*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

Uçkun, Mustafa,
University of İnönü , 44069
Malatya, Turkey (muckun@inonu.edu.tr)
and Öztürk,
Mehmet Ali, University of Cumhuriyet,
58140 Sivas, Turkey (maozturk@cumhuriyet.edu.tr).

On Trace of Symmetric
Bi-Gamma-Derivations in Gamma-Near-Rings, pp. 323-339.

ABSTRACT.
Let M be a 2-torsion free 3-prime left gamma-near-ring with multiplicative
center C. Let x be an element of M and C(x) the centralizer of x in M. The
aim of this paper is to study the trace of symmetric bi-gamma-derivations
(also symmetric bi-generalized gamma-derivations) on M. Main results are the
following theorems: Let D(.,.) be a non-zero symmetric bi-gamma-derivation
of M and F(.,.) a symmetric bi-additive mapping of M. Let d and f be traces
of D(.,.) and F(.,.), respectively. In this case (1) If d(M) is a subset of
C, then M is a commutative ring. (2) If d(y), d(y) + d(y) are elements of
C(D(x,z)) for all x, y, z in M, then M is a commutative ring. (3) If F(.,.)
is a non-zero symmetric bi-generalized gamma-derivation of M associated with
D(.,.) and f(M) is a subset of C, then M is a commutative ring. (4) If
F(.,.) is a non-zero symmetric bi-generalized gamma-derivation of M
associated with D(.,.) and f(y), f(y) + f(y) are elements of C(D(x,z)) for
all x, y, z in M, then M is a commutative ring.

**Weixing Chen, **Mathematics and Information
Science School, Shandong Institute of Business and Technology, Yantai 264005, P.
R. China (wxchen5888@163.com)
and **Wenting Tong****,
**Department of Mathematics, Nanjing University,
Nanjing 210093, P. R. China
(wttong@nju.edu.cn).

On skew Armendariz rings and
rigid rings, pp. 341-353.

ABSTRACT. In this paper we study skew Armendariz rings
and rigid rings, extending and improving some results of Hong et al. (2003) and
some known results on Armendariz rings. New families of skew Armendariz rings
are presented including the one in which the endomorphism is not monomorphic and
the ring is not reduced.

**Bezhanishvili, Guram ** and **Harding, John,** New Mexico State
University, Las Cruces, NM, USA 88003 (gbezhani@nmsu.edu),
(jharding@nmsu.edu).

MacNeille completions of modal
algebras, pp. 355-384.

ABSTRACT.
For a modal algebra (B,f), there are two natural ways to extend f to an
operation on the MacNeille completion of B. The resulting structures are
called the lower and upper MacNeille completions of (B,f). In this paper we
consider lower and upper MacNeille completions for various varieties of
modal algebras. In particular, we characterize the varieties of closure
algebras and diagonalizable algebras that are closed under lower and upper
MacNeille completions. We also introduce the variety of Sierpinski algebras,
and show that although this variety is not closed under lower or upper
MacNeille completions, it follows from the axiom of choice that each
Sierpinski algebra has a MacNeille completion that is also a Sierpinski
algebra, and that this result implies the Boolean ultrafilter theorem.

**Chang, Gyu Whan,** Department of Mathematics, University of Incheon,
Incheon 402-749, Korea
(whan@incheon.ac.kr).

Quasi-invertible prime t-ideals,
pp. 385-389.

ABSTRACT.
Let G be a group and let cent(G) denote the set of centralizers of single
elements of G. A group G is called n-centralizer if |cent(G)|=n. In this
paper, for a finite group G, we give some interesting relations between
|cent(G)| and the maximum number of the pairwise non-commuting elements in
G. Also we characterize all n-centralizer finite groups for n=7 and 8. Using
these results we prove that there is no finite group G with the property
that |cent(G)|=|cent(G/Z(G))|=8, where Z(G) denotes the centre of G. This
latter result answers positively a conjecture posed by A. R. Ashrafi.

**Padmanabhan, R.,**
Department of Mathematics, University of Manitoba, Winnipeg, Manitoba R3T
2N2, Canada (padman@cc.umanitoba.ca),
**McCune, W.,**
Mathematics and Computer Science Division, Argonne National Laboratory,
Argonne, Illinois 60439-4844, U.S.A.
(mccune@mcs.anl.gov)
and
**Veroff, R.,**
Department of Computer Science, University of New Mexico, Albuquerque, New
Mexico 87131, U.S.A. (veroff@cs.unm.edu).

Lattice laws forcing
distributivity under unique complementation., pp. 391-401.

ABSTRACT.
We give several new lattice identities valid in nonmodular lattices such that
a uniquely complemented lattice satisfying any of these identities is
necessarily Boolean. Since some of these identities are consequences of
modularity as well, these results generalize the classical result of Birkhoff
and von Neumann that every uniquely complemented modular lattice is Boolean. In
particular, every uniquely complemented lattice in M∨V(N_{5}),
the least nonmodular variety, is Boolean.

