HOUSTON JOURNAL OF
MATHEMATICS

Electronic Edition Vol. 39, No. 4 , 2013

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

Jemal Abawajy and  Andrei Kelarev, School of Information Technology, Deakin University, 221 Burwood Highway,  Burwood, Victoria 3125, Australia (jemal.abawajy@deakin.edu.au), (a.kelarev@deakin.edu.au), and J.L. Yearwood and C. Turville, School of Science, Information Technology and  Engineering, University of Ballarat, P.O. Box 663, Ballarat, Victoria 3353, Australia (j.yearwood@ballarat.edu.au), (c.turville@ballarat.edu.au).
A data mining application of the incidence semirings, pp. 1083-1093.
ABSTRACT.This paper is devoted to a combinatorial problem for incidence semirings, which can be viewed as sets of polynomials over graphs, where the edges are the unknowns and the coefficients are taken from a semiring. The construction of incidence rings is very well known and has many useful applications. The present article is devoted to a novel application of the more general incidence semirings. Recent research on data mining has motivated the investigation of the sets of centroids that have largest weights in semiring constructions. These sets are valuable for the design of centroid-based classification systems, or classifiers, as well as for the design of multiple classifiers combining several individual classifiers. Our article gives a complete description of all sets of centroids with the largest weight in incidence semirings.

Andreas Reinhart, Institut für Mathematik und wissenschaftliches Rechnen, Karl-Franzens-Universität, Heinrichstrasse 36, 8010 Graz, Austria, (andreas.reinhart@uni-graz.at).
On integral domains that are C-monoids, pp. 1095-1116.
ABSTRACT. C-monoids are a special class of Mori monoids which play a central role in arithmetical investigations of higher dimensional noetherian domains which are not integrally closed. Mori domains with complete integral closure S and conductor f are C-monoids, provided that both the v-class group of S and the residue class ring S/f, are finite. We provide characterizations for several classes of integral domains to be C-monoids.

Gouveia, M.J., Faculdade de Ciências da Universidade de Lisboa and CAUL, P-1749-016 Lisboa, Portugal (mjgouveia@fc.ul.pt) and Priestley, H.A., Mathematical Institute, University of Oxford, 24/29 St Giles, Oxford OX1 3LB, United Kingdom (hap@maths.ox.ac.uk).
Profinite completions and canonical extensions of semilattice reducts of distributive lattices, pp. 1117-1136.
ABSTRACT. A bounded distributive lattice L has two unital semilattice reducts. These three ordered structures have a common canonical extension. As algebras, they also possess profinite completions and the profinite completion of L itself is well known to coincide with the canonical extension. Depending on the structure of L, the three profinite completions may coincide or may be different. Necessary and sufficient conditions are obtained for the canonical extension of L to coincide with the profinite completion of one, or of each, of its semilattice reducts. The techniques employed here draw heavily on duality theory and on results from the theory of continuous lattices.

Schweizer, Andreas, Department of Mathematics, Korea Advanced Institute of Science and Technology (KAIST), Daejeon 305-701, South Korea  (schweizer@kaist.ac.kr).
Entire functions sharing simple a-points with their first derivative, pp. 1137-1148.
ABSTRACT. We show that if a nonconstant complex entire function f and its derivative f' share their simple zeroes and their simple a-points for some nonzero constant a, then f is equal to f'. We also discuss how far these conditions can be relaxed or generalized. Finally, we determine all entire functions f such that for 3 distinct complex values at every point where f takes one of these values with multiplicity one, f' also takes this value.

