bluuebunny/crossref_metadata_2025_split huggingface dataset:
Building a Stationary Stochastic Process From a Finite-Dimensional Marginal
Authors: Pivato Marcus 
Published: December 2010

AbstractIfis a finite alphabet,, andis a probability measure onthat “looks like” the marginal projection of a stationary stochastic process on, then can we “extend”to such a process? Under what conditions can we make this extension ergodic, (quasi)periodic, or (weakly) mixing? After surveying classical work on this problem when D = 1, we provide some sufficient conditions and some necessary conditions forto be extendible for D > 1, and show that, in general, the problem is not formally decidable.
Hyperbolic Polynomials and Convex Analysis
Authors: Bauschke Heinz H. , Güler Osman , Lewis Adrian S. , Sendov Hristo S. 
Published: December 2010

AbstractA homogeneous real polynomialpishyperbolicwith respect to a given vector d if the univariate polynomial t ⟼ p(x − td) has all real roots for all vectorsx. Motivated by partial differential equations, Gårding proved in 1951 that the largest such root is a convex function ofx, and showed various ways of constructing new hyperbolic polynomials. We present a powerful new such construction, and use it to generalize Gårding’s result to arbitrary symmetric functions of the roots. Many classical and recent inequalities follow easily. We develop various convex-analytic tools for such symmetric functions, of interest in interior-point methods for optimization problems over related cones.
Correction to: Upper Bounds for the Resonance Counting Function of Schrödinger Operators in Odd Dimensions
Authors: Froese Richard 
Published: December 2010

AbstractThe proof of Lemma 3.4 in [F] relies on the incorrect equality μj(AB) = μj(BA) for singular values (for a counterexample, see [S, p. 4]). Thus, Theorem 3.1 as stated has not been proven. However, with minor changes, we can obtain a bound for the counting function in terms of the growth of the Fourier transform of |V|.
Decompositions of the Hilbert Function of a Set of Points in ℙn
Authors: Geramita Anthony V. , Harima Tadahito , Shin Yong Su 
Published: December 2010

AbstractLet H be the Hilbert function of some set of distinct points in ℙn and let α = α(H) be the least degree of a hypersurface of ℙn containing these points. Write α = ds + ds–1 + … + d1 (where di > 0). We canonically decompose H into s other Hilbert functions and show how to find sets of distinct points , lying on reduced hypersurfaces of degrees ds, …, d1 (respectively) such that the Hilbert function of is and the Hilbert function of is H. Some extremal properties of this canonical decomposition are also explored.
Classification of Certain SimpleC*-Algebras with Torsion inK1
Authors: Mygind Jesper 
Published: December 2010

AbstractWe show that the Elliott invariant is a classifying invariant for the class of${{C}^{*}}$-algebras that are simple unital infinite dimensional inductive limits of finite direct sums of building blocks of the form$$\left\{ f\in C\left( \mathbb{T} \right)\otimes {{M}_{n}}:f\left( {{x}_{i}} \right)\in {{M}_{{{d}_{i}}}},i=1,2,...,N \right\},$$where${{x}_{1}},\,{{x}_{2.}},...,{{x}_{N\,}}\in \mathbb{T},{{d}_{1}},{{d}_{2}},.\,.\,.,{{d}_{N}}$are integers dividing$n$, and${{M}_{{{d}_{i}}}}$is embedded unitally into${{M}_{n}}$. Furthermore we prove existence and uniqueness theorems for$*$-homomorphisms between such algebras and we identify the range of the invariant.
Small Prime Solutions of Quadratic Equations
Authors: Choi Kwok-Kwong Stephen , Liu Jianya 
Published: December 2010

AbstractLet b1,…,b5 be non-zero integers and n any integer. Suppose that b1 + … + b5 ≡ n (mod 24) and (bi, bj) = 1 for 1 ≤ i < j ≤ 5. In this paper we prove that(i)if all bj are positive and , then the quadratic equation is soluble in primes pj, and(ii)if bj are not all of the same sign, then the above quadratic equation has prime solutions satisfying .
Intégrales orbitales pondérées sur les algèbres de Lie : le cas p-adique
Authors: Chaudouard Pierre-Henri 
Published: December 2010

