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

**Hammack, Richard, **
Wake Forest University, Winston-Salem, NC 27109, USA
(hammack@mthcsc.wfu.edu).
*Circularity of Planar Graphs, *
pp. 213-221.

ABSTRACT.
A *circular cover* of a graph G is a cover {X_{0}, ... ,X_{n-1}}
of the topological space G by closed connected subsets (indexed over the cyclic
group Z_{n}) with the following properties: Each element in the cover
contains a vertex of G, each vertex of G is contained in at most two elements of
the cover, and the intersection of X_{a} and X_{b} is nonempty
if and only if
*b-a* is in {-1,0,1}. The *circularity* of G is the largest integer *
n* for which there is a circular cover of G with *n* elements. It is
known that the circularity of a planar graph is even. We sharpen this result by
proving that the circularity of a plane graph is twice the maximum number of
disjoint paths joining two faces of G. This result leads to a polynomial-time
algorithm which computes the circularity of any connected planar graph.

**Gorodnik, Alexander, **The Ohio State University, Columbus OH 43210
(gorodnik@math.ohio-state.edu).
*Local near-rings with
commutative groups of units,* pp. 223-234.

ABSTRACT.
Properties of a local near-ring with a commutative group of units are studied in
the paper. For this purpose, a method of reduction to the radical ring is
introduced. It is proven that the additive group of such near-ring will also
have some commutative properties. Several known results about groups of units of
rings are extended to the groups of units of local near-rings. Specifically, the
equivalence of finite generation for the additive group and the multiplicative
group of a local near-ring is established, and a comprehensive classification of
local near-rings with cyclic groups of units is given.

**Bertram Yood, **Department of Mathematics, 218 McAllister Building, The
Pennsylvania State University, University Park, PA 16803
*On Prime and Primitive Ideals, *
pp. 235-246.

ABSTRACT. Conditions are given which force a prime
ideal in a semi-simple ring R to be a primitive ideal. A study is made of rings
R whose structure space has a dense set of isolated points.

**Young Ho Kim, ** Department of Mathematics, Teachers College, Kyungpook
National University, Taegu 702-701, Korea (yhkim@kyungpook.ac.kr ) and **
Dong-Soo Kim, ** Department of Mathematics, Chonnam National University,
Kwangju 500-757, Korea (dosokim@chonnam.chonnam.ac.kr).
*A Basic Inequality for
Submanifolds in Sasakian Space Forms,* pp. 247-257.

ABSTRACT. A basic inequality for submanifolds in
Sasakian space forms with arbitrary codimension and some applications for the
inequality are obtained. In particular, we obtain a classification of
3-dimensional submanifolds in an odd-dimensional sphere satisfying the basic
equality.

**Balogh, Zoltan M., **Institute of Mathematics, University of Berne,
Sidlerstrasse 5, 3012 Berne, Switzerland, (zoltan@math-stat.unibe.ch)
*Equivariant Contactomorphisms
of Circular Surfaces,* pp. 259-266.

ABSTRACT. We construct equivariant contactomorphisms
from the 3-sphere onto theboundary of a strictly pseudoconvex circular domain by
lifting of symplectomorphisms. This method gives a simple proof of a result of
Epstein concerning the imbeddability of equivariant CR structures. Also a result
of Semmes on the existence of Riemann maps onto circular domains folows. An
example of a strictly pseudoconvex circular domain is constructed with the
property that no equivariant contactomorphism minimizes the Koranyi-Reimann
quasiconformal distortion.

**S. García-Ferreira,** Instituto de Matematicas, Ciudad Universitaria
(UNAM), 04510, D.F., Mexico, **S. Romaguera,** Escuela de Caminos, Depto. de
Matematica Aplicada, Universidad Politecnica de Valencia, 46071 Valencia, Spain
and **M. Sanchis, ** Departament de Matematiques, Universitat Jaume I, Campus
de Riu Sec s/n, 12071, Castello, Spain (sanchis@mat.uji.es).
*Bounded Subsets and
Grothendieck's Theorem for Bispaces, *pp. 267-283.

ABSTRACT.
Several kinds of bounded subsets in a bispace are studied. In particular, both
the classical Hewitt's characterizations of pseudocompactness and others
well-known characterizations of these spaces due to Glicksberg and Colmez are
generalized and extended. We apply our results to obtain a characterization of
those T_{0}topological spaces for which every lower semicontinuous
function is bounded and to study several interesting quasi-pseudometric spaces
which appear in Theorical Computer Science. Finally, we give a generalization
for bounded subsets of Grothendieck's Theorem in the setting of bispaces.

**Kazuo Tomoyasu, **Institute of Mathematics University of Tsukuba,
Tsukuba-shi Ibaraki 305-8571, Japan (tomoyasu@math.tsukuba.ac.jp).
*The product of two one-point
compactifications is an ESH-compactification,* pp. 285-296.

ABSTRACT. Let X and Y be non-compact locally compact
spaces. J.L. Blasco showed that if X is pseudocompact, then the product of two
one-point compactifications is not a weakly singular compactification of the
product of X and Y. A. Caterino, G.D. Faulkner and M.C. Vipera posed the
following problem: Are all compactifications of a locally compact space
ESH-compactifications? Here it is known that every weakly singular
compactification is an ESH-compactification. Therefore, the question of whether
the product of two one-point compactifications is an ESH-compactification arises
naturally. In this paper, we give an affirmative answer for the above question.

**Huaipeng Chen, **Institute of Mathematics, University of Tsukuba,
Tsukuba-shi Ibaraki, 305 Japan (hpchen@math.tsukuba.ac.jp).
*Weak Neighborhoods and
Michael-Nagami's Question, *pp. 297-309.

