Electronic Edition Vol. 38, No. 1 , 2012

Editors: G. Auchmuty (Houston), D. Bao (San Francisco, SFSU), D. Blecher (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), 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


Vassilev, Janet, University of New Mexico, Albuquerque, NM 87131 (jvassil@math.unm.edu).
A look at the prime and semiprime operations of one-dimensional domains. , pp. 1-15.
ABSTRACT.   We continue the analysis of prime and semiprime operations over one-dimensional domains started in Vassilev's 2009 paper, Structure on the set of closure operations of a commutative ring. We first show that there are no bounded semiprime operations on the set of fractional ideals of a one-dimensional domain. We then prove the only prime operation is the identity on the set of ideals in semigroup rings where the ideals are minimally generated by two or fewer elements. This is not likely the case in semigroup rings with ideals of three or more generators since we are able to exhibit that there is a non-identity prime operation on the set of ideals of k[[t,3,t4,t5]].

Dobbs, David E., University of Tennessee, Knoxville, Tennessee 37996-0612, USA (dobbs@math.utk.edu ), and Hetzel, Andrew J., Tennessee Technological University, Box 5054, Cookeville, Tennessee 38505, USA (ahetzel@tntech.edu ).
Using going-up to characterize going-down domains, pp. 17-28.
ABSTRACT. A (commutative integral) domain R is called an AGU-domain if R inside T satisfies the going-up property: Whenever T is an algebraic extension domain of R such that the natural map that sends Spec(T) into Spec(R), sends the maximal spectrum Max(T) onto Max(R). Any domain of (Krull) dimension 1 is an AGU-domain, as is any absolutely injective (ai-) domain. A quasilocal domain is an AGU-domain if and only if it is a going-down domain. A partial generalization is given for rings with nontrivial zero-divisors. An example is given of a two-dimensional Prüfer (hence going-down) domain with exactly two maximal ideals which is not an AGU-domain.
Mathematica Code

Konstantinos A. Draziotis (drazioti@gmail.com) and Dimitrios Poulakis, Aristotle University Of Thessasloniki, 541 24, Thessaloniki, Greece, (poulakis@math.auth.gr).
An effective version of Chevalley-Weil theorem for projective plane curves, pp. 29-39.
ABSTRACT.We obtain a quantitative version of the classical Chevalley-Weil theorem for curves.Let Φ: C→W be an unramified morphism of non-singular plane projective curves defined over a number field K. We calculate an effective upper bound for the norm of the relative discriminant of the number field K(Q) over K for any point P of C(K) and Q in the inverse image of P through Φ.

Xiaohuan Mo, Key Laboratory of Pure and Applied Mathematics, School of Mathematical Sciences, Peking University, Beijing 100871, China (moxh@pku.edu.cn).
On some Finsler metrics of constant (or scalar) flag curvature, pp. 41-54.
ABSTRACT. This paper presents many new Finsler metrics of scalar curvature. In particular, we show at least there is an n(n-1)/2-dimensional family of new Finsler metrics of constant flag curvature.

Hu, Wenchuan,School of Mathematics, Sichuan University, Chengdu 610064, P.R.China (huwenchuan@gmail.com).
The Chow group of zero cycles for the quotient of certain Calabi-Yau varieties, pp. 55-67.
ABSTRACT.  In this paper, we compute the Chow group of zero cycles for the quotient of certain Calabi-Yau varieties. Those are new examples that the generalized Bloch Conjecture on zero cycles is shown to hold. As an application of Bloch-Srinivas method on the decomposition of the diagonal, we compute the rational coefficient Lawson homology for 1-cycles and codimension two cycles for these quotient varieties. The (Generalized) Hodge Conjecture is shown to hold for codimension two cycles (and hence also for 2-cycles) on these quotient varieties.

Rongmu Yan, School of Mathematical Science, Xiamen university, 361005, P.R.China (yanrm@xmu.edu.cn).
Deicke's Theorem on complex Minkowski spaces, pp. 69-75.
ABSTRACT. The Cartan tensor is a non-Euclidean quantity of complex Minkowski spaces. We prove that the vanishing of the Cartan tensor is equivalent to the vanishing of the mean Cartan tensor on complex Minkowski spaces.

