*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

**Jack Maney, ** Department of Mathematical Sciences, The University of
South Dakota, 414 E. Clark St., Vermillion, SD 57069 (jmaney@usd.edu).

On the boundary map and overrings,
pp. 325-335.

ABSTRACT. This paper uses a generalization of the length
function, due to Coykendall, to study the overrrings of an half factorial
domain.

**David E. Dobbs,** Department of Mathematics, University of
Tennessee, Knoxville, Tennessee 37996-1300 (dobbs@math.utk.edu) and **Jay
Shapiro,** Department of Mathematics, George Mason University, Fairfax,
Virginia 22030-4444 (jshapiro@gmu.edu).

Descent of Divisibility Properties
of Integral Domains to Fixed Rings, pp. 337-353.

ABSTRACT.
Let G be a finite group acting via ring automorphisms on an integral domain R.
The operation R goes to R^{G} is shown to commute with the formations of
integral closure and complete integral closure, as well as with the formations
of certain rings of fractions and certain conductor overrings. The extension R^{G}
a subring of R satisfies GD (the going-down property). As a result, the
following are among the classes of integral domains that are stable under the
operation R goes to R^{G}: integrally closed domains, seminormal
domains, completely integrally closed domains, Krull domains, Prufer domains,
going-down domains, locally divided domains, divided domains, locally
pseudo-valuation domains, pseudo-valuation domains, and almost pseudo-valuation
domains.

**S. Hedayat **and

Prime and Radical Submodules of Free Modules over a PID, pp. 355-367.

ABSTRACT. In this paper the notion of prime matrix is introduced. It is shown that if R is a PID then every full rank prime submodule of a free module of finite rank is the row space of a prime matrix. Hence the notion of a prime matrix may be regarded as a generalization of the notion of a prime element. Finally, using prime matrices, we

obtain the radical of submodules of a free module of finite rank, as well as the radical submodules.

**S. Hedayat **and

Primary Decomposition of Submodules of a Finitely Generated Module over a PID, pp. 369-377.

ABSTRACT. In this paper we present a method for calculating a reduced primary decomposition for submodules of a finitely generated module over a PID.

** Ayman Badawi, ** Department of Mathematics and Statistics, The
American Universit of Sharjah, P.O. Box 26666 Sharjah, United Arab Emirates
(abadawi@aus.ac.ae) and **David E. Dobbs, **Department of
Mathematics, The University of Tennessee, Knoxville, TN, 37996-1300, U. S. A.
(dobbs@math.utk.edu).

Strong Ring Extensions and
phi-pseudo-valuation rings, pp. 379-398.

ABSTRACT.
In this paper, we extend the concept of strong extensions of domains to the
context of (commutative) rings with zero-divisors. We show that the theory of
strong extensions of rings resembles that of strong extensions of domains.

**P. Malcolmson,** Department of Mathematics, Wayne State
University, Detroit MI 48202 (petem@math.wayne.edu) and** Frank Okoh, **
Department of Mathematics, Wayne State University, Detroit MI 48202
(okoh@math.wayne.edu).

A class of integral domains
between factorial domains and idf-domains, pp. 399-421.

ABSTRACT.
For a non-zero element a in an integral domain R, consider the set D(a) of
non-associate irreducible divisors of all of the powers of that element. The
domain R is idpf (irreducible divisors of powers finite) if for every non-zero
element a in R, the set D(a) is finite. The domain is idf (irreducible divisors
finite) if the set of non-associate irreducible divisors of a is finite for
every non-zero element a. We locate these concepts amongst other generalizations
of factorial domains. A modification of a construction due to Samuel leads to a
domain that is idf but not idpf. We determine the idpf-subrings of the ring of
Gaussian integers. A canonical problem is the determination of the irreducible
affine varieties that are idpf. We show that every Krull domain, in particular
every Dedekind domain, is idpf; hence the coordinate ring of a nonsingular curve
is idpf. The coordinate rings of some familiar singular affine plane curves are
shown to be idpf in positive characteristic but fail to be idpf in zero
characteristic.

**Guido, Daniele** and **Isola, Tommaso,** Dipartimento di Matematica,
Univ. Roma "Tor Vergata", Via della Ricerca Scientifica 1, I-00133 Roma - Italy
(guido@mat.uniroma2.it), (isola@mat.uniroma2.it).

Tangential dimensions II. Measures,
pp. 423-444.

