*Editors*: H. Amann (Zürich), G. Auchmuty (Houston), D. Bao (Houston),
H. Brezis (Paris), S. S. Chern (Berkeley), 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), G. Pisier
(College Station and Paris), S. W. Semmes (Rice)
*Managing Editor*: K. Kaiser (Houston)

**B.A. Davey
** and **M. Haviar, **La Trobe University Bundoora, Victoria 3083 Australia
(B.Davey@latrobe.edu.au), (M.Haviar@latrobe.edu.au).

* A Schizophrenic Operation which
aids the Efficient Transfer of Strong Dualities ,
* pp. 215-222.

ABSTRACT.
We show that, in many cases, if **DB** and **MB** are finite algebras
which generate the same quasi-variety *CCD*, then a strong duality for *
CCD* based on **DB** may be transferred to a strong duality for *CCD*
based on **MB** by the addition some endomorphisms of **MB** and just one
further partial operation. This additional operation exhibits the schizophrenia
so typical of the theory of natural dualities. We show how the result may be
applied to yield an efficient strong duality in the case when **MB**
is a distributive lattice, a semilattice or an abelian group.

**H. P. Goeters,
** Department of Mathematics, Auburn University, Auburn, AL 36849-5310
(goetehp@mail.auburn.edu), and
** W. J. Wickless , **Mathematics Department, University of Connecticut,
Storrs, CT 06268 (wjwick@UConnVM.UConn.edu).

*
Relative Injectivity and Equivalence Theorems ,* pp. 223-239.

ABSTRACT.
Two subgroups, *H* and *K*, of an abelian group *G* are said to
be equivalent when there is an automorphism of *G* sending *H* onto *
K.*. Here we will consider equivalence theorems for torsion-free reduced
abelian groups of finite rank.

Hill wondered if a homogeneous group *G* with the type of the integers
satisfying the simple test for the equivalence of pure subgroups must be free as
an abelian group. The first author investigated Hill's problem in before and
considered the homogeneous groups *G* with the following property: whenever *
H* and *K* are pure subgroups of *G* and f : H --->K is an
isomorphism, there is an automorphism of *G* restricting to f on *H*.
It was established that the homogeneous group *G* has this isomorphism
lifting property precisely when *G* is quasi-pure injective. In particular,
*G *must be free as a module over the center of its endomorphism ring but *
G* need not be free as an abelian group, thus answering Hill's query in the
negative.

In this article we will classify the torsion-free abelian groups of finite
rank which have the isomorphism lifting property lips defined above. Unlike the
homogeneous situation, we show that groups having lips need not be quasi-pure
injective qpi, but qpi groups have the lips property. A notion related to the
lips condition is the *mteps* condition; a group *G *has the *
minimal test for the equivalence of pure subgroups*( *mteps)*, if any
two isomorphic pure subgroups of *G* are equivalent in *G*. We
characterize the groups with mteps below, showing in particular the only
circumstance when a homogeneous group *G* with mteps fails to be qpi is
when rank(*G*) = 3 and when the set of primes where p*G* is not equal
to *G*
excludes an infinite set of primes.

**H. P. Goeters**
Department of Mathematics, Auburn University, Auburn, AL 36849-5310
(goetehp@mail.auburn.edu), and **Bruce Olberding, **
Department of Mathematics, Northeast Louisiana University, Monroe, LA 71209
(maolberding@alpha.nlu.edu).

* On the Multiplicative
Properties of Submodules of the Quotient Field of an Integral Domain , *
pp. 241-254.

ABSTRACT. The notions of cancellation and invertiblity
for ideals are generalized to submodules of the quotient field of an integral
domain.

**M. Crampin
**, Department of Applied Mathematics, The Open University, Walton Hall,
Milton Keynes MK7 6AA, UK (M.Crampin@open.ac.uk).
*The second variation formula
in Lagrange and Finsler geometry , *pp. 255-275.

ABSTRACT.
A relatively straightforward derivation is given of the second variation
formula for an arbitrary problem in the calculus of variations, which leads to a
covariant form of the formula. The relation between this formulation of the
Lagrangian second variation formula, and the corresponding formula in Finsler
geometry, is investigated. In particular, it is shown that it is not necessary
to invoke a connection in order to derive the second variation formula in
Finsler geometry; and that if one does use a connection, each of the four
standard Finslerian connections produces the same result.

**Bell, Steven R. ** Department of Mathematics, Purdue University, West
Lafayette, IN 47906-1395
(bell@math.purdue.edu).
* A Riemann surface attached to
domains in the Plane and Complexity in Potential Theory ,* pp. 277-297.

ABSTRACT. We prove that if either of the Bergman or
Szegö kernel functions associated to a multiply connected domain *D* in the
plane is an algebraic function, then there exists a compact Riemann surface *R*
such that *D* is a domain in *R* and such that a long list of
classical domain functions associated to *D* extend to *R* as single
valued meromorphic functions. Because the field of meromorphic functions on a
compact Riemann surface is generated by just two functions, it follows that all
the classical domain functions associated to *D*
are rational combinations of just two functions of one variable. This result
gives rise to some very interesting questions in potential theory and conformal
mapping. We discuss how it may yield information about complexity in potential
theory in a much more general context.

**Kunzi, Hans-Peter A., **Department of Mathematics, University of Berne,
Sidlerstrasse 5, CH-3012 Berne, Switzerland
(kunzi@math-stat.unibe.ch) and **Losonczi, Attila,
**Alfred Renyi Institute of Mathematics, Hungarian Academy of Sciences,
Realtanoda u. 13-15, H-1364 Budapest, Hungary
(losonczi@math-inst.hu).
* On Some Cardinal Functions
Related to Quasi-uniformities, * pp. 299-313.

