HOUSTON JOURNAL OF
MATHEMATICS

Expected Edition Vol. 43, No. 3, 2017

Editors:  D. Bao (San Francisco, SFSU), D. Blecher (Houston), B. 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 Editors: B. G. Bodmann and K. Kaiser (Houston)

 Houston Journal of Mathematics



Contents

Pat Goeters, Department of Mathematics, Auburn University, Auburn, Al 36849-5310 (goetehp@auburn.edu).
A-divisorial Matlis domains, pp. 691-701
ABSTRACT. We study the integral domains R with the property that HomR(-,A) defines a self-canceling duality with respect to a natural collection of submodules of the quotient field Q of R for a given submodule A of Q with EndR(A)=R. In case there is such a duality when R is a Matlis domain, we show that locally, A must necessarily be a fractional ideal. Additionally, under the presence of this duality, we examine the relation between the domain being Noetherian and having Krull dimension 1.

Enochs, Edgar, University of Kentucky, Lexington, KY 40506 (e.enochs@uky.edu), Jenda, Overtoun, Auburn University, Auburn, AL 36849 (jendaov@auburn.edu), and Ozbek, Furuzan, Auburn University, Auburn, AL 36849 (fzo0005@auburn.edu).
Submonoids of the formal power series, pp. 703-711.
ABSTRACT. Formal power series come up in several areas such as formal language theory, algebraic and enumerative combinatorics, number theory. In this paper we focus on the the subset of formal power series consisting of the ones with zero constant term. This subset forms a monoid with composition operation of series. We classify the sets T of strictly positive integers, for which the set of formal power series consisting of terms with powers from the set T, that forms a monoid with composition as the operation. We prove that in order for that set to be a monoid, T itself has to be a submonoid of (N,.). Unfortunately, this condition is not enough to guarantee the desired result. But if a monoid is strongly closed, then we get the desired result. We also consider an analogous problem for power series in several variables in the last section.

Mahdi Rahmatinia
, Department of Mathematics and Applications, University of Mohaghegh Ardabili, P.O.Box 179, Ardabil, Ir, (m.rahmati@uma.ac.ir), (mahdi.rahmatinia@gmail.com).
On φ-almost Bezoüt rings and φ-almost Prüfer rings, pp. 713-723.
ABSTRACT. The porpuse of this paper is to introduce some new classes of rings that are closely related to the classes of almost Bezoüt domains and almost Prüfer domains. This paper is devoted to study the φ-almost Bezoüt rings (φ-AB rings) and φ-almost Prüfer rings (φ-AP rings). A ring R is a φ-AB ring (respectively, φ-AP ring) if for nonnil elements a,b of R, there exists an n=n(a,b) with (an,bn) is a nonnil principal (respectively, φ-invertible) ideal of R.

Duc Thai Do,
Department of Mathematics, Hanoi National University of Education, 136 Xuan Thuy str., Hanoi, Viet Nam (doducthai@hnue.edu.vn) and Duc-Viet Vu, UPMC Univ. Paris 06, UMR 7586, Institut de Mathematiques de Jussieu, Paris Rive Gauche, 4 place Jussieu, F-75005 Paris, France (duc-viet.vu@imj-prg.fr).
Holomorphic mappings into compact complex manifolds, pp. 725-762.
ABSTRACT. The purpose of this article is to show a second main theorem with the explicit truncation level for holomorphic mappings of the complex plane (or of a compact Riemann surface) into a compact complex manifold sharing divisors in subgeneral position.

Shengjiang Chen,
Department of Mathematics, Ningde Normal University, Fujian, 352100, P.R.China (ndsycsj@126.com) and  Weichuan Lin (corresponding author), Department of Mathematics, Fujian Normal University, Fuzhou, 350007, P.R.China (sxlwc963@fjnu.edu.com).
Periodicity and uniqueness of meromorphic functions concerning sharing values, pp. 763-781.
ABSTRACT. In this paper, we obtain two suffcient conditions for periodicity of mermorphic functions of infinite order concerning three sharing values (2CM+1IM), which are improvements of the related results on meromorphic functions of finite order. As applications, we prove an uniqueness theorem of a meromorphic function g(z) when g(z) shares two values CM and one value IM with a periodic meromorphic function f(z) by a new method. Examples are given to show that our results are precise.

Hongyan Xu,
Department of Informatics and Engineering, Jingdezhen Ceramic Institute, Jingdezhen, Jiangxi, 333403, China (xhyhhh@126.com) and  YinYing Kong (corresponding author), School of Mathematics and Statistics, Guangdong University of Finance and Economics, Guangzhou, Guangdong 510320, China (kongcoco@hotmail.com).
The approximation of analytic function defined by Laplace-Stieltjes transformations convergent in the left half-plane, 783-806.
 ABSTRACT. By introducing the error in approximating Laplace-Stieltjes transformation, we study the growth of the analytic function defined by Laplace-Stieltjes transformation of X-order, which converges on the left half plane, and obtain the relation theorems between the error and X-order of Laplace-Stieltjes transformation.

