bluuebunny/crossref_metadata_2025_split huggingface dataset:
On Multiple Mixed Interior and Boundary Peak Solutions for Some Singularly Perturbed Neumann Problems
Authors: Gui Changfeng , Wei Juncheng 
Published: December 2010

AbstractWe consider the problemwhere Ω is a bounded smooth domain in RN, ε > 0 is a small parameter and f is a superlinear, subcritical nonlinearity. It is known that this equation possesses multiple boundary spike solutions that concentrate, as ε approaches zero, at multiple critical points of the mean curvature function H(P), P ∈ ∂Ω. It is also proved that this equation has multiple interior spike solutions which concentrate, as ε → 0, at sphere packing points in Ω.In this paper, we prove the existence of solutions with multiple spikes both on the boundary and in the interior. The main difficulty lies in the fact that the boundary spikes and the interior spikes usually have different scales of error estimation. We have to choose a special set of boundary spikes to match the scale of the interior spikes in a variational approach.
Small Solutions of ϕ1x12 + . . . + ϕnxn2 = 0
Authors: Ou Zhiming M. , Williams Kenneth S. 
Published: December 2010

AbstractLet ϕ1, . . . , ϕn (n ≥ 2) be nonzero integers such that the equationis solvable in integers x1, . . . , xn not all zero. It is shown that there exists a solution satisfyingand that the constant 2 is best possible.
Operator Estimates for Fredholm Modules
Authors: Sukochev F. A. 
Published: December 2010

AbstractWe study estimates of the typewhere φ(t) = t(1 + t2)−1/2, D0 = D0* is an unbounded linear operator affiliated with a semifinite von Neumann algebra , D − D0 is a bounded self-adjoint linear operator from and , where E(, τ) is a symmetric operator space associated with . In particular, we prove that φ(D) − φ(D0) belongs to the non-commutative Lp-space for some p ∈ (1,∞), provided belongs to the noncommutative weak Lr-space for some r ∈ [1, p). In the case and 1 ≤ p ≤ 2, we show that this result continues to hold under the weaker assumption . This may be regarded as an odd counterpart of A. Connes’ result for the case of even Fredholm modules.
Compact Groups of Operators on Subproportional Quotients of l1m
Authors: Mankiewicz Piotr 
Published: December 2010

AbstractIt is proved that a “typical” n-dimensional quotient Xn of l1m with n = mσ, 0 < σ < 1, has the propertyAverage for every compact group G of operators acting on Xn, where dG(T) stands for the normalizedHaar measure on G and the average is taken over all extreme points of the unit ball of Xn. Several consequences of this estimate are presented.
Essential Dimensions of Algebraic Groups and a Resolution Theorem for G-Varieties
Authors: Reichstein Zinovy , Youssin Boris 
Published: December 2010

AbstractLet G be an algebraic group and let X be a generically free G-variety. We show that X can be transformed, by a sequence of blowups with smooth G-equivariant centers, into a G-variety Xʹ with the following property: the stabilizer of every point of Xʹ is isomorphic to a semidirect product U × A of a unipotent group U and a diagonalizable group A.As an application of this result, we prove new lower bounds on essential dimensions of some algebraic groups. We also show that certain polynomials in one variable cannot be simplified by a Tschirnhaus transformation.
Discrete Series of Classical Groups
Authors: Zhang Yuanli 
Published: December 2010

AbstractLetGnbe the split classical groups Sp(2n), SO(2n+ 1) and SO(2n) defined over ap-adic field F or the quasi-split classical groupsU(n, n) andU(n+ 1,n) with respect to a quadratic extensionE/F. We prove the self-duality of unitary supercuspidal data of standard Levi subgroups ofGn(F) which give discrete series representations ofGn(F).
Nest Representations of TAF Algebras
Authors: Hopenwasser Alan , Peters Justin R. , Power Stephen C. 
Published: December 2010

AbstractA nest representation of a strongly maximal TAF algebra A with diagonal D is a representation π for which Lat π(A) is totally ordered. We prove that ker π is a meet irreducible ideal if the spectrum of A is totally ordered or if (after an appropriate similarity) the von Neumann algebra π(D)ʺ contains an atom.
On the Homology of GLnand Higher Pre-Bloch Groups
Authors: Yagunov Serge 
Published: December 2010

