bluuebunny/crossref_metadata_2025_split huggingface dataset:
Locally Compact Pro-C*-Algebras
Authors: Amini Massoud 
Published: December 2010

AbstractLet X be a locally compact non-compact Hausdorff topological space. Consider the algebras C(X), Cb(X), C0(X), and C00(X) of respectively arbitrary, bounded, vanishing at infinity, and compactly supported continuous functions on X. Of these, the second and third are C*-algebras, the fourth is a normed algebra, whereas the first is only a topological algebra (it is indeed a pro-C*- algebra). The interesting fact about these algebras is that if one of them is given, the others can be obtained using functional analysis tools. For instance, given the C*-algebra C0(X), one can get the other three algebras by C00(X) = K(C0(X)), Cb(X) = M(C0(X)), C(X) = Γ(K(C0(X))), where the right hand sides are the Pedersen ideal, the multiplier algebra, and the unbounded multiplier algebra of the Pedersen ideal of C0(X), respectively. In this article we consider the possibility of these transitions for general C*-algebras. The difficult part is to start with a pro-C*-algebra A and to construct a C*-algebra A0 such that A = Γ(K(A0)). The pro-C*-algebras for which this is possible are called locally compact and we have characterized them using a concept similar to that of an approximate identity.
ℤ[] is Euclidean
Authors: Harper Malcolm 
Published: December 2010

AbstractWe provide the first unconditional proof that the ring ℤ[] is a Euclidean domain. The proof is generalized to other real quadratic fields and to cyclotomic extensions of ℚ. It is proved that if K is a real quadratic field (modulo the existence of two special primes of K) or if K is a cyclotomic extension of ℚ then:the ring of integers of K is a Euclidean domain if and only if it is a principal ideal domain.The proof is a modification of the proof of a theorem of Clark and Murty giving a similar result when K is a totally real extension of degree at least three. The main changes are a new Motzkintype lemma and the addition of the large sieve to the argument. These changes allow application of a powerful theorem due to Bombieri, Friedlander and Iwaniec in order to obtain the result in the real quadratic case. The modification also allows the completion of the classification of cyclotomic extensions in terms of the Euclidean property.
Linear Operators on Matrix Algebras that Preserve the Numerical Range, Numerical Radius or the States
Authors: Li Chi-Kwong , Sourour Ahmed Ramzi 
Published: December 2010

AbstractEvery norm v on Cn induces two norm numerical ranges on the algebra Mn of all n × n complex matrices, the spatial numerical rangewhere vD is the norm dual to v, and the algebra numerical rangewhere is the set of states on the normed algebra Mn under the operator norm induced by v. For a symmetric norm v, we identify all linear maps on Mn that preserve either one of the two norm numerical ranges or the set of states or vector states. We also identify the numerical radius isometries, i.e., linear maps that preserve the (one) numerical radius induced by either numerical range. In particular, it is shown that if v is not the ℓ1, ℓ2, or ℓ∞ norms, then the linear maps that preserve either numerical range or either set of states are “inner”, i.e., of the formA ⟼ Q*AQ, where Q is a product of a diagonal unitary matrix and a permutation matrix and the numerical radius isometries are unimodular scalar multiples of such inner maps. For the ℓ1 and the ℓ∞ norms, the results are quite different.
A Central Limit Theorem and Law of the Iterated Logarithm for a Random Field with Exponential Decay of Correlations
Authors: Schmuland Byron , Sun Wei 
Published: December 2010

AbstractIn [6], Walter Philipp wrote that “… the law of the iterated logarithm holds for any process for which the Borel-Cantelli Lemma, the central limit theorem with a reasonably good remainder and a certain maximal inequality are valid.” Many authors [1], [2], [4], [5], [9] have followed this plan in proving the law of the iterated logarithm for sequences (or fields) of dependent random variables.We carry on this tradition by proving the law of the iterated logarithm for a random field whose correlations satisfy an exponential decay condition like the one obtained by Spohn [8] for certain Gibbs measures. These do not fall into the ϕ-mixing or strong mixing cases established in the literature, but are needed for our investigations [7] into diffusions on configuration space.The proofs are all obtained by patching together standard results from [5], [9] while keeping a careful eye on the correlations.
An Elementary Proof of a Weak Exceptional Zero Conjecture
Authors: Orton Louisa 
Published: December 2010