Jing Zhang,
Department of Mathematics, Division of Computing, Mathematics and Technology, Governors State University, University Park, IL 60484 (jzhang@govst.edu)
Complex manifolds with vanishing Hodge cohomology, pp. 807-827.
ABSTRACT. Let Y be a connected complex manifold and F the sheaf of holomorphic j-forms on Y. If the i-th cohomology of F on Y vanishes for all positive integer i and nonnegative integer j, is Y a Stein manifold? This is a question raised by J-P. Serre in 1953. In this paper, we investigate the properties of this type of complex manifolds, assuming that Y is an open subset of a compact complex manifold X and the boundary X-Y is support of a Cartier divisor D on X. Particularly, we compute the number of algebraically independent nonconstant meromorphic functions with poles in X-Y (This number is called the Itaka D-dimension).

Xiaohuan, Mo,
Peking University, Beijing, 100871 (moxh@math.pku.edu.cn), Linfeng Zhou, East China Normal University, Shanghai, 200241, and Hongmei Zhu, Henan Normal University, Xinxiang, 453007.
On a class of Finsler metrics with constant flag curvature, pp. 829-846.
ABSTRACT: By finding two partial differential equations equivalent to a class of Finsler metrics being of constant flag curvature we explicitly construct new locally projectively flat Finsler metrics of constant flag curvature −1 and 0. They are counterexamples of Theorem 7.3 and 7.2 in Benling Li's paper.

Guanwei Chen,
University of Jinan, Jinan 250022, Shandong Province, P.R. China (guanweic@163.com) and Guo-Ping Zhan, Department of Mathematics, Zhejhang University of Technology, hangzhou 310023, P.R. China (zhangp@zjut.edu.cn).
Infinitely many small negative energy periodic solutions for second order Hamiltonian systems without spectrum 0, pp. 847-860.
ABSTRACT. In this paper, we consider a class of second order Hamiltonian systems, where 0 belongs to a spectral gap and the nonlinearities are subquadratic growth at infinity. The existence of infinitely many small negative energy periodic solutions is obtained by a variant fountain theorem.

Gardella, Eusebio,
Mathematisches Institut, Fachbereich Mathematik und Informatik der Universität Münster, Einsteinstrasse 62, 48149 Muenster, Germany (gardella@uni-muenster.de), (eusegardella@gmail.com).
Regularity properties and Rokhlin dimension for compact group actions, pp. 861-889.
ABSTRACT. We show that formation of crossed products and passage to fixed point algebras by compact group actions with finite Rokhlin dimension preserve the following regularity properties: finite decomposition rank, finite nuclear dimension, and tensorial absorption of the Jiang-Su algebra, the latter in the formulation with commuting towers. Finally, we also show how our results yield new informaticon in some cases of interest. 

Sangani Monfared, Mehdi
, Department of Mathematics and Statistics, University of Windsor, Windsor, ON, N9B 3P4 (monfared@uwindsor.ca).
Relative boundaries for normed spaces, pp. 891-904.
ABSTRACT. We define relative boundaries for subsets of normed spaces. Extending a result of Bishop and de Leeuw, we show that if E is a Banach space and K is a subset of the unit ball of the dual of E, then the (α , β)-points of E relative to K, are strong boundary points of E relative to K. As an application, we show that if A is a unital (left) character amenable Banach algebra, then the spectral Choquet boundary of A is the entire spectrum of A. We give sufficient conditions for character amenability of finitely generated commutative Banach algebras.

Balan, Radu, University of Maryland, College Park, MD 20742 (rvbalan@math.umd.edu).
Stability of frames which give phase retrieval, pp. 905-918.
ABSTRACT. In this paper we study the property of phase retrievability by redundant sysems of vectors under perturbations of the frame set. Specifically we show that if a set F of m vectors in the complex Hilbert space of dimension n allows for vector reconstruction from magnitudes of its coefficients, then there is a perturbation bound r>0 so that any frame set within r from F has the same property. In particular this proves a recent construction for the case m=4n-4 is stable under perturbations. Additionally we provide estimates of the stability radius.

Mbekhta, Mostafa, UFR de Mathématiques, Laboratoire CNRS-UMR 8524 P. Painlevé, Université Lille 1, 59655 Villeneuve Cedex, France (Mostafa.Mbekhta@math.univ-lille1.fr), and Oudghiri, Mourad, Faculté des Sciences d'Oujda, Laboratoire LAGA, 60000 Oujda, Morocco (m.oudghiri@ump.ac.ma)
Additive preservers of group invertible operators, pp. 919-936.
ABSTRACT. Let B(X) be the algebra of all bounded linear operators on an infinite-dimensional complex or real Banach space X. We prove that an additive surjective map Φ on B(X) preserves group invertible operators in both directions if and only if Φ is either of the form Φ(T)=cATA-1 or the form Φ(T)=cBT*B-1 where c is a non-zero scalar, A:X→ X and B:X*→ X are two bounded invertible linear or conjugate linear operators.

