*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), W. B. Johnson (College Station), J. Nagata (Osaka), V. I. Paulsen
(Houston), , S.W. Semmes (Rice)

*Managing Editor*: K. Kaiser (Houston)

Houston Journal of Mathematics

**Enochs, Edgar, **University of Kentucky at Lexington, Kentucky, KY
40506-0027 (enochs@ms.uky.edu) and **
Estrada, Sergio, **Universidad de Murcia, Campus del Espinardo, Espinardo
(Murcia), 30100 Spain, (sestrada@ual.es) **
** The structure of compact
coGalois groups,
pp. 961-970.

ABSTRACT. The coGalois groups of torsion free covers were defined in E. Enochs, J.R. García Rozas, O.M.G. Jenda and L. Oyonarte:

**McCasland, R.L., **University of Edinburgh, Edinburgh EH8 9LE, Scotland
UK (rmccasla@inf.ed.ac.uk), **Moore,
M.E., **University of Texas at Arlington, Arlington, Texas 76019-0408 USA
(moore@uta.edu), and **Smith, P.F., **
University of Glasgow, Glasgow G12 8QW, Scotland UK
(pfs@maths.gla.ac.uk).

Subtractive Bases of Zariski
Spaces, pp. 971-983.

ABSTRACT.
The notion of a subtractive basis for a Zariski Space is defined and examined.
Such bases provide a means of generating Zariski Spaces, which exploits both the
algebraic and topological-type properties of these spaces. In particular, it is
shown that for every finitely-generated module M over a commutative ring with
identity, then the Zariski Space of M has a (finite) subtractive basis.
Moreover, it is shown that, provided M has the additional property of being a
radical module (i.e., rad 0 = 0), then every subtractive basis of the Zariski
Space of M corresponds to a direct sum decomposition of M. For such a module M,
it then follows that every direct summand A of M must have the following
property: if B is a submodule of M and rad B = A, then B = A.

Axtell, Michael, Wabash College,
Crawfordsville, IN 47933
(axtellm@wabash.edu), Stickles, Joe,
Dept. of Mathematics, Millikin University, Decatur IL 62522 and
Warfel, Joseph, Wabash College,
Crawfordsville, IN 47933.

Zero-Divisor Graphs of Direct
Products of Commutative Rings,
pp. 985-994.

ABSTRACT.
We recall several results of zero divisor graphs of commutative rings. We then
examine the preservation of diameter and girth of the zero divisor graph of
direct products of commutative rings.

**Peter, Ioan Radu,** Department of Mathematics, Technical University of

Cluj-Napoca, G. Baritiu, nr. 15, RO-3400 Cluj-Napoca, Romania
(Ioan.Radu.Peter@math.utcluj.ro).

On the Morse Index theorem where the
ends are submanifolds in Finsler geometry, pp. 995-1009.

ABSTRACT.
In this paper we prove two cases of the Morse Index Theorem for Finsler
manifolds. In the first case one of the endpoint of the geodesic is fixed,
the other is variable in a submanifold. The second theorem deals with the
case of two variable endpoints in submanifolds of a Finsler manifold.

**Huff, Robert, **Saint Louis University, Mathematics and CS
Department, 221 N. Grand Blvd, Saint Louis, MO 63103 (rhuff2@slu.edu).

Flat structures and the triply
periodic minimal surfaces C(H) and tC(P), pp. 1011-1027.

ABSTRACT.
The C(H) and tC(P) surfaces are one-parameter families of embedded, triply
periodic minimal surfaces, with the former derived by A. Schoen and the latter
derived by Fischer and Koch. Existence proofs of these surfaces using the
conjugate Plateau method have been given by Karcher. In this paper, an
alternative proof is presented using flat structures on the surfaces. This proof
uses a different fundamental region than Karcher, and the geometry of this
region makes clear a network of straight lines on the surfaces.

**Tetsuya Hosaka, **Department of Mathematics, Utsunomiya University,
Mine-machi, Utsunomiya 321-8505, Japan
(hosaka@cc.utsunomiya-u.ac.jp)**.**

A class of rigid Coxeter groups,
pp. 1029-1036.

