Electronic Edition Vol. 24, No. 4, 1998

Editors: G. Auchmuty (Houston), H. Brezis (Paris), S. S. Chern (Berkeley), J. Damon (Chapel Hill), K. Davidson (Waterloo), L. C. Evans (Berkeley), 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)


R. Santos, Universidade de Lisboa, Faculdade de Ciências, Rua Ernesto de Vasconcelos Bloco C1 , 3 Piso-1700 Pisboa, Portugal (rsantos@fc.ul.pt)
Involutive Stone algebras and Regular alpha-De Morgan Algebras, pp.571-592.
ABSTRACT. A piggyback duality and a translation process between this one and a Priestley duality for each subvariety of involutive Stone algebras and regular alpha-De Morgan algebras is presented. As a consequence we describe free algebras and the prime spectrum of each subvariety.

Weidong Gao, Department of Computer Science and Technology, University of Petroleum, Beijing, Shuiku Road, Changping, Beijing 102200, P.R. China (wdgao@mail.bjpeu.edu.cn) and Alfred Geroldinger, Institut für Mathematik , Karl-Franzens Universität, Heinrichstrasse 36, 9010 Graz, Austria
Half-Factorial Domains and Half-Factorial Subsets of Abelian Groups, pp. 593-611.

Forian Kainrath, Institut für Mathematik , Karl-Franzens Universität, Heinrichstrasse 36, A-8010 Graz, Austria (florian.kainrath@funigraz.ac.at)
A Note on Quotients Formed by Unit Groups of Semilocal Rings , pp. 613-618.
ABSTRACT. For a commutative ring R let U(R) be its unit group. Let S/R be an extension of noetherian semilocal rings such that S is a finitely generated R-module. It is shown that U(S)/U(R) is finite if and only if U(S)/U(R) is finitely generated if and only if S/R is finite.

Yakov Berkovich, Department of Mathematics, University of Haifa, Mount Carmel, Haifa 31905, Israel, and Lev Kazarin, Department of Mathematics, Yaroslavl State university, Yaroslavl 150000, Russia.
Finite Groups in Which the Zeros of Every Nonlinear Irreducible Character are Conjugate Modulo Its Kernel , pp. 619-630.
ABSTRACT. In this note we classify the groups G in which the zeros of every nonlinear irreducible character chi are conjugate in G/ker(chi). Our proof depends on the classification of finite simple groups. We prove a related result for monolithic characters. Some open questions are posed and discussed.

Yakov Berkovich, Department of Mathematics, University of Haifa, Mount Carmel, Haifa 31905, Israel.
Subgroups with the Character Restriction Property and Related Topics, pp. 631-638.

Yakov Berkovich, Department of Mathematics, University of Haifa, Mount Carmel, Haifa 31905, Israel.
Frattini Like Properties of Kernels of Some Characters, pp. 639-647.
ABSTRACT. Let K be minimal among the kernels of the irreducible characters of a finite group G, and let Q/K be a normal subgroup of G/K. Then Q is pi-closed, where pi is a set of primes, if and only if Q/K is. This result improves Theorem 12.24 in I.M. Isaacs, Characters of Finite Groups, Academic Press, New York, 1976. In particular, G is pi-closed if and only if G/K is. The analog of the result above holds for minimal quasikernels too. Some related results are proved.

Jaigyoung Choe, Department of Mathematics, Seoul National University, Seoul, 151-742 (choe@math.snu.ac.kr).
The Isoenergy Inequality for a Harmonic Map, pp. 649-654.
ABSTRACT. Given a harmonic map u from a unit ball B in an n-dimensional Euclidean space to a nonpositively curved Riemannian manifold, we prove that n-1 times the energy of u cannot be larger than the energy of u restricted on the boundary of B. This inequality, called the isoenergy inequality, is sharp.

Chuan Liu, Department of Mathematics, Guangxi University, Nanning, Guangxi, P.R. China and Yoshio Tanaka, Department of Mathematics, Tokyo Gakugei University, Koganei, Tokyo 184, Japan
Star-Countable k-Networks, Compact-Countable k-Networks, and Related Results, pp. 655-670.
ABSTRACT. In the theory of generalized metric spaces, the notion of k-networks has played an important role. Every locally separable metric space or CW-complex, more generally, every space dominated by locally separable metric spaces has a star-countable k-network. Every Lanev space, as well as, every space dominated by Lasnev spaces has a sigma-compact-finite k-network. We recall that every space has a compact-countable k-network if it has a star-countable k-network, a sigma-hereditarily closure preserving k-network, or a sigma-compact-finite k-network. We investigate around spaces with a star-countable k-network, or a compact-countable k-network.

