*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), B. H. Neumann (Canberra), V. I. Paulsen (Houston),
G. Pisier (College Station and Paris), S. W. Semmes (Rice)
*Managing Editor*: K. Kaiser (Houston)

Houston Journal of Mathematics

*Contents*

**James A. Schafer, ** Department of Mathematics, University of Maryland,
College Park, Maryland 20742( jas@math.umd.edu).

Acyclic covers with finite
fundamental group, pp. 1-11.

ABSTRACT.
Abstract: J.H.C. Whitehead's Asphericity Problem states that every subcomplex of
a 2-dimensional aspherical complex is aspherical. Adams showed that any
connected subcomplex of an aspherical complex must possess an acyclic regular
covering which is obviously non-aspherical if the subcomplex is. In this paper
it is shown that the existence of an acyclic cover with non-trivial finite
fundamental group is equivalent to the purely algebraic problem of constructing
an efficient presentation of some product group Q x P, where P is a non-trivial
finite, perfect group and Q is of type FL and of cohomological dimension two.

**Chatham, R. Douglas, **Department of Mathematical Sciences, Morehead State
University, Morehead KY 40351
(d.chatham@moreheadstate.edu)
and **Dobbs, David E., **University of Tennessee, Knoxville, TN 37996
(dobbs@math.utk.edu).

On Pseudo-Valuation Domains
Whose Overrings are Going-Down Domains, pp. 13-19.

ABSTRACT.
It is proved that if R and T are distinct going-down domains with R contained in
T such that Spec(R) = Spec(T) as sets (for instance, a proper field extension)
and M denotes the common maximal ideal of R and T, then each ring between R and
T is a going-down domain if and only if the transcendence degree of T/M over R/M
is at most 1. As a consequence, transcendence degree is used to characterize the
pseudo-valuation domains all of whose overrings are going-down domains.

**Sadettin Erdem, ** Middle East Technical University, Department of
Mathematics, 06531 Ankara, Turkey (serdem@metu.edu.tr).

On Almost (Para)contact
(Hyperbolic) Metric Manifolds And Harmonicity of (φ,φ')-Holomorphic Maps Between
Them., pp. 21-45.

ABSTRACT.
A Theorem is given stating about the harmonicity of 'holomorphic' maps between
manifolds of even and odd dimensions (namely almost indefinite (para)-Hermitian
and almost (para)- contact (hyperbolic) metric manifolds) in the most general
form which gives new results and also covers almost all the known ones. On the
way, some new classes of almost (para)contact (hyperbolic) metric manifolds are
introduced and some examples of these kinds are provided.

**Young Jin Suh ,** **Young Suk Choi, ** and **Hae Young Yang, **
Department of Mathematics, Kyungpook National University, Taegu, 702-701, Korea
(yjsuh@bh.knu.ac.kr).

On space-like hypersurfaces with
constant mean curvature in a Lorentz manifold, pp. 47-70.

ABSTRACT.
The purpose of this paper is to give two theorems of Lorentz-type for complete
space-like hypersurfaces with constant mean curvature as an extension of
theorems of Akutagawa, Cheng and Nakagawa , and Nishikawa.

**Chang, Jeongwook,** Seoul National University, Seoul, Korea 151-742
(jwchang@math.snu.ac.kr), and
**Yun, Gabjin,** Myong Ji University, Yongin, Kyunggi, Korea 449-728
(gabjin@wh.myongji.ac.kr).

Spectral Geometry of Harmonic Maps
into Warped Product Manifolds with a Circle, pp. 71-87.

ABSTRACT.
Let (M^{n}, g) be a closed Riemannian manifold and N = S^{1} × _{
f} S_{c}^{m-1} be a warped product space with
the warped product metric h = dt^{2} + f^{2}(t) ds^{2}.
Let φ, ψ : M --> N be two base projectively harmonic maps. We prove
that if the Jacobi operators J_{φ} and J_{ψ} of φ and ψ are
isospectral, then the energy of φ and ψ are equal up to constant. Besides we
show some properties of harmonic maps and its relation with the spectral
geometry of warped product Riemannian manifolds with a circle.