ABSTRACT.
Notions of (pointwise) tangential dimension are considered, for measures of **R**^{n}.
Under regularity conditions (volume doubling), the upper resp. lower tangential
dimension at a point
*x* of a measure can be defined as the supremum, resp. infimum, of local
dimensions of the measures tangent to the given measure at *x*. Our main
purpose is that of introducing a tool which is very sensitive to the
"multifractal behaviour at a point" of a measure, namely which is able to detect
the "oscillations" of the dimension at a given point, even when the local
dimension exists, namely local upper and lower dimensions coincide. These
definitions are tested on a class of fractals, which we call translation
fractals, where they can be explicitly calculated for the canonical limit
measure. In these cases the tangential dimensions of the limit measure coincide
with the metric tangential dimensions of the fractal defined in D. Guido, T.
Isola, "Tangential dimensions I. Metric spaces", Houston
J. Mathematics 31(4), 2005, 1023-1045, and they are constant, i.e. do not
depend on the point. However, upper and lower dimensions may differ. Moreover,
on these fractals, these quantities coincide with their noncommutative
analogues, defined in [1] and [2] in the framework of Alain Connes'
noncommutative geometry.

[1] D. Guido, T. Isola, *Dimensions and singular traces for spectral triples,
with applications to fractals,
*Journal of
Functional Analysis, Vol. 203(2), , 2003, pp. 362-400.

[2] D. Guido, T. Isola, *Dimensions and spectral triples for fractals in R ^{N }*
, Advances in Operator Algebras and Mathematical Physics; Proceedings of the
Conference held in Sinaia, Romania, June 2003, F. Boca, O. Bratteli, R. Longo H.
Siedentop Eds., Theta Series in Advanced Mathematics, Bucharest 2005. Paper
available through ArXiv.

**Labouriau, Isabel S., **Centro de Matemática da Universidade do Porto,
R. do Campo Alegre, 687, 4 169 Porto, Portugal
(islabour@fc.up.pt) and **Ruas, Maria A. S.,**Departamento de Matemática,
Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo,
13560-970, São Carlos, SP, Brazil
(maasruas@icmc.usp.br).

Invariants for Bifurcations,
pp. 445-458.

ABSTRACT. Bifurcation problems with one parameter are
studied here. We develop a method for computing a topological invariant, the
number of fold points in a stable one-parameter unfolding for any given
bifurcation of finite codimension.

We introduce another topological invariant, the algebraic number of folds. The
invariant gives the number of complex solutions to the equations of fold points
in a stabilization, an upper bound for the number of fold points in any
unfolding. It can be computed by algebraic methods, we show that it is finite
for germs of finite codimension. An open question is whether this value is
always attained as the maximum number of fold points in a stable unfolding.

We compute these two invariants for simple bifurcations in one dimension,
answering the question above in the affirmative. We discuss other invariants in
the literature and verify that the algebraic number of folds and the Milnor
number form a complete set of invariants for simple bifurcations in one
dimension.

**Popvassilev, Strashimir G.,**
Department of Mathematics, University of Louisiana at Lafayette, 217 Maxim D.
Doucet Hall, P.O. Box 41010, Lafayette, Louisiana 70504-1010, U.S.A.
(pgs2889@louisiana.edu),
(www.louisiana.edu/~pgs2889).

Base-family paracompactness,
pp. 459-469.

ABSTRACT.
Call a topological space base-family paracompact if it has an open base every
subfamily of which has a subfamily with the same union, such that the latter
subfamily is locally finite at each point of its union. Proto-metrizable spaces
are base-family paracompact. A T_{1} space is metrizable if and only if
its product with a converging sequence is base-family paracompact.

**Francis Jordan, **Department of Mathematical Sciences, Georgia
Southern University, Statesboro, Ga. 30458
(fjordan@georgiasouthern.edu).

The S4 continua in the sense of
Michael are precisely the dendrites, pp. 471-487.

ABSTRACT. A continuum X is said be S4 if for every
partition P of X into compacta there is a continuous selector for P. It is
known that every S4 continuum is a dendrite. In this paper we prove the
opposite implication. The result will follow from a general theorem on the
existence of continuous selectors and a structure theorem on partitions of
dendrites.

**Jan van Mill, ** Faculty of Sciences, Department of Mathematics,
Vrije Universiteit, De Boelelaan 1081a, 1081 HV Amsterdam, The Netherlands
(vanmill@cs.vu.nl).

