Electronic Edition Vol. 40, No. 2 , 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


Kamal Bahmanpour, Faculty of Mathematical Sciences, Department of Mathematics, University of Mohaghegh Ardabili, 56199-11367, Ardabil, Iran; and School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box. 19395-5746, Tehran, Iran (bahmanpour.k@gmail.com), Reza Naghipour,  and Monireh Sedghi, Department of Mathematics, University of Tabriz, Tabriz, Iran and School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box: 19395-5746, Tehran, Iran (naghipour@ipm.ir), (naghipour@tabrizu.ac.ir).
On the finiteness of Bass numbers of local cohomology modules and cominimaxness, pp. 319-337.
ABSTRACT. In this paper, we continue the study of cominimaxness modules with respect to an ideal of a commutative Noetherian ring, and Bass numbers of local cohomology modules.

Abdel-Aziz, M. Khalifa Saad and A. A. Abdel-Salam, Mathematics Department, Faculty of Science, Sohag University, 82524 Sohag, Egypt (mohamed_khalifa77@science.sohag.edu.eg).
 On implicit surfaces and their intersection curve in Euclidean 4-Space, pp. 339-352
ABSTRACT. This paper aims at studying the differential geometry properties of the tangential intersection curve of three implicit surfaces in Euclidean 4-space. These properties include the tangent T, the principle normal N, the binormal vectors (B1; B2) and the curvatures of that curve. Furthermore, we give examples to illustrate our main results.

Zeytuncu, Yunus E., Texas A&M University, College Station, TX, 77843 (zeytuncu@math.tamu.edu).
 A note on the nebenhülle of smooth complete Hartogs domains, pp. 353-357.
ABSTRACT. It is shown that a smooth bounded pseudoconvex complete Hartogs domain in the two dimensional complex Euclidean space has trivial Nebenhulle. The smoothness assumption is used to invoke a theorem of D. Catlin.

Alvaro Arias and Jonathan Von Stroh, Department of Mathematics, University of Denver, John Greene Hall, 2360 S. Gaylord St., Denver, CO 80208  (aarias@du.edu).
Lifting module maps between different noncommutative domain algebras, pp. 359-383.
ABSTRACT. In this paper we use a renorming technique to lift module maps between *-invariant submodules of domain algebras recently introduced by Popescu.

Yehoram Gordon, Department of Mathematics, Technion, Haifa 32000, Israel, (gordon@techunix.technion.ac.il) and Mathieu Meyer, Equipe d'Analyse et Mathematiques Appliquee,  Universite de Marne-la Vallee, 5 boulevard Descartes, Champs sur Marne, 77454 Marne-la-Vallee, Cedex 2, France (mathieu.meyer@univ-mlv.fr).
On the minima of the functional Mahler product, pp. 385-393.
ABSTRACT.  Let P(f) denote the Mahler product of a real convex function on an n-dimensional Euclidean space. We prove that on the set of all convex functions the Mahler product has no local minimum at any function having some regular point.

LuJun Guo, Department of Mathematics, Shanghai University, Shanghai 200444, China, (lujunguo0301@163.com) and Gangsong Leng, Department of Mathematics, Shanghai University, Shanghai 200444, China, (gleng@staff.shu.edu.cn).
 Stable determination of convex bodies from centroid bodies,  pp. 395-406.
ABSTRACT. In 1990, Lutwak showed that an origin-symmetric star body is uniquely determined by its centroid body. Without the symmetry assumption, we show that the star bodies K, L are identical if they have the same centroid bodies and the volumes V(K∩u+)=V(L∩u+) for all unit vectors u, where u+={x:: x is a d-dimensional vector, x⋅u≥0}. For convex bodies we prove a stability version of this result.

Klimczak, Katarzyna, Łódź University, Poland (kkiel@math.uni.lodz.pl).
Noncommutative version of Kolmogorov's three series theorem and some limit theorems, pp. 407-419.
ABSTRACT. In this note a noncommutative version of Kolmogorov's Three Series Theorem, concerning unconditional convergence, is given. As a noncommutative counterpart of the classical almost sure convergence the almost uniform of measurable operators convergence is used. We also provide a method of proving theorems on almost uniform convergence in von Neumann algebras. Finally, we give a noncommutative version of the Kolmogorov's 0-1 law and show that (under appriopriate assumptions concerning independence) the limit of a convergent sequence of elements of a von Neumann algebra is a multiplicity of identity.

