## HOUSTON JOURNAL OF MATHEMATICS

### Electronic Edition Vol. 39, No. 3 , 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)

Contents

Lee, Tsiu-Kwen, National Taiwan University, Taipei 106, Taiwan (tklee@math.ntu.edu.tw) and Liu, Kun-Shan, National Taiwan university, Taipei 106, Taiwan (kunshanliu@ntu.edu.tw).
Generalized skew derivations with algebraic values of bounded degree, pp. 733-740.
ABSTRACT.Let R be a prime algebra over a field F and let g be a nonzero generalized skew derivation of R. We show that if g(x) is algebraic over F of bounded degree for all x in R, then R is a primitive ring with a minimal idempotent e such that eRe is a finite-dimensional central division algebra.

Chun, Sangmin, Seoul National University, Seoul 151-747, Republic of Korea (schun@snu.ac.kr), and Anderson, D. D., The University of Iowa, Iowa City, IA 52242 (dan-anderson@uiowa.edu).
Irreducible elements in commutative rings with zero-divisors, II, pp. 741-752.
ABSTRACT. Let R be a commutative ring with identity. For elements a and b of R, a and b are associates (resp., strong associates, very strong associates) if (a) = (b) (resp., a = ub for some unit u, a and b are associated and either a = b = 0 or a is nonzero and a = rb implies r is a unit). A nonunit a of R is irreducible (resp., strongly irreducible, very strongly irreducible) if a = bc implies a is associate to b or c (resp., a is strongly associate to b or c, a is very strongly associate to a or c) and a is m-irreducible if (a) is a maximal element of the set of proper principal ideals of R. The ring R is said to be atomic (resp., strongly atomic, very strongly atomic, m-atomic) if each nonzero nonunit of R is a finite product of irreducible (resp., strongly irreducible, very strongly irreducible, m-irreducible) elements. In this paper we collect the known various characterizations of the different types of irreducible elements and give a number of new ones. We also continue the investigation of the various forms of atomicity.

Di Bartolo, Alfonso, Dipartimento di Matematica e Informatica, Via Archirafi 34, I-90123 Palermo, Italy (alfonso@math.unipa.it), Falcone, Giovanni, Dipartimento di Matematica e Informatica, Via Archirafi 34, I-90123 Palermo, Italy (giovanni.falcone@unipa.it), and Strambach, Karl, Department Mathematik, Cauerstrasse 11, D-91058 Erlangen, Germany (strambach@mi.uni-erlangen.de).
Near-rings and groups of affine mappings, pp. 753-780.
ABSTRACT. We classify semi-topological locally compact and semi-algebraic near-rings R where the set of non-invertible elements of R forms an ideal I of R such that the multiplicative group of R/I acts sharply transitively on the set of non-zero elements of I. To achieve our results we use as a main tool the classi cation of locally compact and algebraic (2, 2)-transformation groups given in two previous papers.

Escassut, Alain, Laboratoire de Mathematiques, UMR 6620, Université Blaise Pascal, 63171 Aubiere, France (alain.escassut@math.univ-bpclermont.fr) and Ojeda, Jacqueline, Departamento de Matemática, Facultad de Ciencias Físicas y Matemáticas, Universidad de Concepcion, Concepcion, Chile ( jacqojeda@udec.cl).
Branched values and quasi-exceptional values for p-adic meromorphic functions, pp. 781-795.
ABSTRACT. Let K be an algebraically closed field of characteristic 0, complete with respect to an ultrametric absolute value. We show that a transcendental meromorphic function in K or an "unbounded" meromorphic function inside an open disk cannot admit more than 4 perfectly branched values and a transcendental meromorphic function in K cannot admit more that 3 values aj such that all zeroes of f-aj are multiple. An unbounded analytic function inside an open disk cannot admit more than 2 perfectly branched values. And an entire function cannot admit more than 1 perfectly branched value. Completing a previous result by K. Boussaf and J. Ojeda, we prove that given a transcendental meromorphic function f in K, if f admits 0 and ∞ as perfectly branched values, then the function assumes all non-zero values infinitely often. Similarly, if f is an "unbounded" meromorphic function in an "open" disk, if the residue characteristic p is different from 2 and if all zeroes and poles are of even order, but finitely many, then the function assumes all non-zero values infinitely often.

Teresa Monteiro Fernandes, CMAF, Universidade de Lisboa Bloco C6, P 2, Campo Grande, 1749-16, Lisboa, Portugal (tmf@ptmat.fc.ul.pt).
Microsupport of tempered solutions of shd-modules associated to smooth morphisms, pp. 797-821.
ABSTRACT.  Let f from X to Y be a smooth morphism of complex manifolds. Let G be any constructible object on X locally isomorphic to the inverse image by f of a constructible object on Y. We prove that the microsupport of the solution complex of a coherent D-module in Kashiwara-Schapira's tempered holomorphic functions (resp.tempered holomorphic microfunctions) associated to G is contained in the 1-characteristic variety (resp. in the 1-microcharacteristic variety) associated to f.