Not all homogeneous Polish spaces
are products, pp. 489-492.

ABSTRACT.
We prove that not every homogeneous Polish space is the product of one of its
quasi-components and a totally disconnected space. This answers a question of
Aarts and Oversteegen.

** Ofelia T. Alas, **Instituto de Matematica e Estatıstica,
Universidade de Sao Paulo, Caixa Postal 66281, 05311-970 Sao Paulo, Brasil
(alas@ime.usp.br) and** R. G. Wilson**, Departamento de
Matematicas, Universidad Autonoma Metropolitana, Unidad Iztapalapa, Avenida San
Rafael Atlixco, #186, Apartado Postal 55-532, 09340, Mexico, D.F., Mexico
(rgw@xanum.uam.mx).

Minimal properties between T_{1}
and T_{2}, pp. 493-504.

ABSTRACT.
A space is a *US*-space if every convergent sequence has a unique limit;
it is an *SC*-space if each convergent sequence together with its limit
is closed and is a
*KC*-space if every compact subset is closed. We study the existence of
spaces which are minimal with respect to these properties. We develop a number
of results regarding minimal
*SC*-spaces, we show that the class of infinite minimal
*US*-spaces is empty and we give a consistent example of a Tychonoff
topology which contains no minimal *KC-*topology

**I. G. Todorov, **Department of Pure Mathematics, Queen's
University Belfast, Belfast BT7 1NN, N. Ireland} (i.todorov@qub.ac.uk).

Synthetic properties of ternary
masa-bimodules, pp. 505-519.

ABSTRACT.
We provide a detailed description of the support of the masa-bimodules, which
are ternary rings of operators (we call such masa-bimodules ternary). We show
that the reflexive masa-bimodule generated by any synthetic masa-bimodule and a
finite number of ternary masa-bimodules in an appropriate mutual position, is
always synthetic and characterise the hereditarily synthetic masa-bimodules of
this type. We give some corollaries of these results

**Pengtong Li,** Department of Mathematics, Nanjing University of
Aeronautics and Astronautics, Nanjing 210016, China (pengtonglee@vip.sina.com), **
Jipu Ma,** Department of Mathematics, Nanjing University, Nanjing 210093,
China, and **Jing Wu**, Department of Mathematics, University of
Central Florida, Orlando, Florida 32816, USA (ucfjing@yahoo.com).

Additive Derivations of Certain
Reflexive Algebras, pp. 521-530.

ABSTRACT.
Let L be a J-subspace lattice on a Banach space, AlgL be the associated
reflexive algebra and A be a subalgebra of AlgL containing all finite rank
operators in AlgL. Under an assumption, we prove that every additive derivation
from A into AlgL is linear and quasi-spatial. This result can apply to those
reflexive algebras with atomic Boolean subspace lattices and pentagon subspace
lattices, respectively.

**Kucerovsky, D.** and **Ng,P.W.,** University of
New Brunswick at Fredericton, Fredericton, NB E3B 5A3 Canada (dan@math.unb.ca),
(pwn@math.unb.ca).

The corona factorization
property and approximate unitary equivalence,
pp. 531-550.

ABSTRACT.
We study Rordam's group, KL(A,B), and a corona factorization condition. Our key
technical result is a lemma showing that approximate unitary equivalence
preserves the purely large property of Elliott and Kucerovsky. Using this, we
characterize KL(A,B) as a group of purely large extensions under approximate
unitary equivalence, generalizing a theorem of Kasparov's. Then we prove the
following:

Let B be a stable and separable C*-algebra. Then the following are
equivalent (for weakly nuclear extensions):

i. The corona algebra of B has a certain quasi-invertibility property, which we
here call the corona factorization property.

ii. Rordam's group KL^{1}(A,B) is isomorphic to the group of full
essential extensions of A by B.

iii. Every strongly full and positive element of the corona algebra of B is
properly infinite.

iv. Every norm-full extension of B is absorbing with respect to approximate
unitary equivalence.

v. Every norm-full extension of B is absorbing with respect to ordinary unitary
equivalence.

vi. Every norm-full extension of B is absorbing with respect to weak
equivalence.

vii. Every norm-full trivial extension of B is absorbing with respect to unitary
equivalence.

viii. A K-theoretical uniqueness result for maps into M(B)/B.

We show that if X is the infinite Cartesian product of spheres, then the
stabilization of C(X) does not have the corona factorization property.