ABSTRACT. In this paper, we prove several propositions
about weak neighborhoods, show a theorem which positively answers a question of
Y. Tanaka and construct a counterexample which gives a negative answer to
Michael-Nagami's question.

**M. G. Charalambous, ** Department of Mathematics,University of the
Aegean, Karlovassi 83 200 Samos, Greece (mcha@aegean.gr).
*Notes on Paracompact
Coreflections of Frames, *pp. 311-326.

ABSTRACT. We present several common characterizations
of the paracompact, the Lindelöf and the compact coreflections of kappa-frames.
We start with an approach to the three coreflections through direct limits and
subsequently proceed to characterize them, inter alia, as intersections of
certain quotients and in terms of the possibility of lifting kappa-maps with
domain a fixed topology. We deduce some dimension-theoretic results, such as a
factorization theorem for kappa-maps with Lindelöf domain.

**Yoshikazu Yasui, ** Department of Mathematics, Osaka Kyoiku University,
Asahigaoka, Kashiwara, Osaka 582, Japan, (yasui@cc.osaka-kyoiku.ac.jp) and **
Zhi-Min Gao, ** Department of Mathematics, Shantou University, Shantou 515063
Guang-Dong, China (zmgao@mailserv.stu.edu.cn).
*Spaces in Countable Web, *
pp. 327-335.

ABSTRACT. We will introduce two new covering
properties which are called to be in countable web and in countable discrete
web, respectively. As is known, almost covering properties are hereditary with
respect to a closed subspace, but the above properties will not be hereditary.
So in this paper, we shall discuss the basic properties of the above concepts
and discuss the relations among another covering properties.

**Alexander J. Izzo, ** Department of Mathematics and Statistics, Bowling
Green State University, Bowling Green, OH 43403 (aizzo@math.bgsu.edu).
*Nowhere Locally Uniformly
Continuous Functions are Everywhere, * pp. 337-340.

ABSTRACT. It is shown that if X is a nowhere locally
compact metric space, then there is a bounded continuous real-valued function on
X that is nowhere locally uniformly continuous, and that in fact, the collection
of such functions contains a dense G_{delta} in the space of bounded
continuous real-valued functions under the supremum norm.

**Abbott, Stephen D., **Middlebury College,Middlebury, VT 05753,
(abbott@jaguar.middlebury.edu), and **Hanson, Bruce, ** St. Olaf College,
Northfield, MN 55057, (hansonb@stolaf.edu).
*A General Prediction Theorem
for Unbounded Weights,
*pp. 341-350.

ABSTRACT. We solve an extremal problem for a
non-negative, unbounded operator in Hilbert space. Our result generalizes a
previous result by the first author and contains the classical infimum theorems
of Kolmogorov and Szego. A formula for the weighted distance between a
reproducing kernel function and its complement in H_{2}2is also derived.

**Arnaud Simard, **Equipe de Mathematiques de Besancon, Universite de
Franche-Comte 25030 Besancon cedex , France (simard@vega.univ-fcomte.fr).
*Factorization of Sectorial
Operators with Bounded H ^{infty}-Functional Calculus, *pp.
351-370.

ABSTRACT. It is already known that given a bounded operator A on some Lp space, we can build (thanks to a change of density) a bounded operator B on the corresponding space L2 such that A and B are consistent. In this paper we consider an analogous property for sectorial operators. Namely we prove that under the assumption of bounded functional calculus, a sectorial operator on Lp, acts after a change of density as an operator on L2 which admits a bounded functional calculus. We also treat the case of sectorial operators on Banach lattices under suitable assumptions.

**Espínola, Rafael** and ** López, Genaro, **
Unversity of Seville, 41080-Sevilla, Spain (espinola@cica.es, glopez@cica.es).
*On a result of W. A. Kirk, *
pp. 371-378.

ABSTRACT.
Hyperconvex metric spaces were introduced by Aronszajn and Panitchpakdi in 1956
as those metric spaces which satisfy the 2-intersection property. In the present
work we study noncompact problems on location of fixed point for mappings
between hyperconvex spaces. These results have their motivation in a recent
paper of W. A. Kirk (*Continuous mappings in compact hyperconvex metric spaces*,
Numer. Funct. Anal. Optim.**17** (1996), 599-603).

We look mainly for noncompact extensions of the results given by W. A. Kirk,
using the concept of hyperconvex hull of Isbell. Some new properties on
hyperconvex metric spaces and the hyperconvex hull of Isbell are also
introduced.

**Michael D. O'Neill, ** Department of Mathematics, University of Texas at El
Paso , El Paso, TX 79968 (michael@math.utep.edu).
* Random walk and Boundary
Behavior of Functions in the Disk, *pp. 379-386.

ABSTRACT.
Simple martingale proofs of some results of Rohde (from J. London Math. Soc. 48
, 1993 and from Trans. Amer. Math. Soc. 348, 1996) on the boundary behavior of
Bloch functions are presented, making clear their connection with random walk in
the plane.

**Jiahong Wu, ** Department of Mathematics, University of Texas at Austin,
Austin, TX 78712-1082 (jiahong@math.utexas.edu).
*The Complex Ginzburg-Landau
Equation with Data in Sobolev Spaces of Negative Indices, *pp. 387-397.

ABSTRACT.The local well-posedness is established for
the complex Ginzburg-Landau equation with data in Sobolev spaces of negative
indices. The results presented in this article reduce to H^{r} theory
previously obtained by other authors.