Electronic Edition Vol. 34, No. 4, 2008

Editors: H. Amann (Zürich), G. Auchmuty (Houston), D. Bao (Houston), H. Brezis (Paris), K. Davidson (Waterloo), C. Hagopian (Sacramento), R. M. Hardt (Rice), Y. Hattori (Matsue, Shimane), J. Hausen (Houston), J. A. Johnson (Houston), W. B. Johnson (College Station),  V. I. Paulsen (Houston), M. Rojas (College Station), Min Ru (Houston), S.W. Semmes (Rice)
Managing Editor: K. Kaiser (Houston)

Houston Journal of Mathematics


D. D. Anderson and Sangmin Chun, University of Iowa, Iowa City, IA 52242 (dan-anderson@uiowa.edu), (schun@math.uiowa.edu).
Annihilator-Semigroups and Rings, pp. 985-996.
Let R be a commutative ring with 1. We define R to be an annihilator-semigroup ring if R has an annihilator-semigroup S, that is, (S, ·) is a multiplicative subsemigroup of (R, ·) with the property that for each r in R there exists a unique s in S with 0 : r = 0 : s. The quotient monoid R/~ where a ~ b if and only if 0 : a = 0 : b is called the annihilator congruence semigroup of R. If S is an annihilator-semigroup for R, then S is isomorphic to R/~. In this paper we investigate annihilator-semigroups, annihilator congruence semigroups, and annihilator-semigroup rings.

Arnold, David M., Baylor University, One Bear Place, Waco, TX 76798-7328 (David_Arnold@baylor.edu).
Subgroups of Finite Direct Sums of Z[1/n], pp. 997-1007.
ABSTRACT. Let C(n) denote the class of subgroups of finite direct sums of Z[1/n] for a positive integer n. There is a category equivalence from the isomorphism at n category of C(n) to the class of n-local torsion-free abelian groups of finite rank. Included are a number of examples and a classification of groups in C(n) with rank < 4 for the case that n is a prime number.

M.E. Adams, Department of Mathematics, State University of New York, New Paltz, NY 12561, U.S.A. (adamsm@newpaltz.edu) and J. Schmid, Institute of Mathematics, University of Bern, CH-3012 Bern, Switzerland (juerg.schmid@math.unibe.ch).
Minimal extensions of distributive bounded lattices , pp. 1009-1024.
ABSTRACT. There is a considerable literature on (proper) maximal sublattices of distributive bounded lattices. In this note, we consider the dual concept of when L' is a minimal extension of L, that is L is a (proper) maximal sublattice of L'. Minimal extensions occur in one of two ways, so-called "removing a cover" or "splitting a point". The removal of covers is characterised and "special points" that can always be split are identified. For infinite L, there are at least |L| minimal extensions obtained by splitting special points, and examples are given to show that there need be no other minimal extensions.

Takuya Yamauchi, Dept. of Mathematics, Graduate School of Science, Hiroshima University, Higashi-hiroshima 739-8526, Japan (yamauchi@math.sci.hiroshima-u.ac.jp).
The modularity of Q-curves of degree 43, pp. 1025-1035.
ABSTRACT. Using the absolute invariant of elliptic curves on the modular curve of level 43, we construct a family of elliptic curves over number fields which are isogenous to all its Galois conjugates and we prove their modularity under some conditions.

S. Ponnusamy, Department of Mathematics, Indian Institute of Technology Madras, Chennai-600 036, India (samy@iitm.ac.in)A. Vasudevarao, Department of Mathematics, Indian Institute of Technology Madras, Chennai-600 036, India (alluvasu@iitm.ac.in) and Hiroshi Yanagihara, Department of Applied Science, Faculty of Engineering, Yamaguchi University ( hiroshi@yamaguchi-u.ac.jp).
Region of variability of univalent functions f(z) for which zf '(z) is spirallike, pp.1037-1048.
ABSTRACT.  For a complex number α with Re(α) >0 let Sα(λ) be the class of analytic functions f in the unit dist D with f(0)=0=f'(0)-1, f''(0)=2λe-iαcos(α) satisfying Re e(1+zf''(z)/f'(z))>0 for z in D. For a in D fixed, we determine the region of variability for log(f'(a)) when f  ranges over the class Sα(λ). As a consequence, we obtain an estimate for a pre-Schwarzian norm for Sα(0).

Yibing Shen, Department of Mathematics, Zhejiang University, Hangzhou, 310028, China (yibingshen@zju.edu.cn) and Shihshu Walter Wei, Department of Mathematics,
University of Oklahoma, Norman, Oklahoma 73019-0315,  U.S.A (wwei@ou.edu).
The stability of harmonic maps on Finsler manifolds, pp. 1049-1056.
ABSTRACT. In this paper We study the stability of harmonic maps on Finsler manifolds by an extrinsic average variational method in the calculus of variations. Some nonexistence results of nonconstant stable harmonic maps on compact Finsler manifolds are obtained, and the homotopy classes of maps on Finsler manifolds are discussed.

