*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

**J.S. Okon, ** Department of Mathematics, California State University San
Bernardino, CA 92407 (jokon@csusb.edu), **D.E. Rush,** Department
of Mathematics, University of California, Riverside, CA 92521
(rush@math.ucr.edu) and **L.J. Wallace, ** Department of
Mathematics, California State University, San Bernardino, CA 92407
(wallace@csusb.edu).

A Mori-Nagata Theorem for Lattices and
Graded Rings,
pp. 973-997.

ABSTRACT.
We extend the global transform and the Mori-Nagata theorem, from integral
domains to multiplicative lattices.

**R.B.J.T. Allenby,
** Department of Pure Mathematics, University of Leeds, Leeds, LS2 9JT,
England (pmt6ra@leeds.ac.uk).

On the Upper near Frattini
Subgroup of a Generalized Free Product, pp. 999-1005.

ABSTRACT.
Azarian has shown that, for many types of generalized free product, the lower
near Frattini subgroup is a subgroup of the amalgamated subgroup. Together with
earlier work the present results show that, in all cases for which the lower
near Frattini subgroup has been proved to be a subgroup of the amalgamated
subgroup, so, too, is the (potentially larger) upper near Frattini subgroup
contained in the amalgamated subgroup. This answers a question raised by
Azarian.

**David F. Anderson, **Department of Mathematics, The University
of Tennessee, Knoxville, TN 37996, U. S. (anderson@math.utk.edu) and **
Ayman Badawi, **
Department of Mathematics & Statistics, American University Of Sharjah, P.O.
Box 26666, Sharjah, United Arab Emirates (abadawi@ausharjah.edu).

On phi-Dedekind Rings and
phi-Krull Rings, pp. 1007-1022.

ABSTRACT.
The purpose of this paper is to introduce two new classes of rings that are
closely related to the classes of Dedekind domains and Krull domains. Let H = {R
| R is a commutative ring with 1 and Nil(R) is a divided prime ideal of R}. Let
R in H, T(R) be the total quotient ring of R, and let phi be the map from R into
R_{Nil(R)} (the localization of R at Nil(R)) such that phi(a/b) = a/b
for every a in R and b in R\ Z(R). Then phi is a ring homomorphism from T(R)
into R_{Nil(R)}, and phi restricted to R is also a ring homomorphism
from R into R_{Nil(R)} given by phi(x) = x /1 for every x in R. A nonnil
ideal I of R is said to be phi-invertible if phi(I) is an invertible ideal of
phi(R). If every nonnil ideal of R is phi-invertible, then we say that R is a
phi-Dedekind ring. Also, we say that R is a phi-Krull ring if phi(R) is the
intersection of {V_{i}}, where each V_{i} is a discrete
phi-chained overring of phi(R), and for every nonnilpotent element x in R ,
phi(x) is a unit in all but finitely many V_{i}. We show that the
theories of phi-Dedekind and phi-Krull rings resemble those of Dedekind and
Krull domains.

**Daniele Guido** and **Tommaso Isola,**
Dipartimento di Matematica, Universita di Roma ``Tor Vergata'', I--00133 Roma,
Italy (guido@mat.uniroma2.it), (isola@mat.uniroma2.it).

Tangential dimensions I. Metric
spaces,
pp. 1023-1045.

ABSTRACT.
Pointwise tangential dimensions are introduced for metric spaces. Under
regularity conditions, the upper, resp. lower, tangential dimensions of *X*
at *x* can be defined as the supremum, resp. infimum, of box dimensions of
the tangent sets, *a la Gromov*, of *X* at
*x*. Our main purpose is that of introducing a tool which is very sensitive
to the "multifractal behaviour at a point" of a set, namely which is able to
detect the "oscillations" of the dimension at a given point. In particular we
exhibit examples where upper and lower tangential dimensions differ, even when
the local upper and lower box dimensions coincide. Tangential dimensions can be
considered as the classical analogue of the tangential dimensions for spectral
triples introduced in [D.Guido, T.Isola Journ. Funct. Analysis 203, (2003)
362-400], in the framework of Alain Connes' noncommutative geometry.

**Paul Bankston, ** Marquette University, Milwaukee, WI 53201
(paulb@mscs.mu.edu).

Mapping Properties of
Co-existentially Closed Continua,
pp. , 1047-1063.

ABSTRACT.
A continuous surjection between compacta is called
*co-existential* if it is the second of two maps whose composition is a
standard ultracopower projection. A continuum is called *co-existentially
closed* if it is only a co-existential image of other continua. This notion
is not only an exact dual of Abraham Robinson's existentially closed structures
in model theory, it also parallels the definition of other classes of continua
defined by what kinds of continuous images they can be. In this paper we
continue our study of co-existentially closed continua, especially how they (and
related continua) behave in certain mapping situations.

**Stephen Lipscomb, ** 8809 Robert E. Lee Drive, Spotsylvania,
Virginia 22553, USA (slipscom@umw.edu).

A Minimal Extension of the
Iterated Function System for Sierpinski's Gasket to One Whose Attractor is the
2-simplex, pp. 1065-1083.

