Electronic Edition Vol. 28, No. 4, 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

Courtesy  of Professor M. F. Newman
Photographer: Marie Colvill (Austral. Nat. Univ.)

This issue is dedicated to the memory of Bernhard Neumann, who passed away on October 21st, 2002 in Canberra Australia. Professor Neumann was born in Berlin-Charlottenburg and died a few days after celebrating his 93rd birthday.
Professor Neumann's mathematical stature, editorial expertise and general wisdom has been of great help to successive editors of the journal. He greatly helped the development of the journal and will be missed as both an editor and a friend.



Ulrich Albrecht, Department of Mathematics, Auburn University, Auburn, AL 36849 (U.S.A.} (albreuf@mail.auburn.edu) ).
Modules with Morita-Equivalent Endomorphism Rings, pp. 665-681.
ABSTRACT. Let A and B be modules, which are faithfully flat over their endomorphism ring. The categories of A-solvable and B-solvable modules coincide if and only if A and B are similar. While similar modules have Morita equivalent endomorphism rings, the failure of the converse raises the question which module-theoretic properties are shared by modules with equivalent endomorphism rings. This paper addresses this question by investigating equivalences between full subcategories of the categories of A- and B-solvable modules, respectively. In particular, every equivalence between the category of A-solvable and the category of B-solvable modules is induced by a Morita equivalence between E(A) and E(B) if A and B are faithfully flat as modules over their endomorphism ring. Several examples show that these results may fail without the faithfulness condition.

Silvana Franciosi, Francesco de Giovann, Dipartimento di Matematica e Applicazioni, Universita di Napoli ``Federico II'', Via Cintia, Napoli (Italy)} (degiova@matna2.dma.unina.it) and Pavel Shumyatsky, Department of Mathematics, University of Brasilia , 70910-900 Brasilia-DF (Brazil)
On Groups with Finite Verbal Conjugacy Classes, pp. 683-689.
ABSTRACT. In this paper a generalization of groups with finite conjugacy classes, related to a given word is studied. In order to prove the main theorem, certain verbal generalizations of results by R. Baer and B.H. Neumann are also established.

Grzegorz Gromadzki, Institute of Mathematics, University of Gdansk, Wita Stwosza 57, 80-952 Gdansk, (Poland) (greggrom@math.univ.gda.pl) and Beata Mockiewicz, Instytut Matematyki WSP, Chodkiewicza 30, 85-064 Bydgoszcz (Poland) (brmock@ab-byd.edu.pl).
The groups of real genus 6, 7 and 8, pp. 691-699.
ABSTRACT. The real genus of a finite group G is the minimum algebraic genus of any compact bordered Klein surface on which G act faithfully as a group of automorphisms. Its systematic study was initiated and developed by Coy L. May who in a series of papers found, among the other things, all groups of real genera up to 5. Here we determine all groups of the real genera 6, 7 and 8.

B. G. Kang, Department of Mathematics, POSTECH, Pohang 790-784, Korea (bgkang@postech.ac.kr) and M. H. Park, School of Mathematical Sciences, Seoul National University, Seoul 151-747, Korea (mhpark@euclid.postech.ac.kr).
Completion of a Globalized Pseudo-Valuation Domain, pp. 701-710.
ABSTRACT. Let R be a pseudo-valuation domain with associated valuation domain V and I a nonzero proper ideal of R. Let R^ (resp., V^) be the I-adic (resp., IV-adic) completion of R (resp., V). We show that R^ is a pseudo-valuation domain (which may be a field); and that if I is not idempotent, then V^ is the associated valuation domain of R^. Let R be an SFT globalized pseudo-valuation domain with associated Prufer domain T and I a nonzero proper ideal of R. Let R^ (resp., T^) be the I-adic (resp., IT-adic) completion of R (resp., T). We also show that R^ is an SFT globalized pseudo-valuation ring with associated Prufer ring T^; and that R^ is an SFT globalized pseudo-valuation domain if and only if the radical of I is a prime ideal.

Johann Davidov, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria (jtd@math.bas.bg).
Twistorial examples of almost contact metric manifolds, pp. 711-740.
ABSTRACT. The twistor approach is applied for obtaining almost contact metric structures and some relations between the twistor spaces of odd and even dimensional Riemannian manifolds are established. These relations are illustrated by describing the twistor space of certain manifolds.