Tetsuya Hosaka, Department of Mathematics, Utsunomiya University, (hosaka@cc.utsunomiya-u.ac.jp).
Dense subsets of boundaries of CAT(0) groups, pp. 1057-1063.
ABSTRACT.  We study dense subsets of boundaries of CAT(0) groups and we give a sufficient condition of CAT(0) groups whose boundaries are minimal.

R. Lowen, T. Vroegrijk  and C. Van Olmen, Department of Mathematics and Computer Science, University of Antwerp Middelheimlaan 1, 2020 Antwerp, Belgium (bob.lowen@ua.ac.be), (tom.vroegrijk@ua.ac.be),(christophe.vanolmen@ua.ac.be).
Functional ideals and topological theories, pp. 1065-1089.
ABSTRACT.In this paper we give new and unified isomorphic characterizations of approach spaces, pre-approach spaces, convergence approach spaces, uniform gauge spaces, topological spaces, convergence spaces, pretopological spaces, metric spaces and uniform spaces. The unified treatment is made possible by the use of a type of ideals of positive real-valued functions, a concept, richer and more appropriate than filters for our purpose.

Yang,Gao, Capital Normal University, Beijing, 100037 China (gaoyang1203@gmail.com), Lei,Mou, Capital Normal University, Beijing, 100037 China (leimou@sohu.com) and Shangzhi, Wang, Capital Normal University, Beijing, 100037 China (zhyk@vip.sina.com).
Products of base-cover metacompact spaces, pp. 1091-1097.
ABSTRACT. A space X is base-cover metacompact if it has an open base every subcover of which has a point-finite subcover. Answering a question asked by Popvassilev, we prove: (1) The product of the Michael line (or the Sorgenfrey line) and ω1+1 is not base-cover metacompact, where ω1+1 has the order topology. (2) The product of a base-cover metacompact Lindelöf space and a compact metrizable space is base-cover metacompact.

Xuanhao Ding, Department of Mathematics, Guilin University of Electronic Technology, Guilin, 541004, the People's Republic of China (dxh@gliet.edu.cn) and Dechao Zheng Department of Mathematics, Vanderbilt University, Nashville, Tennessee 37240 (zheng@math.vanderbilt.edu).
Finite rank commutator of Toeplitz operators or Hankel perators, pp. 1099-1119.
ABSTRACT. In this paper we completely characterize when the commutator of two Toeplitz operators or two Hankel operators on the Hardy space has finite rank.

Charalampos Charitos and Ioannis Papadoperakis,  Agricultural University of Athens, Laboratory of Mathematics, 118 55 Athens, GREECE, (bakis@aua.gr) and (papadoperakis@aua.gr).
Ergodicity of invariant measures for the geodesic flow on quotient spaces of real trees, pp. 1121-1143.
ABSTRACT. We consider spaces of the form X/Γ where X is a real tree and Γ a group of isometries of X acting properly discontinuously on X. A measure m on the space of geodesics of X/Γ is constructed. The ergodicity of m with respect to the geodesic flow is studied.

Alzer, Horst, Morsbacher Str. 10, 51545 Waldbröl, Germany (H.Alzer@gmx.de).  
Inequalities for the tail of exponential series, II , pp. 1145-1164.
ABSTRACT. We present several new inequalities for the tail of the exponential series with negative variable. Among others, we provide sub - and superadditive properties, monotonicity and convexity theorems, and mean value inequalities.

Jimenez-Vargas, A., University of Almeria, 04071 Almeria, Spain (ajimenez@ual.es) and Villegas-Vallecillos, M., University of Almeria, 04071 Almeria, Spain (mvv042@alboran.ual.es).
Into linear isometries between spaces of Lipschitz functions, pp. 1165-1184.
ABSTRACT. In this paper we state a Lipschitz version of a known Holsztynski's theorem on linear isometries of C(X)-spaces. Let Lip(X) be the Banach space of all scalar-valued Lipschitz functions f on a compact metric space X endowed with the norm ||f|| = max{sup{|f(x)|: x in X}, L(f)}, where L(f) is the Lipschitz constant of f. We prove that any linear isometry T from Lip(X) into Lip(Y) satisfying that L(T1X)< 1 is essentially a weighted composition operator Tf(y) = a(y)f(b(y)) for all f in Lip(X) and all y in Y0, where Y0 is a closed subset of Y, b is a Lipschitz map from Y0 onto X with L(b) less or equal than max{1,diam(X)}, and a is a function in Lip(Y) with ||a|| = 1 and |a(y)| = 1 for all y in Y0. We improve this representation in the case of onto linear isometries and we classify codimension 1 linear isometries in two types.

