Titles and Abstracts
Vol. 25, No. 2, 1999

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 {X0, ... ,Xn-1} of the topological space G by closed connected subsets (indexed over the cyclic group Zn) 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 Xa and Xb 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 T0topological 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 Gdelta 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 H22is 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 Hinfty-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 Hr theory previously obtained by other authors.