Electronic Edition Vol. 31, No. 2, 2005

Editors: H. Amann (Zürich), G. Auchmuty (Houston), D. Bao (Houston), H. Brezis (Paris), J. Damon (Chapel Hill), K. Davidson (Waterloo), C. Hagopian (Sacramento), R. M. Hardt (Rice), J. Hausen (Houston), J. A. Johnson (Houston), J. Nagata (Osaka), V. I. Paulsen (Houston), G. Pisier (College Station and Paris), S. W. Semmes (Rice)
Managing Editor: K. Kaiser (Houston)

Houston Journal of Mathematics


Pedro L. Q. Pergher, Universidade Federal de São Carlos, Departamento de Matemática, São Carlos, SP, Brazil (pergher@dm.ufscar.br).
A Zp-index homomorphism for Zp-spaces, pp. 305-314.
ABSTRACT. Let Zp be the cyclic group of order p and let (X,T) be a Zp-space, that is, a topological space X equipped with a free action of Zp, generated by a periodic homeomorphism T of X with period p. In this paper we construct a Zp-index graded homomorphism associated with (X,T), defined on the equivariant homology Zp-modules of (X,T) and with values in Zp. Using this Zp-index homomorphism we prove that, if (X,T) and (Y,S) are Zp-spaces and p=2q with q odd, then, under certain homological conditions on X and Y, there is no equivariant map from (X,T) into (Y,S). This result includes the particular situation in which the target spaces (Y,S) are spheres of odd dimension, equipped with the standard free periodic homeomorphism of period p. This is a special case of a previous result of T. Kobayashi, which handled this case with no restriction on p.

Bucataru, Ioan,"Al.I.Cuza" University, Faculty of Mathematics, 6600 Iasi, Romania (bucataru@uaic.ro).
Linear connections for systems of higher order differential equations, pp. 315-332.
ABSTRACT. For a system of (k+1) order differential equations (or a semispray of order k on the tangent bundle of order k) we determine a nonlinear connection induced by it. This nonlinear connection induces a linear connection D on the total space of the tangent bundle of order k, that is called the Berwald connection. Using the Cartan's structure equations of the Berwald connection, we determine the conditions by which a system of (k+1) order differential equations is linearizable with respect to the accelerations of order k. This is a generalization for the k=1 case presented in the first part of the paper.

Citti, Giovanna, Universita' di Bologna, Italia (citti@dm.unibo.it), and Manfredini, Maria, Universita' di Bologna, Italia, (manfredi@dm.unibo.it).
Blow-up in non homogeneous Lie groups and rectifiability, pp. 333-353.
ABSTRACT. In this paper we extend the De Giorgi notion of rectifiability of surfaces in non homogeneous Lie groups. This notion and the principal properties of Cacciopoli sets had already been proved in homogeneous Lie group, using a blow-up method, with respect to the natural dilations. In non homogeneous Lie groups no dilations are defined, so that we need to apply a freezing method, locally approximating the non homogeneous structure, with an homogeneous one.

Ko, Seokku, Konkuk University, Choongjusi Choongbuk, Korea 380-701 (seokko@kku.ac.kr).
Embedding Compact Riemann Surfaces in 4-dimensional Riemannian Manifolds, pp. 355-366.
ABSTRACT. Any compact Riemann surface has a conformal model in any orientable Riemannian manifold of dimension 4. Precisely, we prove that, given any compact Riemann surface S0, there is a conformally equivalent model in a prespecified orientable 4-dimensional Riemannian manifold. A model can be constructed by deforming a given topologically equivalent complete Riemann surface S in the normal direction NS of S. This result along with previous Ko Embedding theorem(see "Embedding compact Riemann surfaces in Riemannian Manifolds", Houston Journal of Mathematics, Vol. 27. no. 3, 2001) now shows that a compact Riemann surface admits conformal models in any Riemannian manifold of dimension greater than or equal to 3.

Mihailescu, Eugen, Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, Ro 70700, Bucharest, Romania (Eugen.Mihailescu@imar.ro) and Urbanski, Mariusz, Department of Mathematics, University of North Texas, P.O. Box 311430, Denton, TX 76203-1430, USA (urbanski@unt.edu).
Estimates for the stable dimension for holomorphic maps, pp. 367-389.
ABSTRACT. We study the Hausdorff dimension of the intersection between stable manifolds and basic sets for an Axiom A holomorphic endomorphism on the complex projective space of dimension 2. We improve an upper estimate given in a previous paper by Mihailescu, by taking into consideration the number of preimages, and thus proving for non-invertible maps results parallel to those of Verjovsky and Wu from the case of Henon diffeomorphisms. Also, a lower estimate for the above stable dimension is given by using a concept of preimage entropy modeled after Bowen. If the map is not a homeomorphism, then the preimage entropy may not coincide with the usual forward entropy. We also construct examples of holomorphic Axiom A maps which are injective on their respective basic sets and such that their stable dimension is strictly positive. We study in the end the stable dimension for a class of special quadratic endomorphisms.