ABSTRACT.
In this paper, we give a new class of rigid Coxeter groups. Radcliffe have
proved that right-angled Coxeter groups are rigid. The main theorem of this
paper is an extension of this result.

**Grace, E.E**.,
Department of
Mathematics, Arizona State University, Tempe, Arizona 85287-1804
(egrace@asu.edu) and
**Vought,
E.J**.,
Department of Mathematics and Statistics, California
State University, Chico; Chico, California 95929-0525
(eeevought@worldnet.att.net).

Plane Continua without disjoint
subcontinua with nonvoid interiors
, pp. 1037-1045.

ABSTRACT. It is proved that every plane continuum, in
which each two subcontinua with nonvoid interiors intersect, is not aposyndetic
and semilocally connected at the same point. It is a corollary that any such
continuum has a weak cutpoint.

**Daniel, Dale, **Lamar University, Beaumont, TX 77710-0047
(daniel@math.lamar.edu).

On Metrizability of Images of
Ordered Compacta , pp. 1047-1059.

ABSTRACT.
We consider those Hausdorff spaces that are the continuous image of some
compact ordered space. Utilizing a theorem of Treybig, we characterize those
continuous images of compact ordered spaces that are metrizable. In doing so, we
give a ''best possible" metrization theorem for separable images of compact
ordered spaces. In particular, a Hausdorff space that is the continuous image of
some compact ordered space is metrizable if and only it is separable and may be
embedded as a G-delta subset of some locally connected continuum. We also obtain
some corollaries and related results. .

**Nitta, Shin-ichi.,**Shijonawate-gakuen Junior College,Osaka,Japan
(nitta@jc.shijonawate-gakuen.ac.jp),and **Yoshioka,Iwao, **Department of
Mathematics, Okayama University,Okayama,Japan
(yoshioka@math.okayama-u.ac.jp).

Nagata Spaces and wN-spaces which are
preserved by Quasi-Perfect Maps, pp. 1061-1076.

ABSTRACT.
G.Ying and C.Good (2001) described that Lutzer's example (1971) asserts that
neither Nagata spaces nor wN-spaces are necessarily preserved under
quasi-perfect maps. We introduce some classes of spaces which are contained in
the class of wN-spaces and show that these classes are invariant under
quasi-perfect maps or closed almost-open maps, but not preserved by closed map
nor open finite-to-one maps. We also show that in the realm of paracompact
spaces, these new classes coincide with the class of M-spaces in the sense of
Morita, and study conditions for metrizability of these classes.

**Chatyrko, Vitalij,** Linkoping University, 581 83 Linkoping, Sweden
(vitja@mai.liu.se),** Hattori, Yasunao,**
Shimane University, Matsue, Shimane, 690-8504 Japan

(hattori@riko.shimane-u.ac.jp),
and **Ohta, Haruto, **Shizuoka University, Ohya, Shizuoka, 422-8529 Japan
(echohta@ipc.shizuoka.ac.jp).

Partitions of spaces by locally
compact subspaces, pp. 1077-1091.

ABSTRACT. In this article, we shall discuss the possibility
of different presentations of topological spaces as unions or partitions of
locally compact subspaces.

For a space X, let lc(X) (resp. lcd(X)) denote the minimum cardinality of a
cover (resp. partition) of X by locally compact subspaces. We prove:

(1) For every finite or countably infinite cardinal n, there exists a subspace X
of the real line such that lc(X)=n; (2) for every Hausdorff space X, if lc(X) is
at most countable, then lc(X)=lcd(X); (3) if X is a topologically complete,
nowhere locally compact, Hasudorff space, then lc(X) is uncountable; (4) if a
perfectly normal space X is covered by finitely many subpaces, each of which is
locally compact with at most one exception, then the covering dimension of X
coincides with the maximum of the dimensions of those subspaces. It is open
whether there is an example in ZFC of a Hausdorff space X such that
lc(X)<lcd(X).

