*Editors*: G. Auchmuty (Houston), D. Bao
(San Francisco, SFSU), D. Blecher (Houston), H. Brezis (Paris and Rutgers), B. Dacorogna (Lausanne), K. Davidson (Waterloo), M. Dugas (Baylor), M. Gehrke (LIAFA,
Paris7), C. Hagopian (Sacramento),
R. M. Hardt (Rice), Y. Hattori (Matsue,
Shimane), 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

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

On the typeset of a Butler B(2)-group,
pp. 653-683.

ABSTRACT A Butler B(2)-group G is a sum of finitely many torsionfree
Abelian groups of rank 1, subject to two independent relations.
In a paper which appeared in the Volume in memory of A.L.S. Corner (De Vivo, C. and Metelli, C.,* On direct decompositions
of Butler B(2)-groups*, Volume in memory of A.L.S. Corner, Contributions to
Module Theory; Models, Modules and Abelian Groups, W. De-Gruyter (2008),
201-219) we showed that the decomposability of G depends on the occurrence of a
certain type. We study here the types of G, determining which depend only on the
two main structures of G-the base types and the basic partition- and which
instead depend on the coefficients of the relations. We give an algorithm to
compute the types σ of the first kind, and study the rank of the group G(σ) of
elements of G with type ≥σ.

**John Harding,** and **Qin Yang,** Department of Mathematical Sciences, New Mexico State University, Las Cruces, NM 88003, USA
(jharding@nmsu.edu), (qyang@nmsu.edu).

Regular completions of lattices, pp. 685-691.

ABSTRACT. A variety of lattices admits a meet dense
regular completion if every lattice in the variety can be embedded into a
complete lattice in the variety by an embedding that is meet dense and regular
(preserves existing joins and meets). We show that exactly two varieties of
lattices admit a meet dense regular completion, the variety of one-element
lattices and the variety of all lattices. This extends an earlier result of
Harding showing these are the only two varieties of lattices closed under
MacNeille completions.

**Sarah M. Johansen,** Department of Mathematics, La Trobe University, Victoria 3086, Australia
(S.Johansen@latrobe.edu.au).

Dualisability of relational structures, pp. 693-712.

ABSTRACT.We investigate the dualisability problem for finite relational structures and highlight differences with the more familiar dualisability problem for finite algebras. For example, while many inherently non-dualisable algebras are known, we shall show that there are no inherently non-dualisable relational structures at all. We will also prove that, for every finite set with at least four elements, there are uncountably many non-equivalent relational structures on that set that are all dualised by a fixed alter ego.

**Dobbs, David E.,** University of Tennessee, Knoxville, TN 37996-0614 (dobbs@math.utk.edu)
and **Sahandi, Parviz, **Department of Mathematics, University of Tabriz, Tabriz, Iran, and School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box: 19395-5746, Tehran, Iran (sahandi@ipm.ir).

Semistar normal pairs and related characterizations of P*MDs, pp. 713-739.

ABSTRACT. Given an overring extension of domains D inside T, we introduce the semistar-theoretic analogues of D being integrally closed in T, (D,T) being a normal pair, D inside T being a residually algebraic extension and (D,T) being a residually algebraic pair. Our main result generalizes Davis' characterization of normal pairs (D,T) as (overring) extensions D inside T for which each intermediate ring is D-flat, while also generalizing some celebrated characterizations of Prufer domains and several results of Ayache-Jaballah on residually algebraic pairs. This work also involves extending the connections between the semistar-theoretic notions of primitivity and INC-pair that were given by Chang and Fontana. Applications include several characterizations of P*MDs.

**Nie, Zhaohu, **Department of Mathematics and Statistics, Utah State
University, Logan, UT 84341(zhaohu.nie@usu.edu).

On transgression in associated bundles, pp. 741-749.

ABSTRACT.
We formulate and prove a formula for transgressing characteristic forms in general associated bundles following a method of Chern. As applications, we derive D. Johnson's explicit formula for such general transgression and Chern's first transgression formula for the Euler class.

**Kaliszewski, S., **Arizona State University, Tempe, AZ 85287
(kaliszewski@asu.edu),
**Patani, Nura, **Arizona State University, Tempe, AZ 85287
(nura.patani@asu.edu), and
**Quigg, John, **Arizona State University, Tempe, AZ 85287
(quigg@asu.edu).

Characterizing Graph C*-Correspondences, pp. 751-759.

ABSTRACT. Every separable nondegenerate C*-correspondence over a commutative C*-algebra with discrete spectrum is isomorphic to a graph correspondence.

**Bernhard Burgstaller, **Mathematisches Institut,
Einsteinstrasse 62, 48149 Münster, Germany
(bernhardburgstaller@yahoo.de).

Representations of crossed products by cancelling actions and
applications, pp. 761-774.

ABSTRACT.
The algebraic crossed product of a cancelling
action of an amenable group on a locally matricial algebra allows only one
faithful C*-representation. We give examples, and actually prove a more general
uniqueness theorem for algebraic G-bundles.

Markov operators and C*-algebras, pp. 775-798.

ABSTRACT. A Markov operator P acting on the space of continuous functions on a compact space X gives rise to a natural topological quiver. We use the theory of such quivers to attach a C*-algebra to P in a fashion that reflects some of the probabilistic properties of P.

**Lacey, Michael T, ** Georgia Institute of Technology, Atlanta Georiga
(lacey@math.gatech.edu).

An A_{p}-A_{∞} inequality for the Hilbert transform, pp. 799-814.

