*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), J. Nagata (Osaka), B. H. Neumann (Canberra), V. I. Paulsen (Houston),
G. Pisier (College Station and Paris), S. W. Semmes (Rice)
*Managing Editor*: K. Kaiser (Houston)

Houston Journal of Mathematics

*Contents*

**David E. Rush, ** Department of Mathematics, University of California,
Riverside, California 92521 (rush@newmath.ucr.edu) and **Laura J. Wallace,**(wallace@csusb.edu).

Noetherian Maximal Spectrum and
Coprimely Packed Localizations of Polynomial Rings, pp. 437-448.

ABSTRACT. A ring R is said to be coprimely packed if
for every ideal I of R and for each set S of maximal ideals of R one has that I
is a subset of the union of S only if I is a subset of some member of S.

A ring R is shown to have Noetherian maximal spectrum if and only if R(X) is
coprimely packed.

**M. Gehrke, ** Department of Mathematical Sciences New Mexico State
University Las Cruces, NM 88003 USA (mgehrke@nmsu.edu) and **H. A. Priestley, **
Mathematical Institute 24/29 Oxford OX1 3LB UK ( hap@maths.ox.ac.uk)

Non-canonicity of MV-algebras ,
pp. 449-455.

ABSTRACT. The variety MV of all MV-algebras is shown
to be non-canonical in a strong sense. Specifically it is shown that the
canonical extension of the Chang algebra, K_{2}, is not an MV-algebra.
As a consequence, no non-finitely generated variety of MV-algebras is canonical.

**Nako Nachev, **Department of Algebra, Plovdiv University, 4000 Plovdiv,
Bulgaria (nachev@pu.acad.bg).

Isomorphism of Semisimple
Twisted Group Algebras, pp. 457-464.

ABSTRACT. Let *K* be a field of characteristic
different from 2. In this paper we give sufficient and necessary conditions for
the isomorphism of semisimple twisted group algebras of cyclic 2-groups.

** C. Watt, **
School of Mathematics, Trinity College Dublin, Dublin 2, Ireland
(cwatt@maths1.kst.dit.ie).

Horizontal Complex Curves and
Holomorphic Curvature , pp. 465-495.

ABSTRACT. Horizontal complex curves are defined on a
complex Finsler manifold and are shown to coincide with those complex curves
which realise the holomorphic curvature of the given Finsler metric. An
existence and uniqueness theorem for horizontal complex curves is sketched and
extensions of known characterisations of the Kobayashi metric are derived. The
theory is illustrated for a family of metrics on the Euclidean open unit ball of
a finite dimensional complex vector space.

** Dusan Repovs, ** Institute of Mathematics, Physics and Mechanics,
University of Ljubljana, Jadranska 19, P. O. Box 2964, Ljubljana, Slovenia 1001
(dusan.repovs@fmf.uni-lj.si and **Pavel V. Semenov** Department of
Mathematics, Moscow City Pedagogical University, 2-nd Selskokhozyastvennyi pr.
4, Moscow,Russia 129226 (pavels@orc.ru ).

On Relative Approximation Theorems , pp. 497-509.

ABSTRACT. We consider an approach which reduces the
solution of the approximation problem for a USC mapping to an appropriate
selection-type restriction of the family of values of this mapping. As a
corollary we prove that for every compact, not necessarily ANR, domain *X *
of a USC convex-valued mapping H : *X* → *Y* and for every ε > 0
there exists δ > 0 such that every δ-approximation of *H *defined over a
closed subset *A* ⊂ *X* can be extended to an ε-approximation over the
entire domain. Similar facts are established for selections and ε-selections of *
H* over *A*.

** Manuel Sanchis, ** Departament de Matematiques, Universitat Jaume I,
Campus del Riu Sec s/n, 12071, Castelló, Spain
(sanchis@mat.uji.es) and **Angel
Tamariz-Mascarúa**, Universidad Nacional Autónoma de México, Facultad de
Ciencias, Departamento de Matemáticas, 04510 México D.F., México
(atamariz@servidor.unam.mx).

A note on p-bounded and
quasi-p-bounded subsets, pp. 511-527.

ABSTRACT.
We discuss the relationship between p-boundedness and quasi-p-boundedness in the
realm of Generalized Linearly Ordered Spaces (GLOTS) for free ultrafilters p on
the natural numbers. We show that p-pseudocompactness, p-compactness, and
quasi-p-compactness are equivalent properties for GLOTS; that bounded subsets of
a GLOTS are strongly bounded; and that C-compact subsets of a GLOTS are strongly
C-compact. We also show that a topologically orderable group is locally
precompact if and only if it is metrizable. For bounded subsets of a GLOTS, a
version of the classical Glicksberg's theorem on pseudocompactness is obtained.
Also we prove that there exists an ultrapseudocompact topological group which is
not quasi-p-compact for any free ultrafilter p on the natural numbers. To see
this example, p-pseudocompactness and p-compactness are investigated in the
field of spaces of continuous functions defined on a space X with values in
[0,1], and considered with the pointwise convergence topology: Cp(X,[0,1]);
proving that ultracompactness, quasi-p-compactness and countable compactness
(respectively, ultrapseudocompactness, quasi-p-pseudocompactness and
pseudocompactness) are equivalent properties in these spaces.

**Byung-Jay Kahng, ** Department of Mathematics, University of
Kansas, Lawrence, KS 66045 (bjkahng@math.ukans.edu).

^{* }-representations of
a quantum Heisenberg group algebra , pp. 529-552.

