*Editors*: G. Auchmuty (Houston), H. Brezis (Paris), S.S. Chern
(Berkeley), J. Damon (Chapel Hill), L.C. Evans (Berkeley), R.M. Hardt (Rice),
J.A. Johnson (Houston), A. Lelek (Houston), J. Nagata (Osaka), B. H. Neumann
(Canberra), V. Paulsen (Houston), G. Pisier (College Station and Paris), R.
Scott (Houston), S.W. Semmes (Rice), K. Uhlenbeck (Austin)
*Managing Editor*: K. Kaiser (Houston)

**Lu, Chin-Pi, **University of Colorado, Denver, CO 80217-3364.
*Unions of Prime
Submodules, *pp. 203-213.

ABSTRACT.
A proper submodule P of a module M over a ring R is said to be prime if re is in
P for r in R and e in M implies that either e is in P or r is in P:_{R}M.
In this paper we investigate the following two topics which are related to
unions of prime submodules:

i) The Prime Avoidance Theorem for modules and

ii) S-closed subsets of modules.

**Repovs, D., **University of Ljubljana, 1001 Ljubljana, Slovenia,
**Semenov, P.V., **Moscow State Pedagogical University, 119882 Moscow,
Russia, and **Scepin, E.V., **Steklov Mathematical Institute, 117966 Moscow,
Russia.
*Topologically Regular
Maps with Fibers Homeomorphic to a One-Dimensional Polyhedron*,
pp. 215-229.

ABSTRACT. We introduce the concept of a topologically
regular map as a map with homeomorphic fibers, whose multivalued inverse map is
continuous with respect to the Frechet metric. We prove that every topologically
regular map between compact metric spaces with fibers homeomorphic to some
one-dimensional polyhedron is a locally trivial bundle.

In our proof two nontrivial facts are used. First one is Michael's Selection
theorem for maps with convex but nonclosed values. Second one is that the
restriction of a locally 1-soft map onto ``small'' closed neighborhoods, is an
open monotone map. Here we need Anderson's map of the universal Menger curve
onto the Hilbert cube.

**Dontchev, Julian, **University of Helsinki, PL 4, Yliopistonkatu 15, 00014
Helsinki, Finland
(dontchev@cc.helsinki.fi),
**Ganster, Maximilian, **Graz University of Technology, Steyrergasse 30,
A-8010 Graz, Austria
(ganster@weyl.math.tu-graz.ac.at), and **Rose, David, **Southeastern
College of the Assemblies of God, 1000 Longfellow Boulevard, Lakeland, Florida
33801-6099
(darose@secollege.edu).
*Alpha-Scattered
Spaces II,
*pp. 231-246.

ABSTRACT.
A topological space X is scattered if the only perfect or equivalently crowded
subset of X is the empty set. Crowded sets are sometimes called
dense-in-themselves and scattered sets are known as dispersed, zerstreut or
clairseme.

For a topological space X, the Cantor-Bendixson derivative D(X)
is the set of all non-isolated points of X. It is a fact that the
Cantor-Bendixson derivative of every scattered space is nowhere dense. That D(X)
is nowhere dense is equivalent to the assumption that I(X), the sets of all
isolated points of X, is dense in X. The spaces satisfying this last condition
are precisely the spaces whose alpha-topologies are scattered. These spaces are
called alpha-scattered. The concept was recently used to show that in
alpha-scattered spaces the notions of submaximal spaces and alpha-spaces
coincide and thus a recent result of Arhangel'skii and Collins was improved.
Topological spaces with countable Cantor-Bendixson derivative have been also
recently considered. Such spaces are called d-Lindelof.

The aim of this
paper is to continue the study of scattered and alpha-scattered spaces. The
following three open problems are left:

(1) When is an omega-scattered
space alpha-scattered?

(2) When is a sporadic space alpha-scattered? When do the two concepts
coincide?

(3) How are alpha-scattered and C-scattered spaces related?

**Putinar, Mihai, **University of California, Santa Barbara, CA 93106.
*Spectral Sets and
Scalar Dilations,
*pp. 247-265.

**Hashimoto, Takahiro, **Ehime University, 790-77 Matsuyama-shi, Japan
(taka@math.sci.ehime-u.ac.jp),
and **Otani, Mitsuharu, **Waseda University, 169 Tokyo, Japan
(otani@mn.waseda.ac.jp).
*Nonexistence of
Weak Solutions of Nonlinear Elliptic Equations in Exterior Domains, *
pp. 267-290.

ABSTRACT. The nonexistence of nontrivial solution is
discussed for some quasilinear elliptic equations for the case where a domain is
exterior of bounded and starshaped domain. It should be noted that because of
the degeneracy of the equation, the nontrivial solutions of the equation are not
twice differentiable. Therefore there arises the necessity of discussing the
nonexistence of solutions in a framework of weak solutions. When the domain is
bounded, the second author introduced a ``Pohozaev-type inequality'' valid for a
class of weak solutions, which is effective enough for discussing the
nonexistence. We here give an exterior-domain version of Pohozaev-type
inequality, whence some results on the nonexistence of solutions are derived.
These suggest that concerning the existence and nonexistence of nontrivial
solutions, there may exist an interesting duality between the interior problems
and the exterior problems for starshaped domains.

**Tshikuna-Matamba, T., **Institut Superieur Pedagogique, B.P. 282-Kanaga,
Zaire.
*On the
Structure of the Base Space and the Fibres of an Almost Contact Metric
Submersion, *
pp. 291-305.

**Seubert, S., **Bowling Green State University, Bowling Green, OH 43403-0221
(sseuber@math.bgsu.edu).
*Reducing Subspaces of
Compressed Analytic Toeplitz Operators,
*
pp. 307-327.

**Poon, Chi-Cheung, **National Chung Cheng University, Chiayi 621, Taiwan.
*On the Heat Equation for
Harmonic Maps into Round Cones,
*pp. 329-340.

**Fister, Renee, **Murray State University, Murray, KY 42071
(kfister@math.mursuky.edu).
*Optimal Control of
Harvesting in a Predator-Prey Parabolic System, *
pp. 341-355.

**Jung, Michael, **Technische Universitat Berlin, 10623 Berlin, Germany
(mjung@math.tu-berlin.de).
*Evolution Families and
Generators of Semigroups, *
pp. 357-383.

ABSTRACT. In this article we will examine properties
of evolution families and their generators. We start out with the generator of a
semigroup and by perturbation obtain results on non-autonomous, abstract Cauchy
problems. Some results on non-linear problems are also obtained. It is namely
the (Z*)-condition, which will provide us with results and which we will relate
to the (Z)-condition given by W. Desch and W. Schappacher. Some examples are
given in the last section.

**Morayne, M., **and **Ryll-Nardzewski, C. **.
*Errata to
Superpositions with Differences of Semicontinuous Functions, *
p. 384.

(Vol. 22, No. 4, 1996, pp. 719-735.)

**Garity, Dennis J., Jubran, Isa S., **and **Schori, Richard M. **.
*Corrigenda to a
Chaotic Embedding of the Whitehead Continuum, *
pp. 385-390.

(Vol. 23, No. 1, 1997, pp. 33-44.)

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