HOUSTON JOURNAL OF MATHEMATICS

Electronic Edition Vol. 40, No. 1 , 2014

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

Dobbs, David E. University of Tennessee, Knoxville, Tennessee 37996-1320 (dobbs@math.utk.edu), and Shapiro, Jay, George Mason University, Fairfax, Virginia 22030-4444, (jshapiro@gmu.edu).
Pseudo-normal pairs of integral domains, pp. 1-19.
ABSTRACT. If R ⊆ T are (commutative integral) domains with R quasilocal, then (R,T) is called a pseudo-normal pair if there exists a divided prime ideal P of R such that T = R_P and R/P is a PVD. Besides normal pairs with quasilocal base, such pairs can be characterized as having a ring R ⊆ S ⊆ T such that Spec(R) = Spec(S) as sets and (S,T) is a normal pair. There can be at most one finite sequence from a given R to a given T all of whose steps are the second type of pair. Denumerable ascending sequences consisting of such steps are constructed. If R is not necessarily quasilocal, (R,T) is called pseudo-normal if (R_M,T_R\M) is pseudo-normal for each maximal ideal M of R. The class of pseudo-normal pairs is stable under formation of rings of fractions and factor domains. The most natural example of a pseudo-normal pair with non-quasilocal base is given with R an LPVD and T its quotient field. However, for each integer n ≥ 2, there exists a pseudo-normal pair whose base domain has exactly n maximal ideals and is not an LPVD.

Birkenmeier, Gary F., University of Louisiana at Lafayette, Lafayette, LA 70504 (gfb1127@louisiana.edu), and Lennon, Matthew J., University of Louisiana at Lafayette, Lafayette, LA 70504 (mjl4646@louisiana.edu).  
 Dense intrinsic extensions, pp. 21-42.
ABSTRACT. In this paper the idea of a dense intrinsic extension of a ring is introduced and studied in detail. These types of extensions provide a natural generalization of the usual notion of a dense extension. Several important properties transfer to dense intrinsic extensions which include extending, quasi-continuous, and the Kasch property amongst others. The split-null (or trivial) extension is used to provide a variety of examples to illustrate the transfer of these properties. It is also shown that with mild conditions on the base ring, a complete set of centrally primitive idempotents can be constructed for a dense intrinsic extension, T, from a corresponding set in the base ring, R. Examples and applications are given for a variety of rings.

Enochs, Edgar, Dept. of Mathematics, University of Kentucky, Lexington, KY 40506-0027 (enochs@ms.uky.edu), Estrada, Sergio, Depto. de Matematica Aplicada, Universidad de Murcia, Murcia SPAIN 30100 (sestrada@um.es), and Iacob, Alina, Dept. of Mathematical Sciences, Georgia Southern University, Statesboro, GA 30460-8093 (aiacob@georgiasouthern.edu).
Cotorsion pairs, model structures and homotopy categories, pp. 43-61.
ABSTRACT. We will show the interlacing between complete cotorsion pairs, model structures and homotopy categories. This will give a method of constructing adjoint functors between homotopy categories as well as a method for constructing abelian model structures in the category of unbounded complexes of certain abelian categories. We illustrate our methods by recovering some recents results of Murfet and Neeman as particular instances. And we also find new abelian model structures both in C(R) and in C(Qco(X)) attained to classes which are non necessarily closed under direct limits.

Carmelo Antonio Finocchiaro, Dipartimento di Matematica, Università degli Studi Roma Tre, Largo San Leonardo Murialdo 1, 00146 - Roma, Italy (carmelo@mat.uniroma3.it) .
Prüfer-like conditions on an amalgamated algebra along an ideal, pp. 63-79.
ABSTRACT. Let f be a ring homomorphism from a ring A into a ring B, and let b be an ideal of B. In this paper we study Prüfer-like conditions in the amalgamation of A with B along b.

Theofanidis Theoharis and Philippos J. Xenos, Mathematics Division, School of Technology, Aristotle University of Thessaloniki, Thessaloniki 54124, Greece, (theotheo@gen.auth.gr), (fxenos@gen.auth.gr).
 Real hypersurfaces of non-flat complex space forms equipped with Jacobi structure operator of Codazzi type,  pp. 97-107.
ABSTRACT. J.D. Perez, F.G. Santos and Y.J. Suh in 2007, proved that there exist no real hypersurfaces in projective space Pⁿ, n≥3, equipped with structure Jacobi operator of Codazzi type. In the present paper, we generalize the above mentioned problem and we obtain the same result for complex space forms M_n(c), c≠0, n≥3. We have already solved this problem for n=2.

