*Editors*: D. Bao (San Francisco,
SFSU), D. Blecher (Houston), Bernhard G. Bodmann (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), W. B. Johnson (College Station), M. Rojas (College Station),
Min Ru (Houston), S.W. Semmes (Rice).

*Managing Editor*: K. Kaiser (Houston)

Houston Journal of Mathematics

*Contents*

Families of compact RIEMANN surfaces, pp. 727-731.

ABSTRACT.The aim of this article is to indicate how Koebe’s General Uniformisation Theorem for planar Riemann surfaces may be used to construct families of compact Riemann surfaces of every genus (explicitly in case of g=1) in a very concrete way.

**Calvaruso, Giovanni,** Dipartimento di Matematica e Fisica “E. De Giorgi”, Università del Salento, Prov. Lecce-Arnesano, 73100 Lecce, Italy
(giovanni.calvaruso@unisalento.it).

Four-dimendsional para Kähler Lie algebras: classification and geometry, pp. 733-748.

ABSTRACT. Let *g* denote an arbitrary 2n-dimensional Lie algebra. A symplectic structure on
*g* is a closed two-form ω on *g* of maximal rank, that is, such that ω_{n} ≠ 0.
A paraKähler Lie algebra is an even-dimensional Lie algebra \g, equipped with a pair (J,g), where J is a paracomplex structure and g a pseudo-Riemannian metric, such that the fundamental two-form Ω(X,Y)=g(X,JY) is symplectic. We completely classify left-invariant paraKähler structures on four-dimensional Lie algebras and then study the geometry of their paraKähler metrics, emphasizing different behaviors with respect to their Kähler analogues.

**Leobardo Rosales,** Keimyung University, Department of
Mathematics, 1095 Dalgubeol-daero, Daegu, Republic of Korea, 704-701
(lrosales@gw.kmu.ac.kr).

The q-Valued minimal surface equation, pp. 749-765.

ABSTRACT. The q-valued minimal surface equation is a partial differential equation over the unit disk in the plane, but degenerate at the origin, producing solutions which if can be continuously extended at the origin, then have corresponding q-valued graphs which are stable immersed minimal surfaces in the unit cylinder. Here, we give a complete geometric description of the q-valued graph corresponding to a solution to the q-valued minimal surface equation in case we cannot extend the solution continuously across the origin.

**Eunmi Pak, Young Jin Suh and Changhwa Woo,** Department of Mathematics, Kyungpook National University, Daegu 702-701, Republic of Korea,
(legalgwch@knu.ac.kr).

Restricted Ricci conditions for real hypersurfaces in complex two-plane Grassmannians, pp. 767-783.

ABSTRACT. In this paper, we have considered new restricted commuting conditions between the restricted Jacobi operator and the Ricci tensor for real hypersurfaces in complex two-plane Grassmannians G_{2}(**C**^{m+2}). By using a new method of simultaneous diagonalzation for commuting symmetric operators, we verified a complete classification for real hypersurfaces in G_{2}(**C**^{m+2}) with above conditions that become equivalent condition for hypersurfaces of Type~A.

** Sievewright, Daniel,** Western Michigan University, Kalamazoo, MI 49008, (daniel.s.sievewright@wmich.edu).

Deddens algebras for weighted shifts, pp. 785-814.

ABSTRACT. We describe the possible structure of the Deddens algebra associated with a weighted shift, focusing on injective weighted shifts of finite multiplicity. We give necessary and sufficient conditions for such an algebra to have a nontrivial invariant subspace. Then, several examples are given to show that we cannot strengthen the results about the structure of the Deddens algebra.

**Klemes, Ivo**, 3460 Fulton Road, Victoria BC, V9C 3N2 Canada
(klemes@math.mcgill.ca).

More symmetric polynomials related to p-norms, pp. 815-830.

