Electronic Edition
Vol. 26, No. 3, 2000

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)


J. Sichler, Department of Mathematics, University of Manitoba, Winnipeg, Manitoba, Canada R3T 2N2 (sichler@mira.cc.umanitoba.ca ) and V. Trnková, Mathematical Institute of Charles University, Sokolovska 83, 186 75 Praha 8, Czech Republic.
Continuous maps of products of metrizable spaces , pp. 417-450.
ABSTRACT. For a collection A of metrizable spaces, let P(A) denote the category formed by all finite products of members of A and all their continuous maps. For collections A and B indexed by the same set, the categories P(A) and P(B) are compared. The results generalize the existence of two metrizable spaces X and Y whose monoids of continuous selfmaps are isomorphic while the categories PX and PY of their finite powers are not.

Mariagrazia Bianchi and Anna Gillio, Department of Mathematics, ``F. Enriques'' University of Milano, Milano, Italy (bianchi@vmimat.mat.unimi.it), (gillio@vmimat.mat.unimi.it) and David Chillag Department of Mathematics, Technion--Israel Institute of Technology, 32000 Haifa, Israel, (chillag@techunix.technion.ac.il).
Finite Groups in which Every Irreducible Character Vanishes on at Most Two Conjugacy Classes. , pp. 451-461.
ABSTRACT. It is known that if G is a finite non-abelian group in which every irreducible character vanishes on at most one conjugacy class, then G is a Frobenius group with a Frobenius complement of order 2 and Frobenius kernel of odd order. In particular G is solvable. This paper studies the class of finite groups G in which every irreducible character vanishes on at most two conjugacy classes. There are such nonsolvable groups. We show that A5 and PSL(2,7) are the only nonsolvabe groups in this class. We also show that each solvable group in this class is either a certain type of a Frobenius group, or is very close to being one.

R.B.J.T. Allenby, Department of Pure Mathematics, University of Leeds, Leeds, LS2 9JT, England (pmt6ra@leeds.ac.uk).
The existence and location of the near Frattini subgroup in Certain Generalized Free Products , pp. 463-468.
ABSTRACT. Let G be the generalized free product of groups A and B with amalgamated subgroup H. We show that, if H is infinite cyclic, then the upper and lower near frattini subgroups are equal and coincide with either the identity subgroup or the largest subgroup of H which is normal in G. In the case of infinitely many cyclic factors we can determine when each of these two cases occurs. Finally we show that, if H satisfies the minimum condition, then the upper and lower near frattini subgroups of G are both in H but that they need not be equal.

D. E. Dobbs, Department of Mathematics, University of Tennessee, Knoxville, TN 37996-1300 (dobbs@math.utk.edu).
A Conductor Theorem, pp. 469-472.
ABSTRACT. It is proved that if one intersects the localizations of a finite-conductor domain at each of the prime ideals in a linearly ordered collection, the result is the localization of the given domain at the union of the given prime ideals. As a consequence, valuation domains are characterized as the quasilocal treed finite-conductor doamins with the QQR-property.

Ayman Badawi, Department of Mathematics, Birzeit University, Box 14, Birzeit, West Bank, via Israel (abring@birzeit.edu).
On Phi -Pseudo-Valuation Rings II , pp. 473--480.
ABSTRACT. A commutative ring R with 1 is called a pseudo-valuation ring (PVR) if for every a, b in R , either a divides b or b divides ac for each nonunit c in R. Also, R is called a phi-pseudo-valuation ring if Nil(R) ( the set of nilpotent elements of R) is a divided prime ideal of R and for every nonnilpotent elements a,b in R, either a divides b in R or b divides ac in R for each nonunit c in R. In this paper, we show that for each positive integer n(possibly infinite) there is a phi-PVR of Krull dimension n that is not a PVR.

Alan Mason, 2316 Wright Circle, Round Rock, TX 78664 (Alanndg@aol.com; Alan_Mason@email.msn.com).
An Application of Stochastic flows to Riemannian Foliations , pp. 481-515.
ABSTRACT. A stochastic flow is constructed on a frame bundle adapted to a Riemannian foliation on a compact manifold. The generator A of the resulting transition semigroup is shown to preserve the basic functions and forms, and there is an essentially unique strictly positive smooth function phi satisfying A*phi = 0. This function is used to perturb the metric, and an application of the ergodic theorem shows that there exists a bundle-like metric for which the basic projection of the mean curvature is basic-harmonic.

Xiaohuan Mo, School of Mathematical Sciences, Peking University, Beijing 100871, Peoples Republic of China (moxh@pku.edu.cn).
New characterizations of Riemannian spaces, pp. 517-526.
ABSTRACT. We show that a Finsler space is Riemannian if and only if its Finsler bundle is minimal, if and only if its all projective circles are Riemannian.

