Electronic Edition Vol. 41, No. 4 , 2015

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


Guowu Yao, Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, People's Republic of China (gwyao@math.tsinghua.edu.cn).
Gluing quasiconformal mappings in the complex plane, pp. 1107-1117.
ABSTRACT. In this paper, several versions of gluing theorems for quasiconformal mappings in the plane are obtained. The best possibility of gluing quasiconformal mappings is investigated. As an application, we provide a new short proof of the gluing theorem obtained by Jiang and Qi.

Jaume Llibre, Departament de Matemàtiques. Universitat Autònoma de Barcelona, Bellaterra, 08193--Barcelona, Catalonia, Spain (jllibre@mat.uab.cat) and Víctor F. Sirvent, Departamento de Matemáticas, Universidad Simón Bolívar, Apartado 89000, Caracas 1086-A, Venezuela (vsirvent@usb.ve).
C1 self--maps on closed manifolds with all their periodic points hyperbolic, pp. 1119-1127.
ABSTRACT. We present several results providing sufficient conditions for the existence of almost quasi--unipotent maps on different closed manifolds having infinitely many periodic points all of them hyperbolic.

Vladimir S. Matveev, Institute of Mathematics, Friedrich-Schiller-Universität Jena, 07737 Jena, Germany (vladimir.matveev@uni-jena.de) .
On submaximal dimension of the group of almost isometries of Finsler metrics, pp. 1129-1136.
ABSTRACT. We show that the second greatest possible dimension of the group of (local) almost isometries of a Finsler metric is (n2-n)/2 +1 for n= dim(M) different from 4 and (n2-n)/2 +2 =8 for n=4. If a Finsler metric has the group of almost isometries of dimension greater than (n2-n)/2+1, then the Finsler metric is Randers, i.e., F(x,y)= (gx(y,y))1/2+w(y). Moreover, if n is not 4, the Riemannian metric g has constant sectional curvature and, if in addition n is not 2, the 1-form w is closed, so (locally) the metric admits the group of local isometries of the maximal dimension n(n+1)/2. In the remaining dimensions 2 and 4, we describe all examples of Finsler metrics with 3 resp. 8-dimensional group of almost isometries.

Kensuke Onda, Graduate School of Mathematics, Nagoya University, Furocho, Chikusaku, Nagoya 464-8602 JAPAN (kensuke.onda@math.nagoya-u.ac.jp) and Phillip E. Parker, Mathematics Department, Wichita State University, Wichita KS 67260-0033 USA (phil@math.wichita.edu).
Nilsolitons of H-type in the Lorentzian setting, pp. 1137-1151 
ABSTRACT. It is known that all left-invariant pseudo-Riemannian metrics on the three-dimensional Heisenberg group are algebraic Ricci solitons. We consider generalizations of Riemannian H-type, namely pseudoH-type and pH-type. We study algebraic Ricci solitons of left-invariant Lorentzian metrics on 2-step nilpotent Lie groups of both types.

Tang, Tong, Department of Mathematics, Nanjing Normal University, Nanjing 210097, China (tt507010156@126.com), Pan, Yifei, Department of Mathematical Sciences, Indiana University - Purdue University Fort Wayne, Fort Wayne, IN 46805-1499, and School of Mathematics and Informatics, Jiangxi Normal University, Nanchang, China (pan@ipfw.edu), and Wang, Mei, Department of Statistics, University of Chicago, Chicago, IL 60637 (meiwang@galton.uchicago.edu).
An increasing flat function with infinitely changing convexity, pp. 1153-1161.
ABSTRACT. We construct a smooth, strictly increasing function with its second derivative changing signs infinitely many times near a point, then we extend the function to a surface increasing in radial direction with curvatures changing signs infinitely often near the origin. The interesting analytical properties of the functions may serve as examples to understand the reversed Hopf Lemma.