Hisao Kato, Institute of Mathematics, University of Tsukuba, Ibaraki 305, Japan
Attractors in Euclidean Spaces and Shift Maps on Polyhedra, pp. 671-680.

Jiling Cao, Maximilian Ganster and Ivan ReillyDepartment of Mathematics, The University of Auckland, Private Bag 92019, Auckland 1, New Zealand
Submaximality, Extremal Disconnectedness and Generalized Closed Sets, pp. 681-688.
ABSTRACT. In this paper, we continue the study of generalized closed sets in a topologicalspace. In particular, we study the question when some classes of generalized closed sets coincide. A new class of spaces, the class of sg-submaximal spaces, is also introduced. Characterizations of extremally disconnected spaces and sg-submaximal spaces are established via various kinds of generalized closed sets.

Douglas D. Mooney, The Center for Healthcare Industry Performance Studies, 1550 Old Henderson Road, Suite S277, Columbus, Ohio 43220 (dmooney@chipsonline.com)
On the Equivalence of the Fomin Extension and the Banaschewski-Fomin- Sanin Extension, pp. 689-697.
ABSTRACT. In 1947, Katêtov asked for necessary and sufficient conditions on a space X so that its Fomin extension sigma X and its Banaschewski-Fomin-Sanin extension mu( X) are equivalent. This question was raised again by Tikoo in 1985 in his study of the Banaschewski-Fomin- Sanin extension. In this paper we present an answer to this question and look at several examples related to it. Prime open filters and a variant of regularly nowhere dense sets are used as tools in obtaining these results.

Peter Semrl, Institute of Mathematics, Physics, and Mechanics, Jadranska 19, 1000 Ljubljana, Slovenia (peter.semrl@imfm.uni-lj.si.)
Hyers-Ulam Stability of Isometries, pp. 699-705.
ABSTRACT. Let X and Y be real Banach spaces. The maximal possible distance of a surjective approximate isometry from X onto Y to the set of all surjective approximate isometries from X onto Y depends on the Jung constant of X.

Alexander P. Schuster, Department of Mathematics, Washington University, St. Louis, MO 63130-1693 (aschust@math.wustl.edu)
The homogeneous approximation property in the Bergman space, pp. 707-722.
ABSTRACT. It is shown that sets of sampling for the Bergman space A2 have the ``homogeneous approximation property'' (HAP) and that sets with this property are sampling for A2+epsilon. In addition, previous results concerning the boundary behaviour of sampling sets are improved.

Cho, Hong Rae, Department of Mathematics Education, Andong National University, Andong 760-749, Korea (chohr@anu.andong.ac.kr).
Some Lipschitz Regularity for Integral Kernels on Subvarieties of Pseudoconvex Domains in C2, pp. 723-733
ABSTRACT. Let D be a smoothly bounded pseudoconvex domain in C2. Let M be a one-dimensional subvariety of D which has no singularities on bM and intersects bD transversally. If bM consists of the points of finite type, then we can construct an integral kernel CM for M which satisfies the reproducing property of holomorphic functions f on M from their boundary values. Furthermore, we get a Lipschitz estimate of the operator induced by the integral kernel, which depends on the type of the boundary bM.

Q-Heung Choi,Department of Mathematics, Inha University, Incheon 402-751, Korea and Tacksun Jung Department of Mathematics, Kunsan National University, Kunsan 573-701, Korea.
A Fourth Order Nonlinear Elliptic Equation with Jumping Nonlinearity, pp. 735-756.
ABSTRACT. We investigate the existence of solutions of the fourth order nonlinear elliptic boundary value problem under Dirichlet boundary condition in a bounded open subset of an n-dimensional space with smooth boundary and the nonlinearity crossing eigenvalues of the fourth order elliptic operator. We also investigate a relation between multiplicity of solutions and source terms of the equation with the nonlinearity crossing an eigenvalue.

Lang, W. Christopher, Indiana University Southeast, New Albany, Indiana 47150 clang@ius.indiana.edu .
Addendum : Wavelet Analysis on the Cantor Dyadic Group , p. 757
Pictures that were missing in Vol. 24, No. 3, 1998

Yoshio Agaoka, Department of Mathematics, Faculty of Integrated Arts & Sciences, Hiroshima University, Higashi-Hiroshima, 739-8521, Japan (agaoka@mis.hiroshima-u.ac.jp).
Errata (see Vol. 24(3)): A New Example of Higher Order Almost Flat Affine Connections on the Three-Dimensional Sphere, p. 759
Corrections of the article in Vol. 24, No. 3, 1998