**Janusz J. Charatonik**, Instituto de Matematicas, UNAM, Circuito Exterior,
Ciudad Universitaria, 04510 Mexico, D.F., Mexico (jjc@matem.unam.mx),
** Wlodzimierz J. Charatonik**, Department of Mathematics and Statistics,
University of Missouri-Rolla, Rolla, MO 65409, (wjcharat@umr.edu) and **Janusz
R. Prajs**, Department of Mathematics, Idaho State University, Pocatello, ID
83209, (prajs@math.isu.edu)

Gate continua, absolute terminal continua and absolute retracts, pp.
89-117.

ABSTRACT.
The following classes ** K ** of continua are studied in the paper:
(hereditarily decomposable) arc-like, hereditarily irreducible, atriodic, and
containing no

**Chatyrko, Vitalij A., ** University of Linkoping, S-581 83 Linkoping,
Sweden (vitja@mai.liu.se) and **Pasynkov Boris A.,** Moscow State University,
119899, Moscow, Russia (pasynkov@mech.math.msu.su).

On sum and product theorems
for dimension Dind. , pp. 119-131.

ABSTRACT.
For dimension Dind introduced by A. Arhangel'skij (cf. [V.Egorov and
Ju.Pristavkin, On a definition of dimension, Soviet Math. Dokl. 9 (1968),
188-191.]) we prove that Dind is finite iff the large inductive dimension Ind is
finite. We establish also various sum theorems for Dind which lead to
essentially better estimation formulas for Dind of topological products than the
known ones for Ind from [B.A. Pasynkov, On the finite-dimensionality of
topological products, Topol. Appl. 82 (1998), 377-386.]

**Toru Ikeda, **Kochi Medical School, Kohasu, Oko-cho, Nankoku-shi, Kochi
783-8505 JAPAN (ikedator@med.kochi-ms.ac.jp).

PL Finite Group Actions on
3-Manifolds Which Are Conjugate by Homeomorphism , pp. 133--142.

ABSTRACT.
Topological and PL (piecewise linear) equivalences of PL finite group actions on
manifolds are defined by conjugate by topological and PL homeomorphisms
respectively. It has been studied much about PL finite group actions on
3-manifolds up to topological equivalence. The aim of this article is to study
them in terms of PL equivalence. The solution of the Hauptvermutung for
3-manifolds is not enough to fill up the gap. We first study the Hauptvermutung
for polyhedral 3-orbifolds, and thereafter we prove topological equivalence
implies PL equivalence.

**A. B. Raha, ** Stat--Math Division, Indian Statistical Institute, 203, B.
T. Road, Calcutta 700 035, India (abraha@isical.ac.in).

An innocuous problem of continuity : A set-theoretic dilemma , pp. 139-142.

ABSTRACT.
An innocuous problem of continuity has been shown to be undecidable under the
usual axioms of set theory and topology.

**Garcia-Falset, J. , ** Departament d'Anàlisi Matemàtica, Universitat de
València, Dr. Moliner 50, 46100 Burjassot, València, Spain (garciaf@uv.es).

Fixed points for mappings with the range type condition, pp. 143-158.

ABSTRACT.
In this paper , we prove several fixed point results for general nonlinear
mappings satisfying a "range type" condition. Among others things we give a
fixed point theorem for pseudo-contractive mappings and we show that for any
equivalent renorming of l_{2}, some well known fixed point free
continuous mappings are not pseudo-contractive.

**D. A. Robbins, **Department of Mathematics, Trinity College, Hartford,
CT 06106 (david.robbins@trincoll.edu).

Modules over commutative
C*-algebras and the BSE condition., pp. 159-168.