Abu-Omar, Amer, Department of Basic Sciences and Mathematics, Philadelphia University, Amman, Jordan (aabuomar@philadelphia.edu.jo) and Kittaneh, Fuad, Department of Mathematics, The University of Jordan, Amman, Jordan (fkitt@ju.edu.jo).
Numerical radius inequalities for products and commutators of operators, pp. 1163-1173.
ABSTRACT. New numerical radius inequalities are given. These inequalities involve products and commutators of Hilbert space operators. Our results generalize and improve recent numerical radius inequalities.

Bice, Tristan, York University, Toronto, Canada (Tristan.Bice@gmail.com) and Farah, Ilijas, York University, Toronto, Canada, (ifarah@yorku.ca).
Traces, Ultrapowers and the Pedersen-Petersen C*-algebras, pp. 1175-1190.
ABSTRACT. We consider traces on the ultrapower of a C*-algebra A. Given infinitely many extremal tracial states on A, we construct a large family of traces on its ultrapower that are not simply ultrafilter limits of traces on A. Further, we show that there are traces on the ultrapower of A that are not even locally trivial when A is a Pedersen-Petersen C*-algebra. Some other interesting properties of these C*-algebras are also exhibited. 

Hu Bingyang, Le Hai Khoi, Nanyang Technological University, 637371 Singapore, and Kehe Zhu, State University of New York, Albany, NY 12222, USA Zhu, Kehe (kzhu@albany.edu).
Frames and operators in Schatten classes, pp. 1191-1219.
ABSTRACT. For a compact operator T on a separable Hilbert space H and a positive exponent p, we characterize membership of T in the Schatten p-class in terms of the action of T on frames. An interesting difference exists between the case p>2 and the case p<2.

Chan, Kit C., Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, OH 43402 (kchan@bgsu.edu), and Kadel, Gokul R., Department of Mathematical Sciences, Cameron University, Lawton, OK 73505 (gkadel@cameron.edu). Dual hypercyclic extension for an operation on a Hilbert subspace, pp. 1221-1256.
ABSTRACT. Let M be a closed nontrivial subspace of a separable, infinite dimensional Hilbert space H with dim(H/M) = ∞. We show that a bounded linear operator A : M → M has a dual hypercyclic extension T : H → H if and only if its adjoint A* : M → M is hypercyclic.

Byoung Jin Choi, Department of Mathematics, Sungkyunkwan University, Suwon 440-746, Korea (choibj@skku.edu), Un Cig Ji, Department of Mathematics, Research Institute of Mathematical Finance, Chungbuk National University, Cheongju 362-763, Korea (uncigji@chungbuk.ac.kr).
Precise asymptotics of partial sums of noncommutative random variables, pp. 1257-1275.
ABSTRACT. In this paper, we study an asymptotic property, as a general and unifying approach, of a sequence of real valued functions and, as applications, we first prove a general precise asymptotics of partial sums of noncommutative random variables and then we prove a precise asymptotics of partial sums of free random variables in a domains of attraction of boxplus-stable distribution of exponent α (1< α ≦ 2).

Isaia, Florin, Transilvania University of Brasov, Faculty of Mathematics and Computer Science, 50 Iuliu Maniu St, 500091 Brasov, Romania (florin.isaia@unitbv.ro).
On the superposition operator between Sobolev spaces: well-definedness, continuity, boundedness, and higher-order chain rule, pp. 1277-1294.
ABSTRACT. This paper deals with the study of superposition operators between two arbitrary Sobolev spaces. The sufficient conditions which ensure the well-definedness, the continuity, the boundedness, and the validity of the higher-order chain rule for such operators, obtained in two previous papers (see G. Dinca and F. Isaia, On superposition operators between higher-order Sobolev spaces and a multivariate Faá di Bruno formula: the subcritical case, Differ. Integral Equ. 26 (2013), 11-58; G. Dinca and F. Isaia, Superposition operators between higher-order Sobolev spaces and a multivariate Faá di Bruno formula: supercritical case, Adv. Nonlin. Studies, 14 (2014), 137-158.) are heuristically analyzed. This point of view may be a start point in the attempt to prove that these sufficient conditions are necessary as well.

