*Editors*: H. Amann (Zürich), G. Auchmuty (Houston), D. Bao
(Houston), H. Brezis (Paris), K. Davidson (Waterloo), C. Hagopian (Sacramento),
R. M. Hardt (Rice), Y. Hattori (Matsue,
Shimane), J. Hausen (Houston), J. A. Johnson (Houston), W. B. Johnson
(College Station), V. I. Paulsen (Houston), M. Rojas (College Station),
Min Ru (Houston), S.W. Semmes (Rice)

*Managing Editor*: K. Kaiser (Houston)

Houston Journal of Mathematics

**Thomas G. Lucas**, Department of Mathematics and
Statistics, University of North Carolina Charlotte, Charlotte, NC 28223, USA
(tglucas@email.uncc.edu).

The Gaussian property for rings
and polynomials, pp. 1-18.

ABSTRACT.
The content of a polynomial f over a commutative ring R is the ideal c(f) of
R generated by the coefficients of f. If c(fg)=c(f)c(g) for each polynomial
g in R[x], then f is said to be Gaussian. The ring R is Gaussian if each
polynomial in R[x] is Gaussian. It is known that f is Gaussian if c(f) is
locally principal. The converse is established for polynomials over reduced
rings. Also, if the square of the nilradical is zero, then R is Gaussian if
and only if the square of each finitely generated ideal is locally
principal.

**Francisco J. Echarte**, **Juan Nunez**, and
**Francisco Ramirez**, Departamento de Geometria y Topologia,
Facultad de Matematicas, Universidad de Sevilla, Apartado 1160.
41080-Sevilla (Espana) (jnvaldes@us.es).

Description of some families
of filiform Lie algebras, pp. 19-32.

ABSTRACT.
In this paper we describe some families of filiform Lie algebras by giving a
method which allows to obtain them in any arbitrary dimension n starting from
the triple (p, q, m), where m = n and p and q are, respectively, invariants z1
and z2 of those algebras. After obtaining the general law of complex filiform
Lie algebras corresponding to triples (p, q, m), some concrete examples of this
method are shown.

Jackson, Marcel, La Trobe
University, Victoria 3086, Australia
(m.g.jackson@latrobe.edu.au).

Residual bounds for compact
totally disconnected algebras, pp. 33-67.

ABSTRACT.
A Boolean topological algebra is a general algebra with a compatible
topology that is compact and totally disconnected. It is well known that
every Boolean topological semigroup, group or ring is topologically
residually finite; that is, every pair of distinct elements can be separated
by a continuous homomorphism into a (discretely topologised) finite algebra.
We examine the possible residual bounds for Boolean topological algebras in
relation to their non-topological residual bound, with particular emphasis
given to groups and completely simple semigroups. Amongst the results is the
undecidability of the problem of determining if all Boolean topological
models of a finite set of identities are profinite.

**Erne, Marcel**, Faculty for Mathematics and Physics, Leibniz University,
Hannover, Germany
(erne@math.uni-hannover.de).

Distributors and Wallman locales,
pp. 69-98.

ABSTRACT. A distributor in an m-semilattice (a
join-semilattice with an isotone multiplication) is a nonempty upper set
containing both the join of a and c and the join of b and c iff it contains
the join of ab and c. Distributors provide a far-reaching extension of the
filter theory for distributive lattices, quantales and similar objects to
structures where no distributive laws are assumed a priori. The closure
system of all distributors is a universal locale over the given
m-semilattice, and the principal distributors form its universal
distributive lattice quotient. Moreover, distributors are a helpful tool for
the spectral theory of m-semilattices and various related kinds of (ordered)
algebras. We present diverse alternative characterizations of Scott-open
distributors in complete m-semilattices, for example as kernels of
join-preserving homomorphisms onto compact locales, and we establish a
one-to-one correspondence between Scott-open distributors and those nuclei
whose range is a Wallman locale, the pointfree analogue of a compact
T1-topology.

**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).

Kähler and para-Kähler structures
associated with Finsler spaces of non-zero constant flag curvature, pp.
99-114.

