*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

*Contents*

**G. Grätzer, **Department of Mathematics, University of Manitoba,
Winnipeg, MB R3T 2N2, Canada (gratzer@ms.umanitoba.ca), **E.T. Schmidt, **
Mathematical Institute of the Budapest University of Technology and Economics,
Müegyetem rkp. 3, H-1521 Budapest, Hungary (schmidt@math.bme.hu) and ** K.
Thomsen, **Department of Mathematics, University of Manitoba Winnipeg, MB
R3T 2N2, Canada (kurt_thomsen@hotmail.com).

Congruence Lattices of Uniform Lattices, pp. 247-263.

ABSTRACT. A lattice is uniform, if for any congruence, any two congruence classes are of the same size. A classical result of R. P. Dilworth represents a finite distributive lattice as the congruence lattice of a finite lattice. We show that this finite lattice can be constructed as a finite uniform lattice.

**Takahiro Sudo, **Department of Mathematical Sciences, Faculty of
Science, University of the Ryukyus, Nishihara-cho, Okinawa 903-0213, JAPAN
(sudo@math.u-ryukyu.ac.jp ).

Group C*-algebras of Some
Connected Lie Groups with Stable Rank One, pp. 265-280.

ABSTRACT.
We show that group C*-algebras of some connected Lie groups have stable rank
one, connected stable rank one and general stable rank one.

**Bang-Yen Chen, **
Department of Mathematics, Michigan State University, East Lansing, MI
48824-1027, USA (bychen@math.msu.edu).

Constant-Ratio Space-Like
Submanifolds in Pseudo-Euclidean Space, pp. 281-294.

ABSTRACT.
A submanifold of a pseudo-Euclidean space is said to be of constant-ratio if the
ratio of the length of the tangential and normal components of its position
vector function is constant. Submanifolds of constant-ratio relate closely to
the notion of convolution of Riemannian manifolds and to a problem in physics
concerning the motion in a central force field which obeys the inverse-cube law
originated from Newton in 1679. The purpose of this paper is to completely
classify constant-ratio space-like submanifolds in pseudo-Euclidean space.

**Richard H. Escobales, Jr., **Department of Mathematics, Canisius
College, Buffalo, NY 14208
(escobalr@canisius.edu).

Integrability Criteria and
Vector-Bundle Valued Cohomology for Foliations,
pp. 295-311.

ABSTRACT.
We first study a flow **F** on a closed, connected, n-dimensional, Riemannian
manifold (M, g). We assume that the mean curvature one-form κ associated with **
F** is closed. We show that this naturally induces a flat Bott-type connection
D on **V**, the distribution tangent to the flow **F**. We observe that in
fact this connection D depends only on the basic real cohomology class [κ]_{B}.
Then the natural exterior derivative d' associated with this Bott-type
connection on
**V**-valued differential forms has the property that (d')^{2} = 0,
and so one think of a cohomology of
**V**-valued differential forms, H*(M,**V**), canonically determined by
[κ]_{B}. We show that **H**, the distribution orthogonal to **V**
in TM with respect to the metric g, is integrable if and only if a certain
non-trivial cohomology class exists in H^{1}(M, **V**). Hence, in the
integrable case, H^{1}(M, **V**) is not 0. We discuss an analogue of
this result for distribution orthogonal to a foliation of leaf dimension p
greater than or equal to 2. For the foliation **F** itself, we have results
provided the Bott connection B on **H** is flat. B is flat on **H**
provided **F** is bundle-like with respect to the Riemannian g on M and the
base spaces of the local Riemannian submersions which define the bundle-like
foliation **F** are flat. Under these assumptions on **F**, H^{1}(M, **
H**) is not 0. In particular, when **F** is codimension-one foliation on M
which is bundle-like with respect to the metric g, we show that H^{1}(M,**H**)
is not equal to 0.

**Alejandro Illanes** and **Likin C. Simón**
Instituto de Matemáticas, UNAM, Circuito Exterior, Ciudad Universitaria, México
04510, D.F. MÉXICO (illanes@matem.unam.mx, lsimon@matem.unam.mx).

Means with Special Properties,
pp. 313-324.

ABSTRACT.
Let *X* be a metric continuum. A *mean* is a continuous function
*m: X× X → X* such that *m(x,x)=x* and *m(x,y)=m(y,x) *for every
*x, y ∈ X*. In this paper we study means with additional properties,
namely, we consider confluent, monotone and open means. We give examples and we
include some open questions.

