Electronic Edition Vol. 37, No. 3 , 2011

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 (Radboud), 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


Guram Bezhanishvili and Patrick J. Morandi, Department of Mathematical Sciences, New Mexico State University, Las Cruces NM 88003-8001 (gbezhani@nmsu.edu) ,
(pmorandi@nmsu.edu) .
One-point order-compactifications, pp. 699-713.
ABSTRACT  We classify all one-point order-compactifications of a noncompact locally compact order-Hausdorff ordered topological space X. We give a necessary and sufficient condition for a one-point order-compactification of X to be a Priestley space. We show that although among the one-point order-compactifications of X there may not be a least one, there always is a largest one, which coincides with the one-point order-compactification of McCallion. In fact, we prove that whenever X satisfies the condition given in McCartan, then the largest one-point order-compactification of X coincides with the one described by McCartan.

Dobbs, David E., University of Tennessee, Knoxville, Tennessee 37996-0612, USA (dobbs@math.utk.edu), and Sahandi, Parviz, University of Tabriz, Tabriz, Iran (sahandhi@tabrizu.ac.ir).
On semistar Nagata rings, Prüefer-like domains and semistar going-down domains, pp. 715-731.
ABSTRACT. Let star be a semistar operation on a domain D. Then the semistar Nagata ring Na(D, star) is a treed domain if and only if D is star-tilde-treed and the contraction map from Spec(Na(D, star)) to the union of the set of quasi-star-tilde-ideals of D and the singleton set consisting of 0 is a bijection if and only if D is a star-tilde-treed and star-tilde-quasi-Prüefer domain. Consequently, if D is a star-tilde-Noetherian domain but not a field, then D is star- tilde-treed if and only if star-tilde-dim(D)=1. The ring Na(D, star) is a going-down domain if and only if D is a star-tilde-GD domain and a star-tilde-quasi-Prüefer domain. In general, D is a PstarMD if and only if Na(D, star) is an integrally closed treed domain if and only if Na(D, star) is an integrally closed going-down domain. If P is a quasi-star-prime ideal of D, an induced stable semistar operation of finite type, star/P, is defined on D/P. The associated Nagata rings satisfy: Na(D/P, star/P) is isomorphic to Na(D, star)/PNa(D, star). If D is a PstarMD (resp., a star-tilde-Noetherian domain; resp., a star-Dedekind domain; resp., a star-tilde-GD domain), then D/P is a P(star/P)MD (resp., a (star/P)-Noetherian domain; resp., a (star/P)-Dedekind domain; resp., a (star/P)-GD domain).

Hamid Reza Maimani, Department of Mathematics, Shahid Rajaee University, Tehran, Iran and School of Mathematics, Institute for Research in Fundamental Sciences (IPM), Tehran Iran (maimani@ipm.ir) and Siamak Yassemi, Department of Mathematics, University of Tehran, Tehran, Iran and School of Mathematics, Institute for Research in Fundamental Sciences (IPM), Tehran Iran (yassemi@ipm.ir).
On the zero-divisor graphs of commutative semigroups, pp. 733-740.
ABSTRACT. In this paper we study the case where the zero divisor graph of a commutative semigroup is complete r-partite for a positive integer r. Also we bring some results on the commutative semigroups which are finitely colorable.

D.D. Anderson, Department of Mathematics, The University of Iowa, Iowa City, IA 52242 USA  (dan-anderson@uiowa.edu) and Sangmin Chun, Department of Mathematics\\Seoul National University, Seoul 151-747, Republic of Korea (schun@snu.ac.kr).
Irreducible elements in commutative rings with zero-divisors, pp. 741-744.
ABSTRACT. Let R be a commutative ring with zero-divisors. A nonunit element a in R is irreducible if a=bc implies (a)=(b) or (a) =(c). We show that if a,b in R with a irreducible and (a)⊂ (b) ⊂R then a is a zero-divisor and b is a non zero-divisor. It follows that a in R is irreducible if and only if (1) (a) is maximal in the set of proper principal ideals of R or (2) (a) is maximal in the set of principal ideals generated by zero-divisors. Thus a chain (a1) ⊂...(an)  of principal ideals generated by irreducible elements must have n ≤ 2.