AbstractFor every integern> 1 and infinite fieldFwe construct a spectral sequence converging to the homology of GLn(F) relative to the group of monomial matrices GMn(F). Some entries inE2-terms of these spectral sequences may be interpreted as a natural generalization of the Bloch group to higher dimensions. These groups may be characterized as homology of GLnrelatively to GLn-1and GMn. We apply the machinery developed to the investigation of stabilization maps in homology of General Linear Groups.
Merit Factors of Polynomials Formed by Jacobi Symbols
Authors: Borwein Peter , Choi Kwok-Kwong Stephen 
Published: December 2010

AbstractWe give explicit formulas for the L4 norm (or equivalently for the merit factors) of various sequences of polynomials related to the polynomialsandwhere is the Jacobi symbol.Two cases of particular interest are when N = pq is a product of two primes and p = q + 2 or p = q + 4. This extends work of Høholdt, Jensen and Jensen and of the authors.This study arises from a number of conjectures of Erdȍs, Littlewood and others that concern the norms of polynomials with −1, 1 coefficients on the disc. The current best examples are of the above form when N is prime and it is natural to see what happens for composite N.
On the Steinberg Map and Steinberg Cross-Section for a Symmetrizable Indefinite Kac-Moody Group
Authors: Mokler Claus 
Published: December 2010

AbstractLet G be a symmetrizable indefinite Kac-Moody group over . Let be the characters of the fundamental irreducible representations of G, defined as convergent series on a certain part Gtr-alg ⊆ G. Following Steinberg in the classical case and Brüchert in the affine case, we define the Steinberg map as well as the Steinberg cross section C, together with a natural parametrisation . We investigate the local behaviour of χ on C near , and we show that there exists a neighborhood of (0, . . . , 0) × (1, . . . , 1), on which χ ◦ ω is a regular analytical map, satisfying a certain functional identity. This identity has its origin in an action of the center of G on C.
R-Diagonal Elements and Freeness With Amalgamation
Authors: Nica Alexandru , Shlyakhtenko Dimitri , Speicher Roland 
Published: December 2010

AbstractThe concept of R-diagonal element was introduced in [5], and was subsequently found to have applications to several problems in free probability. In this paper we describe a new approach to R-diagonality, which relies on freeness with amalgamation. The class of R-diagonal elements is enlarged to contain examples living in non-tracial *-probability spaces, such as the generalized circular elements of [7].
Values of the Dedekind Eta Function at Quadratic Irrationalities: Corrigendum
Authors: van der Poorten Alfred J. , Williams Kenneth S. 
Published: December 2010

AbstractHabib Muzaffar of Carleton University has pointed out to the authors that in their paper [A] only the resultfollows from the prime ideal theorem with remainder for ideal classes, and not the stronger resultstated in Lemma 5.2. This necessitates changes in Sections 5 and 6 of [A]. The main results of the paper are not affected by these changes. It should also be noted that, starting on page 177 of [A], each and every occurrence of o(s − 1) should be replaced by o(1).Sections 5 and 6 of [A] have been rewritten to incorporate the abovementioned correction and are given below. They should replace the original Sections 5 and 6 of [A].
Spaces of Lorentz Multipliers
Authors: Hare Kathryn E. , Sato Enji 
Published: December 2010

AbstractWe study when the spaces of Lorentz multipliers from Lp,t → Lp,s are distinct. Our main interest is the case when s < t, the Lorentz-improving multipliers. We prove, for example, that the space of multipliers which map Lp,t → Lp,s is different from those mapping Lp,t → Lp,s if either r = p or p′ and 1/s − 1/t ≠ 1/u − 1/v, or r ≠ p or p′. These results are obtained by making careful estimates of the Lorentz multiplier norms of certain linear combinations of Fejer or Dirichlet kernels. For the case when the first indices are different the linear combination we analyze is in the spirit of a Rudin-Shapiro polynomial.
Avoiding Patterns in the Abelian Sense
Authors: Currie J. , Linek V. 
Published: December 2010

AbstractWe classify all 3 letter patterns that are avoidable in the abelian sense. A short list of four letter patterns for which abelian avoidance is undecided is given. Using a generalization of Zimin words we deduce some properties of ω-words avoiding these patterns.
Differential Structure of Orbit Spaces
Authors: Cushman Richard , Śniatycki Jędrzej 
Published: December 2010

