*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), Min Ru (Houston), S.W. Semmes (Rice)

*Managing Editor*: K. Kaiser (Houston)

Houston Journal of Mathematics

**D.D. Anderson** and **John S. Kintzinger**,
Department of Mathematics, The University of Iowa, Iowa City, Iowa 52242
(dan-anderson@uiowa.edu),
(JohnSKintzinger@netscape.net.

General ZPI-rings without
Identity, pp. 631-634.

ABSTRACT.
Abstract - General ZPI-rings without IdentityLet R be a commutative ring not
necessarily having an identity. Then R is a general ZPI-ring if every ideal
of R is a product of prime ideals. S. Mori showed that a general ZPI-ring
without identity is either (1) an integral domain, (2) a ring R where every
ideal of R including 0 is a power of R, (3) K times R where K is a field and
R is a ring as in (2), or (4) K times D where K is a field and D is a domain
with every nonzero ideal of D a power of D. The purpose of this paper is to
prove that if R is a ring as in (2), then there is an SPIR S with S=R[1]
having R as its maximal ideal. Moreover, there is a complete DVR (D,(p))
with D=(p)[1] so that S and R are homomorphic images of D and (p),
respectively.

**Chatham, R. Douglas, **Department of Mathematics and Computer Science,
Morehead State University, Morehead, KY 40351
(d.chatham@moreheadstate.edu)
and **Dobbs, David E., **University of Tennessee, Knoxville, TN 37996
(dobbs@math.utk.edu).

Pairs of commutative rings
in which all intermediate rings have the same dimension, pp. 635-647.

ABSTRACT. If n is a nonnegative integer or infinity,
and R is a (commutative unital) ring contained in a (commutative unital) ring T,
then (R,T) is said to be an n-dimensional pair if every ring S that both
contains R and is contained in T has Krull dimension n. For n greater than zero,
examples are given of n-dimensional pairs that are not integral extensions,
including an infinite family of examples that are neither LO-pairs nor
INC-pairs. The n-dimensional pair property transfers well in constructions
involving pullbacks or passage to the associated reduced rings, but this
property is not stable under passage to factor domains. Special attention is
paid to the n-dimensional pairs whose first coordinate is a Jaffard domain or a
residually Jaffard ring. Also, examples are given of infinity-dimensional pairs
whose intermediate rings have prime ideal chains of arbitrarily large
cardinality; and of a family of n-dimensional pairs arising from minimal
overrings.

**Ko, Seokku,** Konkuk University, Chungjusi Chungbuk Korea 380-701
(seokko@kku.ac.kr).

Embedding Bordered Riemann Surfaces in
4-dimensional Riemannian Manifolds, pp. 649-661.

ABSTRACT. Any bordered Riemann surface has a conformal
model in any orientable Riemannian manifold of dimension 4. Precisely, we
prove that, given any bordered Riemann surface S0, there is a conformally
equivalent model in a prespecified orientable 4-dimensional Riemannian
manifold. A model can be constructed by deforming a compactification surface
of the given topologically equivalent complete Riemann surface S in the
normal direction. This result along with previous Ko Embedding theorem(see
"Embedding bordered Riemann surfaces in Riemannian Manifolds", Journal of
Korean Mathematical Society, Vol. 30. no. 2, 1993) now shows that a bordered
Riemann surface admits conformal models in any Riemannian manifold of
dimension greater than or equal to 3.

**Houston, Kevin,** School of Mathematics, University of Leeds, Leeds, LS2
9JT, U.K. (k.houston@leeds.ac.uk).

Disentanglements and Whitney
equisingularity, pp. 663-681.

ABSTRACT.
A classical theorem of Briançon, Speder and Teissier states that a family of
isolated hypersurface singularities is Whitney equisingular if, and only if,
the mu*-sequence for a hypersurface is constant in the family. This paper
shows that similar results are true for families of finitely A-determined
map-germs from Cn to C3, where n=2 or 3. Rather than the Milnor fibre we use
the disentanglement of a map, and since a disentanglement can be viewed as a
section of a stable discriminant we can apply Damon's theory which defines
an analogue of the mu*-sequence. The constancy of this sequence is
equivalent to Whitney equisingularity of the family in the n=2 case. For the
other case it is shown, using extra information, that the image of the
family is Whitney equisingular.

**Qun He,** Department of Applied Mathematics, Tongji University, Shanghai
200092, China
(hequn@mail.tongji.edu.cn) and **Yi-Bing Shen**, Department of
Mathematics, Zhejiang University, Hangzhou 310028, China
(yibingshen@zju.edu.cn).