ABSTRACT. It was shown by R.,L. Bryant (Houston J.
Math. 28 (2002) 221-262) that there is a canonical Kähler structure on the space
of geodesics of a Finsler manifold whose flag curvature is constant and
positive. A different construction is proposed in the present paper, leading
instead to a Kähler structure on the slit tangent bundle of the Finsler space;
it is based on the identification of an appropriate complex structure. The
construction is easily adapted to apply to a Finsler space with constant
negative flag curvature, when it gives a para-Kähler rather than a Kähler
structure; the properties of this para-Kähler structure are explored.

**Gloria Andablo-Reyes, **Facultad de Ciencias de Fisico-Matematicas, UMSNH,
F. J. Mujica s/n, Felicitas del Rio, 58060. Morelia, Michoacan, Mexico (gloria@fismat.umich.mx)
and **Victor Neumann-Lara, **Instituto de Matematicas, UNAM, Circuito
Exterior, Ciudad Universitaria,04510. Mexico, D. F., Mexico
(neumann@math.unam.mx).

Ordered embeddings of symmetric
products, pp. 115-122.

ABSTRACT.
Let X and Y be metric continua. Let F_{n}(X) (resp., F_{n}(Y))
be the hyperspace of nonempty closed subsets of X (resp., Y) which contain at
most n elements. We say that the hyperspace F_{n}(X) can be orderly
embedded in F_{m}(Y) provided that there exists an embedding h from F_{n}(X)
to F_{m}(Y) such that if A,B are elements of F_{n}(X) and A is
contained in B, then h(A) is contained in h(B). In this paper we prove:

(a) If n is minor or equal than m, m is minor than 2n and F_{n}(X) can
be orderly embedded in F_{m}(Y), then X can be embedded in Y.

(b) There exist continua X and Y such that, for each n greater than 1, F_{n}(X)
can be orderly embedded in F_{2n}(Y) and X can not be embedded in Y.

**Gutiérrez García,** **J.,** Departamento de Matemáticas, Universidad
del País Vasco, 48080 Bilbao, Spain
(javier.gutierrezgarcia@ehu.es), and ** Kubiak, T.,** Wydzial
Matematyki i Informatyki, Uniwersytet im. Adama Mickiewicza, 61-614 Poznań,
Poland
(tkubiak@amu.edu.pl) and **de Prada Vicente, M.A.,** Departamento de
Matemáticas, Universidad del País Vasco, 48080 Bilbao, Spain (mariangeles.deprada@ehu.es).

Generating and inserting continuous
functions with values in bounded complete domains and hedgehog-like structures,
pp. 123-144.

ABSTRACT. The paper deals with functions on a
topological space having values in a bounded complete domain. Our purpose is
two-fold. We first develop a theory of generating such functions from certain
scales or prescales of subsets. We then study lower and upper limits of
functions having bounded complete domain as a range space. We characterize those
limit functions in terms of the (pre)scales generating the original ones. Part
of these developments is then used to prove an insertion-type theorem for
continuous functions from a topological space to an appropriately based bounded
complete domain with its Lawson topology. Examples of those domains include,
among others, hedgehogs with countably many spines, their products as well as
various ‘mutants’ of the hedgehog.

Continua with kernels, pp. 145-163.

ABSTRACT. In this article we introduce the concept of kernels of continua, obtained by combining inverse limits of inverse sequences of unit intervals and one-valued bonding maps with inverse limits of inverse sequences of unit intervals and upper semicontinuous set-valued bonding functions. We also show some of their properties, with special emphasis on arc-like continua.

**Liang-Xue Peng,**** **
College of Applied Science,
Beijing University of Technology, Beijing 100022,
China
(pengliangxue@bjut.edu.cn).

On products of certain D-spaces,
pp. 165-179.