Czerwińska, Małgorzata M., The University of Memphis, Memphis, TN 38152 (mmczrwns@memphis.edu), Kamińska, Anna, The University of Memphis, Memphis, TN 38152 (kaminska@memphis.edu) and Kubiak, Damian, The University of Memphis, Memphis, TN 38152 (dmkubiak@memphis.edu).
Exposed and strongly exposed points in symmetric spaces of measurable operators, pp. 823-852.
ABSTRACT. We investigate the relationships between exposed or strongly exposed points of the unit ball of an order continuous symmetric function space E, and of the unit ball of the space of τ-measurable operators E(M,τ) associated to a semifinite von Neumann algebra M with trace τ. We prove that an operator x is an exposed or strongly exposed point of the unit ball of the symmetric space of measurable operators E(M,τ) if and only if its singular value function μ(x) is an exposed or strongly exposed point of the unit ball in E, respectively.

Dosi Anar, Middle East Technical University Northern Cyprus Campus, Guzelyurt KKTC, Mersin 10, Turkey (dosiev@metu.edu.tr), (dosiev@yahoo.com)
Quantum cones and their duality, pp. 853-887.
ABSTRACT. In this paper we investigate the duality properties of quantum cones. We prove a bipolar theorem for quantum cones and classify all inflated quantum orders over Paulsen's construction as quantum topologies compatible with the given duality.

Mikhail I. Ostrovskii, Department of Mathematics and Computer Science, St. John’s University, 8000 Utopia Parkway, Queens, NY 11439, USA (ostrovsm@stjohns.edu).
Different forms of metric characterizations of classes of Banach spaces, pp. 889-906.
ABSTRACT. For each sequence X of finite-dimensional Banach spaces there exists a sequence H of finite connected unweighted graphs with maximum degree 3 such that the following conditions on a Banach space Y are equivalent: (1) Y admits uniformly isomorphic embeddings of elements of the sequence X. (2) Y admits uniformly bilipschitz embeddings of elements of the sequence H.

Reinhold, Karin, University at Albany, 1400 Washington Avenue, Albany, NY, 12222 (reinhold@albany.edu) and Savvopoulou, Anna K., Indiana University South Bend, 1700 Mishawaka Avenue, South Bend, In, USA, 46634 (annsavvo@iusb.edu).
Variation and Oscillation inequalities for convolution products, pp. 907-918.
ABSTRACT. We establish variation and oscillation inequalities for convolution products of probability measures defined on the integers.

Yasheng Ye, Dept. of Math, University of Shanghai for Science and Technology, Shanghai 200093, P.R.China (yashengye@yahoo.com.cn), Hiaojun Liu, Dept. of Math, University of Shanghai for Science and Technology, Shanghai 200093, P.R.China (xiaojunliu2007@hotmail.com) , and Xuecheng Pang, Dept. of Math，East China Normal University, Shanghai 200241, P.R.China (xcpang@math.ecnu.edu.cn).
A normal criterion about two families of meromorphic functions concerning shared values, pp. 919-928.
ABSTRACT. In this paper, we discuss the normality of two families of functions concerning shared values. In particular, we prove the following result: Let F be a family of meromorphic functions on a domain D, all of whose zeros have   multiplicity at least k, and for every f(z) in F, f=0 iff the k-th derivative of f(z)=1, where k is a positive integer. Let F1 and F2 be two subsequences of F, and F2 be normal on D. If for every f(z) in F1, there exists g(z) in F2, such that f=0 iff  g=0, then F1 is normal.

Barroso, Ana Cristina, Faculdade de Ciências da Universidade de Lisboa, Departamento de Matemática and CMAF, Av. Prof. Gama Pinto, 2, 1649-003 Lisboa, Portugal (abarroso@ptmat.fc.ul.pt), Croce, Gisella, LMAH, Le Havre University, 25 rue Philippe Lebon, 76063 Le Havre, France (gisella.croce@univ-lehavre.fr), and Ribeiro, Ana Margarida, Departamento de Matemática and CMA, Faculdade de Ciências e Tecnologia da Universidade Nova de Lisboa, Quinta da Torre, 2829-516 Caparica, Portugal (amfr@fct.unl.pt).
Sufficient conditions for existence of solutions to vectorial differential inclusions and applications, pp. 929-967.
ABSTRACT.In this paper we discuss the existence of solutions to vectorial differential inclusions, refining a result proved in Dacorogna and Marcellini [1996, Théorèmes d'existence dans les cas scalaire et vectoriel pour les équations de Hamilton-Jacobi, C. R. Acad. Sci. Paris Sér. I Math., 322(3):237--240]. We investigate sufficient conditions for existence, more flexible than those available in the literature, so that important applications can be fitted in the theory. We also study some of these applications.

Jianjun, Zhang, Mathematics and Information Technology School, Jiangsu Institute of Education, Nanjing , 210013 P. R.China (zhangjianjun1982@163.com) and  Liangwen, Liao, Department of Mathematics, Nanjing University, Nanjing, 210093 P. R. China (maliao@nju.edu.cn).
On Malmquist type theorem of complex difference equations, pp. 969-981.
ABSTRACT. In this paper, we will give a result on complex difference equations which is reminiscent of the classical Malmquist theorem in complex differential equations.

