Electronic Edition Vol. 32, No. 3, 2006

Editors: H. Amann (Zürich), G. Auchmuty (Houston), D. Bao (Houston), H. Brezis (Paris), J. Damon (Chapel Hill), K. Davidson (Waterloo), C. Hagopian (Sacramento), R. M. Hardt (Rice), J. Hausen (Houston), J. A. Johnson (Houston), W. B. Johnson (College Station), J. Nagata (Osaka), V. I. Paulsen (Houston), , S.W. Semmes (Rice)
Managing Editor: K. Kaiser (Houston)

Houston Journal of Mathematics


De Vivo, Clorinda and Metelli, Claudia , Dipartimento di Matematica e Applicazioni, Università Federico II di Napoli, 80126 Napoli, Italy (clorinda.devivo@dma.unina.it), (cmetelli@math.unipd.it).
On degenerate B(2)-groups, pp. 633-649.
ABSTRACT. We examine a class of B(2)-groups where types of elements are still determined by partitions. An algorithm is given to determine whether a degenerate B(2)-group which is a direct sum of two strongly indecomposable B(1)-groups is itself a regular B(1)-group.

Enochs, Edgar, University of Kentucky at Lexington, Kentucky, KY 40506-0027 (enochs@ms.uky.edu) and  Estrada, Sergio, Universidad de Murcia, Campus del Espinardo, Murcia (SPAIN), 30100 (sestrada@um.es), and García-Rozas, J.R., University of Almería at Almeria, Almeria (SPAIN), 04071 (jrgrozas@ual.es).
Galois and coGalois groups associated with cotorsion theories, pp. 651-663.
ABSTRACT. The notion of a coGalois group of a torsion free cover was introduced in E. Enochs, J.R. García Rozas, O.M.G. Jenda and L. Oyonarte. Compact coGalois groups. Math. Proc. Cambridge Phil. Soc. (2) 128 (2000), 233-244. But the notion of such a group makes sense whenever we have some sort of a cover. And then the dual notion of a Galois group makes sense when we have an envelope. Covers and envelopes occur whenever we have a perfect cotorsion theory. In such a cotorsion theory we have two orthogonal classes. We argue that in this situation there is a natural way to relate coGalois (or Galois) groups of an object to such a group for an object in the orthogonal class. Our main application is the traditional case of a cotorsion theory but over a Dedekind domain. In this case the orthogonal classes are the torsion free and the cotorsion modules. We show that here we have the stronger result that every coGalois group (or Galois group) occurs as that associated with a cotorsion module which has no nonzero torsion free divisible submodules. We then briefly indicate how this result can be used to study these coGalois groups.

Feng Wei, Department of Applied Mathematics, Beijing Institute of Technology, Beijing 100081, People's Republic of China (daoshuo@bit.edu.cn).
*-Generalized Differential Identities of Semiprime Rings with Involution, pp. 665-681.
ABSTRACT. The main purpose of this paper is to consider the *-generalized differential identities of semiprime ring with involution * of positive characteristic. On the one hand, we extend certain results concerning derivations to the context of generalized derivations. On the other hand, we generalize some existing results on prime rings to the case of semiprime rings

Behrooz Khosravi, Dept. of Pure Math., Faculty of Math. and Computer Sci., Amirkabir University of Technology (Tehran Polytechnic), 424, Hafez Ave., Tehran 15914, IRAN and Institute for Studies in Theoretical Physics and Mathematics (IPM), Bahman Khosravi, and Behnam Khosravi, Dept. of Math., Faculty of Math. Sci., Shahid Beheshti Univ., Evin, Tehran, 19838, IRAN (khosravibbb@yahoo.com)
Characterizability of PSL(p+1,q) by its order component(s), pp. 683-700.
ABSTRACT. The prime graph of a group is the graph whose vertex set is the prime divisors of the order of G and two distinct primes p and q are joined by an edge if and only if G contains an element of order pq. Then the order of every finite group G can be expressed as a product of coprime positive integers m1,...,mt such that the set of prime divisors of mi is a connected component of the prime graph of G. The integers m1,...,mt are called the order components of G. Order components of a finite group are introduced in Chen (J. Algebra 185 (1996) 184). It was proved that PSL(3,q), where q is an odd prime power, is uniquely determined by its order components (J. Pure and Applied Algebra (2002)). Also in Iranmanesh and et al. (Acta Math. Sinica, English Series (2002)) and (Bull. Austral. Math. Soc. (2002)) it was proved that PSL(3,q) for q=2n and PSL(5,q) are uniquely determined by their order components. Also it was proved that PSL(p,q) is uniquely determined by its order components (Comm. Algebra (2004)). In this paper we discuss the characterizability of PSL(p+1,q) by its order component(s), where p is an odd prime number. In fact we prove that PSL(p+1,q) is uniquely determined by its order component(s) if and only if (q-1)|(p+1). A main consequence of our results is the validity of Thompson's conjecture for the groups PSL(p+1,q) where (q-1)|(p+1).