AbstractIn this paper we extend Darmon's theory of “integration on ℋp × ℋ” to cusp forms f of higher even weight. This enables us to prove a “weak exceptional zero conjecture”: that when the p-adic L-function of f has an exceptional zero at the central point, the ℒ-invariant arising is independent of a twist by certain Dirichlet characters.
Cohomology Ring of Symplectic Quotients by Circle Actions
Authors: Mohammadalikhani Ramin 
Published: December 2010

AbstractIn this article we are concerned with how to compute the cohomology ring of a symplectic quotient by a circle action using the information we have about the cohomology of the original manifold and some data at the fixed point set of the action. Our method is based on the Tolman-Weitsman theorem which gives a characterization of the kernel of the Kirwan map. First we compute a generating set for the kernel of the Kirwan map for the case of product of compact connected manifolds such that the cohomology ring of each of them is generated by a degree two class. We assume the fixed point set is isolated; however the circle action only needs to be “formally Hamiltonian”. By identifying the kernel, we obtain the cohomology ring of the symplectic quotient. Next we apply this result to some special cases and in particular to the case of products of two dimensional spheres. We show that the results of Kalkman and Hausmann-Knutson are special cases of our result.
Multisymplectic Reduction for Proper Actions
Authors: Śniatycki Jędrzej 
Published: December 2010

AbstractWe consider symmetries of the Dedonder equation arising from variational problems with partial derivatives. Assuming a proper action of the symmetry group, we identify a set of reduced equations on an open dense subset of the domain of definition of the fields under consideration. By continuity, the Dedonder equation is satisfied whenever the reduced equations are satisfied.
Similarity Classification of Cowen-Douglas Operators
Authors: Jiang Chunlan 
Published: December 2010

AbstractLet ℋ be a complex separable Hilbert space and ℒ(ℋ) denote the collection of bounded linear operators on ℋ. An operator A in ℒ(ℋ) is said to be strongly irreducible, if , the commutant of A, has no non-trivial idempotent. An operator A in ℒ(ℋ) is said to be a Cowen-Douglas operator, if there exists Ω, a connected open subset of C, and n, a positive integer, such that(a)Ω ⊂ σ(A) = ﹛z ∈ C | A – z not invertible﹜;(b)ran(A – z) = ℋ, for z in Ω;(c)Vz∈Ω ker(A – z) = ℋ and(d)dim ker(A – z) = n for z in Ω.In the paper, we give a similarity classification of strongly irreducible Cowen-Douglas operators by using the K0-group of the commutant algebra as an invariant.
Smoothness of Quotients Associated With a Pair of Commuting Involutions
Authors: Helminck Aloysius G. , Schwarz Gerald W. 
Published: December 2010

AbstractLet σ, θ be commuting involutions of the connected semisimple algebraic group G where σ, θ and G are defined over an algebraically closed field , char = 0. Let H := Gσ and K := Gθ be the fixed point groups. We have an action (H × K) × G → G, where ((h, k), g) ⟼ hgk–1, h ∈ H, k ∈ K, g ∈ G. Let G//(H × K) denote the categorical quotient Spec (G)H×K. We determine when this quotient is smooth. Our results are a generalization of those of Steinberg [Ste75], Pittie [Pit72] and Richardson [Ric82] in the symmetric case where σ = θ and H = K.
Central Sequence Algebras of a Purely Infinite Simple C*-algebra
Authors: Kishimoto Akitaka 
Published: December 2010

AbstractWe are concerned with a unital separable nuclear purely infinite simple C*-algebra A satisfying UCT with a Rohlin flow, as a continuation of [12]. Our first result (which is independent of the Rohlin flow) is to characterize when two central projections in A are equivalent by a central partial isometry. Our second result shows that the K-theory of the central sequence algebra A′ ∩ Aω (for an ω ∈ βN\N) and its fixed point algebra under the flow are the same (incorporating the previous result). We will also complete and supplement the characterization result of the Rohlin property for flows stated in [12].
Enriques Diagrams and Adjacency of Planar Curve Singularities
Authors: Alberich-Carramiñana Maria , Roé Joaquim 
Published: December 2010

AbstractWe study adjacency of equisingularity types of planar complex curve singularities in terms of their Enriques diagrams. The goal is, given two equisingularity types, to determine whether one of themis adjacent to the other. For linear adjacency a complete answer is obtained, whereas for arbitrary (analytic) adjacency a necessary condition and a sufficient condition are proved. We also obtain new examples of exceptional deformations,i.e, singular curves of type𝓓′ that can be deformed to a curve of type𝓓without𝓓′ being adjacent to𝓓.
On the Size of the Wild Set
Authors: Somodi Marius 
Published: December 2010