Some properties of harmonic maps for
Finsler manifolds, pp. 683-699.

ABSTRACT.
This paper is to study further some properties of harmonic maps between
Finsler manifolds. Some rigidity theorems for harmonic maps between Finsler
manifolds are given. By introducing the stress-energy tensor of maps between
Finsler manifolds, some integral formulas are obtained. Moreover, it is proved
that any conformal strongly harmonic map from an n(>2)-dimensional Finsler
manifold to a Finsler manifold must be homothetic.

**Rezsõ L. Lovas,** Institute of Mathematics, University of Debrecen H--4010
Debrecen, P.O.B. 12, Hungary
(lovasr@math.klte.hu).

A note on Finsler-Minkowski norms,
pp. 701-707.

ABSTRACT.
By a Finsler--Minkowski norm, we mean a function on a real vector space which is
positively homogeneous and positive on the non-zero vectors. We suppose that its
metric tensor, i.e., the second derivative of its square is non-degenerate. Then
we show that it is automatically positive definite.

The main idea of the proof is as follows. We suppose, without loss of
generality, that our vector space is a Euclidean n-space. The unit sphere is a
compact hypersurface, and therefore it has a point, the furthermost one from the
origin, in which all the n-1 principal curvatures have the same sign. Finally,
we establish a relation between the signs of these principal curvatures and the
signature of the metric tensor.

**Wladimir G. Boskoff,** Department of Mathematics and Computer Science,
Ovidius University, Constanţa, 900527, Romania
(boskoff@univ-ovidius.ro), **
Marian G. Ciucă**, Department of Mathematics and Computer Science, Ovidius
University, Constanţa, Romania
(mgciuca@univ-ovidius.ro) and **Bogdan D. Suceavă,** Department of
Mathematics, California State University, Fullerton, CA 92834-6850, U.S.A.
(bsuceava@fullerton.edu).

Distances induced by Barbilian's
metrization procedure, pp. 709-717.

ABSTRACT. Several authors have pointed out the
connection between Barbilian's metric introduced in 1934 and the recent study of
Apollonian metrics. We provide examples of various distances that can be
obtained by Barbilian's metrization procedure and we discuss the relation
between this metrization procedure and important Riemannian and generalized
Lagrangian metrics. Then we prove an extension of Barbilian's metrization
procedure.

Volumes of principal orbits of isotropy subgroups in compact symmetric spaces, pp. 719-734.

ABSTRACT. Let (G,K) be a Riemannian symmetric pair of compact type such that G is simply connected. Take the compact Riemannian symmetric space G/K and the natural isometric action of the isotropy subgroup K on G/K. In this paper, we discuss the problem how to compute the volumes of the principal orbits in explicit form and how to find the unique principal orbit of maximal volume. Moreover, we study this problem in detail in some rank two irreducible symmetric spaces with different restricted root systems.

**Takamitsu Yamauchi, **Department of Mathematics, Shimane University,
Matsue, 690-8504, Japan
(t_yamauchi@riko.shimane-u.ac.jp).

A characterization of metrizable
finitistic spaces and its applications to upper semicontinuous set-valued
selections, pp. 735-751.

ABSTRACT. In this paper, we give two types of
characterizations of finitistic spaces. One is in terms of perfect mappings from
zero-dimensional metric spaces, which is analogous to K. Morita's
characterization of finite-dimensional metrizable spaces. Another is by means of
upper semicontinuous set-valued selections, which is an analogue of M. M.
Čoban's characterization of finite-dimensional paracompact spaces.
Characterizations of some classes of infinite-dimensional spaces and a
generalization of finitistic spaces will also be given.

**Gerardo Acosta,** Instituto de Matematicas, Circuito Exterior, Ciudad
Universitaria, Area de la Investigacion Cientifica, Mexico, D.F. 04510, Mexico
(gacosta@matem.unam.mx) and **Peyman
Eslami,** Department of Mathematics, University of Alabama at Birmingham,
Birmingham, AL 35294
(peslami@math.uab.edu), and Lex G.
Oversteegen Department of Mathematics, University of Alabama at Birmingham,
Birmingham, AL 35294
(overstee@math.uab.edu).

On open maps between dendrites,
pp. 753-770.