Zheng Jian-Hua, Department of Mathematical Sciences, Tsinghua University, Beijing, P. R. China (jzheng@math.tsinghua.edu.cn).
Conformal and invariant measures of parabolic meromorphic functions, pp. 1149-1159.
ABSTRACT.  A meromorphic function is called parabolic on the Riemann sphere if all singular values of it lie in the Fatou set and there exist only finitely many limit points of the post-singular set in the Julia set and these limit points are rational indifferent periodic points. Therefore, the infinity is not a singular value of a parabolic meromorphic function on the Riemann sphere. That a measure on the Julia set is s-conformal means that s-power of the derivative of the function with respect to the spherical metric is Jacobian. We have known the existence of s-conformal measure for a parabolic meromorphic function on the Riemann sphere where s is the Poincare exponent. The purpose of this paper is to prove that the s-conformal measure is atomless, unique and ergodic, and there exists an equivalent invariant measure if no mass is put on the infinity, which extends the Denker and Urbanski's result on parabolic rational functions.

Cavicchioli, Alberto, University of Modena and Reggio E., 41100 Modena, Italy (cavicchioli.alberto@unimore.it), Spaggiari, Fulvia, University of Modena and Reggio E., 41100 Modena Italy (spaggiari.fulvia@unimore.it),  and Telloni, Agnese I., University of Modena and Reggio E., 41100 Modena, Italy (agneseilaria.telloni@unimore.it).
Cusped hyperbolic 3-manifolds from some regular polyhedra, pp. 1161-1174.
ABSTRACT. We illustrate some topological properties and give surgery descriptions of the cusped hyperbolic orientable 3-manifolds obtained by face pairings of the regular octahedron and the regular cube. Some applications and connections with the work of several authors complete the paper.

Tachikawa, Atsushi, Department of Mathematics, Faculty of Science and Technology, Tokyo University of Science, Noda, Chiba, 278-8510, Japan (tachikawa_atsushi@ma.noda.tus.ac.jp).
C1,α-regularity of energy minimizing maps from a 2-dimentional domain into a Finsler space, pp. 1175-1186.
ABSTRACT. Let (M,g) be a 2-dimentional smooth Riemannian manifold, Ω ⊂ M a bounded domain with smooth boundary ∂Ω, and (Rn, F) a Finsler space with a Finsler structure F which satisfies uniform convexity. Then, for a boundary data φ∈ H1,∞(Ω,Rn), an energy minimizing map u : Ω → (Rn, F) with the boundary condition u = φ on ∂Ω is in the class C1,α(Ω) ∩C0, β(Ω∪∂Ω) for some α∈(0,1) and any β∈(0,1).

Bowers, Adam, Department of Mathematics, University of California San Diego, La Jolla, CA 92093 (abowers@ucsd.edu). 
A generalization of the Varopoulos algebra, pp. 1187-1210.
ABSTRACT. We generalize the notion of the the Varopoulos algebra, which is the projective tensor product of two spaces of bounded measurable functions. We show that this new class of functions can be integrated with respect to bimeasures in a well-defined way, and give a Fubini-type property. We then show connections to Schur multipliers and tilde algebras and then discuss some unanswered questions.

Izuchi, Kei Ji, Department of Mathematics, Niigata University, Niigata 950-2181, Japan (izuchi@m.sc.niigata-u.ac.jp) and  Izuchi, Yuko, Aoyama-shinmachi 18-6-301, Niigata 950-2006, Japan (yfd10198@nifty.com)
Sequential properties of the maximal ideal space of H∞, pp. 1211-1232.
ABSTRACT. Let D be the smallest Douglas algebra containing the Banach algebra of bounded analytic functions on the open unit disk and M be the maximal ideal space of D. It is known that cluster points of a sequence of points in M which are contained in distinct fibers have some remarkable properties. In this paper, we continue this line of research by considering more general sequences. Let {En} be a sequence of subsets of M and x be a cluster point of the union set of {En}. It is proved that if each En is a QC-level set that contains a sparse point (or a point of type G), then so does Q(x), where Q(x) is the QC-level set associated with x. It is also shown that if {Xn} is a sequence of points in M whose k-hull, k(Xn), is minimal, then so does the k-hull of any cluster point x of {Xn}. In the appendix, we shall be concerned with T. Wolff's results, given in his unpublished note, on QC-level sets.