AbstractTo every pair of algebraic number fields with isomorphic Witt rings one can associate a number, called the minimum number of wild primes. Earlier investigations have established lower bounds for this number. In this paper an analysis is presented that expresses the minimum number of wild primes in terms of the number of wild dyadic primes. This formula not only gives immediate upper bounds, but can be considered to be an exact formula for the minimum number of wild primes.
On the Duality between Coalescing Brownian Motions
Authors: Xiong Jie , Zhou Xiaowen 
Published: December 2010

AbstractA duality formula is found for coalescing Brownian motions on the real line. It is shown that the joint distribution of a coalescing Brownian motion can be determined by another coalescing Brownian motion running backward. This duality is used to study a measure-valued process arising as the high density limit of the empirical measures of coalescing Brownian motions.
Unbounded Fredholm Operators and Spectral Flow
Authors: Booss-Bavnbek Bernhelm , Lesch Matthias , Phillips John 
Published: December 2010

AbstractWe study the gap (= “projection norm” = “graph distance”) topology of the space of all (not necessarily bounded) self-adjoint Fredholm operators in a separable Hilbert space by the Cayley transformand direct methods. In particular, we show the surprising result that this space is connected in contrast to the bounded case. Moreover, we present a rigorous definition of spectral flow of a path of such operators (actually alternative but mutually equivalent definitions) and prove the homotopy invariance. As an example, we discuss operator curves on manifolds with boundary.
Some New Results on L2 Cohomology of Negatively Curved Riemannian Manifolds
Authors: Cocos M. 
Published: December 2010

AbstractThe present paper is concerned with the study of the L2 cohomology spaces of negatively curved manifolds. The first half presents a finiteness and vanishing result obtained under some curvature assumptions, while the second half identifies a class of metrics having non-trivial L2 cohomology for degree equal to the half dimension of the space. For the second part we rely on the existence and regularity properties of the solution for the heat equation for forms.
Small Coverings with Smooth Functions under the Covering Property Axiom
Authors: Ciesielski Krzysztof , Pawlikowski Janusz 
Published: December 2010

AbstractIn the paper we formulate a Covering Property Axiom, CPAprism, which holds in the iterated perfect set model, and show that it implies the following facts, of which (a) and (b) are the generalizations of results of J. Steprāns.(a) There exists a family ℱ of less than continuummany functions from ℝ to ℝ such that ℝ2 is covered by functions from ℱ, in the sense that for every 〈x, y〉 ∈ ℝ2 there exists an f ∈ ℱ such that either f (x) = y or f (y) = x.(b) For every Borel function f : ℝ → ℝ there exists a family ℱ of less than continuum many “” functions (i.e., differentiable functions with continuous derivatives, where derivative can be infinite) whose graphs cover the graph of f.(c) For every n > 0 and a Dn function f: ℝ → ℝ there exists a family ℱ of less than continuum many Cn functions whose graphs cover the graph of f.We also provide the examples showing that in the above properties the smoothness conditions are the best possible. Parts (b), (c), and the examples are closely related to work of A. Olevskiĭ.
Local Solvability of Laplacian Difference Operators Arising from the Discrete Heisenberg Group
Authors: Kornelson Keri A. 
Published: December 2010

AbstractDifferential operators Dx, Dy , and Dz are formed using the action of the 3-dimensional discrete Heisenberg group G on a set S, and the operators will act on functions on S. The Laplacian operator is a difference operator with variable differences which can be associated to a unitary representation of G on the Hilbert space L2(S). Using techniques from harmonic analysis and representation theory, we show that the Laplacian operator is locally solvable.
The Resolvent of Closed Extensions of Cone Differential Operators
Authors: Schrohe E. , Seiler J. 
Published: December 2010

AbstractWe study closed extensions of an elliptic differential operator A on amanifold with conical singularities, acting as an unbounded operator on a weighted Lp-space. Under suitable conditions we show that the resolvent exists in a sector of the complex plane and decays like as Moreover, we determine the structure of the resolvent with enough precision to guarantee existence and boundedness of imaginary powers of .As an application we treat the Laplace–Beltrami operator for a metric with straight conical degeneracy and describe domains yielding maximal regularity for the Cauchy problem , u(0) = 0.
Hyperbolic Group C*-Algebras and Free-Product C*-Algebras as Compact Quantum Metric Spaces
Authors: Ozawa Narutaka , Rieffel Marc A. 
Published: December 2010