Ng, P. W., Mathematics Department, University of Louisiana at Lafayette, Lafayette, Louisiana, 70504 (png@louisiana.edu).
Commutators in C*r(F), pp. 421-446.
ABSTRACT. We study commutators in the reduced C*-algebra of the free group in infinitely many generators and in simple unital Jiang-Su stable C*-algebras which are rationally tracially AF. We show that an element of any of the above C*-algebras is a sum of three commutators if and only if it is annihilated by all tracial states.

Rui Shi, School of Mathematical Sciences, Dalian, University of Technology, Dalian, 116024, P. R. China (ruishi@dlut.edu.cn), (ruishi.math@gmail.com).  
On the uniqueness of the strongly irreducible decompositions of operators up to similarity, pp. 447-465.
ABSTRACT. We give a generalization of the Jordan canonical form theorem for a class of bounded linear operators on complex separable Hilbert spaces in terms of abelian von Neumann algebras. Precisely, we study the uniqueness of strongly irreducible decompositions of the operators on the Hilbert spaces up to similarity

ElBialy, Mohamed Sami,  Department of Mathematics and Natural Sciences, American University of Ras Al Khaimah,
UAE (sami.elbialy@aurak.ae).
Smooth conjugacy and linearization near resonant fixed points in Hilbert spaces, pp. 467-509.
ABSTRACT.  In this work we study the problems of smooth conjugacy and smooth linearization near resonant hyperbolic fixed points for local diffeomorphisms of Hilbert spaces.

Ciprian Preda,  Department of Mathematics, 310 Malott Hall, Cornell University, Ithaca, NY 14853-4201, USA (preda@math.cornell.edu)
On the exponential decay of an orbit of a vector under C0-semigroups, pp. 511-525.
ABSTRACT. Consider {T(t)}t ≥ 0 a C0-semigroup on the Banach space X. We prove that the orbit of a vector x0 under T(⋅) has an exponential decay if there exists a pair of Τ-spaces (U(R+,X),V(R+,X)) satisfying a very general technical condition and such that no matter how we choose a locally integrable function f: R+→R, we have that f(⋅)T(⋅)x0 ∈ U(R+,X)⇒ [t→(∫0t f(τ)dτ)T(t)x0 ∈ V(R+,X)]. It is worth to note that the Τ-spaces class includes almost all the important function spaces, as the classical Lp spaces, Orlicz function spaces, etc (we recall the reader that a Τ-space is a Banach function space embedded in the Fréchet space of locally integrable functions that has the ideal property and with the right shift being an isometry on it). An application is also pointed out.

Ding-Gong, Yang Soochow University, Suzhou 215006, P. R. China, and Jin-Lin, Liu, Yangzhou University, Yangzhou 225002, P. R. China (jlliu@yzu.edu.cn).
Certain subclasses of meromorphically multivalent functions, pp. 527-554.
ABSTRACT. The authors introduce two new subclasses of meromorphically multivalent functions. Distortion inequalities and convolution properties are obtained. Some properties of the partial sums of functions belonging to these function classes are also given.

Arhangelskii, Alexander, Moscow, 121165, Russia (arhangel.alex@gmail.com), and van Mill, Jan, Dept. of Mathematics, VU University Amsterdam, 1081 HV Amsterdam, the Netherlands (j.van.mill@vu.nl).  
On uniquely homogeneous spaces, II, pp. 555-568.
ABSTRACT. A space X is uniquely homogeneous provided that for all x and y in X there is a unique homeomorphism of X that takes x onto y.  It is shown that there is an example of a uniquely homogeneous separable metrizable space that is Abelian (all homeomorphisms commute) but not Boolean (all homeomorphisms are involutions). It is also shown that such an example cannot be a Baire space. This answers several problems on (unique) homogeneity.

Clark, Alex, Dept. of Mathematics, University of Leicester, University Road, LE1 7RH, UK (adc20@le.ac.uk), Fokkink, Robbert, DIAM Probability, TU Delft, Mekelweg 4, 2628CD Delft, Netherlands (R.J.Fokkink@tudelft.nl), and Olga Lukina, Department of Mathematics, Statistics and Computer Science University of Illinois at Chicago M/C 249, 851 S. Morgan Street, Chicago IL 60607 (lukina@uic.edu).
The Schreier continuum and ends, pp. 569-599.
ABSTRACT. Blanc showed in his thesis that a compact minimal foliated space with a residual subset of 2-ended leaves can contain only 1 or 2 ended leaves. In this paper we give examples of compact minimal foliated spaces where a topologically generic leaf has 1 end, there is an uncountable set of leaves with 2 ends and a leaf with 2n ends, for a given n > 1. The examples we present are weak solenoids, which allows us to represent the graph of the group action on the fibre as the inverse limit of finite coverings of a finite graph, which we call the Schreier continuum, which we use to obtain the result. While in certain cases the problem can be reduced to the study of a self-similar action of an automorphism group of a regular tree, our geometric technique is more general, as it applies to cases where the action is not self-similar.  

