Editors: H. Amann (Zürich), G. Auchmuty (Houston), D. Bao
(Houston), H. Brezis (Paris), J. Damon (Chapel Hill), K. Davidson (Waterloo), C.
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(Houston), W. B. Johnson (College Station), J. Nagata (Osaka), V. I. Paulsen
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Managing Editor: K. Kaiser (Houston)
Houston Journal of Mathematics
Badawi, Ayman, Department of Mathematics and Statistics, American
University of Sharjah, P.O. Box 26666, Sharjah, United Arab Emirates
(abadawi@aus.ac.ae), and Lucas, Thomas G., Department of
Mathematics and Statistics, University of North Carolina Charlotte, Charlotte,
NC 28223, U.S.A. (tglucas@uncc.edu).
On Φ-Mori Rings,
pp. 1-32.
ABSTRACT.
A commutative ring R is said to be a φ-ring if its
nilradical Nil(R)
is both prime and comparable with each principal ideal. The name is derived from
the natural map φ from the total quotient ring T(R) to R
localized at Nil(R). An ideal I that properly contains
Nil(R) is φ-divisorial if (φ(R): (φ(R):φ(I)))=φ(I). A ring is a φ-Mori
ring if it is a φ-ring that satisfies the ascending chain condition on
φ-divisorial ideals. Many of the properties and characterizations of Mori
domains can be extended to φ-Mori rings, but some cannot.
Coykendall, Jim,
Department of Mathematics, North Dakota State University, Fargo, ND
58105-5075, U.S.A. (jim.coykendall@ndsu.nodak.edu), Dumitrescu, Tiberiu,
Facultatea de Matematica, Universitatea Bucuresti, 14 Academiei Str., Bucharest,
RO 010014, Romania (tiberiu@al.math.unibuc.ro), and
Zafrullah, Muhammad, Department of Mathematics, Idaho State
University, Pocatello, ID 83209, U.S.A. (zafrullah@lohar.com).
The half-factorial property and
domains of the form A+XB[X], pp. 33-46.
ABSTRACT.
In this note, we use the A+XB[X] and A+XI[X] constructions from a new angle to
construct new examples of half factorial domains. Positive results are obtained
highlighting the interplay between the notions of GCD domain, GL domain,
integrally closed domain and half-factorial domain in A+XB[X] constructions. It
is additionally shown that constructions of the form A+XI[X] rarely possess the
half-factorial property.
F. Fontenele, Departamento de Geometria, Instituto de
Matemática, Universidade Federal Fluminense, 24020-140, Niterói, Brazil
(fontenele@mat.uff.br), and Sérgio L. Silva,
Departamento de Estruturas Matemáticas, Universidade Estadual do Rio
de Janeiro, 20550-013, Rio de Janeiro, Brazil (sergiol@ime.uerj.br).
On the m-th mean curvature of
compact hypersurfaces, pp. 47-57.
ABSTRACT.
Let M be an n-dimensional compact Riemannian manifold immersed in the
(n+1)-dimensional Euclidean space. In a previous paper, the authors proved
that if the product of the scalar curvature by the square of some support
function is less than or equal to one then the image of M is a geodesic sphere.
Also we obtained the analogous result in case the ambient is the
(n+1)-dimensional hyperbolic space. In this paper, we obtain the correspondent
result for immersions into (n+1)-dimensional Euclidean sphere and
generalizations of this type of result for high order mean curvatures. The basic
technique is to apply the divergence's theorem in a region containing a subset
of interest. This technique allows us to give a new proof of a theorem of
Vlachos. Some other results are also obtained.
Andreev, Fedor, Western Illinois University, Macomb, IL 61455 (F-Andreev@wiu.edu).
Direct computation of the
monodromy data for P6 corresponding to the quantum cohomology of the projective
plane
, pp. 59-77.
ABSTRACT.
A solution to the sixth Painleve equation (P6) corresponding to the quantum
cohomology of the projective plane is considered. This is one of the solutions
to P6 coming from the Frobenius manifold theory. The resulting generators of the
monodromy group are computed. The main difference in the author's approach is
its directness, so that no references to the Frobenius manifold theory are
needed. The proof presented in the article requires only a) classical results on
the asymptotic expansion of some special cases of the hypergeometric function
and b) simple, but not obvious rational substitution. The proof also directly
demonstrates that the resulting monodromy group is in SL(2,Z).