Daniel Grieser, Institut für Mathematik, Humboldt-Universität at Berlin, Sitz: Rudower Chaussee 25, 10099 Berlin, Germany. (grieser@mathematik.hu-berlin.de)
Quasiisometry of singular metrics, pp. 741-752.
ABSTRACT. We investigate when two Riemannian metrics, defined near zero in Rn and possibly singular at zero, are quasiisometric via a coordinate change that may be singular at zero.

Arenas, F.G. and Sánchez-Granero, M.A. Area of Geometry and Topology, Faculty of Science, Universidad de Almería, 04120 Almería, Spain (farenas@ual.es ), ( misanche@ual.es ).
Hahn-Mazurkiewicz Revisited: A new proof, pp. 753-769.
ABSTRACT. In this paper we study connectivity in metric spaces in terms of fractal structures (introduced by the authors). This approach allow us, for example, to give a new proof of Hahn-Mazurkiewicz Theorem, as well as Alexandroff-Urysohn characterization of compact metrizable spaces as continuous images of the Cantor space, or the Hausdorff characterization of the Cantor space as the only zero-dimensional perfect compact metrizable space. Related results are also proved.

Cao, Jiling, The University of Auckland, Private Bag 92019, Auckland, New Zealand (cao@math.auckland.ac.nz), Ganster, Maximilian, Graz University of Technology, Steyrergasse 30, A-8010 Graz, Austria (ganster@weyl.math.tu-graz.ac.at), Konstadilaki, Chariklia, Aristotle University of Thessaloniki, 54006 Thessaloniki, Greece (xariklia@ccf.auth.gr), and Reilly, Ivan L., The University of Auckland, Private Bag 92019, Auckland, New Zealand (i.reilly@auckland.ac.nz).
On Preclosed Sets and Their Generalizations, pp. 771-780.
ABSTRACT. This paper continues the study of preclosed sets and of generalized preclosed sets in a topological space. Our main objective is to establish results about the relationships between the various types of generalized closed sets. As a by-product, we are able to provide characterizations of certain known classes of topological spaces by using preclosed sets and their generalizations.

J. J. Charatonik, Mathematical Institute, University of Wroclaw, pl. Grunwaldzki 2/4, 50-384 Wroclaw, Poland; current address: Instituto de Matematicas, UNAM Circuito Exterior, Ciudad Universitaria, 04510 Mexico, D. F., Mexico (jjc@hera.math.uni.wroc.pl), (jjc@math.unam.mx) and A. Illanes, S. Macias, Instituto de Matematicas, UNAM Circuito Exterior, Ciudad Universitaria, 04510 Mexico, D. F., Mexico (illanes@math.unam.mx), (macias@servidor.unam.mx)
Induced mappings on the hyperspaces Cn(X) of a continuum X, pp. 781-805.
ABSTRACT. For a given mapping between continua we study the induced mappings between the corresponding hyperspaces of nonempty closed subsets with at most n components, and deduce some fixed point theorems. Our results extend various results that are known for the induced mappings between the hyperspaces of subcontinua.

Sean MacDonald and Lex G. Oversteegen, University of Alabama at Birmingham, Birmingham, AL 35294-1170 (mcdonald@math.uab.edu), (overstee@math.uab.ed).
On Mappings which are not Semi-conjugate to Interval Maps, pp. 807-813.
ABSTRACT. In this paper we provide a simple condition which implies that a given map from a continuum to itself is not semi-conjugate to an interval map. The argument makes use of the linear structure of the arc and reduces to a combinatorial argument.

Nauwelaerts, Mark, University of Antwerp, Groenenborgerlaan 171, B-2020 Antwerpen, Belgium (mnauw@ruca.ua.ac.be).
An alternative description of the topological universe hull of (quasi-)uniform spaces using approach theory, pp. 815-832.
ABSTRACT. The topological universe (= topological quasitopos) hulls of qAUnif and AUnif, the category of (quasi-)approach uniform spaces and uniform contractions, which combines (quasi-)uniform spaces and extended pseudo-(quasi-)metric spaces, are described as subcategories of (q)SAULim, the category of (quasi-)semi-approach uniform limit spaces and uniform contractions, and are shown to be reasonable generalizations of the corresponding hulls of (q)Unif, for which a new and more direct and internal characterization is also provided.