Muzsnay, Zoltán  (muzsnay@math.unideb.hu) and Nagy, Péter T.  (nagypeti@math.unideb.hu) , Institute of Mathematics, University of Debrecen, Hungary, H-4010 Debrecen, Hungary, P.O.B. 12.
Finsler manifolds with non-Riemannian holonomy, pp. 77-92.
ABSTRACT. The aim of this paper is to show that holonomy properties of Finsler manifolds can be very different from those of Riemannian manifolds. We prove that the holonomy group of a positive definite non-Riemannian Finsler manifold of non-zero constant curvature with dimension >2 cannot be a compact Lie group. Hence this holonomy group does not occur as the holonomy group of any Riemannian manifold. In addition, we provide an example of left invariant Finsler metric on the Heisenberg group, so that its holonomy group is not a (finite dimensional) Lie group. These results give a positive answer to the following problem formulated by S. S. Chern and Z. Shen: Is there a Finsler manifold whose holonomy group is not the holonomy group of any Riemannian manifold?

Vassilis J. Papantoniou and Kostas Petoumenos,  University of Patras, Department of Mathematics, GR-26500 Rion, Greece  (bipapant@math.upatras.gr, (copetoum@math.upatras.gr).
Biharmonic hypersurfaces of type M23 in E24, pp. 93-114.
ABSTRACT. An n-dimensional submanifold of index r of an m-dimensional pseudo-Euclidean space of index s is said to have harmonic mean curvature vector field, if the action of the Laplace operator (with respect to the induced pseudo-Riemannian metric) on the mean curvature vector field vanishes. Submanifolds with harmonic mean curvature vecror field are also known as biharmonic submanifolds. In the present paper, we use all possible canonical forms of the shape operator of a three dimensional hypersurface of index two in a four dimensional pseudo-Euclidean space of index two, and prove that every such a nondegenerate biharmonic hypersurface is minimal.

Yu Kawakami, Graduate School of Science and Engineering, Yamaguchi University, Yamaguchi, 753-8512, Japan (ykwkami@yamaguchi-u.ac.jp).
Value distribution of the hyperbolic Gauss maps for flat fronts in hyperbolic three-space, pp. 115-130.
ABSTRACT. We give an effective estimate for the totally ramified value number of the hyperbolic Gauss maps of complete flat fronts in the hyperbolic three-space. As a corollary, we give the upper bound for the number of exceptional values of them in some topological cases. Moreover, we obtain some new examples for this class.

Jincai Wang, School of Mathematical Sciences, Soochow University, P.R. China, 215006 (wwwanggj@163.com) and  Yi Chen, School of Mathematical Sciences, Soochow University, P.R. China, 215006.
Rotundity and uniform rotundity of Orlicz-Lorentz spaces with the Orlicz norm, pp. 131-151.
ABSTRACT.  In this article, we obtain criteria of rotundity and uniform rotundity of Orlicz-Lorentz spaces with the Orlicz norm. .

G. K. Eleftherakis, Department of Mathematics University of Athens, 157 84, Athens, Greece (gelefth@math.uoa.gr).
TRO equivalent algebras, pp. 153-175
ABSTRACT. In this work we study a new equivalence relation between w* closed algebras of operators on Hilbert spaces. The algebras A and B are called "TRO equivalent" if there exists a ternary ring of operators M (i.e. the set MM*M is contained in M) such that A is the w* closure of the span of the set M*BM and B is the w* closure of the span of the set MAM*. We prove that two reflexive algebras are TRO equivalent if and only if there exists a * isomorphism between the commutants of their diagonals mapping the invariant projection lattice of the first algebra onto the lattice of the second one.

Peng Gao, Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, 637371 Singapore (penggao@ntu.edu.sg).
On weighted remainder form of Hardy-type inequalities pp. 177-199.
ABSTRACT. We use different approaches to study a generalization of a result of Levin and Steckin concerning an inequality analogous to Hardy's inequality. Our results lead naturally to the study of weighted remainder form of Hardy-type inequalities.