da Silva, Rosângela M., Instituto de Matemática e Estatística, Universidade Federal de Goiás, 74001-970, Goiânia, GO, Brazil (rosams@mat.ufg.br)  and Tenenblat, Keti, Departamento de Matemática, Universidade de Brasília, 70904-970, Brasília, DF, Brazil  (keti@mat.unb.br) .
Minimal Surfaces in a cylindrical region of R3 with a Randers metric, pp. 745-771.
ABSTRACT.  We consider the Euclidean metric of R3 perturbed by a rotation. This Finsler space, M3, is the open region of R3 bounded by a cylinder with a Randers metric. Using the Busemann-Hausdorff volume form, we prove that the only minimal surfaces of rotation in this space are the catenoids contained in M3, generated by the rotation of a catenary around the axis of the cylinder. There are no minimal surfaces of rotation whose rotational axis is different from the axis of the cylinder. Moreover, we obtain the partial differential equations that characterize the minimal surfaces in M3 that are the graph of a function. We prove that the only planar regions which are minimal M3 are the open disks bounded by the parallels of the cylinder and the strips of planes generated by the intersection of M3 with the planes of R3 that contain the cylinder axis.

Imran Ahmed, Department of Mathematics, COMSATS Institute of Information Technology, M.A. Jinnah Campus, Defence Road, off Raiwind Road Lahore, PAKISTAN (drimranahmed@ciitlahore.edu.pk) and Maria Aparecida Soares Ruas, ICMC-USP, Caixa Postal 668, 13560-970, São Carlos-S.P., Brazil (maasruas@icmc.usp.br).
Invariants of Relative Right and Contact Equivalences, pp. 773-786.
ABSTRACT. We study holomorphic function germs under equivalence relations that preserve an analytic variety. We show that two quasihomogeneous polynomials, not necessarily with isolated singularities, having isomorphic relative Milnor algebras are relative right equivalent. Under the condition that the module of vector fields tangent to the variety is finitely generated, we also show that the relative Tjurina algebra is a complete invariant for the classification of arbitrary function germs with respect to the relative contact equivalence. This is the relative version of a well known result by Mather and Yau.

Jin Hong Kim, Department of Mathematical Sciences, Korea Advanced Institute of Science and Technology, Yuseong-gu, Daejeon 305-701, Republic of Korea (jinkim@kaist.ac.kr) and Hee Kwon Lee, Korea Institute for Advanced Study, 87 Hoegiro, Seoul 130-722, Republic of Korea (heekwon@kias.re.kr
On the fundamental groups of positively curved 5-manifolds with maximal local symmetry rank, pp. 787-792.
ABSTRACT. Let M be a closed oriented Riemannian manifold of dimension 5 with positive sectional curvature. If M admits an effective and isometric torus action of rank 2 or 3 which is invariant under the fundamental group of M, it has been shown by Fang and Rong that M is homeomorphic to a spherical space form. In this paper, we show that if M admits an effective and isometric torus action of rank 3 which is invariant under the fundamental group of M, then its fundamental group is actually cyclic. Furthermore, we show that if the fundamental group of M is not isomorphic to the cyclic group of order 3 as well, then M is diffeomorphic to a lens space.

Gomes, J. Barbosa, Departamento de Matemática, Universidade Federal de Juiz de Fora, Juiz de Fora, MG, Brazil (barbosa.gomes@ufjf.edu.br), and Ruggiero, Rafael O., Departamento de Matemática, Pontifícia Universidade Católica do Rio de Janeiro, Rio de Janeiro, RJ, Brazil (rorr@mat.puc-rio.br).
Smooth k-basic Finsler compact surfaces with expansive geodesic flows are Riemannian, pp. 793-806.
ABSTRACT. We show that C4 k-basic compact Finsler surfaces whose geodesic flows are expansive are in fact Riemannian. A Finsler surface is called k-basic if the Gauss-Finsler curvature does not depend on the vertical variable.

Bos, Rogier, Christelijk Gymnasium Utrecht, Koningsbergerstraat 2, 3531 AJ Utrecht, The Netherlands (rogier_bos@hotmail.com).
Continuous representations of groupoids, pp. 807-844.
ABSTRACT. We introduce unitary representations of continuous groupoids on continuous fields of Hilbert spaces. We investigate some properties of these objects, using several examples. We present a palette of results, including, among others: a comparision of the different notions of continuity for representations, a description of the representations of families of groups, and a version of the Peter-Weyl theorem for groupoids.

Matache, Valentin, Department of Mathematics, University of Nebraska, Omaha, NE 68182, USA (vmatache@mail.unomaha.edu).
Composition operators whose symbols have orthogonal powers, pp. 845-857.
ABSTRACT.  Composition operators on the Hilbert Hardy space H2 whose symbols are analytic selfmaps of the open unit disk having orthogonal powers are considered. The spectra and essential spectra of such operators are described. In the general case of an arbitrary analytic selfmap of the open unit disk, it is proved that the composition operator induced by that map has essential spectral radius less than 1 if and only if the map under consideration is a non--inner map with a fixed point in the unit disk. The canonical decomposition of a non--unitary composition contraction is determined.