AbstractLet ℓ be a length function on a group G, and let Mℓ denote the operator of pointwise multiplication by ℓ on ℓ2(G). Following Connes, Mℓ can be used as a “Dirac” operator for C*r(G). It defines a Lipschitz seminorm on C*r(G), which defines a metric on the state space of C*r(G). We show that if G is a hyperbolic group and if ℓ is a word-length function on G, then the topology from this metric coincides with the weak-* topology (our definition of a “compact quantum metric space”). We show that a convenient framework is that of filtered C*-algebras which satisfy a suitable “Haagerup-type” condition. We also use this framework to prove an analogous fact for certain reduced free products of C*-algebras.
Dupin Hypersurfaces in ℝ5
Authors: Riveros Carlos M.C. , Tenenblat Keti 
Published: December 2010

AbstractWe study Dupin hypersurfaces in ℝ5 parametrized by lines of curvature, with four distinct principal curvatures. We characterize locally a generic family of such hypersurfaces in terms of the principal curvatures and four vector valued functions of one variable. We show that these vector valued functions are invariant by inversions and homotheties.
Motivic Haar Measure on Reductive Groups
Authors: Gordon Julia 
Published: December 2010

AbstractWe define a motivic analogue of the Haar measure for groups of the form G(k((t))), where k is an algebraically closed field of characteristic zero, and G is a reductive algebraic group defined over k. A classical Haar measure on such groups does not exist since they are not locally compact. We use the theory of motivic integration introduced by M. Kontsevich to define an additive function on a certain natural Boolean algebra of subsets of G(k((t))). This function takes values in the so-called dimensional completion of the Grothendieck ring of the category of varieties over the base field. It is invariant under translations by all elements of G(k((t))), and therefore we call it a motivic analogue of Haar measure. We give an explicit construction of the motivic Haar measure, and then prove that the result is independent of all the choices that are made in the process.
Existence and Multiplicity of Positive Solutions for Singular Semipositonep-Laplacian Equations
Authors: Agarwal Ravi P. , Cao Daomin , Lü Haishen , O'Regan Donal 
Published: December 2010

AbstractPositive solutions are obtained for the boundary value problemHeref (t, u)≥–M, (Mis a positive constant) for (t, u) ∈ [0, 1]×(0, ∞). We will show the existence of two positive solutions by using degree theory together with the upper–lower solution method.
Hausdorff and Quasi-Hausdorff Matrices on Spaces of Analytic Functions
Authors: Galanopoulos P. , Papadimitrakis M. 
Published: December 2010

AbstractWe consider Hausdorff and quasi-Hausdorff matrices as operators on classical spaces of analytic functions such as the Hardy and the Bergman spaces, the Dirichlet space, the Bloch spaces and BMOA. When the generating sequence of the matrix is the moment sequence of a measure μ, we find the conditions on μ which are equivalent to the boundedness of the matrix on the various spaces.
Mordell–Weil Groups and the Rank of Elliptic Curves over Large Fields
Authors: Im Bo-Hae 
Published: December 2010

AbstractLet K be a number field, an algebraic closure of K and E/K an elliptic curve defined over K. In this paper, we prove that if E/K has a K-rational point P such that 2P ≠ O and 3P ≠ O, then for each σ ∈ Gal(/K), the Mordell–Weil group of E over the fixed subfield of under σ has infinite rank.
Diametrically Maximal and Constant Width Sets in Banach Spaces
Authors: Moreno J. P. , Papini P. L. , Phelps R. R. 
Published: December 2010

AbstractWe characterize diametrically maximal and constant width sets inC(K), whereKis any compact Hausdorff space. These results are applied to prove that the sum of two diametrically maximal sets needs not be diametrically maximal, thus solving a question raised in a paper by Groemer. A characterization of diametrically maximal sets inis also given, providing a negative answer to Groemer's problem in finite dimensional spaces. We characterize constant width sets inc0(I), for everyI, and then we establish the connections between the Jung constant of a Banach space and the existence of constant width sets with empty interior. Porosity properties of families of sets of constant width and rotundity properties of diametrically maximal sets are also investigated. Finally, we present some results concerning non-reflexive and Hilbert spaces.
Functorial Decompositions of Looped Coassociative Co-H Spaces
Authors: Selick P. , Theriault S. , Wu J. 
Published: December 2010

