Electronic Edition Vol. 34, No. 3, 2008

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


Benjamin, Elliot and  Bresinsky, Henrik, Dept. of Math. and Stat., University of Maine, Orono, Maine 04473 (ben496@prexar.com), (bresinsky@math.umaine.edu).
On homogeneous k-Buchsbaum polynomial ideals T with some algorithms for dim(T) less than or equal to 2, pp. 637-647.
Let G be a finite group of odd order. The symmetric genus G is the minimum genus of any Riemann surface on which G acts faithfully. Suppose G acts on a Riemann surface X of genus g ³ 2. If |G| > 8(g - 1), then |G| = K(g-1), where K is 15, 21/2, 9 or 33/4. We call these four types of groups LO1-groups through LO4-groups, respectively. We determine the characteristics of LO1-groups and LO2-groups and show that there are infinite families of each type. We also show that there are exactly ten odd order groups with genus between 2 and 26 inclusive. Finally, if G is an odd order group with symmetric genus of the form p+1 for an odd prime p or 2k + 1, for some positive integer k, then G is a metacyclic group with certain properties. We determine that, in the range between 26 and 200, most of the numbers of either of these forms are not the genus of an odd order group.

Harding, John, Department of Mathematical Sciences, New Mexico State University, Las Cruces, NM 88003 (jharding@nmsu.edu).
A regular completion for the variety generated by the three-element Heyting algebra , pp. 649-660.
ABSTRACT. We show that the variety generated by the three-element Heyting algebra admits a meet dense, regular completion even though it is not closed under MacNeille completions.

Cornelius, E F Jr., College of Engineering and Science, University of Detroit Mercy, Detroit, MI, USA 48221-3038 (efcornelius@comcast.net) and Schultz, Phill, School of Mathematics and Statistics, The University of Western Australia, Nedlands, Australia 6009 (schultz@maths.uwa.edu.au).
Multinomial points, pp. 661-676.
ABSTRACT. We describe the integer-valued functions which can arise as the image of an integral coefficient polynomial in k variables when it or a related power series is evaluated at k-tuples of integers from the domain {0,1,…, n-1} and also when it is evaluated at k-tuples of natural numbers. There is an interesting duality between the coefficients and the values of such polynomials and power series, which has applications in number theory. The techniques include expanding Lagrange interpolation polynomials to power series with respect to a basis for multivariable polynomials, called the integral root basis, and constructing higher dimensional analogs of Pascal's infinite matrix.

Brozos-Vazquez, Miguel, Department of Geometry and Topology, Faculty of Mathematics, University of Santiago de Compostela, 15782 Santiago de Compostela, Spain (mbrozos@usc.es) and Gilkey, Peter, Mathematics Department, University of Oregon, Eugene, OR 97403, USA (gilkey@uoregon.edu).
Complex Osserman algebraic curvature tensors and Clifford families, pp. 677-702.
ABSTRACT. We use methods of algebraic topology to study the eigenvalue structure of a complex Osserman algebraic curvature tensor. We classify the algebraic curvature tensors which are both Osserman and complex Osserman in all but a finite number of exceptional dimensions.

Stefan Haesen, Steven Verpoort,  and Leopold Verstraelen, K.U. Leuven, Departement Wiskunde, Afdeling Meetkunde, Celestijnenlaan 200B bus 2400, 3001 Leuven, Belgium (stefan.haesen@wis.kuleuven.be), (steven.verpoort@wis.kuleuven.be), (leopold.verstraelen@wis.kuleuven.be).
The mean curvature of the second fundamental form, pp. 703-719.
ABSTRACT.  The critical points of the area functional of the second fundamental form of Riemannian surfaces in three-dimensional semi-Riemannian manifolds are determined. They are characterized by the vanishing of a scalar function, which will be called the mean curvature of the second fundamental form. A property which involves this new mean curvature is distinctive for totally umbilical surfaces.

