*Editors*: H. Amann (Zürich), G. Auchmuty (Houston), D. Bao
(San Francisco, SFSU), H. Brezis (Paris), K. Davidson (Waterloo), M. Gehrke (Radboud), 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

**David E. Dobbs, **Department of Mathematics, University of Tennessee,
Knoxville, TN 37996-1300 U.S.A.
(dobbs@math.utk.edu).

When is a pullback a locally divided domain?, pp. 341-351.

ABSTRACT.
Let P be a property of some (commutative integral) domains such that: if A is a proper subring of a domain B such that Spec(A)= Spec(B) as sets, then A has P if and only if B has P; if A is a domain and Q is a prime ideal of A, then the CPI-extension of A with respect to Q has P if and only if both A/Q and the localization of A at Q have P; and if A is a domain, then A has P if and only if the localization of A at M has P for each maximal ideal M of A. Examples of such P include the property of being a going-down domain and the property of being a locally divided domain. Let T be a domain, Q a maximal ideal of T, p the canonical surjection from T to T/Q, D a subring of T/Q, and R the inverse image of D under p. Then the pullback R (of p and the inclusion map from D to T/Q) has P if and only if both T and D have P. By suitably modifying the above requirements on the property P, we obtain a companion result which applies, in particular, when P is the property of being a locally pseudo-valuation domain.

**Maja Fošner,** Faculty of logistics, University of Maribor, Mariborska cesta 2,
3000 Celje, Slovenia
(maja.fosner@uni-mb.si),
**Joso Vukman,
**Department of Mathematics and Computer Science, Faculty of Natural Sciences and
Mathematics, University of Maribor, Koroška cesta 160, SI-2000 Maribor,
Slovenia, (joso.vukman@uni-mb.si).

An equation related to two-sided centralizers in prime rings, pp. 353-361.

ABSTRACT.
In this paper we prove the following result: Let R be a prime ring and let T
: R → R be an additive mapping satisfying the relation
nT(x^{n})=T(x)x^{n-1} + xT(x)x^{n-2} + ... +
x^{n-1}T(x) for all x in R where n > 1 is some fixed integer. If
char(R) = 0 or n ≤ char(R) ≠ 2, then T is of the form T(x) = λx for all x in R
and some fixed element λ in R where C is the extended centroid of
R.

**Climent Vidal, Juan,** Universidad de Valencia, Departamento de Lógica y Filosofía de la Ciencia, E-46010 Valencia, Spain (juan.b.climent@uv.es) and **
Soliveres Tur, Juan, **Universidad de Valencia, Departamento de Lógica y Filosofía de la Ciencia, E-46010 Valencia, Spain (juan.soliveres@uv.es).

When is the insertion of the generators injective for a sur-reflective subcategory of a category of many-sorted algebras?, pp. 363-372.

ABSTRACT. For a many-sorted signature **Σ** = (S,Σ) we
characterize, by defining the concept of support of an S-sorted
set and a convenient algebraic closure operator
Ex_{Σ} on S, those sur-reflective
subcategories **K** of the category
**Alg**(**Σ**) of all **Σ**-algebras
for which the unit of the adjunction from **Set**^{S} to
**K** is pointwise monomorphic.

**Strugar, Igor,** Limestone College, Gaffney, SC 29340, USA
(istrugar@limestone.edu), and **Thompson, Gerard,** Department of Mathematics, The University of
Toledo, Toledo, Ohio 43606, USA (GTHOMPS@UTNet.UToledo.Edu).

Inverse problem for the canonical Lie group connection, pp. 373-409.

ABSTRACT. The geodesic spray of the canonical symmetric connection for a five dimensional Lie group
is studied. For each corresponding Lie algebra a faithful representation in terms of
vector fields on a five dimensional real space is obtained, thereby providing an effective
realization of Lie's third theorem. Thereafter the inverse problem of the calculus of
variations for each of the geodesic sprays is investigated. In all cases it is determined
whether such spray is of Euler-Lagrange type and in the affirmative case at least one
concrete Lagrangian is written down. All the cases where there is a Lagrangian of metric
type are exhibited.

**Etayo, Fernando, ** Universidad de Cantabria, 39071, Santander, Spain
(etayof@unican.es)
and **Santamaría, Rafael, **Universidad de León, 24071, León, Spain (rsans@unileon.es).

Connections functorially attached to almost complex product structures, pp. 411-434.

