David Brink, Department of Mathematics, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark; email: brink@math.ku.dk

Abstract/Résumé:

It is investigated when a cyclic \(p\)-class field of an imaginary quadratic number field can be embedded in an infinite pro-cyclic \(p\)-extension.

On donne des conditions pour qu’un \(p\)-corps de classes cyclique d’un corps de nombres quadratique imaginaire soit plongeable dans une \(p\)-extension pro-cyclique infinie.

Keywords:

AMS Subject Classification: Galois theory 11R32

PDF(click to download): On $mathbb{Z}_{p}$-embeddability of cyclic ${p}$-class fields

Thomas R. Hagedorn, Department of Mathematics and Statistics, The College of New Jersey, P.O. Box 7718, Ewing, NJ 08628-0718 USA; email: hagedorn@tcnj.edu

Abstract/Résumé:

Let \(S = \{a_i\}_{i=0}^\infty\) be a real linear recurrence of degree \(n\) with companion polynomial \(f_S(x)\). Let \(N_S\) be the zero-multiplicity for \(S\). Assume that the roots of \(f_S(x)\) are simple, real, and nondegenerate. When \(n=3\), Smiley and Picon showed \(N_S\leq 3\). When \(n=4\), we establish the sharp bound \(N_S\leq 5\). In general \(n\), we prove \(N_S \leq 2n-3\).

Soit \(S = \{a_i\}_{i=0}^{\infty}\) une suite définie par une relation de récurence linéaire réels de degré \(n\) avec polynôme charactéristique \(f_S (x)\). Désignons par \(N_S\) le zéro-multiplicité de \(S\). Supposons que les racines de \(f_S(x)\) soient simples, réelles, et non-dégénérées. Dans le cas \(n=3\), Smiley et Picon ont obtenu le resultat \(N_S \leq 3\). Dans le cas \(n=4\), nous démontrons la borne optimale \(N_S \leq 5\). Enfin nous démontrons que, étant donné un entier \(n\) quelconque, \(N_S \leq 2n-3\).

Keywords:

AMS Subject Classification: Recurrences 11B37

PDF(click to download): Zeros of a real linear recurrence of degree $ngeq 4$

Lawrence G. Brown, Department of Mathematics, Purdue University, West Lafayette, IN 47907–2067 USA; email: lgb@math.purdue.edu

Abstract/Résumé:

We show that if \(A\) is a \(C^*\)-algebra of real rank zero and stable rank one, then the Riesz interpolation property holds in the ordered group \(K_0(A) \oplus K_1(A)\).

Nous montrons que si \(A\) est une \(C^*\)-algèbre de rang réel zéro et de rang stable égal à un, donc la propriété d’interpolation de Riesz est valable dans le groupe ordonné \(K_0(A) \oplus K_1(A)\).

Keywords:

AMS Subject Classification: Classifications of $C^*$-algebras; factors 46L35

PDF(click to download): The Riesz interpolation property for $K_0(A) oplus K_1(A)$

Andrew J. Dean, Department of Mathematical Sciences, Lakehead University, 955 Oliver Road, Thunder Bay, Ontario, P7B 5E1; email: andrew.dean@lakeheadu.ca

Abstract/Résumé:

It is shown that two \(C^*\)-dynamical systems of the form \((K\otimes A, \mathbb{R}, \mathrm{Ad} U\otimes id)\), where \(U\) is a unitary representation of \(\mathbb{R}\) that decomposes as a finite direct sum of non-trivial irreducible representations whose multiplicities have greatest common denominator 1, and \(A\) is a simple, unital \(C^*\)-algebra with real rank zero and cancellation, are equivariantly isomorphic if, and only if, the two representations are unitarily equivalent. As a corollary, a classification result for certain inductive limit type actions of \(\mathbb{R}\) on stable UHF algebras is given.

Il est montré que deux systèmes \(C^*\)-dynamiques de la forme \((K\otimes A, \mathbb{R}, \mathrm{Ad} U\otimes id)\) où \(U\) est une representation unitaire de \(\mathbb{R}\), qui décompose comme une somme directe et finie des representations non-triviales et irréductibles dont les multiplicités ont 1 comme le dénominateur commun et le plus grand, et \(A\) est un \(C^*\)-algèbre simple, avec l’unité et avec rang réel zéro et annullation, sont isomorphe équivariantement si et seulement si les deux representations sont équivalentes unitairement. Comme un corollaire, un résultat classification pour quelques actions du type de la limite inductive de \(\mathbb{R}\) sur les algèbres d’UHF stables est aussi donné.