Androulakis, George,University of South Carolina,Columbia, SC 29208, United States (giorgis@math.sc.edu), Kalton, Nigel, University of Missouri,Columbia, MO 65211, United States (nigel@math.missouri.edu) and Tcaciuc, Adi, Grant MacEwan College, Edmonton, Alberta, T5J P2P, Canada (tcaciuc@math.ualberta.ca).
On Banach spaces containing lp or c0, pp. 859-866.
ABSTRACT. We use the Gowers block Ramsey theorem to characterize Banach spaces containing isomorphs of lp (for some 1≤ p<∞) or c0.

Kadets, Vladimir, Department of Mechanics and Mathematics, Kharkov National University, pl.Svobody 4, 61077 Kharkov, Ukraine (vova1kadets@yahoo.com), Shepelska, Varvara, Department of Mechanics and Mathematics, Kharkov National University, pl.Svobody 4, 61077 Kharkov, Ukraine (shepelskaya@yahoo.com), Werner, Dirk, Department of Mathematics, Freie Universität Berlin, Arnimallee 6, D-14195 Berlin, Germany (werner@math.fu-berlin.de).
Thickness of the unit sphere, l1-types, and the almost Daugavet property, pp. 867-878.
ABSTRACT. We study those Banach spaces X for which SX does not admit a finite ε-net consisting of elements of SX for any ε < 2. We give characterisations of this class of spaces in terms of l1-type sequences and in terms of the almost Daugavet property. The main result of the paper is: a separable Banach space X is isomorphic to a space from this class if and only if X contains an isomorphic copy of l1.

Junsheng Fang, Department of Mathematics, Texas A&M University, College Station, TX, 77843 (jfang@math.tamu.edu) and Don Hadwin, Department of Mathematics, University of New Hampshire, Durham, NH, 03824 (don@math.unh.edu).
A note on the invariant subspace problem relative to a type  II1 factor, pp. 879-893.
ABSTRACT. In this paper we prove that every operator in an ultrapower algebra of a type II1 factor has a continuous family of invariant subspaces. We also show that an ultrapower algebra of the hyperfinite type II1 factor is not *-isomorphic to an ultraproduct of matrix algebras.

Benjamin Steinberg, School of Mathematics and Statistics, Carleton University Ottawa, ON K1S 5B6 (bsteinbg@math.carleton.ca).
Strong Morita equivalence of inverse semigroups, pp. 895-927.
ABSTRACT. We introduce strong Morita equivalence for inverse semigroups. This notion encompasses Mark Lawson's concept of enlargement. Strongly Morita equivalent inverse semigroups have Morita equivalent universal groupoids in the sense of Paterson and hence strongly Morita equivalent universal and reduced C*-algebras. As a consequence we obtain a new proof of a result of Khoshkam and Skandalis showing that the C*-algebra of an F-inverse semigroup is strongly Morita equivalent to a cross product of a commutative C*-algebra by a group.

Edmunds, David E., Department of Mathematics,  Pevensey II Building, University of Sussex Falmer, Brighton, BN1 9QH, UK , and Hurri-Syrjanen, Ritva, Department  of Mathematics and Statistics, P.O. Box 68, Gustaf Hallstrominkatu 2 b,  FI-00014 University of Helsinki, Finland (ritva.hurri-syrjanen@helsinki.fi).
The improved Hardy inequality, pp. 929-937.
ABSTRACT.  An inequality of Hardy type, with a remainder term, is proved for functions defined on a bounded domain in Euclidean n-space with plump complement. It is also shown that Rellich's inequality holds in such domains.

Godoy, Tomás, FaMAF, Universidad Nacional de Córdoba, (5000) Córdoba, Argentina,  Kaufmann, Uriel, FaMAF, Universidad Nacional de Córdoba, (5000) Córdoba, Argentina,  and Paczka, Sofía, FaMAF, Universidad Nacional de Córdoba, (5000) Córdoba, Argentina (kaufmann@mate.uncor.edu).
Nonnegative solutions of periodic parabolic problems in the presence of non-well-ordered sub and supersolutions. , pp. 939-954.
ABSTRACT. Let D be a smooth bounded domain in RN, let a,b be two bounded nonnegative T-periodic functions, and let 0<q<1. We study existence and nonexistence of nontrivial nonnegative solutions for periodic parabolic problems of the form Lu = ra(x,t)u - b(x,t)uq in D×R, with Dirichlet homogeneous boundary conditions, where r>0 is a real parameter. We also analyze the behaviour of the solutions with respect to r. All results remain true for the corresponding elliptic problems.