Itza-Ortiz, Benjamin A., Universidad Autonoma del Estado de Hidalgo, Pachuca, Mexico (itza@uaeh.edu.mx).
Classification of generalized Denjoy continua, pp. 1295-1311.
ABSTRACT. We give a topological classification of the minimal proper subspaces of  aperiodic flows on the torus in terms of   the conjugacy invariants of their corresponding Denjoy homeomorphisms. Several examples and some connections to operator algebras are discussed.

 Camargo, Javier, Escuela de Matemáticas, Facultad de Ciencias, Universidad Industrial de Santander, Ciudad Universitaria, Carrera 27 Calle 9, Bucaramanga, Santander, A. A. 678, COLOMBIA (jcam@matematicas.uis.edu.co), and Macías, Sergio, Instituto de Matemáticas, Universidad Nacional Autónoma de México, Circuito Exterior, Ciudad Universitaria, México D. F., C. P. 04510, MEXICO (sergiom@matem.unam.mx).
Locally one-to-one and covering maps, pp. 1313-1324.
ABSTRACT. A map f: X → Y between spaces is said to be locally one-to-one provided that there exists an open cover A of X such that the restriction f↑U: U →Y is a one-to-one map, for each U ∈ A. We study when a locally one-to-one map defined between continua is a covering map.

Alejandro Illanes, Universidad Nacional Autónoma de México, Circuito Exterior, Cd. Universitaria, México, 04510, D.F. (illanes@matem.unam.mx), Piotr Minc, Department of Mathematics and Statistics, Auburn University, Auburn, AL 36849 U.S.A. (mincpio@auburn.edu), and Frank Sturm, Department of Mathematics and Statistics, Auburn University, Auburn, AL 36849 U.S.A.
Extending surjections defined on remainders of metric compactifications of [0,∞), pp. 993-1019.
ABSTRACT. Let Y be a compactification of the real half-line [0,∞) with a hereditarily indecomposable continuum X as the remainder, and let Z be a compactification of [0,∞) with a chainable continuum P as the remainder. Then, every continuous surjection f:X→P can be extended to a continuous surjection f*:Y→Z.

Piotr Minc, Department of Mathematics and Statistics, Auburn University, Auburn, AL 36849. (mincpio@auburn.edu), and Frank Sturm, Department of Mathematics and Statistics, Auburn University, Auburn, AL 36849. 
Homeomorphism killing rays, pp. 1341-1350.
ABSTRACT. We prove that for each metric continuum X there is a compactification Z of the half-line [0,∞) with X as the remainder such that the identity is the only homeomorphism of X that extends to a homeomorphism of Z.

Mine, Kotaro, Graduate School of Mathematical Sciences, The University of Tokyo, Tokyo 153-8914, Japan (mine@ms.u-tokyo.ac.jp), Yamashita, Atsushi, Faculty of Engineering, Chiba Institute of Technology, 2-1-1 Shibazono, Narashino-shi, Chiba, 275-0023, Japan (ayamashita@p.chibakoudai.jp), and Yamauchi, Takamitsu, Graduate School of Science and Engineering, Ehime University, 2-5 Bunkyo-cho, Matsuyama, 790-8677, Japan (yamauchi.takamitsu.ts@ehime-u.ac.jp).
C0 coarse structures on uniform spaces, pp. 1351-1358.
ABSTRACT. The definition of C0 coarse structure introduced by Wright is extended to uniform spaces. It is proved that every topological coarse structure of a locally compact Hausdorff space is the C0 coarse structure associated to some uniformity compatible with its topology.

Abrahamsen, Trond A., University of Agder, Norway, Langemets, Johann, University of Tartu, Estonia, Lima, Vegard, Aalesund University College, Norway,  and Nygaard, Olav, University of Agder, Norway (olav.nygaard@uia.no)
Correction to the paper "On thickness and thinness of Banach spaces", Houston J. Math., 41 (2015), no. 1, 97-111
, pp. 1359-1360.