Ghanmi, Allal, Department of Mathematics, Faculty of Sciences, P.O. Box 1014, Mohammed V University, Agdal, 10 000 Rabat, Morocco (ag@fsr.ac.ma) , and Mouayn, Zouhaïr, Department of Mathematics, Faculty of Sciences and Technics (M'Ghila), P.O. Box 523, Sultan Moulay Slimane University, 23 000 Béni Mellal, Morocco (mouayn@fstbm.ac.ma).
A formula representing magnetic Berezin transforms on the complex unit ball as functions of the Laplace–Beltrami operator, pp. 109-126.
ABSTRACT. We give a formula that represents magnetic Berezin transforms associated with generalized Bergman spaces as functions of the Laplace-Beltrami operator on the unit ball of of the n-complex space. In particular, we recover the result obtained by F.A. Berezin [Izv. Akad. Nauk SSSRSer. Mat. 39 (2) 1975] and restated by J. Peetre [J. Oper. Theory, 24, 1990].

Gonçalves, Daniel, Dept. Matemática, Universidade Federal de Santa Catarina, Florianópolis, SC, Brazil, 88040-900 (daemig@gmail.com), Royer, Danilo, Dept. Matemática, Universidade Federal de Santa Catarina, Florianópolis, SC, Brazil, 88040-900 (royer@mtm.ufsc.br)
C*-algebras associated to stationary ordered Bratteli diagrams, pp. 127-143.
ABSTRACT. In this paper, we introduce a C*-algebra associated to any stationary Bratteli diagram. We show that this C*-algebra contains the partial crossed product C*-algebra of the corresponding Bratteli-Vershik system and show that these algebras are invariant under equivalence of the Bratteli diagrams. We also show that the isomorphism class of the algebras, together with a distinguished set of generators, is a complete invariant for equivalence of Bratteli diagrams.

Hirshberg, I., Department of Mathematics, Ben-Gurion University of the Negev, P.O.B. 653, Beersheva 84105, Israel (ilan@math.bgu.ac.il) and Daniel Markiewicz, Department of Mathematics, Ben-Gurion University of the Negev, P.O.B. 653, Beersheva 84105, Israel (danielm@math.bgu.ac.il).
Continuous families of E₀-semigroups , pp. 145-160.
ABSTRACT. We consider families of E₀-semigroups continuously parametrized by a compact Hausdorff space, which are cocycle-equivalent to a given E₀-semigroup β. When the gauge group of β is a Lie group, we establish a correspondence between such families and principal bundles whose structure group is the gauge group of β.

Izuchi, Kei Ji, Department of Mathematics, Niigata University, Niigata 950-2181, Japan (izuchi@m.sc.niigata-u.ac.jp), Izuchi, Yuko, Aoyama-shinmachi 18-6-301, Niigata 950-2006, Japan (yfd10198@nifty.com), and Ohno, Shûichi, Nippon Institute of Technology, 4-1-1 Gakuendai, Miyashiro, Minami-Saitama 345-8501, Japan (ohno@nit.ac.jp).
 Path connected components in weighted composition operators on h^∞ and H^∞ with the essential operator norm, pp. 161-187.
ABSTRACT.  In the spaces of noncompact weighted composition operators on hⁱ and Hⁱ over the unit disk, we may consider the operator norm and the essential operator norm. We shall show that path connected components are the same for both topologies on hⁱ. Also we shall show that path connected components are different for the operator norm and the essential operator norm topologies on Hⁱ.

Samea, Hojjatollah, Department of Mathematics, Bu-Ali Sina University, Hamedan, Iran (h.samea1356@gmail.com, h.samea@basu.ac.ir).
Amenability and approximate amenability of l¹-Munn algebras, pp. 189-193.
ABSTRACT. We study amenability and approximate amenability of l¹-Munn algebras over Banach algebras. We then show that the l¹-Munn algebra LMI(A) over a unital Banach algebra A is approximately amenable if and only if A is approximately amenable and I is finite. Applications to semigroup algebras are given.

Glotov, Dmitry, Department of Mathematics and Statistics, 221 Parker Hall, Auburn Univeristy, AL 36849 (dglotov@auburn.edu).
 On the local behavior of solutions to systems of elliptic equations with an application to superconducting thin films , pp. 195-208.
ABSTRACT. We prove that thesolutions of the thin-film Ginzburg-Landau equation can vanish only to a finite order even when the variable thickness function is not analytic. This result is related to the description of Ginzburg-Landau vortices provided by Bauman, Carlson, and Phillips (1993) and Elliott, Matano, and Tang (1994). The main tool is an extension of a classical result by Hartman and Wintner (1953) that is also proved in this article.