ABSTRACT. Manifolds endowed with three foliations pairwise transversal are known as 3-webs. Equivalently, they can be algebraically defined as biparacomplex or complex product manifolds, i.e., manifolds endowed with three tensor fields of type (1,1), F, P and J=FP, where the two first are product and the third one is complex, and they mutually anti-commute. In this case, it is well known that there exists a unique torsion-free connection parallelizing the structure. In the present paper, we study connections attached to non-integrable almost biparacomplex manifolds

**Lan Wu, **Renmin University of China, 100872, Beijing, People's Republic
of China (wulan@ruc.edu.cn).

A class of variational problem for submanifolds in a space form, pp. 435-450.

ABSTRACT. In this paper we study a class of variational problem for
n-dimensional submanifolds in an (n+p)-dimensional unit sphere S, we call M be
an extremal submanifold if it satisfies the Euler-Lagrange equation of this
variational problem.

we prove an integral inequality of Simons' type for n-dimensional compact
extremal submanifolds in an (n+p)-dimensional unit sphere S and

give a characterization of Clifford torus and Veronese surface by use of
our integral inequality. Two special cases were studied by H. Li (2002) and Guo-Li
(2007).

**Gerardo Acosta,** Instituto de Matematicas de la Universidad Nacional Autonoma de Mexico, Circuito Exterior, Area de la Investigacion Cientifica, Mexico D.F., 04510, Mexico
(gacosta@matem.unam.mx) and **David Herrera-Carrasco,** Facultad de Ciencias Físico-MatemAticas de la BenemErita Universidad AutOnoma de Puebla, rio verde y San Claudio, Ciudad Universitaria, Puebla Pue., Mexico
(dherrera@fcfm.buap.mx).

Dendrites Without Unique Hyperspace,
pp. 451-467.

ABSTRACT.
Let X be a dendrite whose set of end-points is not closed. The second author asked if there is a dendrite Y, not homeomorphic to X, such that the hyperspaces of subcontinua C(X) and C(Y) are homeomorphic. In this paper we answer this question in the positive.

**J. Gutiérrez García,**
Departamento de Matemáticas,
Universidad del País Vasco-Euskal Herriko Unibertsitatea, Apdo. 644, 48080 Bilbao, Spain,
(javier.gutierrezgarcia@ehu.es),
**T. Kubiak,**
Wydział Matematyki i Informatyki,
Uniwersytet im. Adama Mickiewicza, ul. Umultowska 87, 61-614 Poznań, Poland
(tkubiak@amu.edu.pl),
and
**M.A. de Prada Vicente,**
Departamento de Matemáticas,
Universidad del País Vasco-Euskal Herriko Unibertsitatea, Apdo. 644, 48080 Bilbao, Spain
(mariangeles.deprada@ehu.es)

Controlling disjointness with a hedgehog, pp.
469-484.

ABSTRACT. After Frantz's idea of controlling properties of extensions of continuous functions there has been an interest in extending families of continuous pairwise disjoint real-valued functions on normal spaces.
We make the observation that disjoint extending a disjoint family of continuous functions is the same thing as extending a single continuous function with values in a hedgehog *J*(κ) viewed as a bounded complete domain with its Lawson topology where κ is the amount of pairwise disjoint functions which have to be extended.
We provide a number of characterizations of spaces for which *J*(κ) with its Lawson topology becomes an absolute extensor. In particular, this closes the circle of results related to disjoint extension theorems for normal spaces.

**Jerzy Krzempek, ** Institute of Mathematics, Silesian University of Technology, Kaszubska 23, 44-100 Gliwice, Poland
(j.krzempek@polsl.pl).

Some examples of higher-dimensional rigid continua, pp. 485-500.

ABSTRACT. An attempt is made to find analogues of Anderson, Choquet, and Cook's rigid continua in dimensions greater than one. For each natural number n ≥ 2, two examples of n-dimensional metric continua are presented; the second one is hereditarily indecomposable. Both have the property that for every n-dimensional closed subset P of the continuum in question, call it X, every light continuous map from P into X has a fixed point. Hence, no two disjoint n-dimensional subcontinua of X are homeomorphic.

**Rongxin Shen,** Department of Mathematics, Sichuan University, Chengdu 610064, P. R. China and Department of Mathematics, Taizhou Teacher's College, Taizhou 225300, P. R. China
(srx20212021@163.com) .

On Aleph Zero-weak bases,
pp. 501-514.

ABSTRACT.
In this paper, the author discusses spaces with certain Aleph Zero-weak bases, gives some characterizations of images of metric spaces by certain quotient maps, and studies the covering properties of spaces with special Aleph Zero-weak bases.

Mora-Corral, Carlos.
Mathematical Institute, University of Oxford. Oxford OX1 3LB. UK
(mora-cor@maths.ox.ac.uk).