Christopher Jankowski, University of Pennsylvania, Department of Mathematics, David Rittenhouse Laboratory, 209 South 33rd Street,  Philadelphia, PA 19104-6395 (cjankows@sas.upenn.edu).
Unital q-positive maps on M2(C) and cocycle conjugacy of E0-semigroups, pp. 1233-1266.
ABSTRACT. From previous work, we know how to obtain type II0 E0-semigroups using boundary weight doubles (φ, ν), where φ is a unital q-positive map from Mn(C) to itself and ν is a normalized unbounded boundary weight over L2(0, ∞). In this paper, we classify the unital q-positive maps φ from M2(C) to itself, finding that if φ is in addition q-pure, then it is either rank one or invertible. We also examine the case n=3, obtaining the limit maps Lφ for all unital q-positive maps φ from M3(C) to M3(C). In conclusion, we present a cocycle conjugacy result for E0-semigroups induced by boundary weight doubles (φ, ν) when ν has the form ν((I - Λ(1))1/2 B (I - Λ(1))1/2)=(f,Bf).

Li, Qihui, Department of Mathematics East China University of Science and Technology Meilong Road 130, 200237, Shanghai, China (lqh991978@gmail.com),  and Shen, Junhao, Department of Mathematics and Statistics University of New Hampshire, Durham, NH, 03824, USA (jog2@cisunix.unh.edu).
On MF property of reduced amalgamated free products of UHF algebra, pp. 1267-1289.
ABSTRACT. We concentrate on the MF property of reduced free products of unital C*-algebras with amalgamation over finite dimensional C*-algebras. More specifically, we give a necessary and sufficient condition for a reduced free product of two UHF algebras amalgamated over a finite-dimensional C*-algebra with respect to trace preserving conditional expectations to be MF.

Yoshifumi Matsuda, Department of Mathematics, Kyoto University, Kita-shirakawa Oiwake-cho, Sakyo-ku, Kyoto, 606-8502, Japan (ymatsuda@math.kyoto-u.ac.jp), Shin-ichi Oguni, Department of Mathematics, Faculty of Science, Ehime University, 2-5 Bunkyo-cho, Matsuyama, Ehime, 790-8577 Japan (oguni@math.sci.ehime-u.ac.jp), and  Saeko Yamagata, Faculty of Education and Human Sciences, Yokohama National University, 240-8501 Yokohama, Japan (yamagata@ynu.ac.jp).
C*-simplicity for groups with non-elementary convergence group actions, pp. 1291-1299.
ABSTRACT. We prove that a countable group with an effective minimal non-elementary convergence group action is a Powers group. More strongly we prove that it is a strongly Powers group and thus its non-trivial subnormal subgroups are C*-simple.

Prochno, Joscha, Mathematisches Seminar, Christian-Albrechts-Universitaet zu Kiel, Ludewig-Meyn-Str. 4, 24098 Kiel, Germany (prochno@math.uni-kiel.de) and Riemer, Stiene, Mathematisches Seminar, Christian-Albrechts-Universitaet zu Kiel, Ludewig-Meyn-Str. 4, 24098 Kiel, Germany (riemer@math.uni-kiel.de).
On the maximum of random variables on product spaces, pp. 1301-1311.
ABSTRACT.We study the expectation of the maximum of random variables on product spaces. To be more precise, we show that in the case of sequences X1,...,Xn and Y1,...,Yn of p-stable respectively q-stable random variables (p and q in (1,2) and p less than q) on different probability spaces the expectation of the maximum in i and j of |aij Xi Yj|, is equivalent to the p-norm of the q-norm of the matrix (aij). In case q=2 we obtain the equivalence to the p-norm of the M-norm of (aij), where M is the Orlicz function corresponding to the Gaussians. In Addition, we prove that a sequence (Xi) of iid log-gamma(1,p), p>1, distributed random variables generates the p-norm, i.e., the expectation of the maximum in i of |ai Xi| is equivalent to the p-norm of the vector (ai). As far as we know, the generating distribution for p-norms with p greater or equal to 2 has not been known up to now. The case of the generating the 2-norm is important for applications, e.g., obtaining characterizations of subspaces of L1.