ABSTRACT. In this paper we
mainly present two results, one dynamical and one topological, about open
mappings between dendrites. The dynamical result states that if f is a
homeomorphism from a dendrite X onto itself, then the omega limit set of any
point of X is either a periodic orbit or a Cantor set. In the latter case, the
restriction of f to this omega limit set is an adding machine. The topological
result states that if f is an open map from a dendrite X onto a dendrite Y, then
there exists n subcontinua X_{1}, X_{2}, ..., X_{n} of X
such that X is the union of them, the intersection of any two of those
subcontinua contains at most one element which is a critical point of f and the
restriction of f to any set X_{i} is an open map from X_{i} onto
Y that can be lifted, in a natural way, to a product space Z_{i} x Y,
for some compact and zero-dimensional space Z_{i}

**Guo****-Fang
Zhang**, Department of
Mathematics, Nanjing University, Nanjing 210093, China (tuopmath@nju.edu.cn)
and **Wei-Xue**** Shi,** Department of
Mathematics, Nanjing University, Nanjing 210093, China (wxshi@nju.edu.cn).

Characterizations of relative
paracompactness by relative normality of product spaces, pp. 771-779.

ABSTRACT. In this paper, we mainly study the relative
version of Tamano Theorem and give some characterizations of relative
paracompactness in terms of relative normality of products of paracompact spaces
and compact spaces, which gives an answer to a problem posed by Arhangel'skii in
2002.

A new bound on the cardinality of power homogeneous compacta, pp. 781-793.

ABSTRACT. It was recently proved by R. de la Vega that if X is a homogeneous compactum then the cardinality of X is bounded by 2

**David
Herrera Carrasco, **Facultad de Ciencias Físico-Matemáticas de

Dendrites with unique hyperspace,
pp. 795-805.

ABSTRACT. For a metric continuum X
let C(X) denote the hyperspace of subcontinua of X. The continuum X is said to
have unique hyperspace of subcontinua provided that if Y is a continuum and C(X)
is homeomorphic to C(Y), then X is homeomorphic to Y. We show in this paper the
following: A dendrite which is not an arc has unique hyperspace of subcontinua
if its set of end points is closed.

**Granda, Larry M., **Department of Mathematics, St. Louis University, St.
Louis, MO 63103
(grandalm@slu.edu).

Representing homology classes of a
surface by disjoint curves, pp. 807-813.

ABSTRACT. Conditions are given for
when a collection of homology classes of a closed oriented surface of genus *g*
may be represented by a collection of pairwise disjoint simple closed curves.

**Park, Chun-Gil, **Department of Mathematics, Chungnam National
University, Daejeon 305-764, South Korea
(cgpark@cnu.ac.kr).

Automorphisms on a C*-algebra and
isomorphisms between Lie JC*-algebras associated with a generalized additive
mapping, pp. 815-837.

ABSTRACT.It is shown that if an odd mapping
satisfies a generalized additive functional equation, then the odd mapping
is Cauchy additive, and we prove the Cauchy-Rassias stability of linear
mappings in Banach modules over a unital C*-algebra for the generalized
additive functional equation. As an application, we show that every almost
linear bijective mapping on a unital C*-algebra is an automorphism under
some conditions, and that every almost linear bijective mapping of a unital
Lie JC*-algebra onto a unital Lie JC*-algebra is a Lie JC*-algebra
isomorphism under some conditions.

**Defant, Andreas, **University of Oldenburg, D-26111, Oldenburg, Germany
(defant@mathematik.uni-oldenburg.de),
**García, Domingo, ** Universidad

de Valencia, 46100 Burjasot (Valencia), Spain (domingo.garcia@uv.es),
**Maestre, Manuel, ** Universidad de Valencia, 46100 Burjasot
(Valencia), Spain (manuel.maestre@uv.es),
and **Pérez-García, David, **Universidad Rey Juan Carlos, 28933 Móstoles
(Madrid), Spain (david.perez.garcia@urjc.es).

Extension of multilinear forms and
polynomials from subspaces of L1-spaces, pp. 839-860.

ABSTRACT. Let X be a Banach space which has an
unconditional basis and is a subspace of some * L*_{1}*-space*_{
}Y. We show that X=*l*_{1} if and only if every
m-linear form S on X, has an m-linear extension T to Y satisfying that ||T||
is less than or equal to C^{m} ||S||, where C > 0 is a
constant independent of m. If we replace m-linear forms by m-homogeneous
polynomials, then we can only show that X is ``close'' to *l*_{1}.

**Hopenwasser, Alan,**
University of Alabama, Tuscaloosa, AL 35487 (ahopenwa@bama.ua.edu).

Partial
crossed product presentations for O_{n} and M_{k}(O_{n})
using amenable groups, pp. 861-876.