Chinea, Domingo, Department of Fundamental Mathematics, University of La Laguna, Tenerife, Spain (dchinea@ull.es)
On horizontally conformal (φ,φ′;)-holomorphic submersions, pp. 721-737.
ABSTRACT. In this paper we study horizontally conformal (φ,φ′)-holomorphic submersions between almost contact metric manifolds and we obtain some results on the harmoniciy, the minimality of the fibres and the transference of structures.

Ianus, Stere, University of Bucharest, Department of Mathematics, C.P. 10-119, Post. Of. 10, Bucharest 72200, Romania (ianus@gta.math.unibuc.ro), Ionescu, Adrian Mihai, Politehnica University of Bucharest, Department of Mathematics, Splaiul Independentei, Nr. 313, Sector 6, Bucuresti, Romania (aionescu@math.pub.ro) and Vîlcu, Gabriel Eduard, Petroleum-Gas University of Ploiesti, Department of Mathematics and Computer Science, Bulevardul Bucuresti, Nr. 39, Ploiesti, Romania and also University of Bucharest, Research Center in Geometry, Topology and Algebra, Str. Academiei, Nr.14, Sector 1, Bucuresti, Romania (gvilcu@mail.upg-ploiesti.ro).
Foliations on quaternion CR-submanifolds, pp.739-751.
ABSTRACT.  The purpose of this paper is to study the canonical foliations of a quaternion CR-submanifold of a quaternion Kähler manifold. Necessary and sufficient conditions are provided for these foliations to become totally geodesic and Riemannian, respectively. A characterization of QR-products in quaternion space forms is also given.

Bennett, Harold, Texas Tech University, Lubbock, TX 79409 (harold.bennett@ttu.edu) and Lutzer, David, College of William and Mary, Williamsburg, VA 23187-8795 (lutzer@math.wm.edu).
Domain-representability of certain complete spaces, pp. 753-772.
ABSTRACT. We show that three major classes of spaces are domain-representable, namely: (1) subcompact T3-spaces, (2) complete quasi-developable spaces, and (3) T1-spaces that are strongly α-favorable (with stationary strategies) that either have a Gδ-diagonal or else that have a base of countable order.

Robert Ralowski and Szymon Zeberski, Institute of Mathematics, Wroclaw University of Technology, Wybrzeze Wyspianskiego 27, 50-370 Wroclaw, Poland (robert.ralowski@pwr.wroc.pl), (szymon.zeberski@pwr.wroc.pl).
Complete nonmeasurability in regular families, pp. 773-780.
ABSTRACT. We show that for a sigma-ideal I with a Borel base of subsets of an uncountable Polish space, if A is (in several senses) a "regular" family of subsets from I then there is a subfamily of A whose union is completely nonmeasurable i.e. its intersection with every Borel set not in I does not belong to the smallest sigma-algebra containing all Borel sets and I. Our results generalize results obtained by Brzuchowski, Cichon, Grzegorek, Ryll-Nardzewski and the authors of this paper.

Lili Zhang, Department of Mathematics, Xi'an Jiaotong University, Xi'an, Shaanxi, 710049, P.R. China  and Department of Mathematics and Physics, Xi'an Technological university, Xi'an, Shaanxi, 710032, P.R. China P.R. (313308zhll@163.com), and Zhongqiang Yang, Department of Mathematics, Shantou University, Shantou, Guangdong, 515063, P.R. China P.R. (zqyang@stu.edu.cn) .
The regions below compact-supported upper semicontinuous maps, pp. 781-793.
ABSTRACT. Let X be a non-compact locally compact separable metric space. We use USCC(X) to denote the family of the regions below of all compact-supported upper semi-continuous maps from X to I=[0,1]. We may topologize USCC(X) by the Hausdorff metric. It is proved in this paper that USCC(X) is homemorphic to Σ if X is non-discrete, and USCC(X) is homemorphic to Qf  if X is discrete, where Σ={(xn) in Q: sup|xn|<1} is the radial interior of the Hilbert cube Q=[-1,1]ω and Qf ={(xn) in Q : xn=0 except for finitely many n}

Marín, Josefa, Universidad Politécnica de Valencia, 46071 VALENCIA, SPAIN (jomarinm@mat.upv.es).
An extension of Alaoglu's theorem for topological semicones, pp. 795-806.
ABSTRACT. This paper studies the topological semicones and it is obtain an appropriate extension of Alaoglu's theorem for this structure and a quasi-metrization theorem for the dual space of topological semicones.