Ian N. Deters, 871 Champagne Ave., Bowling Green, OH, 43402 (iandeters@iandeters.com) and Steven M. Seubert, Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, OH, 43403-0221 (sseuber@bgsu.edu).
An application of entire function theory to the synthesis of diagonal operators on the space of entire functions, pp. 201-207.
ABSTRACT. In this paper, sufficient conditions are given for an operator acting on the space of entire functions having the monomials as eigenvectors to admit spectral synthesis, that is, for every closed invariant subspace of the operator to be the closed linear span of some collection of its eigenvectors.

Baudier, Florent, Université de Franche-Comté,25000 Besancon, France, Current Address: Université de Neuchâtel, 2000 Neuchâtel, Switzerland (florent.baudier@unine.ch).
Embeddings of proper metric spaces into Banach spaces, pp. 209-223.
ABSTRACT. We show that there exists a strong uniform embedding from any proper metric space into any Banach space without cotype. Then we prove a result concerning the Lipschitz embedding of locally finite subsets of script Lp-spaces. We use this locally finite result to construct a coarse bi-Lipschitz embedding for proper subsets of any script Lp-space into any Banach space X containing the lpn's. Finally using an argument of G. Schechtman we prove that for general proper metric spaces and for Banach spaces without cotype a converse statement holds. In particular X has no non-trivial cotype if and only if X contains a coarse Lipschitz copy of every locally finite metric space (with uniform constants).

Zunwei Fu, School of Mathematical Sciences, Beijing Normal University, Beijing 100875, P. R. China and Department of Mathematics, Linyi Normal University, Linyi 276005, P. R. China(zwfu@mail.bnu.edu.cn), Loukas Grafakos, Department of Mathematics, University of Missouri, Columbia, MO 65211, USA (grafakosl@missouri.edu), Shanzhen Lu, School of Mathematical Sciences, Beijing Normal University, Beijing 100875, P. R. China (lusz@bnu.edu.cn), Fayou Zhao (Corresponding author), School of Mathematical Sciences, Beijing Normal University, Beijing 100875, P. R. China; Department of Mathematics, University of Missouri, Columbia, MO 65211, USA (zhaofayou2008@yahoo.com.cn).
Sharp bounds for m-linear Hardy and Hilbert Operators, pp. 225-244.
ABSTRACT. The precise norms of m-linear Hardy operators and m-linear Hilbert operators on Lebesgue spaces with power weights are computed. Analogous results are also obtained for Morrey spaces and central Morrey spaces.

Paterson, Alan L. T., 3709 Bluefield Court, Clarksville, TN 37040 (apat1erson@gmail.com).
The stabilization theorem for proper groupoids, pp. 245-264.
ABSTRACT. The equivariant stabilization theorem for Hilbert (H-A)-modules under the action of a compact group was proved by G. G. Kasparov (who also obtained a corresponding result for the case of a non-compact group except that the isomorphism involved is not equivariant). An extension of this theorem (in the case A=C0(Y)) to the case where a general locally compact group H acts properly on a locally compact space Y was established by N. C. Phillips. (A proof of the general case where A is an (H-C0(Y))-algebra has been sketched in a paper of Kasparov and Skandalis.) The Phillips equivariant theorem involves the Hilbert (H,C0(Y))-module C0(Y,L2}H). It can naturally be interpreted in terms of a stabilization theorem for proper groupoids, and the paper proves this theorem within the general, proper groupoid, context. The theorem has applications in equivariant KK-theory and groupoid index theory.

Mark S. Grinshpon, Department of Mathematics and Statistics, Georgia State University, Atlanta, GA 30303, USA (matmsg@langate.gsu.edu),  Peter A. Linnell, Department of Mathematics, Virginia Tech, Blacksburg VA 24061-0123, USA (plinnell@math.vt.edu), Michael J. Puls, Department of Mathematics, John Jay College--CUNY, 445 West 59th Street, New York, NY 10019, USA  (mpuls@jjay.cuny.edu).
Dimensions of lp-cohomology groups, pp. 265-273.
ABSTRACT. Let G be an infinite discrete group of type FP and let p > 1 be a real number. We prove that the lp-homology and cohomology groups of G are either 0 or infinite dimensional. We also show that the cardinality of the p-harmonic boundary of a finitely generated group is either 0, 1, or ∞.