ABSTRACT. Extending a previous result of the author,
we define two additional new families of symmetric polynomials which can be used
to state sufficient conditions for p-norm inequalities between
two real n-tuples x and y, in the range p>2. When x consists of the eigenvalues
of an n by n matrix A, we give a formula for the polynomials in
terms of the entries of A, generalizing sums of
principal subdeterminants of A.

**Johnston, Nathaniel,** Department of Mathematics & Statistics, University of Guelph, Guelph, Ontario N1G~2W1, Canada and Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario N2L~3G1, Canada
(nathaniel.johnston@uwaterloo.ca) and
**Kribs, David W.,** Department of Mathematics & Statistics, University of Guelph, Guelph, Ontario N1G~2W1, Canada and Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario N2L~3G1, Canada
(dkribs@uoguelph.ca).

Duality of entanglement norms, pp. 831-847.

ABSTRACT. We consider four norms on tensor product spaces that have appeared in quantum information theory and demonstrate duality relationships between them. We show that the product numerical radius is dual to the robustness of entanglement, and we similarly show that the S(k)-norm is dual to the projective tensor norm. We show that, analogous to how the product numerical radius and the S(k)-norm characterize k-block positivity of operators, there is a natural version of the projective tensor norm that characterizes Schmidt number. In this way we obtain an elementary new proof of the cross norm criterion for separability, and we also generalize both the cross norm and realignment criteria to the case of arbitrary Schmidt number.

Hardy and Rellich-type inequalities with remainders for Baouendi-Grushin vector fields, pp. 849-874.

ABSTRACT. In this paper we study Hardy and Rellich-type inequalities and their improved versions for the Baouendi-Grushin vector fields.

Binary frames, pp. 875-899.

ABSTRACT. We investigate frame theory over the binary field

**Kunszenti-Kovács, Dávid**, ELTE TTK, Institute of Mathematics and Numerical Analysis
and Large Networks Research Group, Hungarian Academy of Sciences, 1117 Budapest,
Pázmány P. sétány 1/C, Hungary
(daku@fa.uni-tuebingen.de).

Almost weak polynomial stability of operators, pp. 901-913.

ABSTRACT. We investigate whether almost weak stability of an operator *T* on a Banach space *X* implies
its almost weak polynomial stability. We show, using a modified version of the van der Corput Lemma, that if
*X* is a Hilbert space and *T* a contraction, then the implication holds. On the other hand, based on a TDS arising from a two dimensional ODE,
we give an explicit example of a contraction on a *C _{0}* space that is almost weakly stable, but its appropriate polynomial powers fail to converge
weakly to zero along a subsequence of density 1.
Finally we provide an application to convergence of polynomial multiple ergodic averages.

**Banjade, Debendra P., **Department of Mathematics, The University of Alabama, Box 870350, Tuscaloosa, AL 35487
(dpbanjade@crimson.ua.edu) and
**Trent, Tavan** T., Department of Mathematics, The University of Alabama, Box 870350, Tuscaloosa, AL 35487
(ttrent@as.ua.edu).

Wolff's problem of ideals in the multiplier algebra on weighted Dirichlet space, pp. 915-932.

ABSTRACT.
Wolff proved a theorem on ideal membership in the
algebra of bounded analytic functions on the unit disk. We establish an
analogous version for the multiplier algebra on weighted Dirichlet spaces.

**McCann, Shawn**, University of Regina, Regina, SK, S4S 0A2
(mccann1s@uregina.ca).

C*-algebras associated with topological group quivers II: K-groups
, pp. 933-964.