ABSTRACT.
As an iterated function system, a pair of contractions (scalings by 1/2) yield
an attractor, 1-simplex; a code space, Cantor's set; and an address map,
quotient map from Cantor's set onto the 1-simplex known as (classical)
adjacent-endpoint identification. In 1972, the author extended adjacent-endpoint
identification to arbitrary code spaces. And for systems with (n+1) greater than
2 such contractions, (general) adjacent-endpoint identification yields an
attractor that is a fractal known as the n-web. Each such n-web is a proper
subspace of an n-simplex. Indeed, Sierpi\'nski's classical construction of his
gasket begins with a 2-simplex (manifold) and ends with the (fractal) 2-web
subspace. It is therefore natural (inverse of moving from manifolds to fractals)
to seek a minimal (code space and address map) extension of the n-web system to
an n-simplex system. Here, we extend the 2-web system (Sierpi\'nski-gasket
system) to one whose attractor is the 2-simplex. For n > 2, however, it is an
open problem to find such minimal extensions

**Yasushi Hirata, **Graduate School of Mathematics, University of Tsukuba,
Ibaraki 305-8571, Japan (yhira@jb3.so-net.ne.jp).

Subnormal finite products of
subspaces of ω _{1}, pp. 1085-1095.

ABSTRACT.
The author and Kemoto characterized mild normality of finite products of
subspaces of ω _{1} in terms of stationarity. In this paper, we will
show that the subshrinking property, subnormality, mild subnormality, and mild
normality coincide for every finite product of subspaces of ω _{1}.

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

On relatively absolutely
star-Lindelöf spaces, pp. 1097-1102.

ABSTRACT.
The author defines and studies the spaces mentioned in the title.

**Taras Banakh, **Department of Mathematics and Mechanics, Lviv
University, Universytetska 1, Lviv, 79000, Ukraine (tbanakh@franko.lviv.ua) and **
Dusan Repovs, ** Institute of Mathematics, Physics and Mechanics,
Jadranska 19, Ljubljana, Slovenia 1001 (dusan.repovs@fmf.uni-lj.si).

On linear realizations and local
self-similarity of the universal Zarichnyi map, pp. 1103- 1114.

ABSTRACT.
Answering a question of M.Zarichnyi we show that the universal Zarichnyi map is
not locally self-similar. We also characterize linear operators homeomorphic to
this map and on this base give a simple construction of it.

**T. Mizokami, ** Department of Mathematics, Joetsu University
of Education, Joetsu, Niigata 943-8512 Japan (mizokami@juen.ac.jp} and **
F. Suwada, **
Joint graduate school(PhD Program) Hyougo University of Teacher Education,
Yashiro, Hyougo 673-1494 Japan.

On General Resolutions due to
Networks, pp. 1115-1126.

ABSTRACT.
We study the general resolutions of spaces such as M_{3}-spaces,
metrizable spaces and developable spaces under the condition that families of
subsets of the initial spaces on which the resolutions are defined are
σ-discrete closed networks.

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

Controlled extensions of products
of continuous functions, pp. 1127-1133.

ABSTRACT.
For a topological space X and a subspace A of X, we prove that: A is C-embedded
in X if and only if for any real-valued continuous function f on A, any
non-negative real-valued function g on A, and any real-valued function H on X
satisfying that the product of f and g equals the restriction of H to A and the
zero-set of g is contained in that of f, there exist continuous extensions F and
G of f and g, respectively, over X such that the product of F and G equals H and
the zero-set of G is contained in that of F. The result essentially extends an
original theorem of M. Frantz on compact metrizable domains (1995) and a
subsequent theorem of S. Barov and J. J. Dijkstra on normal domains (2002). A
version of complex-valued functions is also given.

**Rajeev Kumar** and ** Romesh Kumar, ** Department of
Mathematics, University of Jammu, Jammu--180 006, (raj1k2@yahoo.co.in) (
omesh_jammu@yahoo.com).

On Finite Dimensional Algebras
Generated by Composition Operators on Orlicz Sequence Spaces with Weight,
pp. 1135-1152.

ABSTRACT.
In this paper, we characterise the algebraic composition operators and the
essentailly algebraicity of the Calkin image of composition operators on Orlicz
sequence spaces with weight when the Orlicz function is having atmost polynomial
growth. We also classify the essentially characteristic polynomials.

**Bernhard Haak, **Mathematisches Institut I, Universität
Karlsruhe, Englerstrasse 2, 76128 Karlsruhe, Germany
(Bernhard.Haak@math.uni-karlsruhe.de) and **Christian Le Merdy, **
Laboratoire de Mathematiques,Universite de Franche-Comte, 25030 Besancon Cedex,
France (lemerdy@math.univ-fcomte.fr).

α-Admissibility of Observation and
Control Operators, pp. 1153-1167.

