*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. Bossard,** Equipe d'Analyse, Universite Paris VI, Case 186, 4, place
Jussieu, 75252 - Paris Cedex 05.

* On a Problem of H. P. Rosenthal,
* pp. 1-15.

ABSTRACT.
Let *X *be a non reflexive separable Banach space. H.P. Rosenthal
associates with *X * an ordinal index defined on the elements of the
bidual, and shows that *X*contains no isomorph of c_{0} iff for
any element of the bidual which is not in the space the value of the index is
countable. Using tools of analytic set theory and ordinal ranks on Baire class 1
functions, we prove that if *X* contains no isomorph of c_{0},
then in some cases the ordinal index is uniformly bounded on the elements of the
bidual which are not in the space by a countable ordinal. In particular it is
true when * X* contains no isomorph of l_{1}.

**Sidney A. Morris,
** School of Mathematics, University of South Australia, Mawson Lakes, S.A.
5095, Australia, **Peter Nickolas, **School of Mathematics and Applied
Statistics, University of Wollongong, Wollongong, NSW 2522, Australia, and **
Vladimir Pestov, ** School of Mathematical and Computing Sciences, Victoria
University of Wellington, PO Box 600, Wellington, New Zealand

* Limit Laws for Wide Varieties of
Topological Groups II,* pp. 17-27.

ABSTRACT. A class of topological groups is a wide
variety if it is closed under the formation of subgroups, products and
continuous homomorphic images. Walter Taylor introduced limit laws as analogues
for topological groups of algebraic laws for abstract groups, and proved a
Birkhoff-style characterisation: a class is a wide variety if and only if it is
the class of models for some set of algebraic laws and some perhaps proper class
of limit laws. The class of wide varieties T(m) , for infinite cardinals m , has
played a central role in the theory to date. A group is in T(m) if and only if
each neighbourhood of its identity contains a normal subgroup of index strictly
less than m . This paper contributes to our knowledge of the T(m) , and of the
relation of other wide varieties to the T(m) . In particular, it is shown that
the T(m) are definable by a set (rather than a proper class) of limit laws;
indeed, the same is true of any wide subvariety of any T(m) . Further, the class
of wide varieties lying in each T(m) is a set. On the other hand, it is also
shown that there exists a proper class of wide varieties which do not lie in any
T(m) , and constructions are given of certain families of such varieties, each
defined by sets of particularly simple limit laws.

**Gerhard Gierz, ** Department of Mathematics University of California at
Riverside, Ca 92526 (gierz@math.ucr.edu), and **Albert R. Stralka, **
Department of Mathematics University of California at Riverside, Ca 92526
(stralka@math.ucr.edu).

* Quotients of Full Sublattices of
Euclidean Space, *pp. 29-53.

ABSTRACT. In this note, we show that every full
sublattice of Euclidean space is a quotient of a sublattices for which primes
and coprimes are closed subsets.

**Mollov, Todor Zh.**, University of Plovdiv, 4000 Plovdiv, Bulgaria
(mollov@ulcc.uni-plovdiv.bg) and **Nachev, Nako A.**, University of
Plovdiv, 4000 Plovdiv, Bulgaria
(nachev@ulcc.uni-plovdiv.bg).
*On the semisimple twisted
group algebras of primary cyclic groups, *pp. 55-66.

ABSTRACT.
Let KtG be a twisted group algebra of a finite cyclic p-group G over a field K
of characteristic different from p and of the second kind with respect to p. In
this paper we have given, up to an isomorphism, the decomposition of KtG into a
direct sum of fields, precising their type and multiplicity of appearance and
specifying the multiplicative group U(KtG) of KtG. We have found a sufficient
and necessary condition for the isomorphism of KtG and KtH as K-algebras, where
G and H are finite cyclic p-groups of the same order.

**Byung Gyun Kang ,** Department of Mathematics, POSTECH, Pohang, 790-600,
South Korea.

* When Are the Prime Ideals of the
Localization R[X] _{T} Extended from R ,* pp. 67-81.

ABSTRACT. Let

**O. T. Alas, **University of Sao Paulo, Caixa Postal 66281, 05315-970 Sao
Paulo, Brazil (Alas@ime.usp.br), **W.W. Comfort, ** Wesleyan University,
Middletown CT 06459, (Wcomfort@wesleyan.edu), **S. Garcia-Ferreira,**
Instituto de Matematicas, Ciudad Universitaria (UNAM), 04510 Mexico D.F., Mexico
(garcia@servidor.unam.mx), **M. Henriksen,** Harvey Mudd College, Claremont
CA 91711 (Henriksen@hmc.edu), **R.G. Wilson**, Departamento de Matematicas,
Universidad Autonoma Metropolitana, Unidad Iztapalapa, 09340, Mexico D.F.,
Mexico (rgw@xanum.mx) and **R.G. Woods,** University of Manitoba, Winnipeg,
Man. R3T 2N2 (Rgwoods@cc.umanitoba.ca).
* When is |C(Xx Y)| = |C(X)| x
|C(Y)|? ,* pp. 83-115.