Chuan Liu, Department of Mathematics, Ohio University Zanesville Campus, Zanesville, OH 43701 (LIUC1@OHIO.EDU) and Lewis D. Ludwig, Department of Mathematics and Computer Science, Denison University, Granville, OH 43023 (LUDWIGL@DENISON.EDU).
κ-Fréchect Urysohn Spaces, pp. 75-391-401.
ABSTRACT. In 1999, Arhangel'skii defined the following property: A Hausdorff topological space X is called κ-Fréchect Urysohn if for every open subset A of X and every x in the closure of A there exists a sequence of points of A converging to x. We discuss the properties of κ-Fréchect Urysohn spaces, the conditions under which a κ-Fréchect Urysohn space is Fréchect Urysohn, and the behavior of κ-Fréchect Urysohn spaces under products. Two questions are posed.

Pellicer-Covarrubias, Patricia, Departamento de Matemáticas, Facultad de Ciencias, Circuito Exterior s/n, Ciudad Universitaria, Coyocán 04510, México, D.F. (paty@ciencias.unam.mx).
The Hyperspaces C(p,X) for Atriodic Continua , pp 403-426.
ABSTRACT. Let C(X) denote the hyperspace of subcontinua of a continuum X. For an element A of C(X), define the hyperspace C(A,X) as the set of elements of C(X) which contain A. We prove that nondegenerate Whitney levels of C(p,X) are arcs when X is an atriodic continuum. The main result is a characterization of the hyperspaces C(p,X) for atriodic continua. Moreover, as a consequence of the characterization, we obtain that a continuum X is atriodic if and only if C(A,X) is planar for every element A of C(X).

Ofelia T. Alas,Instituto de Matematica e Estatistica, Universidade de Sao Paulo, Caixa Postal 66281, 05311-970 Sao Paulo, Brasil (alas@ime.usp.br) and Richard G. Wilson, Departamento de Matematicas, Universidad Autonoma Metropolitana, Unidad Iztapalapa, Avenida San Rafael Atlixco, #186, Apartado Postal 55-532, 09340, Mexico, D.F., Mexico (rgw@xanum.uam.mx).
Weaker connected Hausdorff topologies on spaces with a σ-locally finite base, pp. 427-439.
ABSTRACT. We show that if (X,t) is a disconnected Hausdorff space with a sigma locally finite base, then there is a weaker connected Hausdorff topology on X if and only if X is not H-closed.

Charatonik, Janusz J., Instituto de Matematicas, UNAM, Circuito Exterior, Ciudad Universitaria, 04510 Mexico, D. F., Mexico, (jjc@matem.unam.mx) and Prajs, Janusz R., Department of Mathematics and Statistics, California State University Sacramento, Sacramento, 6000 J Street, CA 95819-6051 U. S. A. (prajs@csus.edu)
Generalized epsilon-push property for certain atriodic continua, pp. 441-462.
ABSTRACT. We show that an absolute retract for hereditarily unicoherent continua that contains no simple triod must be an arc-like continuum. More general results are proved for a class of continua having only arcs as their proper subcontinua.

Sergey A. Antonyan, Departamento de Matematicas, Facultad de Ciencias, Universidad Nacional Autonoma de Mexico, Mexico D.F. 04510, Mexico (antonyan@servidor.unam.mx)
A characterization of equivariant absolute extensors and the equivariant Dugundji theorem, pp. 451-462.
ABSTRACT. Let G be a compact Lie group. We prove that a metrizable G-space X is a G-ANE (resp., a G-AE) iff X is an ANE (resp., an AE) and, for any subgroup H of G which is the intersection of finitely many stabilizers in X, the H-fixed point set X[H] is a strong neighborhood H-deformation retract (resp., a strong H-deformation retract) of X. If a G-space X has no G-fixed point, then X is a G-ANE provided that X is an H-ANE for any subgroup H of G that occurs as a stabilizer in X. As an application, we give a new proof of the equivariant Dugundji extension theorem in the metrizable case.