RésuméSoit G un groupe réductif connexe défini sur un corps p-adique F et son algèbre de Lie. Les intégrales orbitales pondérées sur (F) sont des distributions JM(X, f)—f est une fonction test— indexées par les sous-groupes de Lévi M de G et les éléments semi-simples réguliers . Leurs analogues sur G sont les principales composantes du côté géométrique des formules des traces locale et globale d’Arthur.Si M = G, on retrouve les intégrales orbitales invariantes qui, vues comme fonction de X, sont borńees sur : c’est un résultat bien connu de Harish-Chandra. Si M ⊊ G, les intégrales orbitales pondérées explosent au voisinage des éléments singuliers. Nous construisons dans cet article de nouvelles intégrales orbitales pondérées (X, f), égales à JM(X, f) à un terme correctif près, qui tout en conservant les principales propriétés des précédentes (comportement par conjugaison, développement en germes, etc.) restent borńees quand X parcourt . Nous montrons également que les intégrales orbitales pondérées globales, associées à des éléments semi-simples réguliers, se décomposent en produits de ces nouvelles intégrales locales.
Framed Stratified Sets in Morse Theory
Authors: Lebel André 
Published: December 2010

AbstractIn this paper, we present a smooth framework for some aspects of the “geometry of CW complexes”, in the sense of Buoncristiano, Rourke and Sanderson [3]. We then apply these ideas to Morse theory, in order to generalize results of Franks [5] and Iriye-Kono [8].More precisely, consider a Morse function f on a closed manifold M. We investigate the relations between the attaching maps in a CW complex determined by f, and the moduli spaces of gradient flow lines of f, with respect to some Riemannian metric on M.
Mahler’s Measure and the Dilogarithm (I)
Authors: Boyd David W. , Rodriguez-Villegas Fernando 
Published: December 2010

AbstractAn explicit formula is derived for the logarithmicMahler measurem(P) of P(x, y) = p(x)y− q(x), where p(x) and q(x) are cyclotomic. This is used to find many examples of such polynomials for which m(P) is rationally related to the Dedekind zeta value ζF(2) for certain quadratic and quartic fields.
On the Lusternik-Schnirelmann Category of Maps
Authors: Stanley Donald 
Published: December 2010

AbstractWe give conditions which determine if cat of a map go up when extending over a cofibre. We apply this to reprove a result of Roitberg giving an example of a CW complex Z such that cat(Z) = 2 but every skeleton of Z is of category 1. We also find conditions when cat(f × g) < cat(f) + cat(g). We apply our result to show that under suitable conditions for rational maps f, mcat(f) < cat(f) is equivalent to cat(f) = cat(f × idSn). Many examples with mcat(f) < cat(f) satisfying our conditions are constructed. We also answer a question of Iwase by constructing p-local spaces X such that cat(X × S1) = cat(X) = 2. In fact for our spaces and every Y ≄ *, cat(X × Y) ≤ cat(Y) + 1 < cat(Y) + cat(X). We show that this same X has the property cat(X) = cat(X × X) = cl(X × X) = 2.
Strongly Projective Graphs
Authors: Larose Benoit 
Published: December 2010

AbstractWe introduce the notion of strongly projective graph, and characterise these graphs in terms of their neighbourhood poset. We describe certain exponential graphs associated to complete graphs and odd cycles. We extend and generalise a result of Greenwell and Lovász [6]: if a connected graph G does not admit a homomorphism to K, where K is an odd cycle or a complete graph on at least 3 vertices, then the graph G × Ks admits, up to automorphisms of K, exactly s homomorphisms to K.
On Graded Categorical Groups and Equivariant Group Extensions
Authors: Cegarra A. M. , Garćia-Calcines J. M. , Ortega J. A. 
Published: December 2010

AbstractIn this article we state and prove precise theorems on the homotopy classification of graded categorical groups and their homomorphisms. The results use equivariant group cohomology, and they are applied to show a treatment of the general equivariant group extension problem.
Fully Nonlinear Elliptic Equations on General Domains
Authors: Bao Jiguang 
Published: December 2010

AbstractBy means of the Pucci operator, we construct a function u0, which plays an essential role in our considerations, and give the existence and regularity theorems for the bounded viscosity solutions of the generalized Dirichlet problems of second order fully nonlinear elliptic equations on the general bounded domains, which may be irregular. The approximation method, the accretive operator technique and the Caffarelli's perturbation theory are used.
An Exactly Solved Model for Mutation, Recombination and Selection
Authors: Baake Michael , Baake Ellen 
Published: December 2010