ABSTRACT. Sufficient conditions on the Tychonoff spaces *
X* and *Y* are found that imply that the equation in the title holds.
Sufficient conditions on the Tychonoff space *X* are found that ensure that
the equation holds for every Tychonoff space *Y*. A series of examples
(some using rather sophisticated cardinal arithmetic) are given that witness
that these results cannot be generalized much.

**Jawad Sadek** Northwest Missouri State University
(jawads@mail.nwmissouri.edu)
*Normal Limits and
Star-Invariant Subspaces of Bounded Mean Oscillatio in Multiply Connected
Domains, *pp. 117-129.

ABSTRACT. Let *D* be a domain in the plain bounded
by *n+1* analytic Jordan curves. Let H^{2} be the usual Hardy class
of analytic functions in *D*. Denote by *BMOA* the space of analytic
functions of bounded mean oscillation in *D *and let K_{2} be the
star-invariant subspace generated by an inner function *phi* in *D*.
Let K_{*} be the intersection of K_{2}and *BMOA*. In this
paper, we give a necessary and sufficient condition for the normal limit to
exist at a point on the boundary of *D *for a function in K_{*}.

**Efton Park,**Department of Mathematics Texas Christian University Fort
Worth, Texas 76129 (e.park@tcu.edu)
* Isometries of Unbounded
Fredholm Modules over Manifolds *, pp. 131-144 .

ABSTRACT. A self-adjoint first-order elliptic
differential operator
*D *acting on sections of a Hermitian vector bundle over a compact
Riemannian manifold
*M*determines an unbounded Fredholm module over
**M**_{n}*(C(M))* for each positive integer *n*. We
show that the group of automorphisms of **M**_{n}*(C(M))*
that respect the unbounded Fredholm module is a compact topological group in the
topology of pointwise convergence. If *D* is an operator of Dirac type and
we restrict to scalar functions, then this group is also a Lie group.

**Joel D. Avrin** Department of Mathematics, University of North Carolina
at Charlotte, Charlotte, North Carolina 28223.
*Flame propagation in Models of
Complex Chemistry
,* pp. 145-163.

ABSTRACT. We consider models of laminar flames with
Arrhenius kinetics in long thin tubes. In previous studies of a model of a
one-step reaction of the form A--> B, we identified certain conditions imposed
on the initial temperature that guarantee a rough sense of flame propagation
resulting in complete asymptotic burning of the fuel. We now extend these
studies to a model of a two-step reaction of the form A -->B --> C, and to some
models of one-step reactions with multiple species. We again identify sufficient
conditions on the initial temperature that guarantee a rough sense of flame
propagation and complete asymptotic burning.For these results to hold we need to
add some restrictions on other parameters for technical reasons, but we show
that our results nonetheless apply to a wide range of cases.

**Srdjan Petrovic, **
Department of Mathematics & Statistics, Western Michigan University, Kalamazoo,
MI 49008-5152
(petrovic@wmich.edu).
*An Extremal Problem in
Interpolation Theory,* pp. 165-181.

ABSTRACT. If z_{1},z_{2},...,z_{n}
are complex numbers in the open unit disk **D** and A_{1},A_{2},...,A_{n}
are N-by-N matrices, let **F **denote the family of analytic functions,
bounded in **D**, such that for each F in **F**, F(z_{k})=A_{k},
k=1,2,...,n. For z in **D **and F in
**F**, let

|F(z)|_{sp }be the spectral radius of F(z). We
consider the supremum of |F(z)|_{sp }over all z in **D **and
the infimum of the last quantity when F ranges over all functions in
**F**. H. Bercovici has raised the question whether this infimum is
attained. We will show that the answer is affirmative for N=2 and N=3, and we
point out at the obstructions to generalize this result to the case N>3.

**Porretta, Alessio,** Universita di Roma I, P.le A. Moro 2, 00185 Roma,
ITALY (porretta@mat.uniroma1.it).
* Some remarks on the
regularity of solutions for a class of elliptic equations with measure data, *
pp. 183-213 .

ABSTRACT. We deal with a class of Dirichlet problems
in an open bounded subset of the N-euclidean space for second order nonlinear
elliptic operators in divergence form of the type -div(a(x,u,Du)) where a(x,s,p)
is a Caratheodory function monotone, coercive and with linear growth with
respect to p, while no growth assumption from above is made on a(x,s,p) as a
function of s. We consider the equation -div(a(x,u,Du))=f with Dirichlet
boundary conditions assuming that f is a bounded Radon measure, proving the
existence of a weak solution and some regularity results on the summability of
both u and Du in the case that a(x,s,p), as a function of s, grows like s to the
power m. In this latter case, we also prove the existence of a solution to the
perturbated problem -div(a(x,u,Du)+H(x,u,Du)=f, where H(x,s,p) is a Caratheodory
function satisfying a sign condition (H(x,s,p)s>0 except for s=0) and which has
quadratic growth with respect to p and, as a function of s, it grows, for s
large, at most like s to the power r, with r+1<m. This restriction in the link
between m and r is in fact necessary, in order to have solutions for every
measure f, as a consequence of some recent results on removable singularities by
H. Brezis and L. Nirenberg.