ABSTRACT.
In our earlier work, we constructed a specific non-compact quantum group whose
quantum group structures have been constructed on a certain twisted group
C*-algebra. In a sense, it may be considered as a ``quantum Heisenberg group
C*-algebra''. In this paper, we will find, up to equivalence, all of its
irreducible *-representations. We will point out the Kirillov type
correspondence between the irreducible representations and the so-called
dressing orbits. By taking advantage of its comultiplication, we will then
introduce and study the notion of ``inner tensor product representations''. We
will show that the representation theory satisfies a ``quasitriangular'' type
property, which does not appear in ordinary group representation theory.

**Leo B. Jonker and Ole A. Nielsen**, Queen's University, Kingston ON K7L
3N6, Canada (leo@mast.queensu.ca,
nielseno@post.queensu.ca).

An Example Concerning the Order-Two Density of a Set , pp. 553-563.

ABSTRACT. For each real number s strictly between 0
and 1 we construct a subset of the unit interval whose Hausdorff dimension is s,
whose upper density (relative to the Hausdorff measure in that dimension) is
almost everywhere equal to 1, and whose order-two density and lower density are
both everywhere equal to 0.

**Fred Richman, **
Florida Atlantic University, Boca Raton FL 33431 (richman@fau.edu), **Douglas
Bridges** University of Waikato, Hamilton, New Zealand
(d.bridges@math.canterbury.ac.nz) and **Peter Schuster, **Universität
München, 80333 München (pschust@rz.mathematik.uni-muenchen.de).

Trace-class operators,
pp. 565-583.

ABSTRACT. In this paper we give a direct definition of
the von Neumann-Schatten classes of operators in terms of the existence of a
certain supremum. The theory is developed without appeal to separability, or to
the existence of an orthonormal basis, and without using countable choice or the
law of excluded middle. We construct the singular values of compact operators,
and characterize compact operators, and the von Neumann-Schatten classes, in
terms of singular values.

** N.J. Kalton, ** Department of Mathematics, University of
Missouri-Columbia, Columbia, MO 65211 (nigel@math.missouri.edu) and **A.E.
Litvak**, Department of Mathematics, Technion, Haifa, Israel, 32000
(alex@math.technion.ac.il) (current address: Department of Math. and Stat. Sc.,
University of Alberta, Edmonton, AB, Canada (alexandr@math.ualberta.ca).

Quotients of finite-dimensional
quasi-normed spaces , pp. 585-598.

ABSTRACT. We study the existence of cubic quotients of
finite-dimensional quasi-normed spaces, that is, quotients well isomorphic to
k-dimensional cube for some k. We give two results of this nature. The first
guarantees a proportional dimensional cubic quotient when the envelope is cubic;
the second gives an estimate for the size of a cubic quotient in terms of a
measure of non-convexity of the quasi-norm.

** K. S. Ryu, ** Department of Mathematics, Han Nam University, Taejon
306-791, Korea (ksr@math.hannam.ac.kr) and
**S. C. Yoo, **Jaeneung College, Incheon 401-714, Korea
(yky3ng@mail.jnc.ac.kr).

The existence theorem and formula
for an operator-valued function space integral over paths in abstract Wiener
space , pp. 599-620.

ABSTRACT. In 1973, Kuelbs and LaPage showed the
existence of analogy of Wiener measure over continuous paths in abstract Wiener
space [1]. In 1992, Ryu found the formula, similar to the Wiener integration
formula, for this measure [2]. In this article, we introduce the definition of
scale-invariant weak integral and investigate some basic properties of this
integral. We establish an existence theorem and formula for an operator-valued
function space integral over continuous paths in an abstract Wiener space, which
are represented by the scale-invariant weak integral. The work here is patterned
to some extent on earlier work involving Wiener and Feynman path integrals but
the present setting requires a number of new concepts and results.

*References*

[1] J. Kuelbs and R. LaPage, The law of the iterated Logarithm for Brownian
Motion in a Banach space, Trans. Amer. Math. Soc., 185 (1973), 253-264.

[2] K.S. Ryu, The Wiener integral over paths in abstract Wiener space, J. Korean
Math. Soc., Vol. 29, No. 2, (1992), 317-331.

** B. Scarpellini, **Mathematisches Institut der Universität, Rheinsprung
21, 4051 Basel, Switzerland (bscarpellini@hotmail.com).

On a family of large
solutions of Navier-Stokes , pp. 621-647.

ABSTRACT.
It is well known that large, smooth initial data give rise to local strong
solutions of the Navier-Stokes equations, while small smooth initial data give
rise to global strong solutions. Here we describe three classes of initial data
w_{0} for which ||∇w_{0}|| may be arbitrarily large, which give
rise to global strong solutions.

** Peihao Zhao, ** Department of Mathematics, Lanzhou University, Lanzhou,
730000, P. R. of China (zhaoph@lzu.edu.cn) and **Chengkui Zhong. **

Positive Solutions of Elliptic
Equations Involving both Supercritical and Sublinear Growth , pp. 649-663.

ABSTRACT. Positive solutions of elliptic problem
involving both supercritical and sublinear growth on the unit ball with
Dirichlet boundary condition are analysed as their supremum norm tend to
infinity. It is shown that they converge, uniformly away from the origin, as
well as in H^{1}, to the unique singular solution. Then we prove that
there is only one solution when the sublinear term is small enough, this give a
negative answer to the open problem in J.Funct.Anal.122(1994),519-543. And, an
infinitely number of positive solutions has been obtained.