*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 Z_{p}-index
homomorphism for Z_{p}-spaces,
pp. 305-314.

ABSTRACT.
Let Z_{p} be the cyclic group of order p and let (X,T) be a Z_{p}-space,
that is, a topological space X equipped with a free action of Z_{p},
generated by a periodic homeomorphism T of X with period p. In this paper we
construct a Z_{p}-index graded homomorphism associated with (X,T),
defined on the equivariant homology Z_{p}-modules of (X,T) and with
values in Z_{p}. Using this Z_{p}-index homomorphism we prove
that, if (X,T) and (Y,S) are Z_{p}-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 S_{0}, 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

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).

L^{p}-estimates for a
class of elliptic operators with unbounded coefficients in **R**^{N},
pp. 605-620.

ABSTRACT.
We consider second-order elliptic partial differential operators defined in
**R**^{N}, 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 L^{p} 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.