Electronic Edition
Vol. 25, No. 1, 1999

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)


Edgar E. Enochs, Department of Mathematics, University of Kentucky, Lexington, KY 40506-0027 (enochs@ms.uky.edu), Ivo Herzog, Department of Mathematics, The Ohio State University at Lima, Lima, OH 45804 and Sangwon Park, Department of Mathematics, Dong-A University, Pusan Korea
Cyclic Quiver rings and Polycyclic-by-Finite Group Rings, pp.1-13.
ABSTRACT. It is shown that polynomial rings, group rings over polycyclic-by-finite groups, and path rings over cyclic quivers are all Iwanaga-Gorenstein if the coefficient ring is such.

D.D. Anderson, Department of Mathematics, The University of Iowa, Iowa City, IA 52242 (dan-anderson@uiowa.edu) , David F. Anderson, Department of Mathematics, The University of Tennessee, Knoxville, TN 37996 (anderson@novell.math.utk.edu) and Jeanam Park, Department of Mathematics, Inha University, Inchon, Korea, 402-751 (jnpark@inha.ac.kr)
GCD-Sets in Integral Domains, pp. 15-34.
ABSTRACT. Let R be an integral domain. A saturated multiplicative subset S of R different from the unit group of R is a GCD-set if gcd(a,b) exists for each element a and b of S. We study the structure of GCD-sets of R, with emphasis on the case where R is a Dedekind domain. We show that if R is atomic, then each GCD-set is generated by completely irreducible elements, and that if R is a Dedekind domain and x is a nonzero nonunit of R, then some positive power of x has a completely irreducible factor. Let R be a Dedekind domain with torsion realizable pair {Cl(R),A}. If S is a GCD-set of R, then there is a subgroup G(S) of Cl(R) generated by an independent subset of A with Cl(R)/G(S) isomorphic to Cl(T) where T is R localized at S. Conversely, suppose that G is a subgroup of Cl(R) generated by an independent subset of A. Then there is a GCD-set S(G) of R with Cl(R)/G isomorphic to Cl(T) where T is R localized at S(G).

Hiroshi Hosokawa, Department of Mathematics, Tokyo Gakugei University, Japan (hosokawa@u-gakugei.ac.jp).
The Span of Hyperspaces, pp. 35-41.
ABSTRACT. The concept of the span was introduced by A.Lelek in 1964. It assigns a real number for a metric space. The hyperspace C(X) of a continuum X is the continuum consisting of all subcontinua of X with the Hausdorff metric. A Whitney continuum of C(X) is, roughly speaking, a subcontinuum of C(X) with a same size. In this paper, it is proved that if some Whitney continuum has zero span, then every Whitney continuum consisting of subcontinua of X with a larger size has also zero span. Furthermore, we show that the span is a continuous function from the space of all Whitney continua into the real numbers.

Michael Pearson , Department of Mathematics and Statistics Mississippi State University Mississippi State, MS 39762 (pearson@math.msstate.edu)
Extremals for a Class of Convolution Operators, pp. 43-54.
ABSTRACT. Extremals, or maximizers, are shown to exist for a class of convolutionoperators. Tools used include rearrangement inequalities and the duality between inequalities for an operator and its inverse. Applications to and extensions of well known results for fractional integration and Sobolev inequalities are also discussed.

Vicumpriya S. Perera, Department of Mathematics and Computer Science, Kent State University, 4314 Mahoning Avenue N.W., Warren, OH 44483-1998 (pererav@trumbull.kent.edu).
Real Valued Spectral Flow in a Type II_Infinity Factor, pp. 55-66.
ABSTRACT. . In this article, we generalize the integer-valued spectral flow (sf) of Atiyah-Patodi-Singer (APS,1970) to self adjoint Breuer-Fredholm elements in a  type II_Infinity von Neumann algebra factor to obtain a real valued spectral flow.
We then obtain the generalization of the isomorphism (see APS-1970) between the fundamental group of the non-trivial path
component,  Fsa of  self-adjoint Fredholm opeartors Fsa and the integers, Z, to type II_Infinity case via sf.

