bluuebunny/crossref_metadata_2025_split huggingface dataset:
Group Actions and Codes
Authors: Puppe V. 
Published: December 2010

AbstractA 2-action with “maximal number of isolated fixed points” (i.e., with only isolated fixed points such that dimk(⊕iHi (M; k)) = |M2|, k = ) on a 3-dimensional, closed manifold determines a binary self-dual code of length = . In turn this code determines the cohomology algebra H*(M; k) and the equivariant cohomology . Hence, from results on binary self-dual codes one gets information about the cohomology type of 3-manifolds which admit involutions with maximal number of isolated fixed points. In particular, “most” cohomology types of closed 3-manifolds do not admit such involutions. Generalizations of the above result are possible in several directions, e.g., one gets that “most” cohomology types (over ) of closed 3-manifolds do not admit a non-trivial involution.
Nombres premiers de la forme ⌊nc⌋
Authors: Rivat Joël , Sargos Patrick 
Published: December 2010

AbstractFor c > 1 we denote by πc(x) the number of integers n ≤ x such that ⌊nc⌋ is prime. In 1953, Piatetski-Shapiro has proved thatholds for c < 12/11. Many authors have extended this range, which measures our progress in exponential sums techniques. In this article we obtain c < 1.16117….
Descending Rational Points on Elliptic Curves to Smaller Fields
Authors: Akbary Amir , Kumar Murty V. 
Published: December 2010

AbstractIn this paper, we study the Mordell-Weil group of an elliptic curve as a Galois module. We consider an elliptic curve E defined over a number field K whose Mordell-Weil rank over a Galois extension F is 1, 2 or 3. We show that E acquires a point (points) of infinite order over a field whose Galois group is one of Cn×Cm (n = 1, 2, 3, 4, 6, m = 1, 2), Dn×Cm (n = 2, 3, 4, 6, m = 1, 2), A4×Cm (m = 1, 2), S4 × Cm (m = 1, 2). Next, we consider the case where E has complex multiplication by the ring of integers of an imaginary quadratic field contained in K. Suppose that the -rank over a Galois extension F is 1 or 2. If ≠ and and h (class number of ) is odd, we show that E acquires positive -rank over a cyclic extension of K or over a field whose Galois group is one of SL2(/3), an extension of SL2(/3) by /2, or a central extension by the dihedral group. Finally, we discuss the relation of the above results to the vanishing of L-functions.
Ideal Structure of Multiplier Algebras of Simple C*-algebras With Real Rank Zero
Authors: Perera Francesc 
Published: December 2010

AbstractWe give a description of the monoid of Murray-von Neumann equivalence classes of projections for multiplier algebras of a wide class of σ-unital simple C*-algebras A with real rank zero and stable rank one. The lattice of ideals of this monoid, which is known to be crucial for understanding the ideal structure of themultiplier algebra , is therefore analyzed. In important cases it is shown that, if A has finite scale then the quotient of modulo any closed ideal I that properly contains A has stable rank one. The intricacy of the ideal structure of is reflected in the fact that can have uncountably many different quotients, each one having uncountably many closed ideals forming a chain with respect to inclusion.
Zeta Functions and ‘Kontsevich Invariants’ on Singular Varieties
Authors: Veys Willem 
Published: December 2010

AbstractLet X be a nonsingular algebraic variety in characteristic zero. To an effective divisor on X Kontsevich has associated a certain motivic integral, living in a completion of the Grothendieck ring of algebraic varieties. He used this invariant to show that birational (smooth, projective) Calabi-Yau varieties have the same Hodge numbers. Then Denef and Loeser introduced the invariant motivic (Igusa) zeta function, associated to a regular function on X, which specializes to both the classical p-adic Igusa zeta function and the topological zeta function, and also to Kontsevich's invariant.This paper treats a generalization to singular varieties. Batyrev already considered such a ‘Kontsevich invariant’ for log terminal varieties (on the level of Hodge polynomials of varieties instead of in the Grothendieck ring), and previously we introduced a motivic zeta function on normal surface germs. Here on any ℚ-Gorenstein variety X we associate a motivic zeta function and a ‘Kontsevich invariant’ to effective ℚ-Cartier divisors on X whose support contains the singular locus of X.
Ranks of Algebras of ContinuousC*-Algebra Valued Functions
Authors: Nagisa Masaru , Osaka Hiroyuki , Phillips N. Christopher 
Published: December 2010