AbstractIt is well known that rather generalmutation-recombination models can be solved algorithmically (though not in closed form) by means of Haldane linearization. The price to be paid is that one has to work with a multiple tensor product of the state space one started from.Here, we present a relevant subclass of such models, in continuous time, with independent mutation events at the sites, and crossover events between them. It admits a closed solution of the corresponding differential equation on the basis of the original state space, and also closed expressions for the linkage disequilibria, derived by means of Möbius inversion. As an extra benefit, the approach can be extended to a model with selection of additive type across sites. We also derive a necessary and sufficient criterion for the mean fitness to be a Lyapunov function and determine the asymptotic behaviour of the solutions.
Higher Order Tangents to Analytic Varieties along Curves
Authors: Braun Rüdiger W. , Meise Reinhold , Taylor B. A. 
Published: December 2010

AbstractLet V be an analytic variety in some open set in which contains the origin and which is purely k-dimensional. For a curve γ in , defined by a convergent Puiseux series and satisfying γ(0) = 0, and d ≥ 1, define Vt := t−d(V − (t)). Then the currents defined by Vt converge to a limit current Tγ,d[V] as t tends to zero. Tγ,d[V] is either zero or its support is an algebraic variety of pure dimension k in . Properties of such limit currents and examples are presented. These results will be applied in a forthcoming paper to derive necessary conditions for varieties satisfying the local Phragmén-Lindelöf condition that was used by Hörmander to characterize the constant coefficient partial differential operators which act surjectively on the space of all real analytic functions on .
On the Nonsquare Constants of Orlicz Spaces with Orlicz Norm
Authors: Yan Yaqiang 
Published: December 2010

AbstractLet lΦ and LΦ(Ω) be the Orlicz sequence space and function space generated by N-function Φ(u) with Orlicz norm. We give equivalent expressions for the nonsquare constants CJ(lΦ), CJ(LΦ(Ω)) in sense of James and CS(lΦ), CS(LΦ(Ω)) in sense of Schäffer. We are devoted to get practical computational formulas giving estimates of these constants and to obtain their exact value in a class of spaces lΦ and LΦ(Ω).
Infinitely Divisible Laws Associated with Hyperbolic Functions
Authors: Pitman Jim , Yor Marc 
Published: December 2010

AbstractThe infinitely divisible distributions onof random variablesCt,StandTtwith Laplace transformsrespectively are characterized for various t > 0 in a number of different ways: by simple relations between their moments and cumulants, by corresponding relations between the distributions and their Lévy measures, by recursions for their Mellin transforms, and by differential equations satisfied by their Laplace transforms. Some of these results are interpreted probabilistically via known appearances of these distributions for t = 1 or 2 in the description of the laws of various functionals of Brownian motion and Bessel processes, such as the heights and lengths of excursions of a one-dimensional Brownian motion. The distributions ofC1andS2are also known to appear in the Mellin representations of two important functions in analytic number theory, the Riemann zeta function and the Dirichlet L-function associated with the quadratic character modulo 4. Related families of infinitely divisible laws, including the gamma, logistic and generalized hyperbolic secant distributions, are derived fromStandCtby operations such as Brownian subordination, exponential tilting, and weak limits, and characterized in various ways.
Integrable Systems Associated to a Hopf Surface
Authors: Moraru Ruxandra 
Published: December 2010

AbstractA Hopf surface is the quotient of the complex surface by an infinite cyclic group of dilations of . In this paper, we study the moduli spaces of stable -bundles on a Hopf surface , from the point of view of symplectic geometry. An important point is that the surface is an elliptic fibration, which implies that a vector bundle on can be considered as a family of vector bundles over an elliptic curve. We define a map that associates to every bundle on a divisor, called the graph of the bundle, which encodes the isomorphism class of the bundle over each elliptic curve. We then prove that the map G is an algebraically completely integrable Hamiltonian system, with respect to a given Poisson structure on . We also give an explicit description of the fibres of the integrable system. This example is interesting for several reasons; in particular, since the Hopf surface is not Kähler, it is an elliptic fibration that does not admit a section.
Cohomology of Complex Torus Bundles Associated to Cocycles
Authors: Lee Min Ho 
Published: December 2010

AbstractEquivariant holomorphic maps of Hermitian symmetric domains into Siegel upper half spaces can be used to construct families of abelian varieties parametrized by locally symmetric spaces, which can be regarded as complex torus bundles over the parameter spaces. We extend the construction of such torus bundles using 2-cocycles of discrete subgroups of the semisimple Lie groups associated to the given symmetric domains and investigate some of their properties. In particular, we determine their cohomology along the fibers.
Poisson Brackets and Structure of Nongraded Hamiltonian Lie Algebras Related to Locally-Finite Derivations
Authors: Su Yucai 
Published: December 2010