**Dijkstra, Jan J.,** Vrije Universiteit, Amsterdam, The Netherlands (dijkstra@cs.vu.nl).

A homogeneous space that is
one-dimensional but not cohesive, pp. 1093-1099.

ABSTRACT. A separable metric space is called cohesive if
every point of the space has a neighbourhood that fails to contain nonempty
clopen subsets of the space. A topological group is cohesive if and only if it
is not zero-dimensional. We present a homogeneous, one-dimensional, almost
zero-dimensional space that is not cohesive.

We also show that a complete homogeneous space is cohesive if and only if it is
not zero-dimensional.

Zero-dimensional Closed Set Aposyndesis and Hyperspaces., pp. 1101-1105.

ABSTRACT. A continuum is a compact metric space. It is said that a continuum X is zero-dimensional closed set aposyndetic provided that for each zero-dimensional closed subset A of X and for each p in X minus A, there exists a subcontinuum M of X such that p is in the interior of M and M does not intersect A. It is shown that if X is a continuum and n is a natural number, then both the hyperspace of nonempty closed subsets of X and the n-fold hyperspace of X are zero-dimensional closed set aposyndetic

**Antonio Peláez,** Instituto de
Matemáticas, UNAM, Circuito Exterior, Ciudad
Universitaria, México D. F., C. P. 04510,
MEXICO, (pelaez@matem.unam.mx)

Generalized inverse limits,
pp. 1107-1119.

ABSTRACT.
Recently, Professor W. Mahavier defined an inverse limit of a sequence of closed
subsets of the unit square. We use that definition to construct, for a given
positive integer m, an inverse limit of a sequence of closed subsets of the unit
square having dimension equal to m. We extend Professor Mahavier's definition
and define an inverse sequence of closed subsets and its generalized inverse
limit. In this case, the closed sets are not necessarily contained in the unit
square. We also extend some results obtained by Professor Mahavier in his paper
"Inverse limits with subsets of [0,1]× [0,1], Topology and Its Applications,
141(2004), 225-231" and we give a condition to induce maps between those new
spaces.

**MacCluer, Barbara D.**, University of Virginia, Charlottesville, VA 22904
(bdm3f@virginia.edu) and **Pons,
Matthew A.**, University of Virginia, Charlottesville, VA 22904
(map6h@virginia.edu).

Automorphic Composition Operators
on Hardy and Bergman Spaces in the Ball, pp.1121-1132.

ABSTRACT.
We determine which composition operators with automorphism symbol are
essentially normal on the Hardy and Bergman space of the ball. To do this, we
first show that modulo the compact operators, the product of an automorphic
composition operator followed by its adjoint is a Toeplitz operator with
positive symbol.

**Jupiter, Daniel**, Texas A & M Health Science Center, Temple, TX 76504
(djupiter@tamu.edu), and **Redett, David, ** Indiana University -
Purdue University Fort Wayne, Fort Wayne, IN 46805
(redettd@ipfw.edu).

Invariant Subspaces of RL^{1},
pp. 1133-1138.

ABSTRACT.
In this note we extend D. Singh and A. A. W. Mehanna's invariant subspace
theorem for RH^{1}
(the real Banach space of analytic functions in H^{1} with real Taylor
coefficients) to the simply invariant subspaces of RL^{1} (the real
Banach space of functions in L^{1} with real Fourier coefficients.

**Mykhaylyuk, Volodymyr,** Chernivtsi National University str.
Kotsjubyn'skogo 2, Chernivtsi, 58012 Ukraine
(mathan@chnu.cv.ua) and **Popov, Mykhaylo**, Chernivtsi National
University str. Kotsjubyn'skogo 2, Chernivtsi, 58012 Ukraine
(popov@chv.ukrpack.net).

On "weak" embeddings of L_{1},
pp. 1139-1152.

ABSTRACT.
We study the relationships between some notions of "weak" embeddings
(semi-embeddings, sign-embeddings, etc.) of the space of the Lebesgue summable
functions on the unit segment. First kind of problems - which "weak" embeddings
are automatically other ones - are simple and we answer them completely. The
questions of the second kind - which "weak" embeddabilities imply others - are
difficult and some of them remain still open.

