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 a_j such that all zeroes of f-a_j 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.

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.

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.