Pop, Florin, Dept. of Mathematics, Wagner College, Staten Island, NY 10301 (fpop@wagner.edu)
Remarks on the Completely Bounded Approximation Property for C*-algebras, pp. 937-945.
ABSTRACT. In this paper we show that if the range C*-algebra has the Weak Expectation Property, then completely bounded maps have tensor product extension properties similar to those of completely positive maps. This result, combined with an argument of Huruya, allows us a new look at the Completely Bounded and Matricial approximation properties for C*-algebras.

Gilles Godefroy
, Institut de Mathématiques de Jussieu, 4 place Jussieu, 75252 Paris Cedex 05, France (gilles.godefroy@imj-prg.fr)
The isomorphism classes of lp are Borel, pp. 947-951.
ABSTRACT. It is proved for 1<p<∞ that the set of subspaces of C(2ω) that are isomorphic to lp is Borel.

Pilarczyk, Dominika,
University of Wroc³aw, Wroc³aw (dominika.pilarczyk@math.uni.wroc.pl).
Linear evolution equation with fractional Laplacian and singular potential, pp. 953-967.
ABSTRACT. We show the existence of weak and mild solutions to the Cauchy problem for the linear evolution equation with fractional Laplacian and singular potential. Moreover we describe their large time behavior and obtain asymptotic stability of self-similar solutions.

Tomonori Hirasa,
Faculty of Mathematics, Kyushu University, Motooka 744, Nishi-ku, Fukuoka, 819-0395, Japan  (tomonori_hirasa@yahoo.co.jp).
Liftability for orientable immersed surfaces and triple points, pp. 969-973.
ABSTRACT. In this paper, we consider generic immersions of orientable closed surfaces into 3-space and show that there is a non-liftable example if and only if its number of triple points is 2n (n > 0).

Yao Wei, Hebei University of Science and Technology, Shijiazhuang 050018, Hebei Province, China (yaowei0516@163.com) and Wu, Hengyang, Hangzhou Dianzi University, Hangzhou 310018, Zhejiang Province, China (wuhengy_1974@aliyun.cn)
Dualities for lower semicontinuous maps in the framework of interior spaces, pp. 975-991.
ABSTRACT. This paper studies dualities for lower semicontinuous maps in the framework of interior spaces. For an interior space (X,O(X)) and a complete lattice L, let [X→L] be the set of all lower semicontinuous maps of (X,O(X)). We get three dualities for [X→L]: (1) for every complete lattice L, [X→L] is order isomorphic to the set of all meet-join maps from L to the lattice O(X); (2) a complete lattice L is completely distributive iff [X→L] is order isomorphic to the set of all join-meet maps from O(X) to L for every interior space (X,O(X)); (3) an interior space (X,O(X)) is totally continuous iff [X→L] is order isomorphic to the set of all join-meet maps from O(X) to L for every complete lattice L.

Robert J. Daverman,
Department of Mathematics, University of Tennessee, Knoxville, TN, 37996 (daverman@math.utk.edu).
Smearing the wildness of crumpled cubes via cell-like maps, pp. 993-1018.
ABSTRACT. We consider the set of triples (C,C',f) consisting of crumpled n-cubes C and C' and surjective cell-like maps f of C onto C' such that such that the restriction of f to the Interior of C is 1-1. Generally the overarching goal is to compare the wildness of C and C' in the presence of such a cell-like map. Specifically, we strive to show a wide variety of ways in which target can be more complicated than the domain.

Richard N. Ball
, Dept. of Math, Univ. of Denver, Denver, CO 80208 (rball@du.edu), Anthony W. Hager,  Dept. of Math and CS, Wesleyan Univ. Middletown, CT 06459  (ahager@wesleyan.edu)Donald G. Johnson, 4351 Nambe Arc, Las Cruces, NM 88011 (dgjohnson@member.ams.org)James J. Madden,  Dept. of Math, LSU, Baton Rouge, LA 70803 (jamesjmadden@gmail.com), and Warren Wm. McGovern, Wilkes Honors College, Florida Atlantic Univ., Jupiter, FL 33458 (warren.mcgovern@fau.edu).
The Yosida space of the vector lattice hull of an archimedean l-group with unit, pp. 1019-1030.
ABSTRACT. For an object G in the category of archimedean l-groups with distinguished weak order unit,we have the contravariantly functorial compact Yosida space, YG. When G is embedded in H,the resulting map of YH to YG is a surjection, and when it is also one-to-one, we write "YH=YG"; for divisible hulls, we have always YdG=YG. For vector lattice hulls vG, we frequently have YvG and YG differing. Theorem. A compact space X is quasi-F iff whenever YG=X then also YvG=X. ("quasi-F" means each dense cozero set is C*-embedded.)