Hiroshi, Hosokawa, 3-14-94, Kita-machi, Kokubunji-shi,Tokyo, 185-0001, Japan (hosokawa@u-gakugei.ac.jp).
Strong size levels of n-fold hyperspaces, pp. 955-965.
ABSTRACT. We define an open monotone map on the n-fold hyperspace called a strong size map which is an extention of a Whitney map on C(X). We proved some properties of point inverse of a strong size map.

W.J. Charatonik, Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, MO 65409 (wjcharat@mst.edu) and Janusz R. Prajs, Department of Mathematics, California State University, Sacramento (prajs@csus.edu).
Maps of absolute retracts for tree-like continua, pp. 967-976.
ABSTRACT. It is shown that the class \artl of absolute retracts for tree-like continua is invariant with respect to monotone maps. From the past results it follows that the inverse limit of trees with confluent bonding maps is an absolute retract for tree-like (and more generally, hereditarily unicoherent) continua. In this paper we provide the first example of a member of \artl that is not such a limit.

Beane, Robbie A., Department of Mathematics, Lindenwood University, 209 S. Kingshighway, Saint Charles, MO 63301 (rbeane@lindenwood.edu).
Local compactness of the hyperspace CLC(X), pp. 977-994.
ABSTRACT. We provide a necessary condition and a sufficient condition for local compactness of CLC(X), the hyperspace of closed connected subsets of a metric space X, as well as a sufficient condition for metrizability of CLC(X). To simplify the statement of these conditions we introduce the terms buffer and totally buffered . Some basic theory relating to these new concepts is developed.

Angelo Bella, Dipartimento di Matematica e Informatica, Università di Catania, Viale Andrea Doria 6, 95125 Catania, (bella@dmi.unict.it), Camillo Costantini, Dipartimento di Matematica, Università di Torino, via Carlo Alberto 10, 10123 Torino, Italy, (camillo.costantini@unito.it), Santi Spadaro Department of Mathematics and Statistics, Auburn University, 221 Parker Hall, Auburn, Alabama 36849-5310. Current address: Department of Mathematics, Ben Gurion University of the Negev, Be'er Sheva, 84105 Israel (santi@cs.bgu.ac.il).
 P-spaces and the Whyburn property, pp. 995-1015.
ABSTRACT. We investigate the Whyburn and weakly Whyburn property in the class of P-spaces, that is spaces where every countable intersection of open sets is open. We construct examples of non-weakly Whyburn P-spaces of size continuum, thus giving a negative answer under CH to a question of Pelant, Tkachenko, Tkachuk and Wilson. In addition, we show that the weak Kurepa Hypothesis (an assumption weaker than CH) implies the existence of a non-weakly Whyburn P-space of size aleph2. Finally, we consider the behavior of the above-mentioned properties under products; we show in particular that the product of a Lindelöf weakly Whyburn P-space and a Lindelöf Whyburn P-space is weakly Whyburn, and we give a consistent example of a non-Whyburn product of two Lindelof Whyburn P-spaces.

Varagona, Scott, Mathematics and Statistics, 221 Parker Hall, Auburn University, Auburn, AL, 36849 (varagsm@auburn.edu).
Inverse limits with upper semi-continuous bonding functions and indecomposability, pp. 1017-1034.
ABSTRACT. In their recent work on inverse limits with upper semi-continuous bonding functions, Ingram and Mahavier give various sufficient conditions for such an inverse limit space to be a continuum. Here, we present additional conditions on the bonding functions that are sufficient conditions for the inverse limit to be a decomposable (or indecomposable) continuum. Several examples are given illustrating these results.

Leandro F. Aurichi,  Instituto de Ciências Matemáticas e de Computação (ICMC-USP), Universidade de São Paulo, São Carlos, SP - CEP 13566-590 - Brazil (aurichi@icmc.usp.brD-spaces, separation axioms and covering properties, pp. 1035-1042.
ABSTRACT. We show some properties that imply D. Some of such properties involve preservation of separations axioms over products, some other are about subspaces of a compact space. We also define a stronger condition than D. Its definition is motivated by several proofs that certain spaces are D. We show that such property implies Lindelöfness.