ABSTRACT. Topological quivers generalize the notion of directed graphs in which the sets of vertices and edges are locally compact Hausdorff spaces. Associated to a topological quiver Q is a C*-correspondence, and in turn, a Cuntz-Pimsner algebra C*(Q). Given Γ a locally compact group and endomorphisms α and β of Γ, one may construct a topological quiver Q_{α, β}(Γ) with vertex set Γ, and edge set E_{α, β}(Γ)={(x, y) in Γ x Γ where α(y)=β(x)}. In a previous paper, the author examined the Cuntz-Pimsner algebra O_{α, β}(Γ)= C*(Q_{α, β}(Γ)) and found generators (and their relations) of O_{α, β}(Γ). In this paper, the author uses this information to create a six term exact sequence in order to calculate the K-groups of O_{α, β}(Γ) and in particular, those K-groups resulting from choosing Γ to be the d-torus with endomorphisms α and β as integral matrices with non-zero determinant.

**Changguo Wei,** School of Mathematical Sciences, Ocean University of China, Qingdao, 266100, P.R. China
(weicgqd@163.com).

On the classification of certain unital extensions of C*-algebras,
pp. 965-991.

ABSTRACT. We pursue the classification of unital essential extensions up to unitary equivalence or
isomorphism. We characterize the six-term exact sequences with base points of the unital extensions which are
weakly unitarily equivalent and give a necessary and sufficient condition for their six-term exact sequences with
base points being congruent. Using these results, we prove several UCTs for unital extensions which generalizes
the UCT of Brown and Dadarlat. As an application, we give a generalization of the classic BDF-theory
and classify certain classes of unital full extensions up to unitary.

**Hou, Chunjuan,** Huashang College, Guangdong University of
Business Studies, Guangzhou, 511300, China (houchunjuanhao@163.com), **
Hu, Shouchuan,** Department of Mathematics, Missouri State
University, Springfield, MO 65804 (shu@missouristate.edu),
and **Papageorgiou, Nikolas S.,** Department of
Mathematics, National Technical University, Zografou Campus, Athens 15780,
Greece (npapg@math.ntua.gr).

Positive solutions for parametric
nonlinear neumann problems with competing nonlinearities,
pp. 993-1019.

ABSTRACT. We consider a parametric nonlinear Neumann problem driven by
the p-Laplacian and with a reaction exhibiting the competing effects of a
concave (p-sublinear) and of a convex (p-superlinear) term. Using critical
point theory together with truncation and comparison techniques, we prove a
bifurcation type theorem describing the set of positive solutions as the
parameter varies.

**Banič, Iztok,** Faculty of Natural Sciences and Mathematics, University of Maribor, 2000 Maribor, Slovenia
(iztok.banic@uni-mb.si), **Črepnjak, Matevž,** Faculty of Natural Sciences and Mathematics, University of Maribor, 2000 Maribor, Slovenia
(matevz.crepnjak@um.si), **Erceg, Goran,** Faculty of Natural Sciences and Mathematics, University of Split, 21000 Split, Croatia
(gorerc@pmfst.hr), **Merhar, Matej,** Faculty of Natural Sciences and Mathematics, University of Maribor, 2000 Maribor, Slovenia
(matej.merhar@uni-mb.si), and
**Milutinović, Uroš,** Faculty of Natural Sciences and Mathematics, University of Maribor, 2000 Maribor, Slovenia
(uros.milutinovic@uni-mb.si).

Inducing functions between inverse limits with upper semicontinuous bonding functions,
pp. 1021-1037.

ABSTRACT. In this paper we introduce the category CU in which the compact metric spaces are objects and upper semicontinuous functions from X to 2^{Y} are morphisms from X to Y. We also introduce the category ICU of inverse sequences in CU. Then we investigate the induced functions between inverse limits of compact metric spaces with upper semicontinuous bonding functions. We provide criteria for their existence and prove that under suitable assumptions they have surjective graphs.
We also show that taking such inverse limits is very close to being a functor (but is not a functor) from ICU to CU, if morphisms are mapped to induced functions. At the end of the paper we give a useful application of the mentioned results.

**Van Nall,** Department of Mathematics and Computer Science, University of
Richmond, Richmond, VA 23173
(vnall@richmond.edu).

More continua which are not the inverse limit with a closed subset of a unit square, pp. 1039-1050.

