Electronic Edition Vol. 24, No. 1, 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)


Bell, Howard E. Department of Mathematics, Brock University, St. Catharines, Ontario, Canada L2S 3A1 (hbell@spartan.ac.brocku.ca) and Abraham A. Klein School of Mathematical Sciences, Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, Israel 69978 (aaklein@math.tau.ac.il)
Ideals Contained in Subrings, pp.1-8.
ABSTRACT. Lewin has proved that if S is a ring and R a subring of finite index in S , then R contains an ideal of S which is also of finite index; and Feigelstock has recently shown that other classes of subrings must contain ideals belonging to the same class. We provide some extensions of these results, and apply them to prime rings. In the final section, we investigate finiteness of rings having only finitely many n -th powers, where n s a fixed positive integer that is greater or equal to 2.

Gilmer, Robert, Department of Mathematics, Florida State University, Tallahassee, FL 32306-4510 (gilmer@math.fsu.edu) and Heinzer, William, Department of Mathematics, Purdue University, W. Lafayette, IN 47907-1395 (heinzer@math.purdue.edu).
Prime Ideals of Finite Height in Polynomials Rings, pp. 9-20.
ABSTRACT. We investigate the structure of prime ideals of finite height in polynomial extension rings of a commutative unitary ring R . We consider the question of finite generation of such prime ideals. The valuative dimension of prime ideals of R plays an important role in our considerations. If X is an infinite set of indeterminates over R , we prove that every prime ideal of R[X] of finite height is finitely generated if and only if each P in Spec(R) of finite valuative dimension is finitely generated and for each such P every finitely generated extension domain of R/P is finitely presented. We prove that an integrally closed domain D with the property that every prime ideal of finite height of D[X] is finitely generated is a Pr\"ufer v-multiplication domain, and that if D also satisfies d.c.c. on prime ideals, then D is a Krull domain in which each height-one prime ideal is finitely generated.

Charatonik J.J., Charatonik W. J. , Miklos, S. , Mathematical Institute, University of Wroclaw pl. Grunwaldzki 2/4, 50-384 Wroclaw, Poland (J. J. Charatonik: jjc@hera.math.uni.wroc.pl; W. J. Charatonik: wjcharat@hera.math.uni.wroc.pl; S. Miklos: miklos@hera.math.uni.wroc.pl) and Spyrou, P. Department of Mathematics, University of Athens, Panepistemiopolis, Athens 157 84, Greece, (pspirou@atlas.uoa.ariadne-t.gr).
On Open mappings of Locally Connected Continua onto Arcs, pp. 21-44.
ABSTRACT. Several structural characterizations of locally connected continua that admit an open mapping onto an arc are obtained.

Nikiel, J.,American University of Beirut, Beirut, Lebanon (nikiel@layla.aub.ac.lb), Purisch, S., Barry University, Miami Shores, FL 33161-6695 (purisch@buvax.barry.edu) Treybig, L.B., Texas A&M University, College Station, TX 77843-3368 (treybig@math.tamu.edu).
Separable zero-dimensional spaces which are continuous images of ordered compacta, pp. 45-56.
ABSTRACT. A structure theorem is proved about separable zero-dimensional spaces which are continuous images of ordered compacta and it is shown that not all spaces in this class are orderable themselves.

Fu, Joseph H.G. , University of Georgia Mathematics Department Athens, GA 30602 (fu@math.uga.edu).
On the Total Curvature of Parallel Families of Convex Sets in 3-dimensional Riemannian Manifolds with Nonnegative Sectional Curvature, pp. 57-64.

Wu, Hongyou, Department of Mathematics, Northern Illinois University, DeKalb, Il 60115, USA (wu@math.niu.edu).
Foliations on Constant Curvature Surfaces Foliations on Constant Curvature Surfaces and Nonlinear Partial Differential Equations, pp. 65-84

Coman, D., University of Notre Dame, Notre Dame IN 46556-5683 (Dan.F.Coman.2@nd.edu) and Dabija, M., University of Michigan, Ann Arbor MI 48109-1109 (mardab@math.lsa.umich.edu).
On the dynamics of some diffeomorphisms of C2 near parabolic fixed points, pp. 85-96.
ABSTRACT. In this paper we consider diffeomorphisms of C2 of the special form F(z,w)=(w,-z+2G(w)), where G is holomorphic near 0 and G(0)=0, G'(0)=1. For such maps F the origin is a parabolic fixed point. Under certain hypotheses on G we prove the existence of invariant complex curves under F (and F-1 respectively), on which the forward (and backward) iterates of F converge to the origin. These invariant curves are "one sided": they are given as graphs of holomorphic functions defined on a domain in C containing 0 on its boundary.

Adrian Ionesco, Department of Mathematics and Computer Science, Texas Lutheran University, Seguin, TX 78155.
A Functional Calculus for Pairs of Commuting Polynomially Bounded Operators, pp. 97-104.
ABSTRACT. A functional calculus valid for the class of absolutely continuous pairs of commuting polynomially bounded operators is defined.

Androulakis, George, University of Missouri, Cazacu, Constantin D., University of Missouri, and Kalton, Nigel J., University of Missouri, Columbia, MO 65211 ( nigel@math.missouri.edu ).
Twisted Sums, Fenchel-Orlicz Spaces and Property (M) , pp. 105-126.
ABSTRACT. We study certain twisted sums of Orlicz sequence spaces with non-trivial type with themselves which can be viewed as Fenchel-Orlicz spaces over the real plane. We then show that a large class of Fenchel-Orlicz spaces over finite dimensional spaces can be renormed to have property (M). In particular this gives a new construction of certain twisted Hilbert spaces and shows they have property (M), after an appropriate renorming.

Fugarolas, M. A. , Universidad de Santiago de Compostela, Facultad de Matematicas, Departamento de Analisis matematico, Campus Universitario Sur, 15706-Santiago de Compostela, Spain, (mafuga@zmat.usc.es).
Absolutely Summing Operators On Besov Spaces, pp. 127-136.
ABSTRACT. Let In be the identity operator on an n-dimensional Banach space En. In this paper we establish upper estimates, in terms of the cotype of En, for some ideal norms of In. This results are applied to study absolutely summing operators on Besov spaces.

Van Neerven, J.M.A.M., Alfred P. Sloan Laboratory of Mathematics, California Institute of Technology, CA 91125 Pasadena, U.S.A. (J.vanNeerven@twi.tudelft.nl) and Straub, B. Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, U.S.A. (bernd@maths.unsw.edu.au).
On the existence and growth of mild solutions of the abstract Cauchy problem for operators with polynomially bounded resolvent, pp. 137-172.

Kim, Sang Dong Department of Mathematics, Teachers College, Kyungpook National University, Taegu, Korea, (skim@sobolev.kyungpook.ac.kr) and Shin, Byeong Chun, Basic Science Research Institution, Ajou University, Suwon, Korea, (cshin@gauss.kyungpook.ac.kr).
On the exponential decay of C1 cubic Lagrange splines on non-uniform meshes and for non-uniform data points, pp. 173-183.
ABSTRACT. The space of C1 cubic splines on a given arbitrary mesh for [0,1] provides a unique interpolant to arbitrary data given at 0 and 1 and at two arbitrary points in the interior of each mesh interval. Sufficient conditions for the exponential decay of the corresponding Lagrange functions are given, in terms of the distribution of the data points.

Return to HJM