*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

**De Vivo, Clorinda** and **Metelli, Claudia **,
Dipartimento di Matematica e Applicazioni, Università Federico II di Napoli,
80126 Napoli, Italy
(clorinda.devivo@dma.unina.it),
(cmetelli@math.unipd.it).

On degenerate *B*^{(2)}-groups,
pp. 633-649.

ABSTRACT.
We examine a class of *B*^{(2)}-groups where types of elements are
still determined by partitions. An algorithm is given to determine whether a
degenerate *B*^{(2)}-group which is a direct sum of two strongly
indecomposable *B*^{(1)}-groups is itself a regular *B*^{(1)}-group.

**Enochs, Edgar,** University of Kentucky at Lexington, Kentucky, KY
40506-0027 (enochs@ms.uky.edu) and
**Estrada, Sergio, **Universidad de Murcia, Campus del Espinardo, Murcia
(SPAIN), 30100
(sestrada@um.es), and **García-Rozas,
J.R.,** University of Almería at Almeria, Almeria (SPAIN), 04071
(jrgrozas@ual.es).

Galois and coGalois groups
associated with cotorsion theories, pp. 651-663.

ABSTRACT.
The notion of a coGalois group of a torsion free cover was introduced in E.
Enochs, J.R. García Rozas, O.M.G. Jenda and L. Oyonarte. Compact coGalois
groups. Math. Proc. Cambridge Phil. Soc. (2) 128 (2000), 233-244. But the notion
of such a group makes sense whenever we have some sort of a cover. And then the
dual notion of a Galois group makes sense when we have an envelope. Covers and
envelopes occur whenever we have a perfect cotorsion theory. In such a cotorsion
theory we have two orthogonal classes. We argue that in this situation there is
a natural way to relate coGalois (or Galois) groups of an object to such a group
for an object in the orthogonal class. Our main application is the traditional
case of a cotorsion theory but over a Dedekind domain. In this case the
orthogonal classes are the torsion free and the cotorsion modules. We show that
here we have the stronger result that every coGalois group (or Galois group)
occurs as that associated with a cotorsion module which has no nonzero torsion
free divisible submodules. We then briefly indicate how this result can be used
to study these coGalois groups.

**Feng Wei,** Department of Applied Mathematics, Beijing Institute of
Technology, Beijing 100081, People's Republic of China
(daoshuo@bit.edu.cn).

*-Generalized Differential Identities
of Semiprime Rings with Involution,
pp. 665-681.

ABSTRACT.
The main purpose of this paper is to consider the *-generalized differential
identities of semiprime ring with involution * of positive characteristic. On
the one hand, we extend certain results concerning derivations to the context of
generalized derivations. On the other hand, we generalize some existing results
on prime rings to the case of semiprime rings

**Behrooz Khosravi,** Dept. of Pure Math., Faculty of Math. and Computer
Sci., Amirkabir University of Technology (Tehran Polytechnic), 424, Hafez
Ave., Tehran 15914, IRAN and Institute for Studies in Theoretical Physics
and Mathematics (IPM), **
Bahman Khosravi,** and **Behnam Khosravi, **Dept. of Math., Faculty of
Math. Sci., Shahid Beheshti Univ., Evin, Tehran, 19838, IRAN
(khosravibbb@yahoo.com) .

Characterizability of PSL(p+1,q)
by its order component(s), pp. 683-700.

ABSTRACT.
The prime graph of a group is the graph whose vertex set is the prime
divisors of the order of G and two distinct primes p and q are joined by an
edge if and only if G contains an element of order pq. Then the order of
every finite group G can be expressed as a product of coprime positive
integers m_{1},...,m_{t} such that the set of prime divisors
of m_{i} is a connected component of the prime graph of G. The
integers m_{1},...,m_{t} are called the order components of
G. Order components of a finite group are introduced in Chen (J. Algebra 185
(1996) 184). It was proved that PSL(3,q), where q is an odd prime power, is
uniquely determined by its order components (J. Pure and Applied Algebra
(2002)). Also in Iranmanesh and et al. (Acta Math. Sinica, English Series
(2002)) and (Bull. Austral. Math. Soc. (2002)) it was proved that PSL(3,q)
for q=2^{n} and PSL(5,q) are uniquely determined by their order
components. Also it was proved that PSL(p,q) is uniquely determined by its
order components (Comm. Algebra (2004)). In this paper we discuss the
characterizability of PSL(p+1,q) by its order component(s), where p is an
odd prime number. In fact we prove that PSL(p+1,q) is uniquely determined by
its order component(s) if and only if (q-1)|(p+1). A main consequence of our
results is the validity of Thompson's conjecture for the groups PSL(p+1,q)
where (q-1)|(p+1).