AbstractXu introduced a class of nongraded Hamiltonian Lie algebras. These Lie algebras have a Poisson bracket structure. In this paper, the isomorphism classes of these Lie algebras are determined by employing a “sandwich” method and by studying some features of these Lie algebras. It is obtained that two Hamiltonian Lie algebras are isomorphic if and only if their corresponding Poisson algebras are isomorphic. Furthermore, the derivation algebras and the second cohomology groups are determined.
Some Convexity Results for the Cartan Decomposition
Authors: Graczyk P. , Sawyer P. 
Published: December 2010

AbstractIn this paper, we consider the set = a(eXKeY) where a(g) is the abelian part in the Cartan decomposition of g. This is exactly the support of the measure intervening in the product formula for the spherical functions on symmetric spaces of noncompact type. We give a simple description of that support in the case of SL(3; F) where F= R, Cor H. In particular, we show that is convex.We also give an application of our result to the description of singular values of a product of two arbitrary matrices with prescribed singular values.
Classification des représentations tempérées d'un groupe p-adique
Authors: Bettaïeb Karem 
Published: December 2010

RésuméSoit G le groupe des points définis sur un corps p-adique d'un groupe réductif connexe. A l'aide des caractères virtuels supertempérés de G, on prouve (conjectures de Clozel) que toute représentation irréductible tempérée de G est irréductiblement induite d'une essentielle d'un sousgroupe de Lévi de G.
Admissible Majorants for Model Subspaces of H2, Part II: Fast Winding of the Generating Inner Function
Authors: Havin Victor , Mashreghi Javad 
Published: December 2010

AbstractThis paper is a continuation of [6]. We consider the model subspaces Kϴ = H2 ϴ ϴH2 of the Hardy space H2 generated by an inner function ϴ in the upper half plane. Our main object is the class of admissible majorants for Kϴ, denoted by Adm ϴ and consisting of all functions ω defined on ℝ such that there exists an f ≠ 0, f ∈ Kϴ satisfying |f(x)| ≤ ω(x) almost everywhere on ℝ. Firstly, using some simple Hilbert transformtechniques, we obtain a general multiplier theorem applicable to any Kϴ generated by a meromorphic inner function. In contrast with [6], we consider the generating functions ϴ such that the unit vector ϴ(x) winds up fast as x grows from –∞ to ∞. In particular, we consider ϴ = B where B is a Blaschke product with “horizontal” zeros, i.e., almost uniformly distributed in a strip parallel to and separated from ℝ. It is shown, among other things, that for any such B, any even ω decreasing on (0,∞) with a finite logarithmic integral is in Adm B (unlike the “vertical” case treated in [6]), thus generalizing (with a new proof) a classical result related to Adm exp(iσz), σ > 0. Some oscillating ω's in Adm B are also described. Our theme is related to the Beurling-Malliavin multiplier theorem devoted to Adm exp(iσz), σ > 0, and to de Branges’ space ℋ(E).
Complex Uniform Convexity and Riesz Measures
Authors: Blower Gordon , Ransford Thomas 
Published: December 2010

AbstractThe norm on a Banach space gives rise to a subharmonic function on the complex plane for which the distributional Laplacian gives a Riesz measure. This measure is calculated explicitly here for LebesgueLpspaces and the von Neumann-Schatten trace ideals. Banach spaces that areq-uniformly PL-convex in the sense of Davis, Garling and Tomczak-Jaegermann are characterized in terms of the mass distribution of this measure. This gives a new proof that the trace idealscpare 2-uniformly PL-convex for 1 ≤p≤ 2.
Group Actions and Singular Martingales II, The Recognition Problem
Authors: Rosenblatt Joseph , Taylor Michael 
Published: December 2010

AbstractWe continue our investigation in [RST] of a martingale formed by picking a measurable set A in a compact group G, taking random rotates of A, and considering measures of the resulting intersections, suitably normalized. Here we concentrate on the inverse problem of recognizing A from a small amount of data from this martingale. This leads to problems in harmonic analysis on G, including an analysis of integrals of products of Gegenbauer polynomials.
Défaut de semi-stabilité des courbes elliptiques dans le cas non ramifié
Authors: Cali Elie 
Published: December 2010

AbstractLet be an algebraic closure of ℚ2 and K be an unramified finite extension of ℚ2 included in . Let E be an elliptic curve defined over K with additive reduction over K, and having an integral modular invariant. Let us denote by Knr the maximal unramified extension of K contained in . There exists a smallest finite extension L of Knr over which E has good reduction. We determine in this paper the degree of the extension L/Knr.
Bump Functions with Hölder Derivatives
Authors: Gaspari Thierry 
Published: December 2010