AbstractWe present a new approach to singular reduction of Hamiltonian systems with symmetries. The tools we use are the category of differential spaces of Sikorski and the Stefan-Sussmann theorem. The former is applied to analyze the differential structure of the spaces involved and the latter is used to prove that some of these spaces are smooth manifolds.Our main result is the identification of accessible sets of the generalized distribution spanned by the Hamiltonian vector fields of invariant functions with singular reduced spaces. We are also able to describe the differential structure of a singular reduced space corresponding to a coadjoint orbit which need not be locally closed.
AsymptoticK-Theory for Groups Acting onÃ2Buildings
Authors: Robertson Guyan , Steger Tim 
Published: December 2010

AbstractLet Γ be a torsion free lattice inG= PGL(3,) whereis a nonarchimedean local field. Then Γ acts freely on the affine Bruhat-Tits building ℬ ofGand there is an induced action on the boundary Ω of ℬ. The crossed productC*-algebra(Γ) =C(Ω) ⋊ Γ depends only on Γ and is classified by itsK-theory. This article shows how to compute theK-theory of(Γ) and of the larger class of rank two Cuntz-Krieger algebras.
Explicit Upper Bounds for Residues of Dedekind Zeta Functions and Values ofL-Functions ats= 1, and Explicit Lower Bounds for Relative Class Numbers of CM-Fields
Authors: Louboutin Stéphane 
Published: December 2010

AbstractWe provide the reader with a uniform approach for obtaining various useful explicit upper bounds on residues of Dedekind zeta functions of numbers fields and on absolute values of values at$s=1$of$L$-series associated with primitive characters on ray class groups of number fields. To make it quite clear to the reader how useful such bounds are when dealing with class number problems for CM-fields, we deduce an upper bound for the root discriminants of the normal CM-fields with (relative) class number one.
Quasi-Poisson Manifolds
Authors: Alekseev A. , Kosmann-Schwarzbach Y. , Meinrenken E. 
Published: December 2010

AbstractA quasi-Poisson manifold is a G-manifold equipped with an invariant bivector field whose Schouten bracket is the trivector field generated by the invariant element in associated to an invariant inner product. We introduce the concept of the fusion of such manifolds, and we relate the quasi-Poisson manifolds to the previously introduced quasi-Hamiltonian manifolds with group-valued moment maps.
Parametric Representation of Univalent Mappings in Several Complex Variables
Authors: Graham Ian , Hamada Hidetaka , Kohr Gabriela 
Published: December 2010

AbstractLet B be the unit ball of with respect to an arbitrary norm. We prove that the analog of the Carathéodory set, i.e. the set of normalized holomorphic mappings from B into of “positive real part”, is compact. This leads to improvements in the existence theorems for the Loewner differential equation in several complex variables. We investigate a subset of the normalized biholomorphic mappings of B which arises in the study of the Loewner equation, namely the set S0(B) of mappings which have parametric representation. For the case of the unit polydisc these mappings were studied by Poreda, and on the Euclidean unit ball they were studied by Kohr. As in Kohr’s work, we consider subsets of S0(B) obtained by placing restrictions on the mapping from the Carathéodory set which occurs in the Loewner equation. We obtain growth and covering theorems for these subsets of S0(B) as well as coefficient estimates, and consider various examples. Also we shall see that in higher dimensions there exist mappings in S(B) which can be imbedded in Loewner chains, but which do not have parametric representation.
On Connected Components of Shimura Varieties
Authors: Haines Thomas J. 
Published: December 2010

AbstractWe study the cohomology of connected components of Shimura varieties coming from the group GSp2g, by an approach modeled on the stabilization of the twisted trace formula, due to Kottwitz and Shelstad. More precisely, for each character ϖ on the group of connected components of we define an operator L(ω) on the cohomology groups with compact supports Hic(, ), and then we prove that the virtual trace of the composition of L(ω) with a Hecke operator f away from p and a sufficiently high power of a geometric Frobenius , can be expressed as a sum of ω-weighted (twisted) orbital integrals (where ω-weighted means that the orbital integrals and twisted orbital integrals occuring here each have a weighting factor coming from the character ϖ). As the crucial step, we define and study a new invariant α1(γ0; γ, δ) which is a refinement of the invariant α(γ0; γ, δ) defined by Kottwitz. This is done by using a theorem of Reimann and Zink.
Rational Solutions of Painlevé Equations
Authors: Wenjun Yuan , Yezhou Li 
Published: December 2010