AbstractWe prove a number of results about the stable and particularly the real ranks of tensor products ofC*-algebras under the assumption that one of the factors is commutative. In particular, we prove the following:(1)IfXis any locally compact σ-compact Hausdorff space andAis anyC*-algebra, then RR(C0(X) ⊗A) ≤ dim(X) + RR(A).(2)IfXis any locally compact Hausdorff space andAis any purely infinite simpleC*-algebra, then RR(C0(X) ⊗A) ≤ 1.(3)RR(C([0, 1]) ⊗A) ≥ 1 for any nonzeroC*-algebraA, and sr(C([0, 1]2) ⊗A) ≥ 2 for any unitalC*-algebraA.(4)IfAis a unitalC*-algebra such that RR(A) = 0, sr(A) = 1, andK1(A) = 0, then sr(C([0, 1]) ⊗A) = 1.(5)There is a simple separable unital nuclearC*-algebraAsuch that RR(A) = 1 and sr(C([0, 1]) ⊗A) = 1.
The Donaldson-Hitchin-Kobayashi Correspondence for Parabolic Bundles over Orbifold Surfaces
Authors: Steer Brian , Wren Andrew 
Published: December 2010

AbstractA theorem of Donaldson on the existence of Hermitian-Einstein metrics on stable holomorphic bundles over a compact Kähler surface is extended to bundles which are parabolic along an effective divisor with normal crossings. Orbifold methods, together with a suitable approximation theorem, are used following an approach successful for the case of Riemann surfaces.
Elementary Symmetric Polynomials in Numbers of Modulus 1
Authors: Cartwright Donald I. , Steger Tim 
Published: December 2010

AbstractWe describe the set of numbersσk(z1,…,zn+1), wherez1,…,zn+1are complex numbers of modulus 1 for whichz1z2…zn+1= 1, andσkdenotes thek-th elementary symmetric polynomial. Consequently, we give sharp constraints on the coefficients of a complex polynomial all of whose roots are of the same modulus. Another application is the calculation of the spectrum of certain adjacency operators arising naturally on a building of typeÃn.
Approximations fortes pour des processus bivariés
Authors: Castelle Nathalie 
Published: December 2010

RésuméNous établissons un résultat d’approximation forte pour des processus bivariés ayant une partie gaussienne et une partie empirique. Ce résultat apporte un nouveau point de vue sur deux théorèmes hongrois bidimensionnels établis précédemment, concernant l’approximation par un processus de Kiefer d’un processus empirique uniforme unidimensionnel et l’approximation par un pont brownien bidimensionnel d’un processus empirique uniforme bidimensionnel. Nous les enrichissons un peu et montrons que sous leur nouvelle forme ils ne sont que deux énoncés d’un même résultat.
Local L-Functions for Split Spinor Groups
Authors: Asgari Mahdi 
Published: December 2010

AbstractWe study the local L-functions for Levi subgroups in split spinor groups defined via the Langlands-Shahidi method and prove a conjecture on their holomorphy in a half plane. These results have been used in the work of Kim and Shahidi on the functorial product for GL2 × GL3.
Cuntz Algebra States Defined by Implementers of Endomorphisms of the CAR Algebra
Authors: Gabriel Michael J. 
Published: December 2010

AbstractWe investigate representations of the Cuntz algebraon antisymmetric Fock spaceFa(𝒦1) defined by isometric implementers of certain quasi-free endomorphisms of the CAR algebra in pure quasi-free states φP1. We pay special attention to the vector states oncorresponding to these representations and the Fock vacuum, for which we obtain explicit formulae. Restricting these states to the gauge-invariant subalgebra, we find that for natural choices of implementers, they are again pure quasi-free and are, in fact, essentially the states φP1. We proceed to consider the case for an arbitrary pair of implementers, and deduce that these Cuntz algebra representations are irreducible, as are their restrictions to.The endomorphisms ofB(Fa(𝒦)) associated with these representations ofare also considered.
Structure Theory of Totally Disconnected Locally Compact Groups via Graphs and Permutations
Authors: Möller Rögnvaldur G. 
Published: December 2010

AbstractWillis's structure theory of totally disconnected locally compact groups is investigated in the context of permutation actions. This leads to new interpretations of the basic concepts in the theory and also to new proofs of the fundamental theorems and to several new results. The treatment of Willis's theory is self-contained and full proofs are given of all the fundamental results.
Octahedral Galois Representations Arising From Q-Curves of Degree 2
Authors: Fernández J. , Lario J-C. , Rio A. 
Published: December 2010