ABSTRACT.
In a series of papers, S.-E. Takahasi and collaborators have defined and studied
the notion of a BSE Banach module* X* over a commutative Banach algebra *
A* with bounded approximate identity. The author has used Banach bundles to
further investigate the BSE condition. The present note uses Banach bundles to
add to the catalog of modules which satisfy the BSE condition. Specifically, we
show that if *A*is a commutative C*-algebra, then each Banach module *X *
over * A* is BSE.

**D. Cruz-Uribe, SFO,
** Dept. of Mathematics, Trinity College, Hartford, CT 06106-3100, USA,
(david.cruzuribe@mail.trincoll.edu) and **A. Fiorenza, ** Dipartimento di
Costruzioni e Metodi Matematici in Architettura, Universita di Napoli Via
Monteoliveto, 3 I-80134 Napoli, Italy (fiorenza@cds.unina.it).

The **A**_{∞ }property for Young functions and weighted norm
inequalities, pp. 169-182.

ABSTRACT.
Using Orlicz space norms we define a set function property analogous to the **
A**_{∞} condition for weights, and we characterize the Young functions
which produce set functions with this property.

**Guoxing Ji , ** Department of Mathematics, Shaanxi Normal University,
Xian 710062, Shaanxi, People's Republic of China (gxji@snnu.edu.cn).

Relative lattices of certain analytic operator algebras, pp. 183-191.

ABSTRACT.
In this note, We prove that the relative invariant subspace lattices of a finite
subdiagonal algebra **A** with respect to a faithful normal expectation Φ
and of an analytic operator algebra H^{∞}(α) determined by a flow α are
commutative.

**George Dinca, ** University of Bucharest, Department of Mathematics,
St. Academiei, no. 14, 70109-Bucharest, ROMANIA (dinca@math.math.unibuc.ro), **
Petru Jebelean, ** West University of Timisoara, Department of Mathematics Bv.
V. Parvan, no. 4, 1900-Timisoara, ROMANIA (jebelean@hilbert.math.uvt.ro) and
**Dumitru Motreanu, ** Universite de Perpignan, Departement de Mathematiques,
52 , Avenue de Villeneuve, 66860 Perpignan Cedex, FRANCE
(motreanu@univ-perp.fr).

Existence and Approximation for
a General Class of Differential Inclusions, pp. 193-215.

ABSTRACT.
This paper is concerned with existence and approximation results for
differential inclusions involving a duality mapping and a set-valued operator
which is a generalized gradient in the sense of Clarke of some locally Lipschitz
functional. The applications which we consider focus on the case when the
duality mapping is an elliptic partial differential operator of degenerate type
as, e.g. the p-Laplacian.

** Anderson, D. D., ** University of Iowa, Iowa City, IA 52242-1419
(ddanders@math.uiowa.edu),
**Dobbs, David E.,**
University of Tennessee, Knoxville, TN 37996-1300 (dobbs@math.utk.edu), and **
Mullins, B.,** Birmingham-Southern College, Birmingham, AL 35254
(bmullins@panther.bsc.edu..

Corrigendum: The
primitive element theorem for commutative algebras, pp. 217-221.

ABSTRACT.
Theorem 2.6 of our earlier paper HJM Vol.25(4), is
wrong. This Corrigendum identifies the erroneous step in the published "proof"
of Theorem 2.6; describes and verifies a counterexample to Theorem 2.6 (due to
Robert Gilmer); indicates that a weaker but valid version of Theorem 2.6 can be
proved by adapting the published "proof" by assuming a condition that is
violated in Gilmer's example; states a new result, Theorem 0.1, which answers
the question that was studied in Theorem 2.6; shows how to adapt the published
"proof" of Theorem 2.6 in order to obtain a proof of Theorem 0.1; isolates as a
new result, Corollary 0.2, the valid case of Theorem 2.6 (also a consequence of
Theorem 0.1) in which the base domain is integrally closed; notes how the
addition of one sentence serves to correct the published "proof" of Corollary
2.7; and notes that all the other proofs in the paper are correct.