Matija Cencelj and Dusan Repovs, Institute for Mathematics, Physics and Mechanics, University of Ljubljana, P. O. Box 2964, 1001 Ljubljana, Slovenia (matija.cencelj@imfm.uni-lj.si), (dusan.repovs@imfm.uni-lj.si).
On Compacta of Cohomological Dimension One Over Nonabelian Groups, pp. 527-535.
ABSTRACT. We construct a 2-dimensional homogeneous Cannon-\v Stan'ko compactum which fails to be nonabelian. We also introduce a new class of compact metric spaces, called Daverman compacta and we investigate their applications in the theory of cohomological dimension over nonabelian groups.

Takemi Mizokami, Department of Mathematics, Joetsu University of Education Joetsu, Niigata 943, Japan (mizokami@juen.ac.jp) and Norihito Shimane , The joint Graduate School (Ph. D. Program) in Science of School Education, Department of Natural Science Education Yashiro, Kato-gun, Hyogo 673-14, Japan (d96501@juen.ac.jp).
A Lasnev space is LF-netted , pp. 537-542.
ABSTRACT. Junnila and Yajima defined a new class of LF-netted spaces in terms of special networks and asked whether any Lasnev space is Lf-betted. We give the positive answer.

R. Drnovsek, Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia.
Hyperinvariant subspaces for Operator Semigroups with Commutators of Rank at most One, pp. 543-548.
ABSTRACT. Let X be a Banach space of dimension at least 2 and let M be a non-commutative multiplicative semigroup of operators on X such that the rank of ST-TS is at most 1 for all S and T in M. The existence of non-trivial invariant subspaces for such semigroups has been studied very recently. In this paper we show that if M is generated by two operators, then it has a non-trivial hyperinvariant subspace.

Juan Carlos Cabello and Eduardo Nieto, Departamento de Analisis Matematico, Facultad de Ciencias, Universidad de Granada, 18071 Granada (Spain) (cabello@goliat.ugr.es), (enieto@goliat.ugr.es).
On M-type structures and the Fixed Point Property , pp. 549-560.
ABSTRACT. It is well-known that if a Banach space X satisfies the property (M) (resp. (M*)) then X (resp. X*) has the weak (resp. weak*) fixed point property (fpp). The aim of this work is to extend these results (w-fpp,w*-fpp-in fact weak* normal structure-), to a more wide class of Banach spaces. We exhibit several subclasses of Banach spaces that show the significance of this improvement.

Michael Sever, Department of Mathematics, The Hebrew University, Jerusalem, Israel (sever@math.huji.ac.il)
A Variational Formulation of Symmetric Systems of Conservation Laws , pp. 561-573.
ABSTRACT. Systems of conservation laws admitting an entropy obtain from a simple variational principle. This approach leads to a simplified treatment of a symmetry group for such systems, and to a simplified proof of the equivalence of systems obtained by a change of coordinates.
The case of systems which are hyperbolic, in the sense of a convex extensions, is identified with local extremum values of corresponding functionals.

Suzanne Lenhart and Min Liang , Department of Mathematics, University of Tennessee, Knoxville, TN 37996-1300 (lenhart@math.utk.edu ), (mliang@math.utk.edu).
Bilinear Optimal Control for a Wave Equation with Viscous Damping, pp. 575-595.
ABSTRACT. We treat optimal control of a wave equation, in which the control acts as a damping term. The objective functional measures closeness to a desired profile. A characterization of the unique optimal control is given in terms of the solution of the optimality system which is the original damped wave equation coupled with an adjoint equation.

John M. Davis, Department of Mathematics, Baylor University, Waco, TX 76710 USA (John_M_Davis@baylor.edu) (http://www.baylor.edu/~John_M_Davis/), K. Rajendra Prasad, Department of Mathematics, Auburn University, Auburn, AL 36849 USA and Department of Applied Mathematics, Andhra University, Visakhapatnam 530003 INDIA (rajendra92@hotmail.com), and William K. C. Yin, Department of Mathematics, LaGrange College, LaGrange, GA 30240 USA (wyin@lgc.edu).
Nonlinear Eigenvalue Problems Involving Two Classes of Functional Differential Equations , pp. 597-608.
ABSTRACT. We consider an eigenvalue problem consisting of a nonlinear functional differential equation, an initial condition, and either conjugate or right focal boundary conditions. Values of a parameter (eigenvalues) are determined for which this problem has a positive solution. The methods used here extend recent works by allowing for a much broader class of functions on the right hand side and by providing optimal eigenvalue intervals. The usual assumptions of sublinearity or superlinearity are not needed with this approach. We accomplish this with a new, sharper bounding technique on the Green's function of the associated homogeneous problem using "tent functions".