AbstractGenerically, one can attach to a Q-curve C octahedral representations ρ: Gal() → GL2() coming from the Galois action on the 3-torsion of those abelian varieties of GL2-type whose building block is C. When C is defined over a quadratic field and has an isogeny of degree 2 to its Galois conjugate, there exist such representations ρ having image into GL2(F9). Going the other way, we can ask which mod 3 octahedral representations ρ of Gal() arise from Q-curves in the above sense. We characterize those arising from quadratic Q-curves of degree 2. The approach makes use of Galois embedding techniques in GL2(F9), and the characterization can be given in terms of a quartic polynomial defining the S4-extension of Q corresponding to the projective representation .
The Continuous Hochschild Cochain Complex of a Scheme
Authors: Yekutieli Amnon 
Published: December 2010

AbstractLet X be a separated finite type scheme over a noetherian base ring . There is a complex of topological -modules, called the complete Hochschild chain complex of X. To any -module —not necessarily quasi-coherent—we assign the complex of continuous Hochschild cochains with values in . Our first main result is that when X is smooth over there is a functorial isomorphismin the derived category , where .The second main result is that if X is smooth of relative dimension n and n! is invertible in K, then the standard maps induce a quasi-isomorphismWhen this is the quasi-isomorphism underlying the Kontsevich Formality Theorem.Combining the two results above we deduce a decomposition of the globalHochschild cohomologywhere is the relative tangent sheaf.
Short Kloosterman Sums for Polynomials over Finite Fields
Authors: Banks William D. , Harcharras Asma , Shparlinski Igor E. 
Published: December 2010

AbstractWe extend to the setting of polynomials over a finite field certain estimates for short Kloosterman sums originally due to Karatsuba. Our estimates are then used to establish some uniformity of distribution results in the ring [x]/M(x) for collections of polynomials either of the form f−1g−1 or of the form f−1g−1 + afg, where f and g are polynomials coprime to M and of very small degree relative to M, and a is an arbitrary polynomial. We also give estimates for short Kloosterman sums where the summation runs over products of two irreducible polynomials of small degree. It is likely that this result can be used to give an improvement of the Brun-Titchmarsh theorem for polynomials over finite fields.
Graph Subspaces and the Spectral Shift Function
Authors: Albeverio Sergio , Makarov Konstantin A. , Motovilov Alexander K. 
Published: December 2010

AbstractWe obtain a new representation for the solution to the operator Sylvester equation in the form of a Stieltjes operator integral. We also formulate new sufficient conditions for the strong solvability of the operator Riccati equation that ensures the existence of reducing graph subspaces for block operator matrices. Next, we extend the concept of the Lifshits-Krein spectral shift function associated with a pair of self-adjoint operators to the case of pairs of admissible operators that are similar to self-adjoint operators. Based on this new concept we express the spectral shift function arising in a perturbation problem for block operator matrices in terms of the angular operators associated with the corresponding perturbed and unperturbed eigenspaces.
Automorphismes modérés de l'espace affine
Authors: Edo Eric 
Published: December 2010

RésuméLe problème de Jung-Nagata (cf. [J], [N]) consiste à savoir s'il existe des automorphismes dek[x; y; z] qui ne sont pas modérés. Nous proposons une approche nouvelle de cette question, fondée sur l'utilisation de la théorie des automates et du polygone de Newton. Cette approche permet notamment de généraliser de façon significative les résultats de [A].
Higher Dimensional Asymptotic Cycles
Authors: Schwartzman Sol 
Published: December 2010

AbstractGiven a p-dimensional oriented foliation of an n-dimensional compact manifold Mn and a transversal invariant measure τ, Sullivan has defined an element of Hp(Mn; R). This generalized the notion of a μ-asymptotic cycle, which was originally defined for actions of the real line on compact spaces preserving an invariant measure μ. In this one-dimensional case there was a natural 1—1 correspondence between transversal invariant measures τ and invariant measures μ when one had a smooth flow without stationary points.For what we call an oriented action of a connected Lie group on a compact manifold we again get in this paper such a correspondence, provided we have what we call a positive quantifier. (In the one-dimensional case such a quantifier is provided by the vector field defining the flow.) Sufficient conditions for the existence of such a quantifier are given, together with some applications.
A Note on Cyclotomic Euler Systems and the Double Complex Method
Authors: Anderson Greg W. , Ouyang Yi 
Published: December 2010