**Yang, Jae-Hyun,** Inha University, Incheon 402-751, Republic of Korea
(jhyang@inha.ac.kr).

A note on a fundamental domain for
Siegel-Jacobi space, pp. 701-712.

ABSTRACT.
We find a fundamental domain for the Siegel-Jacobi space and present Riemannian
metrics on the Siegel-Jacobi space invariant under the natural action of the
Jacobi group. We also investigate the spectral theory of the Laplacian on the
abelian variety associated to a point in the moduli space of principally
polarized abelian varieties.

**Cole, Daniel R., **Department of Mathematics -- MS 136, Rice University,
6100 S. Main St., Houston, TX 70005, USA
(dcole@math.rice.edu)
** **and** Pauls, Scott D., **Department of Mathematics, 6188 Bradley
Hall, Dartmouth College, Hanover, NH 03755, USA (scott.pauls@dartmouth.edu).

*C** ^{1}*
Hypersurfaces of the Heisenberg Group are N-rectifiable, pp. 713-724.

ABSTRACT. For the standard three-dimensional Heisenberg group

**Tojeiro, Ruy,** Universidade Federal de São Carlos, 13565-905 São
Carlos, Brazil (tojeiro@dm.ufscar.br).

Conformal de Rham decomposition of
Riemannian manifolds, pp. 725-743.

ABSTRACT. We prove conformal versions of the local
decomposition theorems of de Rham and Hiepko of a Riemannian manifold as
aRiemannian or a warped product of Riemannian manifolds. Namely, we give
necessary and sufficient conditions for a Riemannian manifold to be locally
conformal to either a Riemannian or a warped product. We also obtain other
related de Rham-type decomposition theorems. As an application, we study
Riemannian manifolds that admit a Codazzi tensor with exactly two distinct
eigenvalues everywhere.

**Charatonik, Janusz J., **deceased July 11, 2004 and **Illanes,
Alejandro,** Universidad Nacional Autonoma de Mexico, 04510, Mexico, D.F. (illanes@matem.unam.mx).

N-Sequences and
Contractibility in Hyperspaces, pp. 745-756.

ABSTRACT. The existence of an N-sequence in a continuum
is an obstruction that implies noncontractibility of the continuum. The aim of
the present paper is to show that the existence of an N-sequence in the
continuum X does not imply noncontractibility of some hyperspaces of X.

**Gary Gruenhage,** Department of Mathematics and Statistics, Auburn
University, Auburn, AL 36849}
(garyg@auburn.edu).

Products of cozero complemented
spaces, pp. 757-773.

ABSTRACT.
We answer several questions of Levy and Shapiro, and Henriksen and Woods, on
products of cozero complemented spaces. Among other things, we show that the
product of a cozero complemented space with a metrizable space need not be
cozero complemented unless the metrizable factor is separable, the product of a
non-cozero complemented space and a metrizable space can be cozero complemented,
the product of a cozero complemented space and a countable regular space need
not be cozero complemented, and that it is consistent that the product of two
compact spaces satisfying the countable chain condition need not be cozero
complemented.

**Lisan, Amha T.,** Louisiana State University, Baton Rouge, LA 70803 (lisan@math.lsu.edu).

Quasifactors, proximal extensions and
other structures of nondiscrete minimal flows, pp. 775-782.

ABSTRACT.
The classical theory of dynamical systems arose in the context of the study of
differential equations. In recent years the study of these systems has been
extended beyond discrete or continuous (real) phase groups or semigroups to the
theory of flows of more general topological groups or semigroups. Let S be a
semitopological semigroup, not necessarily discrete. An action of S on a compact
phase space can then be extended to a compactification associated to the space
of left norm continuous functions on S such that all minimal flows are flow
isomorphic to quotients of this compactification. Furthermore we can associate a
subgroup of the maximal group to each minimal flow.

**Veronica Martinez-de-la-Vega,** Instituto de Matematicas, Universidad
Nacional Autonoma de Mexico, Ciudad Universitaria, Mexico D.F. 04510 and
California State

University at Sacramento (vmvm@matem.unam.mx).

Dimension of n-fold Hyperspaces of
Graphs, pp. 783-799.

ABSTRACT. Given a finite graph X, the n-fold hyperspace of
X, Cn(X)={A: A is closed, nonempty and has at most n components}. For n=1 C1(X)
is denoted by C(X). On 1968 Duda showed formulas to compute dim[C(X)] and for
each element A of C(X) he showed how to compute dim A [C(X)]. In this paper we
prove that dim[Cn(X)]=2n+dim[C(X)] and for every element A of Cn(X), where A has
k components, A=A1( ...( Ak, then dim A [Cn(X)]=2(n-k)+(i dim Ai [C(X)] where
i({1,...,k}.