Muzsnay, Zoltán, University of Debrecen, Debrecen,
H-4010, PBox 12, Hungary,
(muzsnay@math.klte.hu).
The Euler-Lagrange PDE and Finsler
metrizability,
pp. 79-98.
ABSTRACT.
We investigate the following question: under what conditions can a second-order
homogeneous ordinary differential equation (spray) be the geodesic equation of a
Finsler space. We show that the Euler-Lagrange partial differential system on
the energy function can be reduced to a first order system on this same
function. In this way we are able to give effective necessary and sufficient
conditions for the local existence of a such Finsler metric in terms of the
holonomy algebra generated by horizontal vector-fields. We also consider the
Landsberg metrizability problem and prove similar results. This reduction is a
significant step in solving the problem whether or not there exists a
non-Berwald Landsberg space.
Yoshio Tanaka, Tokyo Gakugei University, Tokyo 184-8501,
Japan (ytanaka@u-gakugei.ac.jp), and Ying Ge, Suzhou
University, Suzhou 215006, P.R.China (geying@pub.sz.jsinfo.net).
Around quotient compact images of
metric spaces, and symmetric spaces, pp. 99-117.
ABSTRACT.
We give some new characterizations for certain compact-covering (or
sequence-covering) quotient, compact (or ƒÎ-) images of metric spaces in terms
of weak bases or symmetric spaces, and consider relations between these
compact-covering images and sequence-covering images. Also, we pose some
questions around quotient compact images of metric spaces.
Ingram, W. T., University of Missouri - Rolla, Rolla, MO 65409-0020
(ingram@umr.edu), and Mahavier, William S., Emory University,
Atlanta, GA 30322 (wsm@mathcs.emory.edu).
Inverse Limits of Upper
Semi-continuous Set Valued Functions, pp. 119-130.
ABSTRACT.
In this article we define the inverse limit of an inverse sequence (X1,ƒ1),
(X2,ƒ2), (X3,ƒ3), ... where
each Xi
is a compact Hausdorff space and each
ƒi
is an upper semi-continuous function from Xi+1
into 2Xi . Conditions are given under which the
inverse limit is a Hausdorff continuum and examples are given to illustrate the
nature of these inverse limits.
S. Oltra and E.A. Sanchez Perez, Departamento de Matematica Aplicada,
Universidad Politecnica de Valencia, Valencia 46071, Spain (soltra@mat.upv.es),
(easancpe@mat.upv.es).
Order properties and p-metrics on
Köthe function spaces, pp. 131-142.
ABSTRACT.
If L is a Köthe function space, we define and characterize a class of p-pseudo
metrics on L using the representation of the dual space by means of integrals.
We show that it provides an adequate framework for the study of the relation
between the to pology and the order on L. In particular, we obtain in this
context new characterizations of the lattice properties of L. We a lso show that
these results can be applied in the case of the dual complexity spaces that are
used as models for the complexity analysis of algorithms and programs in
Theoretical Computer Science.
Milutinovic, Uros, University of Maribor, PEF, Koroska 160,
2000 Maribor, Slovenia
(uros.milutinovic@uni-mb.si).
Approximation of maps into
Lipscomb's space by embeddings, pp. 143- 159.
ABSTRACT.
Let J(t) be Lipscomb's one-dimensional space and let Ln(t) be
Lipscomb's n-dimensional universal space of weight t, i.e. the set of all
elements of J(t)n+1
having at least one irrational coordinate. In this paper we prove that if X is a
metrizable space and dim X≤n, wX ≤t, then any mapping from X to J(t)n+1
can be approximated arbitrarily close by an embedding from X to Ln(t).
Also, in the separable case an analogous result is obtained, in which the
classic triangular Sierpinski curve (homeomorphic to J(3)) is used instead of
J(aleph0).
S. Macias, Instituto de Matematicas, U.N.A.M., Circuito
Exterior, Ciudad Universitaria, Mexico, D.F., C.P. 04510
(macias@servidor.unam.mx)..
A class of one-dimensional,
nonlocally connected continua for which the set function T
is continuous, pp. 161-165.
ABSTRACT.
We present a class of one--dimensional, nonlocally connected continua for which
the set function T is continuous.