Approximation by piecewise affine homeomorphisms of Sobolev
homeomorphisms that are smooth outside a point,
pp. 515-539.

ABSTRACT. This paper is concerned with the
problem of approximating in the
Sobolev norm a homeomorphism by piecewise affine homeomorphisms. The
homeomorphism we want to approximate is supposed to be smooth except at one
point. As a corollary of our main result, we prove the following: Let Ω be a
subset of `R`² be an open set
containing 0 with polygonal boundary. Let `h`: Ω → `R`²
be
a Lipschitz homeomorphism such that `h`^{-1} is also
Lipschitz, `h` is of class C^{2} in Ω \ {0} and ||D^{2}`h`(`x`)||
= O(|`x`|^{-1}) as `x` → 0. Then, for all 1
≤ `p` < 2,
the
function `h` can be approximated in the norm of the
intersection space
L^{∞} ∩ W^{1,p} by a piecewise affine
homeomorphism `f`.
Several results in the same spirit are also proved, where we suppose
that `h` and `h`^{-1} are smooth except at
one point, and their
derivatives may have one singularity. The construction of `f`
is
explicit. We also show examples of functions satisfying the assumptions
of the main theorem of the paper and for which the piecewise affine
function on a regular triangulation of Ω that coincides with `h`
at
the vertices of the triangulation is not always a homeomorphism.

**Rodriguez, Jose, **Dpto. de Matematica Aplicada, Facultad de Informatica,
Universidad de Murcia, 30100 Espinardo (Murcia), Spain
(joserr@um.es).

Convergence theorems for the Birkhoff integral. pp. 541-551.

ABSTRACT.
We study the validity of Vitali's convergence theorem for the Birkhoff integral of functions taking values in a Banach space X. On the one hand, we show that the theorem is true whenever X has weak*-separable dual unit ball. On the other hand, we prove that if X is super-reflexive and has density character the continuum, then there is a uniformly bounded sequence of Birkhoff integrable X-valued functions (defined on [0,1] with the Lebesgue measure) converging pointwise to a non Birkhoff integrable function.

**Jiri Spurny,** Faculty of Mathematics and Physics, Charles University, Sokolovska 83, 186 75 Praha 8, Czech Republic
(spurny@karlin.mff.cuni.cz).

Automatic boundedness of affine functions, pp. 553-561.

ABSTRACT.
Let f be an affine function on a compact convex set X. We prove that f is bounded provided f has the restricted Baire property on X or is universally Radon measurable on X. We also show that the result of J.P.R. Christensen on weak* universally Baire measurable functionals on spaces of measurable functions can be strengthened for functionals with the restricted Baire property..

**Boaz Tsaban,** Department of Mathematics, Weizmann Institute of Science,
Rehovot 76100, Israel; and Department of Mathematics, Bar-Ilan University,
Ramat-Gan 52900, Israel,
(tsaban@math.biu.ac.il),
(http://www.cs.biu.ac.il/~tsaban/) and **Lyubomyr Zdomskyy,** Department of Mechanics and Mathematics, Ivan
Franko Lviv National University, Universytetska 1, Lviv 79000, Ukraine; and
Department of Mathematics, The Weizmann
Institute of Science, Rehovot 76100, Israel
(lzdomsky@gmail.com).

On the Pytkeev property in spaces of continuous functions (II), pp. 563-571.

ABSTRACT.
We prove that for each Polish space X, the space C(X) of continuous
real-valued functions on X satisfies (a strong version of) the Pytkeev property,
if endowed with the compact-open topology.

We also consider the Pytkeev property in the case where C(X) is endowed with the
topology of pointwise convergence.

**Bennett, Grahame, ** Department of Mathematics, Indiana University,
Bloomington, Indiana 47405, U.S.A.
(bennettg@indiana.edu).

Meaningful sequences and the Theory of Majorization, pp. 573-589.

ABSTRACT.
The fundamental Theorem on Means suggests many new elementary
inequalities, yet it offers no hint at all for proving them. Our
aim here is to explore this gap, especially in the context of
arithmetic progressions. There are applications to the Theory of
Majorization.

**Aviv Censor**, Department of Mathematics, University of California at
Riverside, Riverside, CA, 92521, U.S.A.
(avivc@math.ucr.edu) and **Daniel Markiewicz,** Department of
Mathematics, Ben-Gurion University of the Negev, P.O.B. 653, Beersheva 84105,
Israel (danielm@math.bgu.ac.il)

Limits of groupoid C*-algebras arising from open covers, pp.
591-618.