Justin R. Peters, Department of Mathematics, Iowa State University, 400 Carver Hall, Ames, IA 50011, USA (peters@iastate.edu), and Ryan J. Zerr, Mathematics Department, University of North Dakota, PO Box 8376, Grand Forks, ND 58202, USA (ryan.zerr@und.nodak.edu).
Partial Dynamical Systems and AF C*-algebras, pp. 463-494.
ABSTRACT. We obtain a characterization in terms of dynamical systems of those r-discrete groupoids for which the groupoid C*-algebra is approximately finite-dimensional (AF). These ideas are then used to compute the K-theory for AF algebras by utilizing the actions of these partial homeomorphisms, and these K-theoretic calculations are applied to some specific examples of AF algebras. Finally, we show that, for a certain class of dimension groups, a groupoid can be obtained directly from the dimension group's structure whose associated C*-algebra has its dimension group isomorphic to the original dimension group.

Donsig, Allan P.,University of Nebraska-Lincoln, Lincoln, NE, 68508-0323 (adonsig@math.unl.edu) and Hopenwasser, Alan, University of Alabama, Tuscaloosa, AL, 35487 (ahopenwa@bama.ua.edu).
Analytic Partial Crossed Products, pp. 495-527.
ABSTRACT. Partial actions of discrete abelian groups can be used to construct both groupoid C*-algebras and partial crossed product algebras. In each case there is a natural notion of an analytic subalgebra. We show that for countable subgroups of the real numbers and free partial actions, these constructions yield the same C*-algebras and the same analytic subalgebras. We also show that under suitable hypotheses an analytic partial crossed product preserves all the information in the dynamical system in the sense that two analytic partial crossed products are isomorphic as Banach algebras if, and only if, the partial actions are conjugate.

Ronald G. Douglas, Department of Mathematics, Texas A&M University, College Station, Texas 77843-3368} (rdouglas@math.tamu.edu).
Ideals in Toeplitz Algebras, pp. 529-539.
ABSTRACT. We determine the ideal structure of the Toeplitz C*-algebra on the bidisk.

Bennett, G., Indiana University, Bloomington, Indiana 47405, U.S.A., (bennettg@indiana.edu), and K.-G. Grosse-Erdmann, Fernuniversitaet Hagen, D-58084 Hagen, Germany.
On Series of Positive Terms, pp.541-586.
ABSTRACT. Three new techniques are developed for handling series of positive terms.

I.R. Nezhmetdinov, 15 Wyandotte St., Bethlehem, PA 18015, USA (inezh@member.ams.org) and S. Ponnusamy, Department of Mathematics, Indian Institute of Technology, IIT-Madras, Chennai 600 036, India (samy@iitm.ac.in).
New coefficient conditions for the starlikeness of analytic functions and their applications, pp. 587-604.
ABSTRACT. We obtain some tests for the starlikeness of analytic functions in terms of their Taylor coefficients. This leads to an improvement of several relevant results about hypergeometric functions. The approach is extended for other well-known subclasses of univalent functions.

Giorgio Metafune, Diego Pallara, Dipartimento di Matematica ``E. De Giorgi'', Universita' di Lecce (Italy) (giorgio.metafune@unile.it) (diego.pallara@unile.it) and Vincenzo Vespri, Dipartimento di Matematica "Ulisse Dini'', Universita' di Firenze (Italy) (vespri@math.unifi.it).
Lp-estimates for a class of elliptic operators with unbounded coefficients in RN, pp. 605-620.
ABSTRACT. We consider second-order elliptic partial differential operators defined in RN, with the coefficients of the second-order terms bounded and continuously differentiable, with bounded derivatives, and globally Lipschitz continuous but possibly unbounded coefficients of the first-order terms. We prove a-priori estimates in Lp spaces, and deduce a characterisation of the domain under which these opersators are generators of strongly continuous semigroups.

Massimo Grossi, Dipartimento di Matematica P.le A.Moro 2, 00185 , Roma , Italy (grossi@mat.uniroma1.it) and Angela Pistoia, Dipartimento Me. Mo. Mat. Via Scarpa 16, 00161, Roma, Italy (pistoia@dmmm.uniroma1.it).
Locating the Peak of Ground States of Nonlinear Schrödinger Equations, pp. 621-635..
ABSTRACT. In this paper we study standing wave solutions arising from the nonlinear Schrodinger equation It is known that the peak of the ground state approaches an absolute minimum point of the potential V. Here we prove that if the absolute minimum value of V is achieved at more than one point, then the ground state concentrates where the potential V is flatter.