Xiao-Min Li, Department of Mathematics, Ocean University of China, Qingdao, Shandong 266100, People's Republic of China (xmli01267@gmail.com) and Hong-Xun Yi, Department of Mathematics, Shandong University, Jinan, Shandong 250100, People's Republic of China (hxyi@sdu.edu.cn).
Results on certain meromorphic functions sharing a nonconstant polynomial with their derivatives, pp. 209-227.
ABSTRACT. Let B be the class of meromorphic functions f such that the set sing (f^-1) is bounded, where ing (f^-1) is the set of critical and asymptotic values of f. Suppose that f has at most finitely many poles in the complex plane, and that f^(k)-P and f-P share 0 CM, where k is a positive integer, P is a non-constant polynomial. Then, the hyper-order of f is a nonnegative integer or ∞. Applying this result, we obtain some uniqueness results for transcendental meromorphic functions sharing a nonconstant polynomial with their derivatives, where the meromorphic functions belong to B and have at most finitely many poles in the complex plane. The results in this paper are concerning a conjecture of Brück (On entire functions which share one value CM with their first derivative, Results in Math. 30 (1996), 21-24.

Rossitza Semerdjieva, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 8, 1113 Sofia, Bulgaria (rsemerdjieva@yahoo.com).
Global existence of classical solutions for a nonlocal one dimensional parabolic free boundary problem, pp. 229-253.
ABSTRACT. In this paper we study one dimensional parabolic free boundary value problem with a nonlocal (integro-differential) condition on the free boundary. We establish global existence-uniqueness of classical solutions assuming that the initial-boundary data are sufficiently smooth and satisfy some compatibility conditions. Our approach is based on analysis of an equivalent system of nonlinear integral equations.

Basile Désirée (basile@dmi.unict.it), Bella Angelo, Dipartimento di Matematica e Informatica, Università degli Studi di Catania, 95125 Catania, Italy, (bella@dmi.unict.it), and Ridderbos Guit-Jan, Technische Universiteit Delft, Delft, The Netherlands (G.F.Ridderbos@tudelft.nl).
Weak extent, submetrizabiliy and diagonal degrees, pp. 255-266.
ABSTRACT. We show that if a topological space X has a zero-set diagonal and X² has countable weak extent, then X is submetrizable. This generalizes earlier results from Martin and Buzyakova. Furthermore we show that if X has a regular G_δ-diagonal and X² has countable weak extent, then X condenses onto a second countable Hausdorff space. We also prove several cardinality bounds involving various types of diagonal degree. .

Buzyakova, Raushan, University of North Carolina at Greensboro, Greensboro, NC 27402 (Raushan_Buzyakova@yahoo.com) and Vural, Cetin, Department of Mathematics, Faculty of Arts and Sciences, Gazi University, 06500 Ankara, Turkey (cvural@gazi.edu.tr).
Stationary sets in topological and paratopological groups, pp. 267-273.
ABSTRACT.We show that if a topological or paratopological group G contains a stationary subset of some regular uncountable cardinal, then G contains a subspace which is not collectionwise normal. This statement implies that if a monotonically normal space (in particular, any generalized ordered space) is a paratopological group then the space is hereditarily paracompact.

Yan-Kui Song,  Institute of Mathematics, School of Mathematical Science, Nanjing Normal University, Nanjing 210046, P.R.China (songyankui@njnu.edu.cn)
A note on star covering properties, pp. 275-283.
ABSTRACT. In this paper, we construct the following three examples: (1) There exists a pseudocompact centered Lindelöf Tychonoff space that is not star countable; (2) There exists a pseudocompact star countable Tychonoff space having a regular-closed subspace which is not star countable; (3) Assuming 2^ℵ₀ = 2^ℵ₁, there exists a star countable normal space having a regular-closed subspace which is not star countable.

Szymon Dolecki,  Mathematical Institute of Burgundy, Burgundy University, B.P. 47 870, 21078 Dijon, France  (dolecki@u-bourgogne.fr) and Frédéric Mynard, Department of Mathematical Sciences, Georgia Southern University,PB 8093, Statesboro GA 30460, U.S.A. (fmynard@georgiasouthern.edu).
A unified theory of function spaces and hyperspaces: local properties, pp. 285-318.
ABSTRACT. Every convergence (in particular, every topology) on the hyperspace C(X,$) of a topological space X determines "preimagewise" a convergence on C(X,Z) by the convergence of the respective preimages of open sets. Here X and Z are topological spaces and $ is the Sierpinski topology.  Classical instances of function space structures that are determined this way by their hyperspace counterparts are the pointwise, compact-open and Isbell topologies, and the natural (that is, continuous) convergence.  It is shown that several fundamental local properties hold for a hyperspace convergence C(X,$) at X if and only if they hold for the preimagewise convergence on C(X,R) at the origin, provided that the underlying topology of X have some R-separation properties. This concerns character, tightness, fan tightness, strong fan tightness, and various Fréchet properties (from the simple through the strong to that for finite sets) and corresponds to various covering properties (like Lindelöf, Rothberger, Menger) of the underlying space X. This way, many classical results are unified, extended and improved. Among new surprising results: the tightness and the character of the natural convergence coincide and are equal to the Lindelöf number of the underlying space; the Fréchet property coincides with the Fréchet property for finite sets for the hyperspace topologies generated by compact networks.