Takashi Ishii, Department of Mathematical Science, Graduate School of Science and Technology, Niigata University, Niigata. 950-2181, Japan and Keiji Izuchi, Department of Mathematics, Faculty of Science, Niigata University, Niigata 950-2181, Japan (izuchi@math.sc.niigata-u.ac.jp)
Trivial Points in the Maximal Ideal Space of Hinfinity, pp. 67-77.
ABSTRACT. It is proved that there exists a trivial point in the maximal ideal space of Hinfinity, excluding those in the Shilov boundary, which is not contained in the closure of any nontrivial Gleason parts except the open unit disk. This answers Budde's problem.

Alvaro Arias and G. Popescu, Division of Mathematics and Statistics, University of Texas at San Antonio (arias@math.utsa.edu, gpopescu@math.utsa.edu).
Noncommutative Interpolation and Poisson Transforms II, pp. 79-98.

Alvaro Arias, Division of Mathematics and Statistics, University of Texas at San Antonio (arias@math.utsa.edu).
Multipliers and Representations of Noncommutative Disc Algebras, pp. 99-120.

S. R. Foguel, Hebrew University, Jerusalem, Israel.
Weak and Strong Convergence of the Iterates of a Markov Operator, pp. 121-131.
ABSTRACT. We prove that if P is an ergodic Harris operator, then the sequence of iterates Pn is asymptotically periodic. In our approach we also obtain an explicit representation of the linear functionals which describe the asymptotic periodicity of Pn.

Tedi C. Draghici, Department of Mathematics, Northeastern Illinois University, 5500 N. St. Louis Avenue, Chicago IL 60625-4699 (TC-Draghici@neiu.edu).
Almost Kähler 4-manifolds with J-invariant Ricci tensor, pp. 133-145.
ABSTRACT. Almost Kähler structures with J-invariant Ricci tensor arise naturally from variational problems on the set of compatible metrics for a given symplectic form on a compact manifold. It is shown that on a compact 4-manifold, an almost Kähler metric with J-invariant Ricci tensor and non-negative scalar curvature is, in fact, a Kähler metric.

Po-Hsun Hsieh, Department of Mathematics, National Chung Cheng University, Minhsiung, Chiayi 621, Taiwan (phhsieh@math.ccu.edu.tw).
Angles of holomorphy and the almost complex structure in a tangent bundle, pp. 147-155.
ABSTRACT. Suppose M is a Riemannian manifold. Then TM is naturally equipped with an almost Kähler structure (J, A), where J is an almost complex structure and A is a symplectic form. We derive a formula for the angles of holomorphy of 2-dimensional subspaces of the tangent spaces of TM in terms of invariants. We also investigate their change under the multiplication by a real number on TM and under the parallel translation along a curve in TM. The covariant derivative of J plays a crucial role in the latter case, and thus we derive a formula for it.

M. A. Sychev Sobolev Institute of Mathematics, Universitetski prospect 4, 630090, Novosibirsk, Russia (masychev@math.nsc.ru).
Minimizers of variational problems with Euler-Lagrange Equations having Measure-Valued Right-Hand Side, pp. 157-179.
ABSTRACT. We consider Euler-Lagrange equations with measures in the right-hand side. We define minimizers of the integral functional, which can be formally attached to the equation, as limits of minimizers of the functional over M-Lipschits functions with M converging to infinity.
We show that minimizers are always distributional solutions of the equation with certain regularity. Moreover, a minimizer is unique and is an entropy solution if measure does not charge sets of zero p-capacity, where p is growth of the integrand at infinity.

Biao Ou, Department of Mathematics, University of Toledo, Toledo, OH 73606 (bou@math.utoledo.edu).
A Remark on a Singular Integral Equation, pp. 181-184.
ABSTRACT. We have a geometric proof on that certain functions satisfy a singular integral equation.

James C. Alexander, Department of Mathematics, University of Maryland, College Park, MD 20742-4015 (jca10@po.cwru.edu) and Thomas I. Seidman, {Department of Mathematics and Statistics, University of Maryland, Baltimore County Baltimore, MD 21250 (seidman@math.umbc.edu).
Sliding modes in intersecting switching surfaces, II: Hysteresis, pp. 185-211.
ABSTRACT. When a flow, discontinuous across a switching surface, points ``inward'' so one cannot leave, it induces a unique flow within the surface, called the sliding mode. Uniqueness of sliding modes does not obtain in general when several such surfaces intersect, and models must be refined. Following our earlier papers, we investigate the consequences of such refinements. We show that a natural mechanism, to wit hysteresis, which has been extensively investigated for one switching surface, generically leads to a well-defined sliding mode in the intersection of two switching surfaces.