**Banks, William D., **Department of Mathematics, University of Missouri,
Columbia, MO 65211, USA
(bbanks@math.missouri.edu) and
**Luca, Florian, **Instituto de Matemáticas, Universidad Nacional
Autónoma de México, C.P. 58089, Morelia, Michoacán, México
(fluca@matmor.unam.mx).

Sums of prime divisors and Mersenne
numbers, pp. 403-413.

ABSTRACT.
In this note, we study those positive integers n with the property that the sum
of the distinct prime factors of n divides the n-th Mersenne number.

**Picozza, Giampaolo, **Dipartimento di Matematica, Università degli Studi
"Roma Tre", Roma, Italy
(picozza@mat.uniroma3.it).

A note on semistar Noetherian
domains , pp. 415-432.

ABSTRACT. We study semistar Noetherian domains, that
is, domains having the ascending chain condition on "quasi semistar ideals''.We
generalize several of the classical results that hold in Noetherian domains to
the case of semistar operations stable and of finite type, for instance, Cohen
Theorem, primary decomposition, principal ideal Theorem, Krull intersection
Theorem, etc. We do this mainly by using a method that allows one to transfer
properties already proved for star operations to the context of semistar
operations. Furthermore, an analogue of the Hilbert basis Theorem for semistar
Noetherian domain (with respect to stable semistar operations) is proved.

ABSTRACT. Group coalgebras and Hopf group coalgebras appeared in the work of Turaev [1] on homotopy quantum field theories. A purely algebraic study of Hopf group coalgebras was initiated by Virelizer [2], and then continued by Scaenepeel and Wang [3]. Virelizer laid the algebraic foundations and gave a generalized version of the Fundamental Theorem for Hopf group coalgebras, Wang introduced the notions of a group entwining structure and of a group coalgebra extension, and Scaenepeel proposed an alternative approach to Hopf group coalgebras and showed that Hopf group coalgebras are essentially Hopf algebras in a symmetric monoidal category. We asked what the weak bialgebras in this category would be. We have found an answer to this question by introducing weak Hopf group coalgebras. This paper is devoted to studying the generalizations of entwining structure and coalgebra Galois extension in the setting of weak semi-Hopf group coalgebras, and have obtained a relation between them, that is, a weak group coalgebra Galois extension can induce a unique compatible weak group entwining structure.

1. V.G. Turaev, Homopoty Field Theory In Dimension 3 And Crossed Group Categories, Preprint GT/0005291

2. Alexis Virelizer, Hopf Group Coalgebras, Journal of Pure And Applied Algebra, 171(2002):75-122

3. S.Wang, Group Entwining Structures And Group Coalgebra Galois Extensions, Comm. Algebra,32(9)(2004):3437-3457

**M. Crampin, **Department of Mathematical Physics and Astronomy, Ghent
University, Krijgslaan 281, B-9000 Gent, Belgium and Department of Mathematics,
King's College,

Strand, London WC2R 2LS, UK
(Crampin@btinternet.com).

Isotropic and R-flat sprays,
pp. 451-459.

ABSTRACT.
It is shown that in dimension greater than 2 a spray is isotropic if and only if
it is locally projectively R-flat.

**Bang-Yen Chen**, Department of Mathematics, Michigan State University, East
Lansing, MI 48824-1029, U.S.A. (bychen@math.msu.edu.

Tension field, iterated Laplacian,
type number and Gauss maps, pp. 461-481.

ABSTRACT.
Let M be a Riemannian manifold. By applying the finite type theory we study maps
from M into a Euclidean space whose tension field is an eigenmap of a p-iterated
Laplacian for some natural number p. First, we prove that such maps are either
of 1-type, of null 2-type, or of infinite type. Several examples are then given
to illustrate that this result is sharp. Some applications of this result are
also presented. The simplest examples of maps whose tension field is an eigenmap
of an iterated Laplacian are those which have constant tension field. Next, we
study hypersurfaces whose (classical or spherical) Gauss map has constant
tension field. Finally, we prove that every spherical hypersurface with 2-type
spherical Gauss map must have non-constant mean curvature.

**
Ralph D. Kopperman**,
Department of Mathematics, City College of New
York, CUNY, New York, NY 10031, U. S. A. (rdkcc@ccny.cuny.edu)
and **Richard 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).

Separation and connectedness in
spectral compactifications, pp. 483-497.

ABSTRACT. We continue the study of the relationship
between properties of an inverse spectrum and those of the inverse limit and
selected subspaces of its minimal points. It is shown that limits of inverse
spectra of joincompact spaces with pairwise continuous bonding maps are
connected if and only if the spaces are connected. Since finite T_{1}-spaces
are discrete, there are not enough finite spaces with higher separation
properties to obtain the infinite spaces with these properties as limits of
inverse systems of such finite spaces.

We show that many higher separation properties of the space of minimal points of
the inverse limit result from conditions imposed on the bonding maps. This
relationship is studied for the separation properties T_{1}, regularity,
complete regularity, normality and hereditary normality.

