Electronic Edition Vol. 28, No. 1, 2002

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


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 (Mn, g) be a closed Riemannian manifold and N = S1 × f   Scm-1 be a warped product space with the warped product metric h = dt2 + f2(t) ds2. Let φ,  ψ : M  -->  N be two base projectively harmonic maps. We prove that if the Jacobi operators Jφ and Jψ 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 n-od. If X,Y,Z,K are continua in K , with Z being the union of X and Y , and K being the intersection of X and Y , and all X,Y,Z are different, then K is called a gate continuum in X for K . We characterize gate subcontinua in members of the above classes K . The characterizations are used to construct absolute terminal continua for K , i.e. continua X in K that are terminal in Y whenever X is a subcontinuum of Y and Y is a member of K . These results are applied to investigate properties of absolute retracts for K .

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 l2, 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 Ais 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 Aproperty 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.