AbstractLetbe a finite real abelian extension of ℚ. LetMbe an odd positive integer. For every squarefree positive integerrthe prime factors of which are congruent to 1 moduloMand split completely in, the corresponding Kolyvagin classsatisfies a remarkable and crucial recursion which for each prime number ℓ dividingrdetermines the order of vanishing of κrat each place ofabove ℓ in terms of κr/ℓ. In this note we give the recursion a new and universal interpretation with the help of the double complex method introduced by Anderson and further developed by Das and Ouyang. Namely, we show that the recursion satis_ed by Kolyvagin classes is the specialization of a universal recursion independent ofsatisfied by universal Kolyvagin classes in the group cohomology of the universal ordinary distributionà laKubert tensored with ℤ=Mℤ. Further, we show by a method involving a variant of the diagonal shift operation introduced by Das that certain group cohomology classes belonging (up to sign) to a basis previously constructed by Ouyang also satisfy the universal recursion.
Adic Topologies for the Rational Integers
Authors: Broughan Kevin A. 
Published: December 2010

AbstractA topology on ℤ, which gives a nice proof that the set of prime integers is infinite, is characterised and examined. It is found to be homeomorphic to ℚ, with a compact completion homeomorphic to the Cantor set. It has a natural place in a family of topologies on ℤ, which includes the p-adics, and one in which the set of rational primes ℙ is dense. Examples from number theory are given, including the primes and squares, Fermat numbers, Fibonacci numbers and k-free numbers.
The Closure Ordering of Nilpotent Orbits of the Complex Symmetric Pair (SOp+q, SOp × SOq)
Authors: Ðoković Dragomir Ž. , Litvinov Michael 
Published: December 2010

AbstractThe main problem that is solved in this paper has the following simple formulation (which is not used in its solution). The group K = Op(C) × Oq(C) acts on the space Mp, q of p × q complex matrices by (a; b) · x = axb–1, and so does its identity component K0 = SOp(C)×SOq(C). A K-orbit (or K0-orbit) in Mp,q is said to be nilpotent if its closure contains the zero matrix. The closure, , of a nilpotent K-orbit (resp. K0-orbit) in Mp,q is a union of and some nilpotent K-orbits (resp. K0-orbits) of smaller dimensions. The description of the closure of nilpotent K-orbits has been known for some time, but not so for the nilpotent K0-orbits. A conjecture describing the closure of nilpotent K0-orbits was proposed in [11] and verièd when min(p, q) ≤ 7. In this paper we prove the conjecture. The proof is based on a study of two prehomogeneous vector spaces attached to and determination of the basic relative invariants of these spaces.The above problem is equivalent to the problem of describing the closure of nilpotent orbits in the real Lie algebra so(p, q) under the adjoint action of the identity component of the real orthogonal group O(p, q).
On a Certain Residual Spectrum of Sp8
Authors: Pogge James Todd 
Published: December 2010

AbstractLet G = Sp2n be the symplectic group defined over a number field F. Let 𝔸 be the ring of adeles. A fundamental problem in the theory of automorphic forms is to decompose the right regular representation of G(𝔸) acting on the Hilbert space L2 (G(F) \ G(𝔸)). Main contributions have been made by Langlands. He described, using his theory of Eisenstein series, an orthogonal decomposition of this space of the form: , where (M, π) is a Levi subgroup with a cuspidal automorphic representation π taken modulo conjugacy. (Here we normalize π so that the action of the maximal split torus in the center of G at the archimedean places is trivial.) and is a space of residues of Eisenstein series associated to (M, π). In this paper, we will completely determine the space , when M ≃ GL2 × GL2. This is the first result on the residual spectrum for non-maximal, non-Borel parabolic subgroups, other than GLn.
Spectral Properties of the Commutator of Bergman's Projection and the Operator of Multiplication by an Analytic Function
Authors: Dostanić Milutin R. 
Published: December 2010

AbstractIt is shown that the singular values of the operator aP–Pa, where P is Bergman's projection over a bounded domain Ω and a is a function analytic on , detect the length of the boundary of a(Ω). Also we point out the relation of that operator and the spectral asymptotics of a Hankel operator with an anti-analytic symbol.
The Geometry of Quadratic Differential Systems with a Weak Focus of Third Order
Authors: Llibre Jaume , Schlomiuk Dana 
Published: December 2010

AbstractIn this article we determine the global geometry of the planar quadratic differential systems with a weak focus of third order. This class plays a significant role in the context of Hilbert's 16-th problem. Indeed, all examples of quadratic differential systems with at least four limit cycles, were obtained by perturbing a system in this family. We use the algebro-geometric concepts of divisor and zero-cycle to encode global properties of the systems and to give structure to this class. We give a theorem of topological classification of such systems in terms of integer-valued affine invariants. According to the possible values taken by them in this family we obtain a total of 18 topologically distinct phase portraits. We show that inside the class of all quadratic systems with the topology of the coefficients, there exists a neighborhood of the family of quadratic systems with a weak focus of third order and which may have graphics but no polycycle in the sense of [15] and no limit cycle, such that any quadratic system in this neighborhood has at most four limit cycles.
Predual of the Multiplier Algebra of Ap(G) and Amenability
Authors: Miao Tianxuan 
Published: December 2010