Dube, Themba, Department of Mathematical Sciences, University of South Africa, P.O. Box 392, 0003 Unisa, South Afric(dubeta@unisa.ac.za).
 Pseudocompact supports in pointfree topology, pp. 601-620.
ABSTRACT. Let RL denote the ring of real-valued continuous functions on the completely regular frame L. The support of an element of RL is the closed quotient induced by the pseudocomplement of the cozero of that element. We show that the set P(L) of elements of RL which have pseudocompact supports is an ideal. Call L supportively normal if supports are C-quotients. For supportively normal L, this ideal is the intersection of pure parts of the hyper-real maximal ideals of RL. If L is supportively normal and the Lindelof coreflection of L is spatial, then it is a continuous frame if and only if P(L) is contained in no real maximal ideal. Without the spatiality restriction, an example shows that one implication in this latter equivalence fails. We define locally pseudocompact frames conservatively, and show that if L is such a frame, then P(L) is contained in no fixed maximal ideal. The example alluded to above again shows that the converse fails - in contrast with the spatial case.

W. T. Ingram, 284 Windmill Mountain Road, Spring Branch, TX 78070 (ingram@mst.edu).
Concerning dimension and tree-likeness of inverse limits with set-valued functions in plain text., pp. 621-631.
ABSTRACT. From a theorem of Van Nall it is known that inverse limits with sequences of upper semi-continuous set-valued functions with 0-dimensional values have dimension bounded by the dimensions of the factor spaces. Information is also available about the dimension of inverse limits with sequences of upper semi-continuous continuum-valued bonding functions having graphs that are mappings on the factor spaces that have continua appended at each point of a closed set, however the conclusion of this theorem allows the possibility of an infinite dimensional inverse limit. In this paper we show that inverse limits with sequences of certain surjective upper semi-continuous continuum-valued bonding functions have dimension bounded by the dimensions of the factor spaces. One consequence of our investigation is that certain inverse limits on the unit interval with upper semi-continuous continuum-valued functions are tree-like including those that are inverse limits on the unit interval with a single interval-valued bonding function that has no flat spots.

Ozarslan, Nigar Tuncer, Department of Mathematics and Computer Science, Bahcesehir University, Istanbul, TURKEY (nigaroz@yahoo.com).
Concerning inversible fibrations, globalization and triviality of maps, pp. 633-644.
ABSTRACT. Dyer and Eilenberg (1988) in ``Globalizing Fibrations with schedules'' defined inversible fibration and prove a globalization theorem for these kind of fibrations, then they asked whether a locally trivial maps over contractible space is trivial. In this paper we provide some further details concerning inversible fibrations and we define also inversible Hurewicz Fibrations, relate these to the inversible fibrations of Dyer and Eilenberg and study inversibility for path space fibrations. An affirmative answer to a special case of the Dyer and Eilenberg question is given.

Yan-Kui Song, Institute of Mathematics, School of Mathematical Science, Nanjing Normal University, Nanjing 210023, China (songyankui@njnu.edu.cn).
A note on star-Rothberger spaces, pp. 645-653.
ABSTRACT. In this paper, we show the following statements: (1) There exists a Tychonoff pseudocompact, star-Rothberger space having a regular-closed subspace which is not star-Rothberger; (2) There exists a Hausdorff star-Rothberger space having a regular-closed Gδ-subspace which is not star-Rothberger; (3) Assuming some cardinal assumptions, there exists a Tychonoff strongly star-Rothberger space having a regular-closed Gδ-subspace which is not strongly star-Rothberger; (4) A clopen subspace of strongly star-Rothberger (star-Rothberger) space is strongly star-Rothberger (star-Rothberger, respectively). The above statements give some characterizations to a question of Kočinac.

Er-Guang Yang, School of Mathematics & Physics, Anhui University of Technology, Maanshan 243002, P.R. China (egyang@126.com).
 A weak base version of Collins-Roscoe mechanism, pp. 655-661.
ABSTRACT. We define a weak base version (wA) of Collins-Roscoe mechanism and show that (wA) also implies metrizability of a topological space. With this result, some metrization theorems that appeared in the literature are improved.