ABSTRACT. The Cuntz algebra O_{n }is
presented as a partial crossed product in which an amenable group partially acts
on an abelian C*-algebra. The partial action is related to the Cuntz groupoid
for O_{n} and connections are made with non-self-adjoint subalgebras of
O_{n}, particularly the Volterra nest subalgebra. These ideas are also
extended to the context of matrix algebras M_{k}(O_{n}) over the
Cuntz algebra.

**Dutkay, Dorin**** E.,**
University of Central Florida, Department of Mathematics, 4000 Central
Florida Blvd, PO Box 161364, Orlando, FL 32816-1364, USA
(ddutkay@mail.ucf.edu)
and **Jorgensen, Palle E. T.,** The University of Iowa, Department of
Mathematics, Iowa City, IA 52242-1419, USA
(palle-jorgensen@uiowa.edu).

Harmonic analysis and dynamics
for affine iterated function systems, pp. 877-905.

ABSTRACT.
We introduce a harmonic analysis for a class of affine iteration models in
finite dimensions. Our results use Hilbert-space geometry, and we develop a
new duality notion for affine and contractive iterated function systems
(IFSs). Our applications include some new identities for the Fourier
transform of the measures arising from infinite Bernoulli convolutions.

**Amir Khosravi, **Faculty of Mathematical Sciences and Computer Engineering,
University For Teacher Education, 599 Taleghani Ave., Tehran 15614, Iran,
(khosravi_amir@yahoo.com)and
**Mohammad Sadegh Asgari, **Dept. of Math., Science and Research Branch,
Islamic Azad University, Tehran, Iran
(msasgari@yahoo.com).

Frames of subspaces and
approximation of the inverse frame operator,
pp. 907-920.

ABSTRACT. A frame of subspaces in a Hilbert space H allows
that identity operator on H to be written as a sum of some bounded operators on
H. This family of bounded operators on H is called an atomic resolution of the
identity on H. We show the atomic resolution of the identity associated to a
frame of subspaces have a certain minimum property relative to its associated
norm. We further show that under extra condition every atomic resolution of the
identity provides a frame of subspaces for H. We consider direct sum of frames
of subspaces with respect to the same family of weights which is a frame of
subspaces for their direct sum space. Frame theory of subspaces describes how
one can choose the corresponding atomic resolution of the identity, which is
interesting from mathematical point of view, but for applications it is a
problem that requires to know the inverse frame operator S^{-1}_{W,v}
on H. If the underlying Hilbert space is infinite dimensional it is hard to
invert the frame operator S_{W,v}. We show how the inverse of S_{W,v}
can be approximated by using the methods of linear algebra.

**Gal, Nadia J.**, The University of Memphis, Department of Mathematical
Sciences, Memphis, TN 38152
(nadiagal@memphis.edu).

Isometric Equivalence of Differentiated
Composition Operators between Spaces of Analytic Functions,
pp. 921-926.

ABSTRACT. The differentiated composition operator on the Hardy space is
defined as the composition with an analytic self-map of the disk, followed by
differentiation. We consider the isometric equivalence problem of the
differentiated composition operator on Hardy and Bergman spaces. Using
Forrelli's form for the isometric isomorphism on the Hardy space, we obtain a
result similar to the result of R. C. Wright for the isometric equivalence
problem of composition operators on the Hardy space.

**A. C. Ponce**, Laboratoire de Mathématiques et Physique Théorique (UMR
CNRS 6083), Fédération Denis Poisson, Université François Rabelais, 37200 Tours
France (ponce@lmpt.univ-tours.fr)
and **J. Van Schaftingen, **Département de Mathématique, Université
catholique de Louvain, Chemin du Cyclotron 2, 1348 Louvain-la-Neuve, Belgium

(vanschaftingen@math.ucl.ac.be).

The continuity of functions with N-th
derivative measure,
pp. 927-939.

ABSTRACT. We study the continuity of functions *u*
whose mixed derivative ∂_{1}…∂_{N}*u* is a
measure. If *u* ∈ W^{1,1}(**R**^{N}),
then we prove that *u* is continuous. The same conclusion holds for *u*∈
W^{k,p}(*Q*), with *kp* > *N*-1, where *
Q* denotes a cube in **R**^{N}. The key step
in the proof consists in showing that the measure ∂_{1}…∂_{N}*u*
does not charge hyperplanes orthogonal to the coordinate axes.