ABSTRACT.We prove in particular that for the Hilbert transform, for 1<p<∞ and a weight w in A_{p}, that
the norm of H on L^{p}(w) is dominated by a function of the A_{p} and A_{∞} characteristic of w,
and the A_{∞} characteristic of w^{1-p'}.
The case of p=2 is an instance of a recent result of Hytönen-Perez, and
as a corollary we obtain the well-known bound of S. Petermichl, on the linear bound in the A_{2} characteristic.
This supports a conjectural inequality valid for all Calderón-Zygmund operators T, and arbitrary p.

On possible mixing rates for some strong mixing conditions for N-tuplewise independent random fields, pp. 815-832.

ABSTRACT. For a given pair of positive integers d and N with N at least 2, for strictly stationary random fields that are indexed by the d-dimensional integer lattice and satisfy N-tuplewise independence, the dependence coefficients associated with the ρ-, ρ-prime- and ρ*-mixing conditions can decay together at an arbitrary rate. If also d is at least 2 then, together with N-tuplewise independence, the first two mixing conditions can hold with the same arbitrary rate of decay while the third fails to hold. The proofs of these results provide classes of examples pertinent to limit theory for random fields that involve such mixing conditions together with certain types of ``extra'' assumptions on the marginal and bivariate (or N-variate) distributions.

**Theodoros Stavropoulos,** Department of Mathematics,
University of Athens, GR-15784 Zografou, Greece
(tstravrop@math.uoa.gr).

The geometry of extension principles, pp. 833-853.

ABSTRACT. We study the geometric significance of the fundamental function used in the characterization of affine framelets constructed from refinable functions. We prove that the Oblique Extension Principle characterizes affine framelets constructed from refinable functions.

New gradient estimates for parabolic equations, pp. 855-914.

ABSTRACT. We prove sharp Lorentz- and Morrey-space estimates for the gradient of solutions to non homogeneous nonlinear parabolic equations, where the vector field is assumed to satisfy classical growth and ellipticity conditions and where the inhomogeneity is only assumed to be integrable to the some power larger than 1. In particular we investigate the case where the integrability exponent stays below the duality exponent.

**de Morais Filho, Daniel C.,** Departamento de Matemática e
Estatística, Universidade Federal de Campina Grande, Campina Grande,
Caixa Postal 10044, CEP 58429-970, PB, Brazil (daniel@dme.ufcg.edu.br),
**Faria, Luiz F. O., Miyagaki, Olímpio H., and Pereira, Fábio R.,**
Departamento de Matemática - ICE, Universidade Federal de Juiz de
Fora, CEP 36036-330 Juiz de Fora, MG, Brazil
(luiz.faria@ufjf.edu.br),
(ohmiyagaki@gmail.com),(fabio.pereira@ufjf.edu.br).

One sided resonance for a mixed boundary elliptic system
involving critical Sobolev exponent, pp. 915-931.

ABSTRACT. In this work we study the existence of solutions for the mixed
boundary elliptic gradient system, related to the Ambrosetti and Prodi problem,
allowing one sided resonance for this system.

**Baldwin, Stewart, **Department of Mathematics, Auburn University, Auburn, AL 36849-5310
(baldwsl@auburn.edu) and **Cralley, Jay,** 246 Cornell St #2, Roslindale, MA 02131 (jcralley@gmail.com)

Shift conjugacy and Markov tree
maps, pp. 933-961.

ABSTRACT. Given an expansive Markov tree map, we investigate the conjugacy type of the corresponding inverse limit shift map (where the inverse limit uses a single bonding map). We provide a combinatorial algorithm which, given two expansive Markov maps (on perhaps different trees), tests whether or not the corresponding inverse limit shift maps are conjugate.

**Charatonik, Włodzimierz J.,** Missouri University of Science and Technology, Department of Mathematics and Statistics, 65409 Rolla, MO, USA (wjcharat@mst.edu),
**Fernández-Bayort, Tomás,** C.G.A. (Centro de Gestión Avanzada), Consejería de Educación, Junta de Andalucía, 41071 Sevilla, Spain (tfernandez@andaluciajunta.es) and
**Quintero, Antonio, **Departamento de Geometría y Topología, Facultad de Matemáticas,
Universidad de Sevilla, Apartado 1160, 41080 Sevilla, Spain (quintero@us.es).

On the Freudenthal extensions of confluent proper maps, pp.
963-989.

ABSTRACT.
In this paper we study when Freudenthal extensions of proper maps preserve the (weak, semi) confluency. Also the extensions to the Alexandroff one-point compactificaton are considered.

A note on closed discrete subsets of separable (a)-spaces, pp. 991-997.

ABSTRACT.We show that the existence of a T

Between the cofinally complete spaces and the UC spaces, pp. 999-1015.

ABSTRACT.The local finiteness functional for a metric space (X,d) intuitively describes the radius of the "largest" ball about each point of the space containing at most finitely many points of the space. We give characterizations of those metric spaces in which each sequence along which the functional tends to zero necessarily clusters, placing this class of spaces strictly between the well-studied UC metric spaces and the cofinally complete metric spaces. We produce a subtle formula for the values of the functional for the hyperspace of nonempty closed subsets equipped with Hausdorff distance. Finally, we give necessary and sufficient conditions for the hyperspace to be of this type.

γ-spaces and metrization theorems, pp. 1017-1025.

ABSTRACT.We present some equivalent conditions for a topological space to be a γ-space and some criteria for the metrizability of a topological space in terms of (weak base) γ-functions.