AbstractWe study the range of the gradients of aC1,α-smooth bump function defined on a Banach space. We find that this set must satisfy two geometrical conditions: It can not be too flat and it satisfies a strong compactness condition with respect to an appropriate distance. These notions are defined precisely below. With these results we illustrate the differences with the case ofC1-smooth bump functions. Finally, we give a sufficient condition on a subset ofX* so that it is the set of the gradients of aC1,1-smooth bump function. In particular, ifXis an infinite dimensional Banach space with aC1,1-smooth bump function, then any convex open bounded subset ofX* containing 0 is the set of the gradients of aC1,1-smooth bump function.
Fat Points in ℙ1× ℙ1and Their Hilbert Functions
Authors: Guardo Elena , Van Tuyl Adam 
Published: December 2010

AbstractWe study the Hilbert functions of fat points in ℙ1× ℙ1. IfZ⊆ ℙ1× ℙ1is an arbitrary fat point scheme, then it can be shown that for everyiandjthe values of the Hilbert functionHZ(l,j) andHZ(i,l) eventually become constant forl≫ 0. We show how to determine these eventual values by using only the multiplicities of the points, and the relative positions of the points in ℙ1× ℙ1. This enables us to compute all but a finite number values ofHZwithout using the coordinates of points. We also characterize the ACM fat point schemes using our description of the eventual behaviour. In fact, in the case thatZ⊆ ℙ1× ℙ1is ACM, then the entire Hilbert function and its minimal free resolution depend solely on knowing the eventual values of the Hilbert function.
Best Approximation in Riemannian Geodesic Submanifolds of Positive Definite Matrices
Authors: Lim Yongdo 
Published: December 2010

AbstractWe explicitly describe the best approximation in geodesic submanifolds of positive definite matrices obtained from involutive congruence transformations on the Cartan-Hadamard manifold Sym(n, ℝ)++ of positive definite matrices. An explicit calculation for the minimal distance function from the geodesic submanifold Sym(p, ℝ)++ × Sym(q, ℝ)++ block diagonally embedded in Sym(n, ℝ)++ is given in terms of metric and spectral geometric means, Cayley transform, and Schur complements of positive definite matrices when p ≤ 2 or q ≤ 2.
Semi-Classical Behavior of the Scattering Amplitude for Trapping Perturbations at Fixed Energy
Authors: Michel Laurent 
Published: December 2010

AbstractWe study the semi-classical behavior ash→ 0 of the scattering amplitudef(θ, ω, λ,h) associated to a Schrödinger operatorwith short-range trapping perturbations. First we realize a spatial localization in the general case and we deduce a bound of the scattering amplitude on the real line. Under an additional assumption on the resonances, we show that if we modify the potentialV(x) in a domain lying behind the barrier ﹛x:V(x) > λ﹜, the scattering amplitudef(θ, ω, λ,h) changes by a term of order(h∞). Under an escape assumption on the classical trajectories incoming with fixed direction ω, we obtain an asymptotic development off(θ, ω, λ,h) similar to the one established in the non-trapping case.
Kirillov Theory for a Class of Discrete Nilpotent Groups
Authors: Tandra Haryono , Moran William 
Published: December 2010

AbstractThis paper is concerned with the Kirillov map for a class of torsion-free nilpotent groups G. G is assumed to be discrete, countable and π-radicable, with π containing the primes less than or equal to the nilpotence class of G. In addition, it is assumed that all of the characters of G have idempotent absolute value. Such groups are shown to be plentiful.
On Log ℚ-Homology Planes and Weighted Projective Planes
Authors: Daigle Daniel , Russell Peter 
Published: December 2010

AbstractWe classify normal affine surfaces with trivial Makar-Limanov invariant and finite Picard group of the smooth locus, realizing them as open subsets of weighted projective planes. We also show that such a surface admits, up to conjugacy, one or two Ga-actions.
Jordan Structures of Totally Nonnegative Matrices
Authors: Fallat Shaun M. , Gekhtman Michael I. 
Published: December 2010

AbstractAn n × n matrix is said to be totally nonnegative if every minor of A is nonnegative. In this paper we completely characterize all possible Jordan canonical forms of irreducible totally nonnegative matrices. Our approach ismostly combinatorial and is based on the study of weighted planar diagrams associated with totally nonnegativematrices