**Zhongqiang Yang,
**Department of Mathematics, Shantou University, Shantou, Guangdong, 515063,
China P.R. (zqyang@stu.edu.cn) and **Katsuro Sakai,** Institute of
Mathematics, University of Tsukuba, Tsukuba, 305-8571, Japan
(sakaiktr@sakura.cc.tsukuba.ac.jp).

The Space of Limits of Continua
in the Fell Topology, pp. 325-335.

ABSTRACT.
By Cld(X), we denote the hyperspace of non-empty closed sets of a locally
compact metrizable space X with the Fell topology. Let Cont(X) be its subspace
consisting of all continua and Cont(X)
the closure of Cont(X) in Cld(X). It is proved that if X is connected, locally
connected, non-compact and has no free arcs, then the pair (Cont(X),
Cont(X)) is homeomorphic to the pair (Q × [0,1] - Z × {0}, Q × (0,1]), where Q
is the Hilbert cube and Z is a Z-set in Q which is homeomorphic to EX the space
of ends (i.e., the remainder of the Freudenthal compactification of X).

**Katsuya Yokoi, **Department of Mathematics, Interdisciplinary faculty
of Science and Engineering, Shimane University, Matsue, 690-8504, Japan
(yokoi@math.shimane-u.ac.jp).

Bubbly Continua and Homogeneity,
pp. 337-343.

ABSTRACT.
We show that an *n-*dimensional homogeneous ANR continuum which is cyclic
in dimension *n *is an *n*-bubble. As a consequence, we obtain that no
compact subset of such a space *X*, which is acyclic in dimension *n-1*,
separates *X*.

This is a partial answer to a problem of Bing and Borsuk.

**Yan-Kui Song, **Department of Mathematics, Nanjing University, Nanjing,
210093 P. R. China and Department of Mathematics, Nanjing Normal University,
Nanjing, 210097 P. R. China (songyankui@email.njnu.edu.cn)

Spaces with Large Extent and Large
Star-Lindelöf Number, pp. 345-352.

ABSTRACT.
In this paper, we prove the following statements: (1) For every regular
uncountable cardinal *κ*, there exists a centered-Lindelöf, Tychonoff space *
X *such that *St-l(X)≥κ.* (2) For every uncountable cardinal *κ*,
there exists a discretely star-Lindelöf, Tychonoff space *X* with the
property (a) such that *e(X)≥κ* . (3) For every infinite cardinal *κ*,
there exists a discretely star-Lindelöf, pseudocompact, Tychonoff space *X*
such that *e(X)≥κ.* The statement (1) answers negatively three questions of
Matveev and Bonanzinga on spaces with large extent and star-Lindelöf number.

**Kaori Yamazaki, **
Institute of Mathematics, University of Tsukuba, Tsukuba, Ibaraki 305-8571,
Japan (kaori@math.tsukuba.ac.jp).

Extending Point-Finite
Partitions of Unity, pp. 353-359.

ABSTRACT.
We prove that: (1) A subspace *A *of a space *X* is *P ^{ω}*
(point-finite)-embedded in

**Sophia Zafiridou, **Department of Mathematics, University of Patras,
26500 Patras, Greece (zafeirid@math.upatras.gr).

Rim-Scattered Space, Rim-type
of a Space, Containing Continuum, pp. 361-369.

ABSTRACT.
We prove that for every ordinal α = β +m (where β is a limit ordinal or 0 and m
is a positive integer) and for every k=0,..., m+min {β,1}-1 there is no
containing (planar) continuum of rim-type ≤α +k for the family of all (planar)
spaces having a basis B of open sets such that for every U∈B: (α ) the
α-derivative of Bd(U) is empty and (β ) the set Bd(U) has a compactification
with the α +k-derivative empty.

**Alexander E. Richman, **Department of Mathematics, Bucknell University,
Lewisburg, PA 17837 (arichman@bucknell.edu).

Composition Operators with
Complex Symbol having Subnormal Adjoint, pp. 371-384.

ABSTRACT.
Following earlier work by the author on the Bergman space and work by C. Cowen
and T. Kriete on the Hardy and Dirichlet spaces, it has been believed that in
order for C_{φ}* to be subnormal, the Taylor series for φ must contain
only real-valued coefficients. Assuming the linear fractional form which is the
only possible form for a variety of analytic function spaces including those
mentioned above, we identify those with non-real coefficients for which C_{φ}*
may be subnormal on the weighted Bergman space A^{2}_{α} of the
unit disk for each α. Furthermore, we prove that certain of these actually give
rise to subnormal operators. Additionally, using similar techniques when the
coefficients are real, we establish a necessary condition which, as α becomes
large, approaches a long known necessary condition of Cowen due to spectral
radius considerations.