Jimenez-Vargas, A., University of Almeria, 04071 Almeria, Spain (ajimenez@ual.es) and Villegas-Vallecillos, M., University of Almeria, 04071 Almeria, Spain (mvv042@alboran.ual.es).
Order isomorphisms of little Lipschitz algebras, pp. 1185-1195.
ABSTRACT. For compact metric spaces (X,dX) and (Y,dY) and scalars α, β in (0,1), we prove that every order isomorphism T between little Lipschitz algebras lip(X,(dX)α) and lip(Y,(dY)β) is a weighted composition operator of the form Tf(y) = a(y)f(h(y)) for all f in lip(X,(dX)α) and all y in Y, where a is a nonvanishing positive function in lip(Y,(dY)β) and h is a Lipschitz homeomorphism from (Y,(dY)β) onto (X,(dX)α).

Björn, Anders, Department of Mathematics, Linköpings universitet, SE-581 83 Linköping, Sweden (anbjo@mai.liu.se), Björn, Jana, Department of Mathematics, Linköpings universitet, SE-581 83 Linköping, Sweden (jabjo@mai.liu.se), and Shanmugalingam, Nageswari, Department of Mathematical Sciences, University of Cincinnati, P.O. Box 210025, Cincinnati, OH 45221-0025, U.S.A. (nages@math.uc.edu).
Quasicontinuity of Newton-Sobolev functions and density of Lipschitz functions on metric spaces, pp. 1197-1211.
ABSTRACT. We show that on complete doubling metric measure spaces X supporting a Poincaré inequality, all Newton-Sobolev functions u are quasicontinuous, i.e. that for every a>0 there is an open subset U of X with capacity less than a and such that the restriction of u to X\U is continuous. This implies that the capacity is an outer capacity.

Feng Lü, School of Mathematics and System Sciences, Shandong University, Jinan, Shandong, 250100, P.R. China (lvfeng@mail.sdu.edu.cn) and Junfeng Xu, Department of Mathematics, Wuyi University, Jiangmen 529020, Guangdong, P.R. China (xujunf@gmail.com).
Sharing set and normal families of entire functions and their derivatives , pp. 1213-1223.
ABSTRACT. In this paper, we use the idea of sharing set to prove: Let F be a family of functions holomorphic in a domain, let a and b be two distinct complex numbers with a+b≠ 0. If for each f in F, f and f' share S={a, b} CM, then F is normal in D. As an application, we prove a uniqueness theorem.

Ali Ghaffari, Department of Mathematics, Semnan University, Semnan, Iran (ghaffari1380@yahoo.com).
Operators which commute with the conjugation operators, pp. 1225-1232
ABSTRACT. In this paper we show that every bounded linear operator on some kind of group algebras commutes with conjugate operators, if and only if these operators commute with convolution operators. Using some conditions on bounded linear operators on the algebra of essentially bounded functions, we prove that these operators commute with conjugate operators if and only if commute with convolution operators.

Stevo Stevic, Mathematical Institute of the Serbian Academy of Science, Knez Mihailova 35/I, 11000 Beograd, Serbia, (sstevic@ptt.yu; sstevo@matf.bg.ac.yu),
A note on a theorem of Zhu on weighted Bergman projections on the polydisc, pp. 1233-1241.
ABSTRACT. We show that a holomorphic function in the unit polydisc is the image of a bounded holomorphic function by the weighted Bergman projection if and only if some weighted derivations of the function are bounded. This result improves Theorem 4 in the paper K. Zhu, Weighted Bergman projections on the polydisc, Houston J. Math. 20 (2) (1994), 275-292.

Giorgio Metafune and Chiara Spina, Dipartimento di Matematica "Ennio De Giorgi", Universita di Lecce, C.P.193, 73100, Lecce, Italy (giorgio.metafune@unile.it), (chiara.spina@unile.it)
Heat kernel bounds for certain Schrödinger operators with unbounded potentials, pp. 1243-1257.
ABSTRACT. We prove short and long time estimates for the heat kernels of certain Schrödinger operators with regular but unbounded potentials.

Liping Yang, School of Applied Mathematics, Guangdong University of Technology, Guangzhou, Guangdong Province 510090 P.R. China (yanglping2003@126.com)
The equivalence between the convergence of Ishikawa--Mann iterations and multistep iteration, pp. 1259-1269.
ABSTRACT.It is proved that the convergence of Mann, Ishikawa and three-step iterations for some classes of operators is equivalent to the convergence of multi-step iteration. The main results of this paper extend and improve the corresponding results in some aspects.

Miyagaki, Olímpio H., Universidade Federal de Viçosa, 36571-000 Viçosa, MG, Brasil (olimpio@ufv.br) , and Rodrigues, Rodrigo S., Universidade Federal de São Carlos, 13565-905 São Carlos, SP, Brasil (rodrigosrodrigues@ig.com.br).
On multiple solutions for a singular quasilinear elliptic system involving critical Hardy-Sobolev exponents, pp. 1271-1293.
ABSTRACT. This paper is concerned with the existence of nontrivial solutions for a class of degenerate quasilinear elliptic systems involving critical Hardy-Sobolev type exponents. The lack of compactness is overcame by using the Brezis-Nirenberg approach, and the multiplicity result is obtained by combining a version of the Ekeland's variational principle due to Mizoguchi with the Ambrosetti-Rabinowitz mountain pass theorem.