B. Mond, Department of Mathematics, La Trobe University,
Bundoora, Vic. 3083, Australia (b.mond@latrobe.edu.au), J. Pevcaric,
Faculty of Textile Technology, University of Zagreb, 10000 Zagreb, Croatia, and
I. Peric, Faculty of Chemical Engineering & Technology, University of
Zagreb, 10000 Zagreb, Croatia, (iperic@pbf.hr).
On Reverse Integral Mean Inequalities,
pp. 167-181.
ABSTRACT.
If f s a positive integrable function, then it is well-known that for
real numbers p and q, q≤p, the ratio of the p-power
integral mean of f by the q-power integral mean is greater
than or equal to 1. Different authors have given reverse inequalities
for this ratio. Here we present various upper bounds for this ratio for a wider
class of weighted power means and functions. These results are extensions of
results of Muckenhoupt, Nania and Alzer.
Isaac Pesenson,
Department of Mathematics, Temple University, Philadelphia, PA 19122
(pesenson@math.temple.edu).
Deconvolution of band limited
functions on non-compact symmetric spaces, pp. 183-204.
ABSTRACT.
It is shown that a band limited function on a non-compact symmetric space can be
reconstructed in a stable way from some countable sets of values of its
convolution with certain distributions of compact support. A reconstruction
method in terms of frames is given which is a generalization of the classical
result of Duffin-Schaeffer about exponential frames on intervals. The second
reconstruction method is given in terms of polyharmonic average splines.
Boos, Johann, FernUniversität in Hagen, D-58084 Hagen,
Germany (Johann.Boos@FernUni-Hagen.de), and Leiger, Toivo,
Puhta Matemaatika Instituut, Tartu Ülikool, EE 50090 Tartu, Eesti
(Toivo.Leiger@ut.ee), and Zeltser, Maria, Matemaatika osakond,
Tallinna Ülikool, EE 10120 Tallinn, Eesti (mariaz@tln.ee).
The intersection of matrix domains
including a given sequence space, pp. 205-225.
ABSTRACT.
On the one hand, Hahn's theorem tells that each convergence domain containing
the set of all sequences of 0's and 1's includes all bounded sequences. On the
other hand, it is easy to verify that for each unbounded sequence x there exists
a convergence domain that includes all bounded sequences but does not contain x.
Thus the set of all bounded sequences is the intersection of all convergence
domains containing all sequences of 0's and 1's. In this sense the set of all
bounded sequences is the `summability hull' of the set of all sequences of 0's
and 1's. In the present paper the `summability hull' of arbitrarily given
sequence spaces is studied.
Anna, Kaminska, Department of Mathematical Sciences, The University of
Memphis, Memphis, USA
(kaminska@memphis.edu)
and Han Ju, Lee, Department of Mathematics, POSTECH, Pohang-shi, Republic
of Korea
(hahnju@postech.ac.kr).
On uniqueness of extension of
homogeneous polynomials, pp. 227-252.
ABSTRACT.
We study the uniqueness of norm-preserving extension of n-homogeneous
polynomials in Banach spaces. We show that norm-preserving extensions of
n-homogeneous polynomials do not need to be unique for n > 1 in real Banach
spaces, and for n> 2 in a large class of complex Banach function spaces. We find
further a geometric condition, which in particular yields that a unit ball in X
does not possess any complex extreme point, under which for every norm-attaining
2-homogeneous polynomial on a complex symmetric sequence space X there exists a
unique norm-preserving extension from X to its bidual. In particular, if M is a
Marcinkiewicz sequence space and m is its subspace of order continuous elements,
we show that every norm-attaining 2-homogeneous polynomial on m has a unique
norm-preserving extension to its bidual M if and only if no element of a unit
ball of m is a complex extreme point of its unit ball. We then apply these
results to obtain some necessary conditions for the uniqueness of extension of
2-homogeneous polynomials from a complex symmetric space X to its bidual.
Englis, Miroslav, MU AV CR, Zitna 25, 11567 Praha 1, Czech Republic
(englis@math.cas.cz), Hänninen,
Teemu T., Department of Mathematics, University of Helsinki, P.O. Box 4,
00014 Helsinki, Finland
(Teemu.Hanninen@helsinki.fi), and Taskinen, Jari, Department of
Mathematics, University of Joensuu, P.O. Box 111, 80101 Joensuu, Finland;
current address: Dept. of Mathematics, Univ. of Helsinki, P.O.Box 4,
00014 Helsinki, Finland
(jari.taskinen@helsinki.fi).