ABSTRACT.
D--spaces were introduced by van Douwen in 1978 and studied by van Douwen
and many other topologists. It is not yet clear which topological spaces are
D-spaces, and the product theory for D-spaces is not yet complete. In this
paper we use certain topological games of Galvin to obtain any countable
product of paracompact DC--like spaces is a D-space, and consequently that
any countable product of paracompact C-scattered spaces is a D-space. We
also show that a special generalized metric space is a D-space, this result
extends results of R. Z. Buzyakova. For a fixed integer n, any box product
of scattered spaces each with a scattered rank n must be a D-space. The last
conclusion extands results of William G. Fleissner and Adrienne M. Stanley.

**Joe Corneli,** PlanetMath.org, 421 Cedar Ave. S #17 Minneapolis, MN 55454 (jcorneli@planetmath.org
), and **Ivan Corwin, **151 2nd Avenue, Apt 4D, NY NY 10003 (ivan.corwin@gmail.com),
and **Stephanie Hurder,** Harvard University,National Bureau of Economic
Research, 1050 Massachusetts Avenue Cambridge, MA 02138 (
stephanie.hurder@post.harvard.edu), and **Vojislav Sesum,** Williams
College, Omladinskih brigada 232, Belgrade 11070, Serbia (
sevoja@gmail.com), and **Ya** **Xu,** 74 Barnes Ct. #218, Stanford, CA
94305(xulongya@gmail.com),
and **Elizabeth Adams, **715 Oakland Ave Apt 304, Oakland, CA 94611 (
06eaa@williams.edu) , and** Diana Davis, **Williams College, 1637 Baxter
Hall, Williamstown, MA 01267 (
07djd@williams.edu), and** Michelle Lee**, Williams College, 303
Berkshire Drive, Princeton, NJ 08540 (mishlie@gmail.com),
and **Regina Pettit,** 31001 Floralview Drive South, Apt 203, Farmington
Hills, MI 48331(Regina.Pettit@gmail.com)
and **Neil Hoffman, **Department of Mathematics, University of Texas, 1
University Station C1200, Austin, TX 78712
(nhoffman@math.utexas.edu)

Double bubbles in Gauss space and
spheres, pp. 181-204.

ABSTRACT. We prove that a standard Y is an area-minimizing
partition of Gauss space into three given volumes, provided that the standard
double bubble is an area-minimizing partition of high-dimensional spheres. We
prove that the standard double bubble is the area-minimizing partition of
spheres of any dimension where the volumes differ by at most 4%.

**Dziubanski, Jacek, **Institute of Mathematics,
University of Wroclaw, Pl. Grunwaldzki 2/4, 50-384 Wroclaw, Poland (jdziuban@math.uni.wroc.pl).

Hardy spaces
associated with semigroups generated by Bessel operators with potentials,
pp. 205-234.

ABSTRACT. Let *{T _{t}}_{t>0} *be the
semigroup of linear operators generated by the operator

** Janez Bernik, Roman Drnovsek, Damjana
Kokol Bukovsek, Tomaz Kosir, **and** Matjaz** **
Omladic, **Department of Mathematics, University of Ljubljana, 1000
Ljubljana, Slovenia, (janez.bernik@fmf.uni-lj.si).

Reducibility and
triangularizability of semitransitive spaces of operators, pp. 235-247.

ABSTRACT. A linear space L of operators on a vector
space X is called semitransitive if, given two nonzero vectors x, y in X,
there exists an element A in L such that either y=Ax or x=Ay. In this paper
we consider semitransitive spaces of operators on a finite dimensional
vector space X over an algebraically closed field. In particular, we are
interested in the existence of nontrivial invariant subspaces of X for a
semitransitive space L. We are able to relate the existence of an invariant
subspace for L to the properties of some rank varieties that we associate to
L. Using this relation we show that, if the dimension of L is the same as
the dimension of X, which is minimal possible, then L is triangularizable.
By contrast we show that, from n=3 onwards, there exists a minimal
semitransitive space L of dimension n+1 of operators on an n-dimensional
vector space X which is also irreducible. We also give a new
characterization of semitransitive spaces of operators on finite dimensional
vector spaces.

**Fangyan Lu, **
Department
of Mathematics,

Jordan triple isomorphisms of nest
algebras and applications, pp. 249-267.