As a consequence of this formulas we prove that for any natural number n, the
n-fold hyperspace of a finite graph (different from a simple closed curve) is a
cone if and only if X is an arc or a simple k-od

**Bennett, Grahame, **
Department of Mathematics, Indiana University, Bloomington, Indiana 47405,
U.S.A. (bennettg@indiana.edu).

Sums of Powers and the Meaning of *
l*^{p}, pp. 801-831.

ABSTRACT.
The sequence (1^{α}+2^{α}+ ... + n^{α})/(n^{α})(n=1,2,...)
is convex, or concave, no matter what the value of α in *R *is. There are
applications to Sums of Powers and to the classical inequalities of Carleman,
Copson, Hardy and Knopp.

**Cabrelli, Carlos, ** Universidad de Buenos Aires, Argentina
(cabrelli@dm.uba.ar)
and
**Lacey, M.T.** Georgia Institute of Technology, Atlanta GA 30332
(lacey@math.gatech.edu)
and
** Molter, Ursula, ** Universidad de Buenos Aires, Argentina
(umolter@dm.uba.ar)
and
** Pipher, Jill, ** Brown University, Providence RI 02912
(jpipher@math.brown.edu)

Variations on a Theme of Journé's
Lemma , pp. 833-861.

ABSTRACT.
Journé's Lemma ("A covering lemma for product spaces," Proc. Amer. Math. Soc.,
Vol. 96, (1986), pp 593-598) is a critical component of many questions related
to the product BMO theory of S.-Y. Chang and R. Fefferman. This article presents
several different variants of the Lemma, in two and higher parameters, some
known, some implicit in the literature, and some new.

**Mijoung Kim, **National Institute for Mathematical Sciences, 52 Eoeun-dong,
Yuseong-Gu, Daejeon 305-333, South Korea (mijoungtamu@hotmail.com).**
**
Local regularity of the
∂-Neumann operator, pp.
863-869.

ABSTRACT. Using the vector field method, we find a more general condition than finite type that implies a local regularity result for the ∂-Neumann operator. In our result, it is possible for an analytic disk to be on the part of the boundary where we have local regularity.

**B.S. Yadav,** TU-67 Vishakha Enclave, Pitam Pura, Delhi 110088
(bsyadav@indianshm.com).

Systems of N-variable weighted
shifts as universal operators and their invariant subspaces, pp. 871-894.

ABSTRACT.
Systems of N-variable weighted shifts as introduced by N.P. Jewell and A.R.
Lubin are examined a s universal operators in the sense of G.-C Rota with
suitable conditions on the weight net. Also, results on the existence of cyclic
vectors and characterisation of invariant subspace lattices of systems of
N-variable weighted backward and forward shifts are obtained.

Fabrizio Colombo, Dipartimento di
Matematica Politecnico di Milano, Via Bonardi n. 9 ,

20133 Milano, Italy,
(fabcol@mate.polimi.it), and
Alberto Damiano,
MUUK, Sokolovska 83, 186 75 Praha
8, Ceska Republika
(damiano@karlin.mff.cuni.cz).

Identification of the memory kernel
and the heat source for a phase--field model, pp. 895-920.

ABSTRACT.
We prove an existence and uniqueness result for an inverse problem arising from
a for a phase--field system with thermal memory. We identify the convolution
memory kernel and the heat source besides the temperature and the phase--field
parameter. We prove our results in the framework of the Holder continuous
functions spaces with values in a Banach space X. We apply the abstract results
in the case the space X is the space of continuous functions.

**Le, Vy Khoi,** University of Missouri - Rolla,
Rolla, MO 65409 (vy@umr.edu).

Some existence and bifurcation results
for quasilinear elliptic equations with slowly growing principal operators,
pp. 921-943.

ABSTRACT. The paper is about a boundary value problem,
containing a second order elliptic operator, in which the principal term has
very slow growth.We show the Rabinowitz alternative for global bifurcation and
also some existence results by a topological approach. Due to the lack of
coercivity, new arguments and techniques are needed.

**Yan Xu,** Nanjing Normal University, Nanjing 210097, P. R. China
(xuyan@njnu.edu.cn).

Normality Criterion Concerning Sharing
Functions, pp. 945-954.

ABSTRACT.
Let * F* be a family of meromorphic functions in a domain

**Yan Xu,** Nanjing Normal University, Nanjing 210097, P. R. China
(xuyan@njnu.edu.cn).

A note on a result of Pang and Zalcman,
pp. 955-959.

ABSTRACT.
Let * F* be a family of meromorphic functions in a domain