Minimal L-infinity-type spaces
on strictly pseudoconvex domains on which the Bergman projection is continuous ,
pp. 253-275.
ABSTRACT.
We describe the space of functions on a smoothly bounded strictly pseudoconvex
domain such that (i) the Bergman projection is continuous on it; (ii) its
topology is given by a family of weighted sup-norms, with weights depending only
on a given defining function; (iii) it contains all bounded measurable
functions; and (iv) it is contained continuously into any other function space
satisfying (i)-(iii). This generalizes the results obtained by the third author
for the unit disc. We also obtain analogous assertions for the standard weighted
Bergman projections, and, under the additional hypothesis that the domain be
complete circular, also for the Szegö projection on pluriharmonic functions.
Steven M. Seubert, Department of Mathematics and Statistics, Bowling
Green State University, Bowling Green, OH, 43403-0221 (sseuber@bgnet.bgsu.edu).
Dissipative compressed Toeplitz
operators on shift co-invariant subspaces , pp. 277-292.
ABSTRACT.
Necessary and sufficient conditions for an operator commuting with the
compression of the standard unilateral shift on the Hardy space H2 to
a shift co-invariant subspace to be dissipative are given in terms of the coset
of symbols of the operator. The lattice of closed invariant subspaces of a
dissipative operator commuting with the compression of the shift operator is
shown to coincide with the lattices of closed invariant subspaces of the
fractional powers of the dissipative operator using semigroup results.
Sufficient conditions for the lattice of closed invariant subspaces of a
dissipative operator commuting with the compression of the shift operator to
coincide with the lattice of closed invariant subspaces of the compression of
the shift operator are given whenever the shift co-invariant subspace
corresponds to a Blaschke product.
Jim Gleason, Department of Mathematics, University of
Tennessee, Knoxville, TN, USA 37996-1300 (gleason@math.utk.edu). Current
address: Department of Mathematics, The University of Alabama, Tuscaloosa, AL
35487-0350 (jgleason@as.ua.edu).
Quasinormality of Toeplitz Tuples
with Analytic Symbols, pp. 293-298.
ABSTRACT.
We study properties of quasinormality for tuples of Toeplitz operators with
analytic symbols on the Hardy and Bergman space of the unit ball or the polydisc
in C. Also, using examples we show that different notions of
quasinormality for commuting tuples of operators correspond to multiplication by
the coordinate functions on different domains in C.
Kamila Klis, and Marek Ptak, Institute of
Mathematics, University of Agriculture, Al. Mickiewicza 24/28, 30-059 Krakow,
Poland (rmklis@cyf-kr.edu.pl), (rmptak@cyf-kr.edu.pl).
k-Hyperreflexive subspaces, pp.
299-313.
ABSTRACT.
Changing rank-one operators in a suitable definition of hyperreflexivity to rank
k operators we give a definition of
k-hyperreflexivity. We give an example of 2-hyperreflexive
subspace which second ampliation is not hyperreflexive. There are also given
properties and examples of k-hyperreflexivity. It is shown that the
space of all Toeplitz operators is
2-hyperreflexive and each k-dimensional subspace is
k-hyperreflexive.
Bernal-Gonzalez and Calderon-Moreno, M.C.,
Departamento de Analisis Matematico. Facultad de Matematicas, apdo. 1160.
Avenida Reina Mercedes, 41080 Sevilla , Spain (lbernal@us.es), (mccm@us.es) and
Luh, W.,
Fachbereich Mathematik, Universität Trier, D-54286 Trier, Germany
(luh@uni-trier.de}.
Universal matrix transforms of
holomorphic functions , pp. 315-324.
ABSTRACT.
The phenomenon of overconvergence is related with the convergence of
subsequences of the sequence of partial sums of Taylor series at points outside
their disk of convergence. During the seventies Chui and Parnes and the third
author provided a holomorphic function in the unit disk which is universal with
respect to overconvergence. The generic nature of this kind of universality has
been recently shown by Nestoridis. In this paper, we connect the overconvergence
with the summability theory. We show that there are “many” holomorphic functions
in the unit disk such that their sequences of A-transforms have the
overconvergence property, A being an infinite matrix. This strengthens
Nestoridis' result.