**Timur Oikhberg, **
University of California - Irvine, Irvine CA 92697
(toikhber@math.uci.edu).

Operator spaces with complete
bases, lacking completely unconditional bases, pp. 551-561.

ABSTRACT.
We construct a Hilbertian operator space X such that the set of completely
bounded operators on X consists of Hilbert-Schmidt perturbations of a certain
representation of the second dual to the James space. This space possesses an
orthonormal basis (e_{i}) such that all basis projections are completely
contractive, yet any n-dimensional block subspace has complete unconditionality
constant of at least c n^{1/2} (c is a constant).

**Prüss, Jan, **University of Halle, 06099 Halle, Germany
(pruess@mathematik.uni-halle.de),
**Rhandi, Abdelaziz, **University of Marrakesh, 40000 Marrakesh, Morocco
(rhandi@ucam.ac.ma), and ** Schnaubelt, Roland, **University of Halle, 06099
Halle, Germany
(schnaubelt@mathematik.uni-halle.de).

The domain of elliptic operators on
L^{p}(R^{d}) with unbounded drift coefficients, pp.
563-576.

ABSTRACT.
We consider elliptic operators on R^{d} of second order where the
diffusion coefficients are uniformly elliptic and the drift coefficients can
grow as |x| log|x|. We show that the domain in L^{p}(R^{d}) is
the intersection of the Sobolev space W^{2,p}(R^{d}) and the
domain of the drift term, and that A generates a strongly continuous semigroup
on L^{p}(R^{d}). Our approach relies on a Dore-Venni type
theorem on sums of non commuting operators in L^{p}(R^{d}). The
description of the domain implies global regularity of the density of the
invariant measure of the corresponding transition probabilities (if the measure
exists), i.e., the density belongs to W^{2,q}(R^{d}) for all
finite q.

**Anders Olofsson, ** Falugatan 22 1tr, SE-113 32 Stockholm, Sweden
(anderso@math.su.se).

An inequality for sums of
subharmonic and superharmonic functions, pp. 577-588.

ABSTRACT.
We prove a general inequality for the distributional Laplacian of a sum of a
subharmonic and a superharmonic function postcomposed with a convex function of
linear growth. We use this inequality to show that convex functions of linear
growth operate by means of postcomposition on the class of sums of subharmonic
and superharmonic functions.

**Zhihua Chen, ** Department of Mathematics, Tongji University,
Shanghai, P.R. China (zzzhhc@tongji.edu.cn) and **Min Ru, **
Department of Mathematics, University of Houston, Houston, TX 77204-3476, USA
(minru@math.uh.edu).

A uniqueness theorem for moving targets
with truncated multiplicities, pp. 589-601.

ABSTRACT.
After Nevanlinna's result that any two non-constant meromorphic functions f and
g sharing the same inverse images (regardless of multiplicities) for five
distinct values must be equal, H. Cartan declared that there are at most two
meromorphic functions on C which have the same inverse images regardless of
multiplicities. Although Cartan's proof contained a gap, Cartan's declaration is
true if one assumes that meromorphic functions share four distinct values
counted with multiplicities truncated by 2. In 1998, H. Fujimoto extended such a
restricted Cartan's declaration to the case of holomorphic curves sharing
hyperplanes in a n-dimensional projective space. This paper generalizes
Fujimoto's result to the moving targets.

**Robert J. McCann, ** Department of Mathematics, University of
Toronto, Toronto, Ontario, Canada M5S 3G3 (mccann@math.toronto.edu).

Stable rotating binary stars and
fluid in a tube, pp. 603-631.

ABSTRACT.
This paper considers compressible fluid models for a Newtonian rotating star.
For fixed mass and large angular momentum, stable solutions to the associated
Navier-Stokes-Poisson system are constructed in the form of slow, uniformly
rotating binary stars with specified mass ratio. The variational method employed
was suggested by Elliott Lieb; it predicts uniform rotation as a consequence
rather than an assumption. The density profiles of the solutions are local
energy minimizers in the Wasserstein L-infinity metric; no global energy minimum
can be achieved. A one-dimensional toy model admitting explicit solution is also
introduced which caricatures the situation: to any specified number of
components and their masses corresponds a single family of solutions,
parameterized by angular velocity up to the point of equatorial break-up; here
the equilibrium model breaks down as the atmosphere of the lightest star in the
system begins to drift into space.