**Kahng, Byung-Jay, **Department of
Mathematics and Statistics, Canisius College, Buffalo, NY 14208 (kahngb@canisius.edu
).

Quantum double construction in the
C*-algebra setting of certain Heisenberg-type quantum groups, pp.
1153-1189.

ABSTRACT. We carry out the ``quantum double construction''
of the specific quantum groups we constructed earlier, namely, the ``quantum
Heisenberg group algebra'' and its dual, the ``quantum Heisenberg group''. Our
approach is by constructing a suitable multiplicative unitary operator,
retaining the C*-algebra framework of locally compact quantum groups. We also
discuss the dual of the quantum double and the Haar weights on both of these
double objects. Towards the end, a construction of a (quasitriangular) quantum
universal R-matrix is given.

**Pol, Roman,** Department of Mathematics, Banacha 2, 02-097 Warsaw, Poland
(pol@mimuw.edu.pl) .

Evaluation maps on products of
separable metrizable spaces are Borel, pp. 1191-1196.

ABSTRACT.
Given a completely regular space X we denote by C(X) the space of continuous
real - valued functions on X, and let e : X×C(X) → R, e(x,f) = f(x), be the
evaluation map. The function space C(X) is considered with the pointwise
topology. We prove the result stated in the title, and give an example of a
compact separable space X such that the evaluation map e on X is Borel
measurable, but the preimage of some open set under e is not a countable union
of closed sets, answering two questions by M.R.Burke, Borel measurability of
separately continuous functions II, Top. Appl. 134 (2003), 154 - 188.

**García-Falset, Jesus,**
Departament de Matemàtiques , Universitat de València, Dr Moliner 50, 46100
Burjassot, València, Spain (garciaf@uv.es),
and** Reich, Simeon, ** Department of Mathematics, the
Technion-Israel Institute of Technology, 32000 Haifa, Israel (sreich@tx.technion.ac.il).

Zeroes of accretive operators and
the asymptotic behavior of nonlinear semigroups, pp. 1197-1225.

ABSTRACT.
We study necessary and sufficient conditions for an accretive operator which
satisfies the range condition to have a zero. We obtain, in particular, a
characterization of this property for m-accretive operators in L1. We also
study the asymptotic behavior of nonexpansive semigroups in L1 and then
apply our results to certain initial value problems.

**De-xiang Ma,** College of Information Science and
Engineering, Shandong University of Science and Technology, Qingdao, Shandong
Province 266510, China (madexiang@sohu.com),
**Weigao-Ge,** Department of Mathematics, Beijing Institute of Technology,
Beijing 100081, China (gew@bit.edu.cn), and
**Xuegang-Chen, **Department of Mathematics, North China Electric Power
university, Beijing 102206, China**. **

New results on periodic solutions for a
p-Laplacian Lienard equation with a deviating argument, pp. 1227-1239.

ABSTRACT.
The existence of periodic solutions for Lienard equation with a deviating has
been studied extensively. Generally, restricting conditions are imposed on the
value of the deviating function. In this paper, we study the existence of
periodic solutions for the p-laplacian Lienard equation with a deviating
argument. We give no restriction on the deviating function, which is the
significance of the paper. Our result is based on a new lemma which makes it
possible to use Mawhin's continuation theorem as a tool. The methods we used to
estimate a priori bounds on periodic solutions are also new.

**Pigong Han,** Institute of Applied Mathematics,
Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing
100080, P. R. China (pghan@amss.ac.cn)

The Effect of the Domain Topology on
the Number of Positive Solutions of an Elliptic System Involving Critical
Sobolev Exponents, pp. 1241-1257.

ABSTRACT.
In this paper, we consider the Dirichlet problem for an elliptic system of two
equations involving the critical Sobolev exponents. We first establish the
concentration-compactness principle for elliptic systems; then by the
variational method and applying Lusternik-Schnirelmann theory, we study the
effect of the domain topology on the number of positive solutions.