Keywords: C∗-dynamical system, classification

AMS Subject Classification: Derivations; dissipations and positive semigroups in $C^*$-algebras 46L57

PDF(click to download): A classification theorem for certain actions of $mathbb{R}$ on $C^*$-algebras

R.A. Mollin, Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, Canada, T2N 1N4; email: ramollin@math.ucalgary.ca

Abstract/Résumé:

Central norms are given definition according to the infrastructure of the underlying order under discussion, which we define in the introductory section below. We relate these central norms in the simple continued fraction expansion of \(\sqrt{D}\) to solutions of the Eisenstein equation \(x^2-Dy^2 = -4\), with \(\gcd(x,y) = 1\). This provides a criterion for central norms to be \(4\) in the presence of certain congruence conditions on the fundamental unit of the underlying real quadratic order \(\mathbb{Z}[\sqrt{D}]\).

Keywords: Eisenstein equations, central norms, continued fractions

AMS Subject Classification: Quadratic and bilinear equations 11D09

PDF(click to download): Eisenstein Equations and Central Norms

O.I. Bogoyavlenskij, Department of Mathematics and Statistics, Queen’s University, Kingston, Ontario K7L 3N6; email: bogoyavl@mast.queensu.ca

Abstract/Résumé:

For any dynamical system, a hidden structure of its Lie algebra of symmetries is disclosed. The structure is based on a new infinite series of the canonically defined Lie subalgebras and on their commutator relations.

Pour n’importe quel système dynamique, une structure cachée de son algèbre de Lie de symétries est révélée. Cette structure découle d’une nouvelle série de sous-algèbres de Lie canoniquement définies et de leurs relations de commutateurs.

Keywords:

AMS Subject Classification: Completely integrable systems; topological structure of phase space; integration methods 37J35

PDF(click to download): Hidden structure of the Lie algebra of symmetries

Faruk F. Abi-Khuzam, Department of Mathematics, American University of Beirut, P.O. Box 11-0236, Riad El Solh, Beirut 1107 2020, Lebanon; email: farukakh@aub.edu.lb

May F. Hamdan, Division of Computer Science and Mathematics, Lebanese American University, P.O. Box 135053 F 64, Beirut, Lebanon; email: mhamdan@lau.edu.lb

Abstract/Résumé:

For an entire function \(f\) with non-negative Maclaurin coefficients, a region is obtained which is defined in terms of Hayman’s function \(b(r) = r (rf^{\prime} (r)/f(r))^{\prime}\), and which is free of all zeros of \(f\) and those of all its sections. The new region defined improves on previous results. In particular, it is shown that when \(\underset{n\rightarrow \infty}{\limsup}\, b(r) = A^2/4\), \(A>0\), then the zeros \(r_n \exp (i\theta_n)\) of \(f\) satisfy the inequality, \(\underset{n\rightarrow \infty}{\liminf}\, |\theta_n| \geq 4\sin^{-1} (1/A\sqrt{2})\), which is very close to being optimal.

Etant donnée une function entière \(f\) avec des coéfficients positifs, on trouve une région définie en termes de la fonction \(b(r) = r (rf^{\prime}(r)/f(r))^{\prime}\) de Hayman, dépourvue des zéros de \(f\) et de ceux de toutes ses sections. Particulièrement, on démontre qu’au cas où \(\underset{n\rightarrow \infty}{\limsup}\, b(r) = A^2/4\), \(A>0\), les zéros \(r_n \exp (i\theta_n)\) de \(f\) satisfont l’inégalité \(\underset{n\rightarrow\infty}{\liminf} \, |\theta_n| \geq 4\sin^{-1} (1/A\sqrt{2})\), qui est presque optimale.

Keywords:

AMS Subject Classification: Zeros of polynomials; rational functions; and other analytic functions (e.g. zeros of functions with bounded Dirichlet integral) 30C15

PDF(click to download): Radial Distribution of Zeros of Entire Functions and Sections of their Power Series

Kalifa Bodian, Labo LANI, UFR SAT, Universite Gaston Berger, BP 234, St. Louis, Senegal; email: bodiank1@yahoo.fr

Abdoulaye Sene, Departement de Faculte des sciences, Universite Cheikh Anta Diop, Dakar, Senegal; email: abdousen@ucad.sn

Mary Teuw Niane, Labo LANI, UFR SAT, Universite Gaston Berger, BP 234, St. Louis, Senegal; email: niane@ugb.sn

Abstract/Résumé:

We define norm estimates for the trace of solution of the wave equation with initial conditions in irregular Sobolev spaces of fractional order. Then exact controllability results are deduced.

On établit des estimations de normes pour la trace de la solution de l’équation des ondes avec des données initiales dans des espaces de Sobolev non réguliers et à puissances fractionnaires. On déduit les résultats de contrôlabilité exacte correspondants.