AbstractConsider the sixth Painlevé equation (P6) below where α, β, γ and δ are complex parameters. We prove the necessary and sufficient conditions for the existence of rational solutions of equation (P6) in term of special relations among the parameters. The number of distinct rational solutions in each case is exactly one or two or infinite. And each of them may be generated by means of transformation group found by Okamoto [7] and Bäcklund transformations found by Fokas and Yortsos [4]. A list of rational solutions is included in the appendix. For the sake of completeness, we collected all the corresponding results of other five Painlevé equations (P1)−(P5) below, which have been investigated by many authors [1]–[7].
Chief Factor Sizes in Finitely Generated Varieties
Authors: Kearnes K. A. , Kiss E. W. , Szendrei Á. , Willard R. D. 
Published: December 2010

AbstractLet A be a k-element algebra whose chief factor size is c. We show that if B is in the variety generated by A, then any abelian chief factor of B that is not strongly abelian has size at most ck−1. This solves Problem 5 of The Structure of Finite Algebras, by D. Hobby and R. McKenzie. We refine this bound to c in the situation where the variety generated by A omits type 1. As a generalization, we bound the size of multitraces of types 1, 2, and 3 by extending coordinatization theory. Finally, we exhibit some examples of bad behavior, even in varieties satisfying a congruence identity.
Nilpotent Orbits and Whittaker Functions for Derived Functor Modules of Sp(2, ℝ)
Authors: Miyazaki Takuya 
Published: December 2010

AbstractWe study the moderate growth generalized Whittaker functions, associated to a unitary character ψ of a unipotent subgroup, for the non-tempered cohomological representation of G = Sp(2, ℝ). Through an explicit calculation of a holonomic system which characterizes these functions we observe that their existence is determined by the including relation between the real nilpotent coadjoint G-orbit of ψ in and the asymptotic support of the cohomological representation.
Spherical Functions for the Semisimple Symmetric Pair (Sp(2, ℝ), SL(2, ℂ))
Authors: Moriyama Tomonori 
Published: December 2010

AbstractLet π be an irreducible generalized principal series representation of G = Sp(2, ℝ) induced from its Jacobi parabolic subgroup. We show that the space of algebraic intertwining operators from π to the representation induced from an irreducible admissible representation of SL(2, ℂ) in G is at most one dimensional. Spherical functions in the title are the images of K-finite vectors by this intertwining operator. We obtain an integral expression of Mellin-Barnes type for the radial part of our spherical function.
Convexité, complète monotonie et inégalités sur les fonctions zèta et gamma, sur les fonctions des opérateurs de Baskakov et sur des fonctions arithmétiques
Authors: Bastien G. , Rogalski M. 
Published: December 2010

RésuméNous prouvons un encadrement optimal pour la quantité pour x ≥ 0 et s > 1, qui améliore l'encadrement standard par des int égrales. Cet encadrement entraîne des inégalités sur la fonction ζ de Riemann, et amène à conjecturer la monotonie de la fonction . On donne des applications à l'étude de la convexité de fonctions liées à la fonction Γ d'Euler et à la majoration optimale des fonctions élémentaires intervenant dans les opérateurs de Baskakov. Puis, nous étendons aux fonctions complètement monotones sur ]0, +∞[ les résultats établis pour la fonction , et nous en déduisons des preuves élémentaires du comportement, quand z tend vers 1, des séries génératrices de certaines fonctions arithmétiques. Enfin, nous prouvons qu'une partie du résultat se généralise à une classe de fonctions convexes positives décroissantes.
Approximation on Closed Sets by Analytic or Meromorphic Solutions of Elliptic Equations and Applications
Authors: Boivin André , Gauthier Paul M. , Paramonov Petr V. 
Published: December 2010

AbstractGiven a homogeneous elliptic partial differential operator L with constant complex coefficients and a class of functions (jet-distributions) which are defined on a (relatively) closed subset of a domain Ω in Rn and which belong locally to a Banach space V, we consider the problem of approximating in the norm of V the functions in this class by “analytic” and “meromorphic” solutions of the equation Lu = 0. We establish new Roth, Arakelyan (including tangential) and Carleman type theorems for a large class of Banach spaces V and operators L. Important applications to boundary value problems of solutions of homogeneous elliptic partial differential equations are obtained, including the solution of a generalized Dirichlet problem.
Bifurcations of Limit Cycles From Infinity in Quadratic Systems
Authors: Gavrilov Lubomir , Iliev Iliya D. 
Published: December 2010