ABSTRACT. We show that if a topological space possesses
two (distinct) compatible quasi-uniformities, then it admits at least exp c
nontransitive quasi-uniformities. We also prove that if a quasi-uniform space
(X,W) has a subspace A and an entourage V such that either {V(x): x in A} or {V^{-1}(x):
x in A} does not have a subcollection of cardinality smaller than k covering A,
then there are at least exp(exp k) quasi-uniformities belonging to the
quasi-proximity class of W. Finally we show that if the quasi-proximity class
P(W) of a quasi-uniformity W contains more than one quasi-uniformity and its
coarsest member is transitive, then there are at least exp c transitive
quasi-uniformities belonging to the quasi-proximity class P(W). (Here to avoid
typesetting problems 2^{k} is written exp k where k is an infinite
cardinal.)

**Galindo, Jorge, **Departamento de Matemáticas, Universitat Jaume I,
12071-Castellón, Spain.
(jgalindo@mat.uji.es).
* Structure and Analysis on
Nuclear Groups, *pp. 314-334.

ABSTRACT. Nuclear groups form a class of topological
Abelian groups closed under the most common operations which contains LCA groups
and additive groups of nuclear locally convex spaces. In this paper we attempt
to clarify the structure of these groups by giving a representation theorem.
This is used to show that many properties satisfied by LCA groups and
nuclear locally convex spaces are also enjoyed by nuclear groups. Bounded
subsets, the existence of interpolation sets, transmission of compactness to the
Bohr topology and Pontryagin duality for nuclear groups are studied.

**Elzbieta Pol,**Institute of Mathematics, University of Warzaw, Banacha 2
, 02-097 Warzaw, Poland (pol@mimuw.edu.pl)
* Two examples of Perfectly Normal
Spaces
*, pp. 335-341.

ABSTRACT. We construct a perfectly normal space *X *
locally homeomorphic to the irrationals such that for some fixed-point free
homeomorphism its Cech-Stone extension has a fixed point. This example is
related to an example of Good of a normal space of this kind and a recent
construction of van Hartskamp and van Mill. We give also an example of a
perfectly normal space *X* with ind(*X*)=1 no compactification of
which has small transfinite dimension - a modification of a normal space with
these properties constructed by Charalambous. In both our examples we apply a
construction of perfectly normal spaces given by E.Pol and R.Pol in 1979.

**John Akeryod** and **Elias G. Saleeby
**Department of Mathematics, University of Arkansas, Fayetteville, AR 72701,
USA (jakeroyd@comp.uark.edu), (esaleeby@comp.uark.edu).
*Sampling and the Closure of
the Polynomials in a Weighted Hardy Space
,* pp. 343-360.

ABSTRACT. In this paper, we use a recently developed
collection of measures to obtain sampling results for a class of Banach spaces.
Each of these Banach spaces is the closure of the polynomials in a certain
weighted Hardy space of the slit-disk. We then give a representation theorem for
the Hilbert space case that involves the classical Paley-Wiener space E_{phi}^{2}.

**E. Guentner,** Department of Mathematical Sciences, IUPUI, 402 N.
Blackford St., Indianapolis, IN 46202-3216 (eguentner@math.iupui.edu) .
*Wick Quantization and
Asymptotic Morphisms,* pp. 361-375.

ABSTRACT. The E-theory of A. Connes and N. Higson
provides a new realization of K-homology based on the notion of asymptotic
morphisms. In this note we begin to develop the idea that through this
realization K-homology becomes a receptacle for topological invariants of
quantization schemes. We study the example of the Wick quantization of the
complex plane. We show that it determines an element of the E-theory group of
the complex plane and by constructing an explicit homotopy we show that this
element is equal to the one determined by the Cauchy-Riemann operator.

**V. Karunakaran **and **N.V. Kalpakam ** Mathematics, Madurai Kamaraj
University, Madurai - 625 021, India.
* Boehmians Representing
Measures, *pp. 377-386.

ABSTRACT. If X=[f_{n}&DIVIDE;*f*_{n}
is bounded in *L*^{1}- norm around a neighbourhood of origin then X
is represented locally by a measure. This result generalizes a well known
theorem due to Piotr Mikusinski and Mourad Tighiourat. We also deduce that if *
f*_{n}'s are bounded in the
*L*^{p}- norm in a neighbourhood of the origin then also the
Boehmian is represented by a measure. For p>1 we show that the measure is
absolutely continuous with respect to the Lebesgue measure. An example, to show
that if *f*_{n}'s are not bounded in any *L*^{p} for
p>1 but bounded in *L*^{1}
hen the corresponding measure can be singular with respect to the Lebesgue
measure, is also given.

**Hyeong-Ohk Bae, **Department of Mathematics, Hannam University 133
Ojeong-dong, Daeduk-gu 306-791 Taejon, Republic of Korea (
hobae@math.hannam.ac.kr) and **Hi Jun Choe
** Department of Mathematics Korea Advanced Institute of Science and
Technology (KAIST) Gusong-dong 373-1, Yousong-gu 305-701 Taejon, Republic of
Korea (ch@math.kaist.ac.kr).
* Existence of Weak Solutions to a
Class of Non-Newtonian Flows, *pp. 387-408 .

ABSTRACT. We show that there exist weak solutions to a
class of non-Newtonian flows for the periodic domain. Galerkin approximation, an *
W*^{1,r+2} compactness theorem, and Korn type inequalities are main
ingredients for the proof of the existence of weak solutions. Moreover, we
estimate the Hausdorff dimension of the set of singular times for the weak
solutions.

**George O. Golightly , ** Rt. 5, Box 276, Jacksonville, TX 75766
* Laurent Series From Entire
Functions , *pp. 409-416 .

ABSTRACT. Certain series stemming from entire
functions are investigated.