HOUSTON JOURNAL OF
MATHEMATICS

Electronic Edition Vol. 39, No. 1 , 2013

Editors: G. Auchmuty (Houston), D. Bao (San Francisco, SFSU), D. Blecher (Houston), Bernhard G. Bodmann, 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

Fusacchia, Gabriele, Dipartimento di Matematica Pura ed Applicata, Università degli Studi di Padova, 35121 Padova, Italy (gabfus@math.unipd.it).
 Strong semistar Noetherian domains, pp. 1-20.
ABSTRACT. We study the class of semistar Noetherian domains, characterized by having the Ascending Chain Condition on quasi semistar ideals, in the particular case of a stable semistar operation. In analogy with the Strong Mori case, we call these domains Strong semistar Noetherian, and provide many different characterizations for them, all involving local Noetherianity at quasi semistar prime ideals; this condition alone being too weak, we examine which further properties must be required from the set of quasi semistar prime ideals. This brings our attention on primary decompositions of ideals, associated prime ideals and topological Noetherianity on special subsets of the spectrum. In particular, we use the concept of Delta-Noetherian domain, which proves to be useful in describing Strong semistar Noetherian domains when no assumption of finite character conditions is made.

Ischi, Boris, Collège de Candolle, 5 rue d'Italie, 1204 Geneva, Switzerland (boris.ischi@edu.ge.ch), and Seal, Gavin J., Ecole Polytechnique Fédérale de Lausanne, Switzerland (gavin_seal@fastmail.fm).
 The Chu construction for complete atomistic coatomistic lattices, pp. 21-49.
ABSTRACT. The Chu construction is used to define a *-autonomous structure on a category of complete atomistic coatomistic lattices. This construction leads to a new tensor product that is compared with a certain number of other existing tensor products.

Fieldsteel, Nathan, UIUC,  Urbana, IL 61801 (fieldst2@illinois.edu),  Lindberg, Tova, University of Arizona, Tucson, AZ 85719 (tlindberg@math.arizona.edu),  London, Tyler (tyler.a.london@gmail.com),  Tran, Holden (holdentran2007@u.northwestern.edu), and Xu, Haokun, UCLA, Los Angeles, CA 90095 (xuh@math.ucla.edu).
Classification of groups with strong symmetric genus up to twenty-five, pp. 51-60.
ABSTRACT.The strong symmetric genus of a finite group is the minimum genus of a compact Riemann surface on which the group acts as a group of automorphisms preserving orientation. A characterization of the infinite number of groups with strong symmetric genus zero and one is well-known and the problem is finite for each strong symmetric genus greater than or equal to two. May and Zimmerman have published papers detailing the classification of all groups with strong symmetric genus two through four. Using the computer algebra system GAP, we extend these classifications to all groups of strong symmetric genus up to twenty-five. This paper outlines the approach used for the extension.

Chiang-Hsieh, Hung-Jen, National Chung Cheng University, Chia-Yi 621, Taiwan (hchiang@math.ccu.edu.tw), Lee, Pei-Feng, National Chung Cheng University, Chia-Yi 621, Taiwan (yeuns22@mail.djt.ptc.edu.tw), and Wang, Hsin-Ju, National Chung Cheng University, Chia-Yi 621, Taiwan (hjwang@math.ccu.edu.tw)
On the line graphs associated to the zero-divisor graphs of commutative rings, pp. 61-72.
ABSTRACT. Let R be a commutative ring with identity and let Γ(R) be its zero-divisor graph. In this paper, we study various graphical properties of the line graph associated to Γ(R), such as its diameter, girth, and the Eulerian property, and make some classifications of commutative rings (up to isomorphism) using these invariants.

Andrej Bauer and Karin Cvetko-Vah, Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia (Andrej.Bauer@andrej.com), (Karin.Cvetko@fmf.uni-lj.si).
Stone duality for skew Boolean algebras with intersections, pp. 73-109.
ABSTRACT.  We extend Stone duality between generalized Boolean algebras and Boolean spaces, which are the zero-dimensional locally-compact Hausdorff spaces, to a non-commutative setting. We first show that the category of right-handed skew Boolean algebras with intersections is dual to the category of surjective étale maps between Boolean spaces. We then extend the duality to skew Boolean algebras with intersections, and consider several variations in which the morphisms are restricted. Finally, we use the duality to construct a right-handed skew Boolean algebra without a lattice section.

Zhang, Jing, Department of Mathematics and Statistics, State University of New York at Albany, Albany, NY 12222 (jzhang@albany.edu).
Singularity of a holomorphic map, pp. 111-125.
ABSTRACT. Let f be a holomorphic map between two complex manifolds M and N. We will study the singularities of f, specially if f is defined by the linear system of a holomorphic line bundle. We will also investigate the relationships among Milnor number, singularity of the map and the global smooth sections of the line bundle. .