Zhankui, Xiao, School of Mathematical Sciences, Huaqiao University, Quanzhou, 362021, P. R. China (zhkxiao@gmail.com)  and Feng, Wei, School of Mathematcs, Beijing Institute of Technology, Beijing, 100081, P. R. China (daoshuo@hotmail.com).
Jordan higher derivations on some operator algebras, pp. 275-293.
ABSTRACT. In this paper we mainly consider the question of whether any Jordan higher derivation on some operator algebras is a higher derivation. Let A be a torsion free algebra over a commutative ring R, D be the set of all Jordan higher derivations {dn} on A, and G be the set of all sequences {gn} of Jordan derivations on A. Then there is a one to one correspondence between D and G. It is shown via this correspondence that every Jordan higher derivation on some operator algebras is a higher derivation. The involved operator algebras include CSL algebras, reflexive algebras, nest algebras. At last, we describe local actions of Jordan higher derivations on nest algebras.

Bankston, Paul, Mathematics, Statistics and Computer Science, Marquette University, Milwaukee, WI 53201 (paulb@mscs.mu.edu).  
Categoricity and topological graphs, pp. 295-310.
ABSTRACT. A lattice base for a topological space is a closed-set base that is also closed under finite unions and intersections. Let X be a topological graph; i.e., a union of finitely many points and arcs, with arcs joined only at end points. If Y is any locally connected metrizable compactum, and some lattice base for Y is elementarily equivalent (in the sense of model theory) to some lattice base for X, then Y is homeomorphic to X. This is a categoricity statement for topological graphs.

Liang-Xue  Peng,  College of Applied  Science,  Beijing University of Technology,  Beijing 100124,  China (pengliangxue@bjut.edu.cn).
A note on spaces of continuous step functions over LOTS, pp. 311-318.
ABSTRACT. Given a LOTS (linearly ordered topological space) L, the space T(L)=(T, Τ) is defined as follows. The underlying set is the subset T of cL that consists of all Dedekind sections as well as left endpoints of gaps of  L. That is, T(L) is the union of (cL\L) and the set of left endpoints of gaps of L. The base neighborhoods at points of (cL\ L) in Τ are those from the subspace topology on T, while all other points are declared isolated. We prove that if L is a LOTS and Cp(L, n+1) is Lindelöf then  T(L)n  and (dL)n are Lindelöf, where dL=cL\L and n is a natural number. This gives a positive answer to a question of Buzyakova (the question appears in Fund. Math. 192 (2006) 25-35). We also show that if L is a LOTS and T(L)n is Lindelöf for each natural number n then Sp (L, n) is Lindelöf for each natural number n, where Sp (L, n) is the subspace of  Cp (L, n), which consists of all step functions with finitely many steps and constant functions.

Carlson, Nathan, California Lutheran University, Thousand Oaks, CA 91360 (ncarlson@callutheran.edu), and Ridderbos, Guit-Jan, Technische Universiteit Delft, Delft, The Netherlands (G.F.Ridderbos@tudelft.nl).
On several cardinality bounds on power homogeneous spaces, pp. 311-332.
ABSTRACT. We show the cardinality of a homogeneous Hausdorff space X is not necessarily bounded by 2L(X) , where k is the pi-character of X, by providing examples of sigma-compact, countably tight, homogeneous spaces of countable pi-character and arbitrary cardinality. We also generalize a closing-off argument of Pytkeev to show the cardinality of any power homogeneous Hausdorff space X is at most 2L(X)pct(X)t(X). This was previously shown to hold if X is also regular by G.J. Ridderbos. Another consequence of the generalization of Pytkeev's closing-off argument is the well-known cardinality bound 2L(X)t(X)psi(X) for an arbitrary Hausdorff space X.