**Zhe Dong, **Institute of Mathematics, Fudan
University, Shanghai 200433, China and
**Shijie Lu, **Department of Mathematics, Zhejiang University, Hangzhou
310027, China.

The Hyperspace of Closed Connected
Subsets of a Euclidean Space, pp. 385-392.

ABSTRACT.
In this paper, we study module isomorphisms between weakly closed * T*(

**C. L. García ** and **W. B. Johnson, **Department of Mathematics,
Texas A&M University, College Station, TX 77843, U.S.A (clgarcia@itam.mx),
(johnson@math.tamu.edu)

Power Type Uniform Convexity of*
X
*via p-asymptotic Uniform Convexity of L

ABSTRACT. We show that if L

**Thayer, F. Javier**, 9112 Decatur Ave S, Bloomington, MN 55438
(jt@mitre.org).

Nonstandard Analysis of Graphs,
pp. 403-436.

ABSTRACT.
This paper shows certain metric length spaces characterized by volume growth
properties of balls can viewed as graphs with infinitesimal edges. Our approach
is based on nonstandard analysis.

**V. Karunakaran, **School of Mathematics, Madurai Kamaraj University,
Madurai - 625 021, India. vkarun_mku@yahoo.co.in and **R. Vembu, ** SBK
College, Aruppukottai - 626 101, India. ( msrvembu@yahoo.co.in)

Hilbert Transform on
Periodic Boehmians, pp. 437-452.

ABSTRACT.
The theory of Hilbert transform on periodic functions and on periodic
distributions is well known. In this paper we shall extend this theory to a
suitable Boehmian space and identify a subspace of this Boehmian space on which
the Hilbert transform becomes a one-to-one continuous linear map. We shall also
construct examples of Boehmians which admit Hilbert transform in our sense, but
do not represent periodic distributions.

**Tom Hadfield, **
Department of Mathematics, University College, Cork, Republic of Ireland
(T.Hadfield@ucc.ie).

Noncommutative Geometry of
the Discrete Heisenberg Group, pp. 453-481.

ABSTRACT.
Motivated by the search for new examples of ``noncommutative manifolds'', we
study the noncommutative geometry of the group C*-algebra of the three
dimensional discrete Heisenberg group. We present a unified treatment of the
K-homology, cyclic cohomology and derivations of this algebra, placing it
squarely within the framework of Connes' noncommutative geometry.

**J. López-Gómez, ** Departamento de Matemática Aplicada, Universidad
Complutense de Madrid, 28040--Madrid, Spain. (Lopez_Gomez@mat.ucm.es).

Coexistence and Meta-Coexistence
for Competing Species, pp. 483-536.

ABSTRACT.
In this paper we analyze the dynamics of a family of competing species models
where one of the species grows in the presence of finitely many refuges
according to a logistic law. Basically, our results show how the model behaves
like a superlinear indefinite problem for a single equation ( cf. H. Amann and
J. Lopez-Gomez, *A priori bounds and multiple solutions for superlinear
indefinite elliptic problems*, J. Diff. Eqns. **146** (1998), 336-374.).
As a result of the presence of refuges, for certain ranges of values of the
parameters involved in the formulation of the model, the dynamics of its
classical positive solutions is regulated by a
*metacoexistence state*. By a metacoexistence state it is meant a solution
couple consisting of a *metasolution* coupled with a classical regular
solution.

Roughly speaking, metasolutions are continuous extensions by infinity of
*large solutions* (cf. C. Bandle and M. Marcus, *Large solutions of
semilinear elliptic equations: Existence, uniqueness and asymptotic behavior,*
J. D'Analysis Math. **58**(1991), 9-24.) that regulate the dynamics of the
positive solutions of a semilinear elliptic equation or system.

Metasolutions have been introduced and studied by *J. Garcia-Melian, R
Gomez-Renasco, J. Lopez-Gomez and J. C. Sabina de Lis *(Arch. Rat. Mech.
Anal. **145**
(1998)), *R. Gomez-Renasco and J. Lopez-Gomez *(Nonl. Anal. TMA **48**
(2002) ), *J. Lopez-Gomez *( El. J. Diff. Eqns. **Conf. 05** (2000))
and in the dissertation of *R. Gomez-Renasco *(Universidad de La Laguna,
Tenerife, February 1999.)