Ralowski, Robert and Szymon Zeberski, Wroclaw University of Technology, 50-370 Wroclaw, Poland,  (robert.ralowski@pwr.wroc.pl), (szymon.zeberski@pwr.wroc.pl).
Generalized Luzin sets, pp. 983-993.
ABSTRACT. In this paper we investigate the notion of a generalized (I,J) - Luzin set. This notion generalizes the standard notion of a Luzin set and a Sierpinski set. We find set theoretical conditions which imply the existence of a generalized (I,J) - Luzin set.
We show how to construct a large family of pairwise non-equivalent (I,J) - Luzin sets. We find a class of forcings which preserves the property of being a (I,J) - Luzin set.

Escobedo, Raúl, López, María de J.,Facultad de Ciencias Físico Matemáticas, Benemérita Universidad Autónoma de Puebla, Ave. San Claudio y Río Verde, Ciudad Universitaria, San Manuel, Puebla, Pue., 72570, México, (escobedo@fcfm.buap.mx), (mtoriz@fcfm.buap.mx) and Tenorio, Jesús F., Universidad Tecnológica de la Mixteca, carretera a Acatlima km. 2.5, Huajuapan de León, Oaxaca, 69000, México, (jtenorio@mixteco.utm.mx).
Universality of maps on suspensions over products of span zero continua, pp. 995-1004.
ABSTRACT. We prove that the induced map to the topological suspension of a product of maps from continua onto span zero continua is universal. It follows that topological suspension and cone over a product of span zero (chainable) continua have the fixed point property.

Pol, Elzbieta, Institute of Mathematics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland (E.Pol@mimuw.edu.pl) and Pol, Roman, Institute of Mathematics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland (R.Pol@mimuw.edu.pl).
A connected, locally connected infinite metric space without separable sets of positive dimension, pp. 1005-1012.
ABSTRACT. We give an example of a non-separable connected and locally connected metrizable space whose all nonempty connected separable subspaces are singletons. This answers a question of T.Banakh, M.Vovk and M.R.Wojcik.

Bonanzinga, Maddalena, Dipartimento di Matematica e Informatica, Universita' di Messina, Via F. Stagno d'Alcontres N.31, 98166 Messina, Italy (mbonanzinga@unime.it).
On the Hausdorff number of a topological space, pp. 1013-1030.
ABSTRACT.A new cardinal function, called Hausdorff number, is defined. Some known cardinal inequalities for Hausdorff spaces are generalized in terms of the Hausdorff number.

Niemiec, Piotr,  Jagiellonian University, Institute of Mathematics, ul. Lojasiewicza 6, 30-348 Kraków, Poland (piotr.niemiec@uj.edu.pl)
Ultrametrics, extending of Lipschitz maps and nonexpansive selections, pp. 1031-1050.
ABSTRACT.Ultrametric spaces are characterized (among all metric spaces) in aspects of extending of Lipschitz maps and existence of certain nonexpansive selections. Metric spaces every closed nonempty subset of which is a nonexpansive retract are fully characterized. Total orders on ultrametric spaces which induce metrics and partial orders in the class of compact metric spaces (up to isometry) are investigated. Certain results on isometric embeddings of the hyperspace of an ultrametric space into the space of nonexpansive maps of the space into itself and on upper bounded families of compact spaces are proved.

R. A. McCoy, Department of Mathematics, Virginia Tech, Blacksburg VA 24061-0123, U.S.A. (mccoy@math.vt.edu), Varun Jindal, Department of Mathematics, Indian Institute of Technology Delhi, New Delhi 110016, India (varunjindal.iitd@gmail.com), and S. Kundu, Department of Mathematics, Indian Institute of Technology Delhi, New Delhi 110016, India (skundu@maths.iitd.ernet.in).
Homeomorphism spaces under uniform and fine topologies, pp. 1051-1066.
ABSTRACT. A study is made of the countability and connectedness properties of the space H(X) of self-homeomorphisms from a metric space X onto itself, where H(X) has either the uniform topology or the fine topology. Also for the case that X is Euclidean n-space, three different natural compatible metrics are used to generate three different uniform topologies on H(X). These three uniform homeomorphism spaces are shown to be not homeomorphic to each other when n is greater than 1; and, for such X, these spaces are also compared to H(X) with the fine, point-open and compact-compact-open topologies.

Chatyrko, Vitalij , Dept. of Mathematics, Linkoping University, 581 83 Linkoping, Sweden (vitja@mai.liu.se) and  Karassev, Alexandre, Dept. of Computer Science and Mathematics, Nipissing University, 100 College Drive, P.O. Box 5002, North Bay, ON, P1B 8L7, Canada (alexandk@nipissingu.ca).
On mtrizable remainders of locally compact separable metrizable spaces, pp. 1067-1081.
ABSTRACT. In this paper we describe those locally compact noncompact separable metrizable spaces X for which the class R(X) of all metrizable remainders of X consists of all metrizable non-empty compacta. Then we show that for any pair X and X'of locally compact noncompact connected separable metrizable spaces, either R(X) ⊂ R(X') or R(X') ⊂ R(X).