Keywords:

AMS Subject Classification: Quadratic programming 90C20

PDF(click to download): Exact controllability of the wave equation in fractional order spaces

Giovanni Coppola / Saverio Salerno

Abstract/Résumé:

No abstract available but the full text pdf may be downloaded at the title link below.

Keywords:

AMS Subject Classification: Distribution of integers with specified multiplicative constraints, Asymptotic results on arithmetic functions 11N25, 11N37

PDF(click to download): On the symmetry of arithmetical functions in almost all short intervals

Pierre-Antoine Desrousseaux

Abstract/Résumé:

No abstract available but the full text pdf may be downloaded at the title link below.

Keywords:

AMS Subject Classification: Abelian varieties of dimension $\gtr 1$, Complex multiplication and moduli of abelian varieties, Modular and Shimura varieties, Jacobians; Prym varieties, Isogeny, Complex multiplication, Appell; Horn and Lauricella functions, Integral representations of solutions of PDE 11G10, 11G15, 14G35, 14H40, 14K02, 14K22, 33C65, 35C15

PDF(click to download): Fonctions hypergéométriques de Lauricella, périodes de variétés abéliennes et transcendance

Vladimir Vinogradov

Abstract/Résumé:

No abstract available but the full text pdf may be downloaded at the title link below.

Keywords:

AMS Subject Classification: Large deviations, Functional limit theorems; invariance principles, Jump processes, None of the above; but in this section 60F10, 60F17, 60J75, 60K99

PDF(click to download): On a model for stock price movements and the power-variance family

Feng-Zhen Zhao / Tianming Wang

Abstract/Résumé:

No abstract available but the full text pdf may be downloaded at the title link below.

Keywords: Bernoulli polynomials, Euler polynomial, Nôrlund Bernoulli polynomials, Nôrlund Euler polynomial

AMS Subject Classification: Recurrences, Fibonacci and Lucas numbers and polynomials and generalizations, Bernoulli and Euler numbers and polynomials 11B37, 11B39, 11B68

PDF(click to download): Values of Nörlund Euler Polynomials and Nörlund Bernoulli Polynomials

E. Neher

Abstract/Résumé:

No abstract available but the full text pdf may be downloaded at the title link below.

Keywords:

AMS Subject Classification: Infinite-dimensional Lie (super)algebras 17B65

PDF(click to download): Extended affine Lie algebras

E. Neher

Abstract/Résumé:

No abstract available but the full text pdf may be downloaded at the title link below.

Keywords:

AMS Subject Classification: Infinite-dimensional Lie (super)algebras 17B65

PDF(click to download): Lie Tori

W. Herfort / P.A. Zalesskii

Abstract/Résumé:

No abstract available but the full text pdf may be downloaded at the title link below.

Keywords:

AMS Subject Classification: Limits; profinite groups 20E18

PDF(click to download): Virtually Free Pro-p Groups

J.-J. Lee

Abstract/Résumé:

No abstract available but the full text pdf may be downloaded at the title link below.

Keywords:

AMS Subject Classification: Asymptotic results on arithmetic functions, Elliptic curves 11N37, 14H52

PDF(click to download): A remark on the ranks of twists of elliptic curves

P.C. Gibdon / M.P. Lamoureux

Abstract/Résumé:

No abstract available but the full text pdf may be downloaded at the title link below.

Keywords:

AMS Subject Classification: Lattices and convex bodies in $2$ dimensions 52C05

PDF(click to download): Maximally symmetric, minimally redundant partitions of unity in the plane

E. Ballico

Abstract/Résumé:

No abstract available but the full text pdf may be downloaded at the title link below.

Keywords: Banach analytic set, Lipschitz map, holomorphic vector bundle

AMS Subject Classification: Banach analytic spaces, Holomorphic bundles and generalizations 32K05, 32L05

PDF(click to download): On the infinite-dimensional holomorphic structure on topological bundles

S. Walters

Abstract/Résumé:

No abstract available but the full text pdf may be downloaded at the title link below.

Keywords: C*-algebra, Fourier transform, automorphisms, integral transforms, rotation algebras

AMS Subject Classification: General transforms, Special transforms (Legendre; Hilbert; etc.), Automorphisms, K-theory and operator algebras -including cyclic theory 44A05, 44A15, 46L40, 46L80

PDF(click to download): Periodic Integral Transforms and C*-Algebras

R.A. Mollin

Abstract/Résumé:

No abstract available but the full text pdf may be downloaded at the title link below.

Keywords: infrastructure of real quadratic fields, quadratic Diophantine equations, simple continued fractions

AMS Subject Classification: Continued fractions, Quadratic and bilinear equations, Quadratic extensions 11A55, 11D09, 11R11

PDF(click to download): When the Central Norm Equals 2 in the Simple Continued Fraction Expansion of a Quadratic Surd