Dykema, Kenneth J., and  Redelmeier, Daniel, Texas A&M University, College Station TX 77843-3368 (kdykema@math.tamu.edu).
The amalgamated free product of hyperfinite von Neumann algebras over finite dimensional subalgebras, pp. 1313-1331.
ABSTRACT. In this paper we describe the amalgamated free product of two hyperfinite von Neumann algebras over a finite dimensional subalgebra. In general the free product is of the form a direct sum of finitely many interpolated free group factprs and (possibly) a hyperfinite von Neumann algebra. We then show that the class of von Neumann algebras of this form is closed under taking amalgamated free products over finite dimensional subalgebras.

Fernández-Moncada, Paulo, Universidad Carlos III de Madrid, Spain 28911 (pefernan@math.uc3m.es), García, Antonio, Mathematics Department, Universidad Carlos III de Madrid, Spain 28911 (agarcia@math.uc3m.es), Hernández-Medina, Miguel, Applied Mathematics Department, Universidad Politécnica de Madrid, Spain 28040 (miguelangel.hernandez.medina@upm.es).
Sampling associated with resolvent-type kernels and Lagrange-type interpolation series, , pp. 10051333-1347.
ABSTRACT. In this paper a new class of Kramer kernels is introduced, motivated by the resolvent of a symmetric operator with compact resolvent. The article gives a necessary and sufficient condition to ensure that the associated sampling formula can be expressed as a Lagrange-type interpolation series. Finally, an illustrative example, taken from the Hamburger moment problem theory, is included.

Alexandre Eremenko, Department of Mathematics, Purdue University, West Lafayette IN 47907 (eremenko@math.purdue.edu).
Normal holomorphic maps from C* to a projective space, pp. 1349-1357.
ABSTRACT. A theorem of A. Ostrowski describing meromorphic functions f such that the family f(λz): λ ∈ C* is normal, is generalized to holomorphic maps from C* to a projective space.

Caiyun, Fang, Fudan University, Shanghai 200433, P. R. China (10110180020@fudan.edu.cn), and Xuecheng, Pang, East China Normal University, Shanghai 200241, P. R. China (xcpang@math.ecnu.edu.cn).
Two families of meromorphic functions concerning shared functions, pp. 1359-1366.
ABSTRACT. In this paper, we extend recent results of Liu and Pang on families of meromorphic functions with shared values. We consider the normality of two families of meromorphic functions concerning shared function and obtain some related theorems.

Shou Lin, Department of Mathematics, Ningde Normal University, Fujian 352100, P. R. China (shoulin60@163.com), Kedian Li, Department of Mathematics, Zhangzhou Normal University, Zhangzhou 363000, P. R. China (likd56@126.com), and Ying Ge, School of Mathematical Sciences, Soochow University, Suzhou 215006, P. R. China (geying@suda.edu.cn).
Convergent-sequence spaces and sequence-covering mappings, pp. 1367-1384.
ABSTRACT. Based on ideas of mappings characterizing spaces, this paper characterizes the space X, where each sequence-covering mapping (resp. sequentially-quotient mapping, pseudo-sequence-covering mapping) onto X is an almost open mapping (resp. bi-quotient mapping, 1-sequence-covering mapping, almost weak-open mapping, almost sn-open mapping), and describes some properties of a space in which each point has a neighborhood consisting of a convergent sequence, which answers a question posed by F. Siwiec.