ABSTRACT. Let A_{i}
be a subalgebra of the nest algebra
T( N_{i}) which contains
all finite rank operators in T( N_{i}) ,
i=1, 2. Let φ be
a linear bijection from A_{1} onto A_{2}
which satisfies φ (_{1 }. Then φ is
proved to be an
isomorphism,
or a negative of an isomorphism, or an anti-isomorphism,
or a negative of an
anti-isomorphism. As applications,

**Skalski, A. ** and ** Zacharias, J. ** University of Nottingham,
University Park, Nottingham NG7 2RD,
(adam.skalski@maths.nottingham.ac.uk),
(joachim.zacharias@nottingham.ac.uk)..

Entropy of shifts on higher-rank
graph C*-algebras, pp. 269-282.

ABSTRACT. Let O_{Λ} be a higher-rank graph
C*-algebra. For every p in Z_{+}^{r} there is a canonical
completely positive map Φ^{p} on O_{Λ} and a subshift T^{p}
on the path space X=Λ^{∞}. We show that ht(Φ^{p})=h(T^{p}),
where ht is Voiculescu's approximation entropy and h the classical topological
entropy. For a higher rank Cuntz-Krieger algebra O_{M} we obtain ht(Φ^{p})=
log rad(M_{1}
^{p1}... M_{r}
^{pr}), rad being the spectral radius. This generalizes Boca
and Goldstein's result for Cuntz-Krieger algebras.

**Kenneth R. Davidson**
and **Dilian Yang**, University of Waterloo, Waterloo, ON N2L 3G1,
CANADA, (krdavids@uwaterloo.ca),
(dyang@uwaterloo.ca).

A note on
absolute continuity in free semigroup algebras , pp. 283-288.

ABSTRACT.
A free semigroup algebra is the weak operator topology closed
(nonself-adjoint, unital) algebra generated by n isometries with pairwise
orthogonal ranges. The prototype is the algebra generated by the left
regular representation of the free semigroup on n letters. A free semigroup
algebra which is isomorphic to the left regular algebra is called type L. If
the infinite ampliation of the isometries generates a type L algebra, it is
called weak-* type L. A free semigroup algebra is absolutely continuous if
the vector functionals on it are equivalent to (some) vector functionals on
the left regular representation.

The purpose of this note is to show that absolutely continuous free
semigroup algebras are weak-* type L.

**Sakai, Katsuro, **Institute of Mathematics, University of Tsukuba,
Tsukuba, 305-8571, Japan
(sakaiktr@sakura.cc.tsukuba.ac.jp).

The spaces of compact convex sets and
bounded closed convex sets in a Banach space, pp. 289-300.

ABSTRACT. Let X be an infinite-dimensional Banach
space with density τ and let CC(X) and BC(X) be the spaces of all non-empty
compact convex sets in X and of all non-empty bounded closed convex sets
admitting the Hausdorff metric, respectively. In this note, it is proved
that (i) the space CC(X) is homeomorphic to the Hilbert space with density
τ; (ii) the space BC(X) is homeomorphic to the Hilbert space with density τ
if it has the density τ; (iii) the space BC(X) is homeomorphic to the
Hilbert space with density 2τ if X is separable (i.e., τ is countable) or
reflective.

**Guangcun Lu,** Department of Mathematics, Beijing Normal University,
Beijing 100875, P.R. China
(gclu@bnu.edu.cn).

Symplectic fixed
points and Lagrangian intersections on weighted projective spaces, pp.
301-316.

ABSTRACT. In this note we show that Arnold
conjecture for the Hamiltonian maps still holds on weighted complex
projective spaces. For the real part of the weighted complex projective
space, a Lagrange orbifold we also prove that Arnold conjecture for the
Lagrange intersections for it is also true if each weight of this weighted
complex projective space is odd.

**Editorial Addendum concerning the paper " The BMO^{-1} space and its
application to Schechter's Inequality", by Sadek Gala, Houston
Journal of Mathematics, Vol. 33(4), pp. 1059-1066, **
p.317.