AbstractSelick and Wu gave a functorial decomposition of Ω∑X for path-connected, p-local CW-complexes X which obtained the smallest nontrivial functorial retract Amin(X) of Ω∑X. This paper uses methods developed by the second author in order to extend such functorial decompositions to the loops on coassociative co-H spaces.
A Casselman–Shalika Formula for the Shalika Model of GLn
Authors: Sakellaridis Yiannis 
Published: December 2010

AbstractThe Casselman–Shalika method is a way to compute explicit formulas for periods of irreducible unramified representations of p-adic groups that are associated to unique models (i.e., multiplicity-free induced representations). We apply this method to the case of the Shalika model of GLn, which is known to distinguish lifts from odd orthogonal groups. In the course of our proof, we further develop a variant of themethod, that was introduced by Y.Hironaka, and in effect reducemany such problems to straightforward calculations on the group.
Orbites unipotentes et pôles d'ordre maximal de la fonction μ de Harish-Chandra
Authors: Heiermann Volker 
Published: December 2010

RésuméDans un travail antérieur, nous avions montré que l’induite parabolique (normalisée) d’une représentation irréductible cuspidale σ d’un sous-groupe de LeviMd’un groupep-adique contient un sous-quotient de carré intégrable, si et seulement si la fonction μ de Harish-Chandra a un pôle en σ d’ordre égal au rang parabolique deM. L’objet de cet article est d’interpréter ce résultat en termes de fonctorialité de Langlands.
On Fiber Cones of 𝑚-Primary Ideals
Authors: Jayanthan A. V. , Puthenpurakal Tony J. , Verma J. K. 
Published: December 2010

AbstractTwo formulas for the multiplicity of the fiber cone of an 𝑚-primary ideal of a d-dimensional Cohen–Macaulay local ring (R, 𝑚) are derived in terms of the mixed multiplicity ed–1(𝑚|I), the multiplicity e(I), and superficial elements. As a consequence, the Cohen–Macaulay property of F(I) when I has minimal mixed multiplicity or almost minimal mixed multiplicity is characterized in terms of the reduction number of I and lengths of certain ideals. We also characterize the Cohen–Macaulay and Gorenstein properties of fiber cones of 𝑚–primary ideals with a d–generated minimal reduction J satisfying ℓ(I2/JI) = 1 or ℓ(I𝑚/J𝑚) = 1.
Bol Loops of Nilpotence Class Two
Authors: Chein Orin , Goodaire Edgar G. 
Published: December 2010

AbstractCall a non-Moufang Bol loopminimally non-Moufangif every proper subloop is Moufang andminimally nonassociativeif every proper subloop is associative. We prove that these concepts are the same for Bol loops which are nilpotent of class two and in which certain associators square to 1. In the process, we derive many commutator and associator identities which hold in such loops.
Le splitting pour l'opérateur de Klein–Gordon: une approche heuristique et numérique
Authors: Servat E. 
Published: December 2010

AbstractDans cet article on étudie la différence entre les deux premières valeurs propres, le splitting, d’un opérateur de Klein–Gordon semi-classique unidimensionnel, dans le cas d’un potentiel symétrique présentant un double puits. Dans le cas d’une petite barrière de potentiel, B. Helffer et B. Parisse ont obtenu des résultats analogues à ceux existant pour l’opérateur de Schrödinger. Dans le cas d’une grande barrière de potentiel, on obtient ici des estimations des tranformées de Fourier des fonctions propres qui conduisent à une conjecture du splitting. Des calculs numériques viennent appuyer cette conjecture.
Division Algebras of Prime Degree and Maximal Galois p-Extensions
Authors: Mináč J. , Wadsworth A. 
Published: December 2010

AbstractLet p be an odd prime number, and let F be a field of characteristic not p and not containing the group μp of p-th roots of unity. We consider cyclic p-algebras over F by descent from L = F(μp). We generalize a theorem of Albert by showing that if μpn ⊆ L, then a division algebra D of degree pn over F is a cyclic algebra if and only if there is d ∈ D with dpn ∈ F – Fp. Let F(p) be the maximal p-extension of F. We show that F(p) has a noncyclic algebra of degree p if and only if a certain eigencomponent of the p-torsion of Br(F(p)(μp)) is nontrivial. To get a better understanding of F(p), we consider the valuations on F(p) with residue characteristic not p, and determine what residue fields and value groups can occur. Our results support the conjecture that the p torsion in Br(F(p)) is always trivial.