Seubert, Steven M., Bowling Green State University, Bowling Green, OH 43402 (sseuber@bgsu.edu).
Spectral synthesis of diagonal operators on the space of entire functions, pp. 807-816.
ABSTRACT. The purpose of this paper is to study the invariant subspaces of operators on the space of entire functions having as eigenvectors the monomials.

Djordjeviæ Olivera, Fakultet organizacionih nauka, Jove Iliæa 154, Belgrade, Serbia (oliveradj@fon.bg.ac.yu), and Miroslav Pavloviæ, Matematièki fakultet, Studentski trg 16, 110001 Belgrade, Serbia (pavlovic@matf.bg.ac.yu).
Lipschitz conditions for the norm of a vector valued analytic function, pp. 817-826.
ABSTRACT. We prove some quantitative versions of the Thorp-Whitley maximum modulus prnciple as well as extend to vector-valued functions a theorem of Dyakonov (Equivalent norms on Lipschitz type spaces of holomorphic functions, Acta Math. 178(1997), 143-167) on Lipschitz conditions for the modulus of an analytic functions.

Ara, Pere, Departament de Matematiques, Universitat Autonoma de Barcelona, E-08193 Bellaterra,  Barcelona, Spain (para@mat.uab.cat) and  Mathieu, Martin, Department of Pure Mathematics, Queen's University Belfast, Belfast BT7 1NN, Northern Ireland (m.m@qub.ac.uk).
Maximal C*-algebras of quotients and injective envelopes of C*-algebras, pp. 827-872.
ABSTRACT. A new C*-enlargement of a C*-algebra A nested between the local multiplier algebra of A and its injective envelope is introduced. Various aspects of this maximal C*-algebra of quotients are studied, notably in the setting of AW*-algebras. As a by-product we obtain a new example of a type I C*-algebra such that its second iterated local multiplier algebra is strictly larger than its local multiplier algebra.

Steven G. Krantz, American Institute of Mathematics, 360 Portage Avenue, Palo Alto, CA 94306 (skrantz@aimath.org) and Marco M. Peloso, Dipartimetno di Matematica, Universita'degli Studi di Milano, Via C. Saldini 50, 20133 Milano, ITALY (marco.peloso@mat.unimi.it).
The Bergman kernel and projection on non-smooth worm domains, pp. 873-950.
ABSTRACT. We study the Bergman kernel and projection on the worm domain of Diederich-Fornaess, as later modified by Christer Kiselman. We calculate the Bergman kernels explicitly for these domains, up to an error term that can be controlled. As a result, we can determine the Lp-mapping properties of the Bergman projections on these worm domains. We calculate the sharp range of p for which the Bergman projection is bounded on Lp. Along the way, we give a new proof of the failure of Condition R on these worms.
Finally, we are able to show that the singularities of the Bergman kernel on the boundary are not contained in the boundary diagonal.

Cruz-Uribe, D., SFO, Department of Mathematics, Trinity College, Hartford, CT 06106-3100, USA (david.cruzuribe@trincoll.edu),  and   Forzani, L., UNL-IMAL-CONICET, Argentina, and School of Statistics, University of Minnesota, 495 Ford Hall, Minneapolis, MN 55455, USA (liliana.forzani@gmail.com) and Maldonado, D., Department of Mathematics, Kansas State University, 138 Cardwell Hall, Manhattan, KS 66506, USA (dmaldona@math.ksu.edu).
The structure of increasing weights on the real line, pp. 951-983.
ABSTRACT We examine the structure of a variety of related weight classes on the real line and the positive real axis including doubling measures, Muckenhoupt weights, Ariñno and Muckenhoupt weights, and Young functions. We give a number of characterizations of these classes. As applications we compute the Matuszewska-Orlicz indices of a Young function due to Lindberg, give a sufficient condition for a function to be a multiplier of the doubling measures on the positive half-axis, and address questions on quasi-symmetric mappings.