AbstractFor a locally compact group G and 1 < p < ∞, let Ap(G) be the Herz-Figà-Talamanca algebra and let PMp(G) be its dual Banach space. For a Banach Ap(G)-module X of PMp(G), we prove that the multiplier space ℳ(Ap(G); X*) is the dual Banach space of QX, where QX is the norm closure of the linear span Ap(G)X of u f for u 2 Ap(G) and f ∈ X in the dual of ℳ(Ap(G); X*). If p = 2 and PFp(G) ⊆ X, then Ap(G)X is closed in X if and only if G is amenable. In particular, we prove that the multiplier algebra MAp(G) of Ap(G) is the dual of Q, where Q is the completion of L1(G) in the ‖ · ‖M-norm. Q is characterized by the following: f ∈ Q if an only if there are ui ∈ Ap(G) and fi ∈ PFp(G) (i = 1; 2, … ) with such that on MAp(G). It is also proved that if Ap(G) is dense in MAp(G) in the associated w*-topology, then the multiplier norm and ‖ · ‖Ap(G)-norm are equivalent on Ap(G) if and only if G is amenable.
Coinvariant Algebras of Finite Subgroups of SL(3;C)
Authors: Gomi Yasushi , Nakamura Iku , Shinoda Ken-ichi 
Published: December 2010

AbstractFor most of the finite subgroups of SL(3; C) we give explicit formulae for the Molien series of the coinvariant algebras, generalizing McKay's formulae [McKay99] for subgroups of SU(2). We also study the G-orbit Hilbert scheme HilbG(C3) for any finite subgroup G of SO(3), which is known to be a minimal (crepant) resolution of the orbit space C3/G. In this case the fiber over the origin of the Hilbert-Chow morphism from HilbG(C3) to C3/G consists of finitely many smooth rational curves, whose planar dual graph is identified with a certain subgraph of the representation graph of G. This is an SO(3) version of the McKay correspondence in the SU(2) case.
The Heat Kernel and Green's Function on a Manifold with Heisenberg Group as Boundary
Authors: Ni Yilong 
Published: December 2010

AbstractWe study the Riemannian Laplace-Beltrami operator L on a Riemannian manifold with Heisenberg group H1 as boundary. We calculate the heat kernel and Green's function for L, and give global and small time estimates of the heat kernel. A class of hypersurfaces in this manifold can be regarded as approximations of H1. We also restrict L to each hypersurface and calculate the corresponding heat kernel and Green's function. We will see that the heat kernel and Green's function converge to the heat kernel and Green's function on the boundary.
Type Decomposition and the Rectangular AFD Property for W*-TRO’s
Authors: Ruan Zhong-Jin 
Published: December 2010

AbstractWe study the type decomposition and the rectangular AFD property for W*-TRO’s. Like von Neumann algebras, every W*-TRO can be uniquely decomposed into the direct sum of W*- TRO's of type I, type II, and type III. We may further considerW*-TRO's of type Im,n with cardinal numbers m and n, and considerW*-TRO's of type IIλ,μ with λ, μ = 1 or ∞. It is shown that every separable stable W*-TRO (which includes type I∞, ∞, type II∞, ∞ and type III) is TRO-isomorphic to a von Neumann algebra. We also introduce the rectangular version of the approximately finite dimensional property for W*-TRO’s. One of our major results is to show that a separable W*-TRO is injective if and only if it is rectangularly approximately finite dimensional. As a consequence of this result, we show that a dual operator space is injective if and only if its operator predual is a rigid rectangular space (equivalently, a rectangular space).
Regular Embeddings of Generalized Hexagons
Authors: Steinbach Anja , Van Maldeghem Hendrik 
Published: December 2010

AbstractWe classify the generalized hexagons which are laxly embedded in projective space such that the embedding is flat and polarized. Besides the standard examples related to the hexagons defined over the algebraic groups of type G2,3D4and6D4(and occurring in projective dimensions 5, 6, 7), we find new examples in unbounded dimension related to the mixed groups of type G2.
On the Connectedness of Moduli Spaces of Flat Connections over Compact Surfaces
Authors: Ho Nan-Kuo , Melissa Liu Chiu-Chu 
Published: December 2010

AbstractWe study the connectedness of the moduli space of gauge equivalence classes of flat G-connections on a compact orientable surface or a compact nonorientable surface for a class of compact connected Lie groups. This class includes all the compact, connected, simply connected Lie groups, and some non-semisimple classical groups.