ABSTRACT.
I. Raeburn and J. Taylor have constructed continuous-trace C*-algebras
with a prescribed Dixmier-Douady class, which also depend on the choice
of a locally finite open cover of the spectrum. We study the
asymptotic behavior of these algebras with respect to certain
refinements of the cover and appropriate extension of cocycles. This
leads to the analysis of a limit groupoid G and a cocycle σ,
and the algebra C*(G, σ) may be regarded as a
generalized direct limit of the Raeburn-Taylor algebras. As a
special case, all UHF C*-algebras arise from this limit construction.

**Ciprian Preda**, Department of Mathematics, University of California, Los
Angeles, CA 90095, U.S.A. (preda@math.ucla.edu).

On the asymptotic behaviour of individual elements under one-parameter
semigroups, pp. 619-626.

ABSTRACT.
Let **T** = {T(t)}_{t≥0} be a strongly continuous semigroup of linear
operators on the Banach space X. We point out a sufficient condition to
guarantee an exponential decay (as t → ∞) of an individual trajectory t → T(t)x_{0}.

Trond A. Abrahamsen,
Department of Mathematics, University of Agder, Serviceboks 422,
4604 Kristiansand, Norway (Trond.A.Abrahamsen@uia.no), Vegard Lima, Department of
Mathematics, University of Missouri-Columbia,
Columbia, MO 65211, USA (lima@math.missouri.edu), and Åsvald Lima, Department of
Mathematics, University of Agder, Serviceboks 422, 4604
Kristiansand, Norway (Asvald.Lima@uia.no).

Unconditional ideals of finite rank operators II, pp. 627-646.

ABSTRACT.
Let E be a subspace of a normed space F. It is known
that E is an ideal (resp. a u-ideal) in F if and only if E is an
ideal (resp. a u-ideal) in G for every subspace E⊂G⊂F in
which E has finite codimension (resp. codimension
≤ 2). We show that in many cases a space of finite rank operators is an
ideal (resp. a u-ideal) in a larger space if and
only if it is an ideal (resp. a u-ideal) in a space in which it has
codimension 1. In particular, we show that F(Y,X)
is an ideal (resp. a u-ideal) in W(Y,X^{**}) for all Banach spaces Y if
and only if for every reflexive Banach space Y and T in W(Y,X^{**}), F(Y,X) is an ideal
(resp. a u-ideal) in span( F(Y,X),{T}).

**Johnson, Gerald W.,** University of Nebraska-Lincoln, Lincoln,
NE 68588 (gjohnson2@math.unl.edu)
and **Kim, Byoung Soo,** Seoul
National University of Technology, Seoul 139-743, Korea
(mathkbs@snut.ac.kr).

Derivational derivatives and Feynman's operational calculi,
pp. 647-664

ABSTRACT.
This paper explores the differential (or derivational) calculus associated with the disentangled operators arising from
Feynman's operational calculi (FOCi) for noncommuting operators. (We will use the continuous case of the approach to FOCi initiated
by Jefferies and Johnson in 2000.)
The central part of this paper deals with a first order infinitesimal calculus for a function of n noncommuting operators. Here the first derivatives (or differentials) are replaced by the first order derivational derivatives. The derivational derivatives of the first and higher order have been useful in, for example, operator algebras, noncommutative geometry and Maslov's discrete form of Feynman's operational calculus. In the last section of this paper we will develop some special cases of higher order expansions.

**Edmunds, David, **
School of Mathematical sciences,
Cardiff University, Senghennydd Road, Cardiff CF24 4YH, UK
(DavidEEdmunds@aol.com),
**Kokilashvili, Vakhtang, **
A. Razmadze Mathematical Institute, 1, M. Aleksidze
St., 0193 Tbilisi, Georgia; International Black Sea University, Agmashenebeli
Kheivani 13 km, 0131 Tbilisi, Georgia
(kokil@rmi.acnet.ge),
and **Meskhi, Alexander, **A. Razmadze Mathematical Institute, 1, M. Aleksidze
St., 0193 Tbilisi, Georgia; School of Mathematical Sciences, GC University,
Lahore 54600, Pakistan (meskhi@rmi.acnet.ge).

Two-Weight estimates in L^{p(x)} spaces with
applications to Fourier series
, pp. 665-689.

ABSTRACT.
In
the present paper we establish sufficient conditions governing two-weighted
inequalities for Hardy-Littlewood maximal functions and Calderon-Zygmund
operators in variable Lebesgue spaces. Explicit, natural examples are given of pairs of weights
that satisfy these conditions.The norm summability of
Fourier series and a generalization of Bernstein inequality in a two-weighted
setting are proved.