ABSTRACT. There are nice characterizations of continua that are homeomorphic to an inverse limit with a continuous function from [0,1] to [0,1]. Continua that are homeomorphic to an inverse limits with a single upper semi-continuous set valued function from [0,1] into the closed subsets of [0,1] have not been characterized, and so, in order to learn more about them, we add to the list of continua which cannot be obtained as such an inverse limit.

**Dirk Hofmann,** CIDMA -- Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal
(dirk@ua.pt) and
**Gavin J. Seal, **Mathematics Institute for Geometry and Applications, Ecole Polytechnique Federale de Lausanne, 1015 Lausanne, Switzerland
(gavin.seal@fastmail.fm).

Exponentiable approach spaces, pp. 1051-1062.

ABSTRACT. In this note we present a characterisation of exponentiable approach spaces in terms of ultrafilter convergence.

Infinite games and cardinal properties of topological spaces, pp. 1063-1077.

ABSTRACT. Inspired by work of Scheepers and Tall, we use properties defined by topological games to provide bounds for the cardinality of topological spaces. We obtain a partial answer to an old question of Bell, Ginsburg and Woods regarding the cardinality of weakly Lindelof first-countable regular spaces and answer a question recently asked by Babinkostova, Pansera and Scheepers. In the second part of the paper we study a game-theoretic variant of the countable chain condition, introduced by Daniels, Kunen and Zhou in 1994. We prove that it is equivalent to countable pi-weight for spaces having countable local pi-weight at every point, and exploit it to give a new proof of Shapirovskii's classical bound on the number of regular open sets of a regular topological space.

**Michalik, Daria, **Faculty of Mathematics and Natural Sciences,
College of Science, Cardinal Stefan Wyszynski University, Woycickiego 1/3,
01-938 Warsaw, Poland
(d.michalik@uksw.edu.pl).

Embeddings into the product of generalized Sierpiński curves admitting extensions of maps,
pp.1079-1086.

ABSTRACT. For each cardinal number τ we can construct a 1-dimensional space Σ(τ) - called generalization of Sierpiński curve of weight τ.
We prove in this paper that for a metrizable space X and a family {f_{i}}_{i ∈ N} of mappings of X into itself
the set of all embeddings h : X → Σ(τ)^{ω} such that
dim Cl(h(X)) ≤ dim X and all functions hf_{i}h^{-1} are extendable to mappings
f_{i}^{*} : Cl(h(X)) → Cl(h(X)) is residual in C(X,Σ(τ)^{ω}).

**Daniel, D,**. Lamar University, Beaumont, Texas 77710
(dale.daniel@lamar.edu) and **Tuncali, M.,** Nipissing University, North Bay, Ontario P1B 8L7
(muratt@nipissingu.ca).

Embeddings of non-metric products in images of ordered compacta, pp.
1087-1096.

ABSTRACT. We generalize a construction of A. J. Ward to build continuous images of ordered compacta that contain a non-metrizable product. Such spaces have a relatively restricted structure. As a result, one may express in somewhat explicit form a mapping of an ordered compactum onto an appropriate subspace of a compactum containing such a non-metric product.

**Er-Guang Yang,** School of Mathematics & Physics, Anhui
University of Technology, Maanshan 243002, P.R. China (egyang@126.com).

Properties defined with semi-continuous functions and some related spaces, pp.
1097-1106.

ABSTRACT.
The notions of
properties (UL)_{m}^{wl}, (UL)_{m}^{K}
and (UL)_{m} are introduced to generalize the notion of property (USC)_{m}
introduced by Ohta and Sakai. It is shown that spaces having property (UL)_{m}^{wl}
(resp. (UL)_{m}^{K}, (UL)_{m}) coincide with countably
paracompact (resp. countably mesocompact, countably metacompact) spaces. As
applications, some insertion theorems of countably paracompact spaces and
countably mesocompact spaces are obtained.