ABSTRACT.
Given a strongly continuous semigroup T(t) on some Banach space, we introduce a
variant of the admissibility of an operator with respect to this semigroup,
called alpha-admissibility. Let -A be the generator of T(t). In the case when
that semigroup is a bounded analytic one, the second named author had showed
that the validity of the so-called Weiss conjecture is equivalent to A having a
square function estimate. In this paper, we extend that characterisation to our
new setting. Indeed we show that if A has a square function estimate, then
alpha-admissibility is equivalent to an appropriate resolvent estimate.

** Dan Kucerovsky, **University of New Brunwick-- Fredericton,
Fredericton, N.B., Canada E3B 5A3
(dkucerov @ unb.ca).

Properties of Strictly Positive
Elements in C*- algebras, pp. 1169-1177.

ABSTRACT.
We study the relationship of spectral properties of strictly positive elements
of a C*-algebra to other properties of the algebra, in particular establishing
the CS property for stable sigma-unital algebras that are not of real rank zero.

**Benton L. Duncan, ** University of Nebraska-Lincoln, Lincoln, NE
68588-0323
(bduncan@math.unl.edu).

Universal Operator Algebras of
Directed Graphs, pp. 1179-1198.

ABSTRACT.
Given a directed graph, there exists a universal operator algebra and universal
C^{*}-algebra associated to the directed graph. For finite graphs this
algebra decomposes as the universal free product of some building block operator
algebras. For countable directed graphs, the universal operator algebras arise
as direct limits of operator algebras of finite subgraphs. Finally, a method for
computing the K-groups for universal operator algebras of directed graphs is
given.

**Zhijian Qiu, ** Research Institute of Mathematics, HanShan Normal
University, ChaoZhou, GaungDong 521041, P. R. China (qiu@hstc.edu.cn}.

Carleson Measures On Circular Domains,
pp. 1199-1206.

ABSTRACT.
In this article, we study Carleson measures on circular domains. We characterize
the Carleson measures on circular domains and extend the celebrated theorem of
L. Carleson that gives an equivalence between a Carleson measure and the
Carleson measure inequality from the unit disk to circular domains.

**Ravi P. Agarwal,** Department of Mathematical Sciences, Florida
Institute of Technology, Melbourne, FL 32901-6975, USA (agarwal@fit.edu), **
Haishen Lü,** Department of Applied Mathematics, Hohai University, Nanjing,
210098, China and **Donal O'Regan, ** Department of Mathematics, National
University of Ireland, Galway, Ireland.

Positive Solutions for the
Singular p-Laplace Equation, pp. 1207-1220.

ABSTRACT.
An existence theorem concerning positive solutions for a certain singular
equation is established. The result is obtained using a fixed point theorem in
cones.

**Thomas Kühn, ** Mathematisches Institut, Universität Leipzig,
Augustusplatz 10/11, 04109 Leipzig, Germany
(kuehn@mathematik.uni-leipzig.de) and **Tomas Schonbek,** Florida
Atlantic University, Department of Mathematical Sciences, Boca Raton, FL 33431
(schonbek@fau.edu).

Compact Embeddings of Besov spaces
into Orlicz and Lorentz-Zygmund Spaces, pp. 1221-1243.

ABSTRACT.
Let 1 ≤ p,q < ∞, and let Ω be a bounded open subset of
**R**^{n}. Then the Besov space B_{pq}^{n/p}(Ω)
embeds into the exponential Orlicz space E_{ν}
(Ω) generated by the function Φ_{ν}(t) = t exp(t^{ν}) if and
only if 0 < ν ≤ q'. The embedding is even compact if ν < q'. We give two-sided
estimates for the entropy numbers of these compact embeddings, thus generalizing
previous results of H. Triebel (*Approximation numbers and entropy numbers of
embeddings of fractional Besov-Sobolev spaces in Orlicz spaces*, Proc. London
Math. Soc., 66 (1993), 589-618) and the first author (*Compact embeddings of
Besov spaces in exponential Orlicz spaces*, J. London Math. Soc. (2), 67
(2003), 235-244) in the case p=q.

Alternatively, the Orlicz spaces E_{ν}(Ω) can also be seen as special
Lorentz-Zygmund spaces Λ^{∞}(w,Ω). We introduce a scale of weights w
such that the corresponding Lorentz-Zygmund spaces are only minimally larger
than the limiting Orlicz space E_{q'}(Ω), and such that B_{pq}^{n/p}(Ω)
still embeds compactly into Λ^{∞}(w,Ω). We prove sharp estimates for
approximation and entropy numbers of these embeddings.

**Plamen Simeonov, ** Department of Mathematics, University of
Houston-Downtown, One Main Street, Houston, Texas 77002 (simeonovp@uhd.edu).

A Weighted Energy Problem for
a Class of Admissible Weights, pp. 1245-1260.

ABSTRACT.
We study the minimization problem for weighted logarithmic energy integrals over
the set of probability Borel measures supported on a closed subset of the
extended complex plane. The weight is a nonnegative upper semi-continuous
function that behaves like 1/|z| at infinity. We show that there exists a unique
measure that minimizes the energy integral and we give a characterization of
this measure in terms of a weighted logarithmic potential.