*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]].

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.

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.

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 M_{2}^{3} in E_{2}^{4},
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.

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 L_{p}-spaces. We use this locally
finite result to construct a coarse bi-Lipschitz embedding for proper subsets of any script L_{p}-space
into any Banach space X containing the l_{p}^{n}'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=C_{0}(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-C_{0}(Y))-algebra has been
sketched in a paper of Kasparov and Skandalis.) The Phillips equivariant theorem
involves the Hilbert (H,C_{0}(Y))-module C_{0}(Y,L^{2}}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 l^{p-}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 *l*^{p}-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 {d_{n}} on A, and G be the set of all sequences {g_{n}} 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 C_{p}(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 S_{p}
(L, n) is Lindelöf for each natural number n, where S_{p} (L, n) is the
subspace of C_{p} (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
2^{L(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
2^{L(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
2^{L(X)t(X)psi(X)} for an arbitrary Hausdorff space X.