García-Ferreira S., Universidad Nacional Autónoma de México, Campus Morelia, Apartado Postal 61-3, Santa Maria, 58089, Morelia, Michoacan, Mexico (sgarcia@matmor.unam.mx), Miyazaki K., Department of Mathematics, Osaka Sangyo University, Osaka 574-8530, Japan (kmiyazaki@las.osaka-sandai.ac.jp), Nogura T. , Department of Mathematics Faculty of Science, Ehime University, Matsuyama 790-8677, Japan (nogura.tsugunori.mx@ehime-u.ac.jp), and Tomita A. H., Instituto de Matemática e Estatística, Universidade de São Paulo Rua do Matão, 1010, CEP 05508-090, São Paulo, Brazil (tomita@ime.usp.br).
Topologies generated by weak selection topologies, pp. 1385-1399.
ABSTRACT. A weak selection on an infinite set X is a function f: [X]2 → X such that f({x, y}) is an element of {x, y} for each {x, y} in [X]2. A weak selection f on X defines a relation x <f y if f({x, y}) = x whenever x, y are in X are distinct. The topology Tf on X generated by the weak selection f is the one which has the family of all intervals (←, x)f = { y in X : y <f x} and (x, →) = { y in X : x <f y } as a subbase. A weak selection on a space is said to be continuous if it is a continuous function with respect to the Vietoris topology on [X]2 . The paper deals with topological spaces (X,T) for which there is a set W of continuous weak selections satisfying T = V{f in W} Tf (we say that the topology of X is generated by continuous weak selections). We prove that for any infinite cardinal α, there exists a weakly orderable space whose topology cannot be generated by less than or equal to α -many continuous weak selections. We prove that any subspace of a space generated by continuous weak selections is also generated by continuous weak selections. Assuming that c is regular, we construct a suborderable space whose topology is generated by c-many continuous weak selections but not by less than c. Also, under the assumption of GCH , for every infinite successor cardinal α+ we construct a space X that is generated by α+ -many continuous weak selections but cannot be generated by α-many selections.

Kazimierz Alster, Faculty of Mathematics and Natural Science, College of Science, Cardinal Stefan Wyszyński University, Dewajtis 5, 01--815 Warsaw, Poland (kalster@impan.gov.pl).
On paracompactness in Cartesian products products and Telgarsky's game, pp. 1401-1422.
ABSTRACT. We prove that if X is a paracompact space and M is a metric space such that X can be embedded in the product of omega one copies of M in such a way that for each alpha less than omega one the projection p from X into the product of alpha copies of M is such that for each x in X the projection p is closed at x or the preimage of p(x) is closed and open in X then the product of X and Y is paracompact for every paracompact space Y if and only if the first player of the G(DC,X) game introduced by Telgarsky has a winning strategy.

Dow, Alan, University of North Carolina at Charlotte, USA (adow@uncc.edu), and Shelah, Saharon, Institute of Mathematics, Hebrew University, Givat Ram, Jerusalem 91904, Israel (shelah@math.rutgers.edu).
 An Efimov space from Martin's Axiom, pp. 1423-1435.
ABSTRACT. We show that the existence of an Efimov space follows from a weak set-theoretic hypothesis. An Efimov space is a compact space containing no infinite converging sequence and no copy of the Stone-Cech compactification of the integers.

Ai-Jun Xu, School of Mathematical Sciences, Nanjing Normal University,Nanjing 210046, P.R. China; Department of Applied Mathematics, Nanjing Forest University, Nanjing 210037, P.R.China (ajxu@njfu.edu.cn), and Wei-Xue Shi, Department of Mathematics, Nanjing University, Nanjing 210093, P.R. China (wxshi@nju.edu.cn).
A result on monotonically metacompact spaces, pp. 1385-1399.
ABSTRACT. We answer a question of H.R. Bennett, K.P. Hart and D.J. Lutzer by showing that any generalized ordered space is monotonically (countably) metacompact if its subspace consisting of non-isolated points is monotonically (countably) metacompact.