Oscar Perdomo, Department of Mathematics, Central Connecticut State University, New Britain, CT 06050 (perdomoosm@ccsu.edu).
Algebraic constant mean curvature surfaces in Euclidean space , pp. 127-136.
ABSTRACT. In this paper we prove that the only algebraic constant mean curvature (cmc) surfaces in the 3-dimensional Euclidean space of order less than four are the planes, the spheres and the cylinders. The method used heavily depends on the efficiency of algorithms to compute Gröbner Bases and also on the memory capacity of the computer used to do the computations. We will also prove that the problem of finding algebraic constant mean curvature hypersurfaces in the Euclidean space completely reduces to the problem of solving a system of polynomial equations. .

Jintang Li, Department of Mathematics,Xiamen University, Xiamen, Fujian, 361005,China (dli66@xmu.edu.cn).
Hypersurfaces of Minkowski space with constant mean curvature, pp. 137-145.
ABSTRACT. Let M be a compact hypersurface of Minkowski space with parallel unit normal vector and constant mean curvature. In this paper, we prove that M is either an Euclidean sphere or a locally Minkowski space if the norm square of the second fundamental form of M satisfies a pinching condition.

Gabriela P. Ovando, CONICET and Dept. de Mate., ECEN - FCEIA, Universidad Nacional de Rosario, Pellegrini 250, 2000 Rosario, Argentina (gabriela@fceia.unr.edu.ar). 
Naturally reductive pseudo-Riemannian 2-step nilpotent Lie groups , pp. 147-167.
ABSTRACT.This paper deals with naturally reductive pseudo-Riemannian 2-step nilpotent Lie groups for which the metric is invariant under a left action. The case of nondegenerate center is characterized as follows. The simply connected Lie group can be constructed starting from a real representation of a certain Lie algebra which carries an ad-invariant metric. Also a homogeneous structure is given and applications are shown.

Tapdigoglu, Ramiz,Technical University of Lodz,Faculty of Technical Physics,Computer Science and Applied Mathematics,90-924 Lodz,Poland (racer_rmz@hotmail.com).
 On the description of invariant subspaces in the space C(n)[0,1], pp. 169-176.
ABSTRACT.  Recall that a linear bounded operator, acting on a Banach space , is called unicellular if its lattice of invariant subspaces is totally ordered with respect to inclusion. In this paper we study the unicellularity problem for the Volterra integration operator on the space of n-times continuously differentiable functions on the unit segment. By applying Duhamel product technique an alternative proof of the Ostapenko-Tarasov theorem is given.

Moslehian, Mohammad Sal, Ferdowsi University of Mashhad, Mashhad 91775, Iran (moslehian@ferdowsi.um.ac.ir) ( http://profsite.um.ac.ir/~moslehian/ ).
Matrix Hermite-Hadamard type inequalities, pp. 177-189.
ABSTRACT. We present several matrix and operator inequalities of Hermite-Hadamard type. We first establish a majorization version for monotone convex functions on matrices. We then utilize the Mond-Pecaric method to get an operator version for convex functions. We also present some applications. Finally we obtain an Hermite-Hadamard inequality for operator convex functions, positive linear maps and operators acting on Hilbert spaces.

Armengol Gasull, Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain (gasull@mat.uab.cat) and Yulin Zhao, Department of Mathematics, Sun Yat-sen University, Guangzhou, 510275, People's Republic of China (mcszyl@mail.sysu.edu.cn).
 On a family of polynomial differential equations having at most three limit cycles, pp. 191-203.
ABSTRACT. We prove the existence of at most three limit cycles for a family of planar polynomial differential equations. Moreover we show that this upper bound is sharp. The key point in our approach is that the differential equations of this family can be transformed into Abel differential equations.

Cerny, Robert, Charles University, Faculty of Mathematics and Physics, Department of Mathematical Analysis, Sokolovska 83, 186 75 Praha 8, Czech Republic (rcerny@karlin.mff.cuni.cz).
On singular Moser-Trudinger inequality for embedding into exponential and multiple exponential spaces. , pp. 205-230.
ABSTRACT. We give the Moser-Trudinger inequality with singular weights for the Orlicz-Sobolev spaces embedded into exponential and multiple exponential Orlicz spaces. The Concentration-Compactness Alternative for the singular Moser-Trudinger inequality is established to.

Correa, Alvaro, Department of Mathematics, University of Puerto Rico-Bayamon Campus, Bayamon, PR 00959, USA (alvaro.correa@upr.edu), and Li, Yi Department of Mathematics, Wright State University, Dayton, Ohio 45435, USA (yi.li@wright.edu).
Bifurcation theory for a class of second order differential equations, pp. 231-245.
ABSTRACT. In this paper, we consider multiple positive solutions of a nonlinear two points boundary value problem depending on a parameter. Every solution is uniquely identified by its maximum value. We study how the number of solutions changes when the parameter varies and in addition we will narrow regions of bifurcation points.