Thelma West, Department of Mathematics, University of Louisiana, Lafayette, LA 70504-1010, U.S.A. (thelmarwest@yahoo.com).
Spans of Certain Continua Cross Arcs , pp. 833-848.
ABSTRACT. For a continuum X, which satisfies certain conditions, we determine the span of X times J,~where J is an interval. When X satisfies other, less restrictive conditions, we determine the semispan of X times J. Additionally, when X is in real n-space and Y is contained in B times J where B is the complement of U and U is the unbounded component of the complement of X and Y satisfies various other conditions, we determine the surjective span and the surjective semispan of Y. Furthermore, we apply these results to a class of continua known as the concave upward symetric simple closed curves. Also, we calculate the spans for other related spaces.

Ashton, Brenden, University of New South Wales, UNSW Sydney NSW 2052, Australia (bashton@maths.unsw.edu.au), Cheng, Qingping, Murdoch University, Murdoch WA 6150, Australia (qcheng@maths.unsw.edu.au) and Doust, Ian, University of New South Wales, UNSW Sydney NSW 2052, Australia (i.doust@unsw.edu.au).
Some remarks on well-bounded and scalar-type decomposable operators, pp. 849-864.
ABSTRACT. The aim of this paper is to correct and clarify a number of results in the literature about well-bounded operators. In particular we show that if a well-bounded operator is decomposable in X, then it is automatically of type (A).

Grahame Bennett, Department of Mathematics, Indiana University, Rawles Hall, 831 E. 3rd Street, Bloomington, IN 47405-7106 (bennettg@indiana.edu).
Summability Matrices and Random Walk, pp. 865-898.
ABSTRACT. We show how a random walk may be attached to a summability matrix. This leads to two new classes of elementary inequalities.

Alan Lambert, Department of Mathematics, The University of North Carolina at Charlotte, Charlotte, NC 28223 USA} (allamber@email.uncc.edu).
The Sigma Algebra Generated by the Null Space of a Conditional Expectation, pp. 899-905.
ABSTRACT. The smallest sigma algebra for which all members of the null space of a conditional expectation are measurable is studied. Special attention is paid to the case that this sigma algebra is the full sigma algebra.

X. Li, P. Mikusinski and M. D. Taylor, Department of Mathematics, University of Central Florida,Orlando, Fl 32816-1364, USA (piotrm@mail.ucf.edu).
Remarks on convergence of Markov operators, pp. 907-916.
ABSTRACT. We show that for every positive real number p, p-strong convergence of Markov operators is equivalent to convergence in measure and that such convergence is not preserved by taking adjoints of Markov operators.

Menita Carozza, Universita del Sannio, Via Port'Arsa 11, 82100 Benevento, Italy ( carozza@unisannio.it) and Gioconda Moscariello, Antonia Passarelli di Napoli, Dipartimento di Matematica e Applicazioni ``R. Caccioppoli", Universita di Napoli ``Federico II", Via Cintia, 80126 Napoli, Italy (gmoscari@unina.it), (antonia.passarelli@dma.unina.it).
Nonlinear Equations with Growth Coefficients in BMO, pp. 917-929.
ABSTRACT. We prove an existence and uniqueness result for the Dirichlet problem of a class of equations whose model case is div (b(x)Du)=div f . Here b(x) belongs to the space BMO of the functions of bounded mean oscillation and f belongs to a Lebesgue space which summability exponent is less than the natural one, that is 2. Thus, the solutions are considered in a function space as in [CMP], [FS], [IS].
More precisely, we determine a number 1<q <2, depending on the BMO-norm of b(x), such that, if f has summability exponent greater than q, the Dirichlet problem considered, admit a unique solution.
The proof is based on an a priori estimate obtained using a new version of the classical Hodge decomposition and a convenient approximation argument.
[CMP] M. Carozza, G. Moscariello, A. Passarelli di Napoli, Linear elliptic equations with BMO coefficients, to appear on Rend. Lincei.
[FS] A. Fiorenza, C. Sbordone, Existence and uniqueness results of nonlinear equations with right hand side in L1, Studia Math. 127 (3) (1998), pp. 223-231.
[IS] T. Iwaniec, C. Sbordone, Quasiharmonic fields, to appear on Ann. Inst. H. Poincaré.