Yang, Jae-Hyun, Inha University, Incheon 402-751, Republic of Korea (jhyang@inha.ac.kr).
A note on a fundamental domain for Siegel-Jacobi space, pp. 701-712.
ABSTRACT. We find a fundamental domain for the Siegel-Jacobi space and present Riemannian metrics on the Siegel-Jacobi space invariant under the natural action of the Jacobi group. We also investigate the spectral theory of the Laplacian on the abelian variety associated to a point in the moduli space of principally polarized abelian varieties.

Cole, Daniel R., Department of Mathematics -- MS 136, Rice University, 6100 S. Main St., Houston, TX 70005, USA (dcole@math.rice.edu)  and Pauls, Scott D., Department of Mathematics, 6188 Bradley Hall, Dartmouth College, Hanover, NH 03755, USA (scott.pauls@dartmouth.edu).
C1 Hypersurfaces of the Heisenberg Group are N-rectifiable, pp. 713-724.
ABSTRACT. For the standard three-dimensional Heisenberg group H and subgroup N={(0,y,z)} of H, we show that C1 hypersurfaces in the Heisenberg group are countably N-rectifiable. As a corollary, this shows that all intrinsic C1 graphs over the xy-plane are countable N-rectifiable, showing the equivalence of this notion of rectifiability with that of Franchi, Serra Cassano and Serapioni (Math. Ann., 2001) for such surfaces.

Tojeiro, Ruy, Universidade Federal de São Carlos, 13565-905 São Carlos, Brazil  (tojeiro@dm.ufscar.br).
Conformal de Rham decomposition of Riemannian manifolds, pp. 725-743.
ABSTRACT.  We prove conformal versions of the local decomposition theorems of de Rham and Hiepko of a Riemannian manifold as aRiemannian or a warped product of Riemannian manifolds. Namely, we give necessary and sufficient conditions for a Riemannian manifold to be locally conformal to either a Riemannian or a warped product. We also obtain other related de Rham-type decomposition theorems. As an application, we study Riemannian manifolds that admit a Codazzi tensor with exactly two distinct eigenvalues everywhere.

Charatonik, Janusz J., deceased July 11, 2004 and Illanes, Alejandro, Universidad Nacional Autonoma de Mexico, 04510, Mexico, D.F. (illanes@matem.unam.mx).
N-Sequences and Contractibility in Hyperspaces, pp. 745-756.
ABSTRACT. The existence of an N-sequence in a continuum is an obstruction that implies noncontractibility of the continuum. The aim of the present paper is to show that the existence of an N-sequence in the continuum X does not imply noncontractibility of some hyperspaces of X.

Gary Gruenhage, Department of Mathematics and Statistics, Auburn University, Auburn, AL 36849} (garyg@auburn.edu).
Products of cozero complemented spaces, pp. 757-773.
ABSTRACT. We answer several questions of Levy and Shapiro, and Henriksen and Woods, on products of cozero complemented spaces. Among other things, we show that the product of a cozero complemented space with a metrizable space need not be cozero complemented unless the metrizable factor is separable, the product of a non-cozero complemented space and a metrizable space can be cozero complemented, the product of a cozero complemented space and a countable regular space need not be cozero complemented, and that it is consistent that the product of two compact spaces satisfying the countable chain condition need not be cozero complemented.

Lisan, Amha T., Louisiana State University, Baton Rouge, LA 70803 (lisan@math.lsu.edu).
Quasifactors, proximal extensions and other structures of nondiscrete minimal flows, pp. 775-782.
ABSTRACT. The classical theory of dynamical systems arose in the context of the study of differential equations. In recent years the study of these systems has been extended beyond discrete or continuous (real) phase groups or semigroups to the theory of flows of more general topological groups or semigroups. Let S be a semitopological semigroup, not necessarily discrete. An action of S on a compact phase space can then be extended to a compactification associated to the space of left norm continuous functions on S such that all minimal flows are flow isomorphic to quotients of this compactification. Furthermore we can associate a subgroup of the maximal group to each minimal flow.

Veronica Martinez-de-la-Vega, Instituto de Matematicas, Universidad Nacional Autonoma de Mexico, Ciudad Universitaria, Mexico D.F. 04510 and California State
University at Sacramento (vmvm@matem.unam.mx).
Dimension of n-fold Hyperspaces of Graphs, pp. 783-799.
ABSTRACT. Given a finite graph X, the n-fold hyperspace of X, Cn(X)={A: A is closed, nonempty and has at most n components}. For n=1 C1(X) is denoted by C(X). On 1968 Duda showed formulas to compute dim[C(X)] and for each element A of C(X) he showed how to compute dim A [C(X)]. In this paper we prove that dim[Cn(X)]=2n+dim[C(X)] and for every element A of Cn(X), where A has k components, A=A1( ...( Ak, then dim A [Cn(X)]=2(n-k)+(i dim Ai [C(X)] where i({1,...,k}.
As a consequence of this formulas we prove that for any natural number n, the n-fold hyperspace of a finite graph (different from a simple closed curve) is a cone if and only if X is an arc or a simple k-od

Bennett, Grahame, Department of Mathematics, Indiana University, Bloomington, Indiana 47405, U.S.A. (bennettg@indiana.edu).
Sums of Powers and the Meaning of lp, pp. 801-831.
ABSTRACT. The sequence (1α+2α+ ... + nα)/(nα)(n=1,2,...) is convex, or concave, no matter what the value of α in R is. There are applications to Sums of Powers and to the classical inequalities of Carleman, Copson, Hardy and Knopp.