S. Garcia-Ferreira, A. Garcia-Maynez, and M. Hrusak, Instituto de Matematicas, Universidad Nacional Autonoma de Mexico, Campus Morelia, Apartado Postal 61-3, Xangari, 58089, Morelia, Michoacan, Mexico (agmaynez@matem.unam.mx) (sgarcia@matmor.unam.mx) ,  (michael@matmor.unam.mx)
Spaces in which every dense subset is Baire , pp. 247-263.
ABSTRACT. We deal with several types of spaces in which every dense subspace is Baire (D-Baire spaces). Baire almost P-spaces and open-hereditarily irresolvable Baire spaces are examples of D- spaces. We give a characterization of D-Baire spaces and characterize a particular class of them. We give an example of a D-Baire space whose square is not Baire. .

Jan J. Dijkstra and Jurjen Hickmann, Faculteit der Exacte Wetenschappen, Afdeling Wiskunde, Vrije Universiteit, De Boelelaan 1081a , 1081 HV  Amsterdam, The Netherlands (dijkstra@cs.vu.nl), (jurjenh@gmail.com)
On the homeomorphism groups of Brechner's continua, pp. 265-272.
ABSTRACT.In 1966 Brechner introduced a series of continua M with the property that their autohomeomorphism groups H(M) are totally disconnected but not zero-dimensional. In 2001 Brechner and Kawamura showed that these groups are almost zero-dimensional and thus one-dimensional by a theorem of Oversteegen and Tymchatyn. In the present note we show that the spaces H(M) are universal for the class of almost zero-dimensional spaces. We reach this result by constructing an imbedding of complete Erdös space into H(M). An interesting by-product of this imbedding is that it allows us to conclude that H(M) is not homeomorphic to complete Erdos space.

Fucai Lin, Department of Mathematics and Information Science, Zhangzhou Normal University, Fujian, Zhangzhou, 363000, P.R.China (linfucai2008@yahoo.com.cn) and Shou Lin, Institute of Mathematics, Ningde Teachers' College, Ningde, Fujian 352100, P. R. China.
π-metrizable spaces and strongly π-metrizable spaces, pp. 273-285.
ABSTRACT. A space X is said to be π-metrizable if it has a σ-discrete π-base. In this paper, we mainly give an affirmative answers for two questions about π-metrizable spaces. The main results are that: (1) A space X is π-metrizable if and only if X has a σ-hereditarily closure-preserving π-base; (2)A space X is π-metrizable if and only if X is almost σ-paracompact and locally π-metrizable; (3) Open and closed maps preserve π-metrizability; (4) π-metrizability satisfies hereditarily closure π-preserving regular closed sum theorems. Moreover, we define the notions of second-countable -metrizable and strongly π-metrizable spaces, and study some related questions. Some questions about strongly π-metrizability are posed.

Camargo, Javier, Escuela de Matematicas, Facultad de Ciencias, Universidad Industrial de Santander, Ciudad Universitaria, Bucaramanga, Santander A.A. 678, Colombia (jcam@matematicas.uis.edu.co) and Pellicer-Covarrubias, Patricia, Departamento de Matematicas, Facultad de Ciencias, Ciudad Universitaria, C.P.04510, Mexico D.F., Mexico (paty@ciencias.unam.mx)
Arc-smoothness in symmetric products, pp. 287-316.
ABSTRACT. A space X is arc-smooth at a point p provided there exists a continuous function g : X → C(X) satisfying the following conditions: (1) g(p) = {p}; (2) for each element x of X − {p}, the set g(x) is an arc from p to x; (3) if x belongs to g(y), then g(x) is a subset of g(y). A space is arc-smooth if it is arc-smooth at some point p. In this paper we prove that, among hereditarily unicoherent continua, X is arc-smooth if and only if the nth symmetric product Fn(X) is arc-smooth for each natural number n. This allows us to give a positive answer to a question by J.T.Goodykoontz when we replace the hyperspace of subcontinua of a continuum X with Fn(X). We also give a characterization of the arc-smoothness of the hyperspace F2(X) when X is 1-dimensional, and another of Fn(X) when X is a locally connected, 1-dimensional continuum. Further, we give some conditions on a continuum X that imply the arc-smoothness of the hyperspace Fn(X) at some particular elements. Finally, we characterize the arc-smoothness at elements of F3(X) in the class of hereditarily unicoherent continua and of F2(X) in the class of 1-dimensional continua.

Boero, Ana C., Universidade de São Paulo, São Paulo (SP), Brazil (carol@ime.usp.br), (ana.boero@ufabc.edu.br) and Tomita, Artur H., Universidade de São Paulo, São Paulo (SP), Brazil (tomita@ime.usp.br).
A countably compact group topology on abelian almost torsion-free groups from selective ultrafilters, pp. 317-342.
ABSTRACT. Assuming the existence of continuum many incomparable selective ultrafilters, we show that the real line and the unit circle group can be endowed with a countably compact Hausdorff group topology without non-trivial convergent sequences. More generally, we prove that this result remains valid for every abelian almost torsion-free group of cardinality continuum. We also show, under the same assumption, that every abelian almost torsion-free topological group of countable weight and cardinality continuum admits a Hausdorff group topology which is T1-independent of the original one.