A tree-like continuum whose cone admits a fixed-point-free map, pp. 499-518.

ABSTRACT. In this paper we prove that the cone over the continuum which is the union of a simple triod and a spiral surrounding it does not have the fixed point property.

**Antonyan, Natella,** Instituto Tecnológico y de Estudios Superiores de
Monterrey, Campus Ciudad de México, 14380 México D.F., México
(nantonya@itesm.mx).

An intrinsic characterization of
G-pseudocompact spaces, pp. 519-530.

ABSTRACT.
For any locally compact Hausdorff group G we give, in the realm of G-normal
spaces, an intrinsic characterization of G-pseudocompact spaces. On this way we
prove also an equivariant quantitative version of the well known Urysohn's
Lemma.

**Yajima, Yukinobu,** Kanagawa University, Yokohama 221-8686, Japan
(yajimy01@kanagawa-u.ac.jp).

Strong beta-spaces and their
countable products, pp. 531-540.

ABSTRACT.
We introduce a new concept called "strong beta-spaces". Strong beta-spaces are
beta-spaces. Semi-stratifiable spaces, strong Sigma-spaces and strict p-spaces
are all strong beta-space. Thus, the class of strong beta-spaces is well located
in the classes of generalized metric spaces. This class does not coincide with
the class of beta-spaces, but they coincide under the condition of
paracompactness. As a merit of the class of strong beta-spaces, we show that it
is countably productive. Moreover, it is shown that the class of normal strong
beta-spaces (or paracompact beta-spaces) is countably productive if it is
finitely productive.

**Henrik Petersson,** Chalmers/Göteborg University, School of
Mathematical Sciences SE-412 96 Göteborg, Sweden
(henripet@math.chalmers.se).

Complemented hypercyclic
subspaces, pp. 541-553.

ABSTRACT. A sequence T=(T_{n})
of continuous linear operators T_{n}
acting on a space X, is said to be
hypercyclic if there is a vector x,
called hypercyclic for T, such that (T_{n}x)
forms a dense set. A hypercyclic subspace for
T is an infinite dimensional closed
subspace of X formed by, except for
zero, hypercyclic vectors (for T). We
establish a criterion for a sequence T
of operators, acting on a separable Frechet space with a continuous
norm, to have a complemented hypercyclic subspace. Our result complements
previous results by several authors. _{
}

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

Meaningful sequences, pp.
555-580.

ABSTRACT.
The fundamental Theorem on Means suggests many new elementary inequalities,
yet it offers no hint at all for proving them. Our aim here is to explore
this gap.

**Bernal-Gonzalez, Luis,**
Dept. Analisis Matematico, Apdo.41080 Sevilla, Spain
(lbernal@us.es), **
Calderon-Moreno, Maria del Carmen,** Dept. Analisis Matematico, Apdo.41080
Sevilla, Spain (mccm@us.es) and **Bonilla,
Antonio,** Dept. Analisis Matematico, Apdo.38271 La Laguna,
Tenerife, Spain
(abonilla@ull.es).

Compositional hypercyclicity equals supercyclicity, pp. 581-591.

ABSTRACT. In this note it is proved that the sequence of
composition operators generated by automorphisms of a simply connected domain
strictly contained in the complex plane is hypercyclic (that is, possesses some
dense orbit) if and only if it is supercyclic (i.e., possesses some dense
projective orbit). When the domain is the full complex plane, a result in this
direction is also obtained. In addition, a number of statements about the
corresponding cyclicity properties of single composition

**Selby, Christina**, Department of Mathematics, Purdue University, West
Lafayette, IN 47907
(cselby@math.purdue.edu).

An extension and trace theorem for
functions of H-bounded variation in Carnot Groups of step 2,
pp. 593-616.

ABSTRACT.
This paper provides an extension of a function u in BV_{H} (Ω) to a
function u_{0} in BV_{H}(G), when Ω is *H-admissible* and
G is a Carnot group of step 2. It is shown that H-admissible domains include
non-characteristic domains and domains in groups of Heisenberg type which have a
partial symmetry about characteristic points. An example is given of a domain
that is C^{1,α }, α < 1, that is not H-admissible. Further, when Ω is
H-admissible a trace theorem is proved for u in BV_{H}(Ω).

**Brandolini, Barbara**,
**Chiacchio, Francesco** and **Trombetti, Cristina**, Università degli
Studi di Napoli “Federico II”, Complesso Universitario Monte S. Angelo, via
Cintia, 80126 – Napoli, Italy
(brandolini@unina.it),
(francesco.chiacchio@unina.it),
(cristina@unina.it).

Some remarks on nonlinear
elliptic problems involving Hardy potentials,
pp. 617-630.

ABSTRACT. In this note we prove an Hardy type inequality
with a remainder term, where the potential depends only on a group of variables.
Such a result allows us to show the existence of entropy solutions to a class of
elliptic P.D.E.’s.