers. We illustrate the method with some examples of knots in S3.
On Some q-Analogs of a Theorem of Kostant-Rallis
Authors: Wallach N. R. , Willenbring J. 
Published: December 2010

AbstractIn the first part of this paper generalizationsof Hesselink’s q-analog of Kostant’smultiplicity formula for the action of a semisimple Lie group on the polynomials on its Lie algebra are given in the context of the Kostant-Rallis theorem. They correspond to the cases of real semisimple Lie groups with one conjugacy class of Cartan subgroup. In the second part of the paper a q-analog of the Kostant-Rallis theorem is given for the real group SL(4, ) (that is SO(4) acting on symmetric 4 × 4 matrices). This example plays two roles. First it contrasts with the examples of the first part. Second it has implications to the study of entanglement of mixed 2 qubit states in quantum computation.
Two-Weight Estimates For Singular Integrals Defined On Spaces Of Homogeneous Type
Authors: Edmunds D. E. , Kokilashvili V. , Meskhi A. 
Published: December 2010

AbstractTwo-weight inequalities of strong and weak type are obtained in the context of spaces of homogeneous type. Various applications are given, in particular to Cauchy singular integrals on regular curves.