AbstractWe investigate the bifurcation of limit cycles in one-parameter unfoldings of quadractic differential systems in the plane having a degenerate critical point at infinity. It is shown that there are three types of quadratic systems possessing an elliptic critical point which bifurcates from infinity together with eventual limit cycles around it. We establish that these limit cycles can be studied by performing a degenerate transformation which brings the system to a small perturbation of certain well-known reversible systems having a center. The corresponding displacement function is then expanded in a Puiseux series with respect to the small parameter and its coefficients are expressed in terms of Abelian integrals. Finally, we investigate in more detail four of the cases, among them the elliptic case (Bogdanov-Takens system) and the isochronous center S3. We show that in each of these cases the corresponding vector space of bifurcation functions has the Chebishev property: the number of the zeros of each function is less than the dimension of the vector space. To prove this we construct the bifurcation diagram of zeros of certain Abelian integrals in a complex domain.
Large Time Behavior for the Cubic Nonlinear Schrödinger Equation
Authors: Hayashi Nakao , Naumkin Pavel I. 
Published: December 2010

AbstractWe consider the Cauchy problem for the cubic nonlinear Schrödinger equation in one space dimensionCubic type nonlinearities in one space dimension heuristically appear to be critical for large time. We study the global existence and large time asymptotic behavior of solutions to the Cauchy problem (1). We prove that if the initial data are small and such that for some n ∈ Z, and , then the solution has an additional logarithmic timedecay in the short range region . In the far region the asymptotics have a quasilinear character.
Form Domains and Eigenfunction Expansions for Differential Equations with Eigenparameter Dependent Boundary Conditions
Authors: Binding Paul , Ćurgus Branko 
Published: December 2010

AbstractForm domains are characterized for regular 2n-th order differential equations subject to general self-adjoint boundary conditions depending affinely on the eigenparameter. Corresponding modes of convergence for eigenfunction expansions are studied, including uniformconvergence of the first n − 1 derivatives.
The Weil Character of the Unitary Group Associated to a Finite Local Ring
Authors: Gow Roderick , Szechtman Fernando 
Published: December 2010

AbstractLetR/R be a quadratic extension of finite, commutative, local and principal rings of odd characteristic. Denote byUn(R) the unitary group of ranknassociated toR/R. The Weil representation ofUn(R) is defined and its character is explicitly computed.
Finsler Metrics with K = 0 and S = 0
Authors: Shen Zhongmin 
Published: December 2010

AbstractIn the paper, we study the shortest time problem on a Riemannian space with an external force. We show that such problem can be converted to a shortest path problem on a Randers space. By choosing an appropriate external force on the Euclidean space, we obtain a non-trivial Randers metric of zero flag curvature. We also show that any positively complete Randers metric with zero flag curvature must be locally Minkowskian.
Homotopy Decompositions Involving the Loops of Coassociative Co-H Spaces
Authors: Theriault Stephen D. 
Published: December 2010

AbstractJames gave an integral homotopy decomposition of ∑Ω∑X, Hilton-Milnor one for Ω(∑X ∨ ∑Y), and Cohen-Wu gave p-local decompositions of Ω∑X if X is a suspension. All are natural. Using idempotents and telescopes we show that the James andHilton-Milnor decompositions have analogues when the suspensions are replaced by coassociative co-H spaces, and the Cohen-Wu decomposition has an analogue when the (double) suspension is replaced by a coassociative, cocommutative co-H space.
Two Algorithms for a Moving Frame Construction
Authors: Kogan Irina A. 
Published: December 2010

AbstractThe method of moving frames, introduced by Elie Cartan, is a powerful tool for the solution of various equivalence problems. The practical implementation of Cartan's method, however, remains challenging, despite its later significant development and generalization. This paper presents two new variations on the Fels and Olver algorithm, which under some conditions on the group action, simplify a moving frame construction. In addition, the first algorithm leads to a better understanding of invariant differential forms on the jet bundles, while the second expresses the differential invariants for the entire group in terms of the differential invariants of its subgroup.
The Maximum Number of Points on a Curve of Genus 4 over is 25
Authors: Savitt David 
Published: December 2010

AbstractWe prove that the maximum number of rational points on a smooth, geometrically irreducible genus 4 curve over the field of 8 elements is 25. The body of the paper shows that 27 points is not possible by combining techniques from algebraic geometry with a computer verification. The appendix shows that 26 points is not possible by examining the zeta functions.