Cabrelli, Carlos, Universidad de Buenos Aires, Argentina (cabrelli@dm.uba.ar) and Lacey, M.T. Georgia Institute of Technology, Atlanta GA 30332 (lacey@math.gatech.edu) and Molter, Ursula, Universidad de Buenos Aires, Argentina (umolter@dm.uba.ar) and Pipher, Jill, Brown University, Providence RI 02912 (jpipher@math.brown.edu)
Variations on a Theme of Journé's Lemma , pp. 833-861.
ABSTRACT. Journé's Lemma ("A covering lemma for product spaces," Proc. Amer. Math. Soc., Vol. 96, (1986), pp 593-598) is a critical component of many questions related to the product BMO theory of S.-Y. Chang and R. Fefferman. This article presents several different variants of the Lemma, in two and higher parameters, some known, some implicit in the literature, and some new.

Mijoung Kim, National Institute for Mathematical Sciences, 52 Eoeun-dong, Yuseong-Gu, Daejeon 305-333, South Korea  (mijoungtamu@hotmail.com).
Local regularity of the -Neumann operator, pp. 863-869.
ABSTRACT. Using the vector field method, we find a more general condition than finite type that implies a local regularity result for the -Neumann operator. In our result, it is possible for an analytic disk to be on the part of the boundary where we have local regularity.

B.S. Yadav, TU-67 Vishakha Enclave, Pitam Pura, Delhi 110088 (bsyadav@indianshm.com).
Systems of N-variable weighted shifts as universal operators and their invariant subspaces, pp. 871-894.
ABSTRACT. Systems of N-variable weighted shifts as introduced by N.P. Jewell and A.R. Lubin are examined a s universal operators in the sense of G.-C Rota with suitable conditions on the weight net. Also, results on the existence of cyclic vectors and characterisation of invariant subspace lattices of systems of N-variable weighted backward and forward shifts are obtained.

Fabrizio  Colombo, Dipartimento di Matematica  Politecnico di Milano, Via Bonardi n. 9 ,
 20133  Milano, Italy, (fabcol@mate.polimi.it), and   Alberto Damiano, MUUK, Sokolovska 83, 186 75 Praha 8, Ceska Republika (damiano@karlin.mff.cuni.cz).
Identification of the memory kernel and the heat source for a phase--field model, pp. 895-920.
ABSTRACT. We prove an existence and uniqueness result for an inverse problem arising from a for a phase--field system with thermal memory. We identify the convolution memory kernel and the heat source besides the temperature and the phase--field parameter. We prove our results in the framework of the Holder continuous functions spaces with values in a Banach space X. We apply the abstract results in the case the space X is the space of continuous functions.

Le, Vy Khoi, University of Missouri - Rolla, Rolla, MO 65409 (vy@umr.edu).
Some existence and bifurcation results for quasilinear elliptic equations with slowly growing principal operators, pp. 921-943.
ABSTRACT. The paper is about a boundary value problem, containing a second order elliptic operator, in which the principal term has very slow growth.We show the Rabinowitz alternative for global bifurcation and also some existence results by a topological approach. Due to the lack of coercivity, new arguments and techniques are needed.

Yan Xu, Nanjing Normal University, Nanjing 210097, P. R. China (xuyan@njnu.edu.cn).
Normality Criterion Concerning Sharing Functions, pp. 945-954.
ABSTRACT. Let F be a family of meromorphic functions in a domain D and k be a positive integer, and let ψ(z) be not a identically zero analytic function in D such that f ∈ F and ψ(z) have no common zeros, and ψ(z) has no simple zeros in D. If, for every f ∈ F, all zeros of f have multiplicity at least k, f(z)=0 if and only if f (k)(z)=0, and f (k)(z)= ψ(z) implies f(z)=ψ(z), then F is normal in D. This result improves related results of Fang, and Fang-Zalcman. Some examples are given to show the sharpness of our result.

Yan Xu, Nanjing Normal University, Nanjing 210097, P. R. China (xuyan@njnu.edu.cn).
A note on a result of Pang and Zalcman, pp. 955-959.
ABSTRACT. Let F be a family of meromorphic functions in a domain D. Pang and Zalcman proved (Normal families and shared values, Bull. London Math. Soc. 32(2000), 325-331) that if there exist b ≠ 0 and h > 0 such that for each f ∈ F, f = 0 if and only if f' = b and 0 < |f''(z)| ≤ h whenever f(z) = 0, then F is normal in D. In this note, we prove that the condition that |f''(z)| > 0 whenever f(z) = 0 can be omitted.