*Editors*: G. Auchmuty (Houston), H. Brezis (Paris), S.S. Chern
(Berkeley), J. Damon (Chapel Hill), L.C. Evans (Berkeley), R.M. Hardt (Rice),
J.A. Johnson (Houston), A. Lelek (Houston), J. Nagata (Osaka), B. H. Neumann
(Canberra), V. Paulsen (Houston), G. Pisier (College Station and Paris), R.
Scott (Houston), S.W. Semmes (Rice)
*Managing Editor*: K. Kaiser (Houston)

**Wang, Huaxiong, **University of Haifa, Haifa, 31905, Israel.
*On Characters of
Semirings, *pp.
391-405.

ABSTRACT.
A character of a semiring R is a morphism of semirings from R to the boolean
semiring B. In this paper, we investigate various properties of characters of
semirings. The main result is : If R is a commutative semiring which is not a
ring then there exists a morphism of semirings from R to the boolean semiring.
Applying this result, we prove that the Hilbert basis theorem fails in the
semirings which are not the rings; the Krull dimension of the polynomial
semiring R[t] is infinite for any commutative semiring R which is not a ring.
Rational series with coefficients in a commutative semiring are also studied,
and we prove that if R is a quasi-positive commutative semiring then the support
of any rational series with coefficients in R is a rational language.

**Mo, Xiaokang, **University of Kansas, Lawrence, KS 66045
(mo@math.ukans.edu).
*Bianchi Permutability by
Moving Frames,
*pp. 407-420.

ABSTRACT.
We present a new approach to the Bianchi permutability of surface
transformations by moving frames. We give a simple proof to the classical
permutability theorem of Bianchi for W-congruence. We then prove a new
permutability theorem for Chern-Terng's affine Backlund transformation. Our
method is based on Frobenius theorem and some algebraic symmetries of Cartan's
structure equations.

**Paternain, Gabriel P., **Centro de Matematica, Facultad de Ciencias,
Eduardo Acevedo 1139, Montevideo CP 11200, Uruguay
(gabriel@cmat.edu.uy).
*Finsler Structures
on Surfaces With Negative Euler Characteristic*,
pp. 421-426.

ABSTRACT.
We show that real analytic Landsberg structures and real analytic K-basic
structures on closed oriented surfaces of negative Euler characteristic must be
Riemannian.

**Boeckx, E., **Katholieke Universiteit Leuven, Leuven, Belgium
(Eric.Boeckx@wis.kuleuven.ac.be), and **Vanhecke, L., **Katholieke
Universiteit Leuven, Leuven, Belgium
(Lieven.Vanhecke@wis.kuleuven.ac.be).
*Characteristic
Reflections on Unit Tangent Sphere Bundles,
*pp. 427-448.

ABSTRACT.
In Sasakian geometry a locally phi-symmetric space is defined by a certain
curvature condition, which has several equivalent geometric interpretations. In
this paper we extend the notion of a locally phi-symmetric space to the broader
class of contact metric manifolds using reflections with respect to
characteristic curves. We show that the only phi-symmetric unit tangent sphere
bundles are those of spaces of constant curvature. For this class of spaces we
study some further geometric properties relating to the Ricci curvature tensor
and to Jacobi operators.

**Guaschi, John, **Laboratoire de Mathematiques Emile Picard, Universite Paul
Sabatier, 31062 Toulouse Cedex 4, France, and **Llibre, Jaume, **Universitat
Autonoma de Barcelona, 08193 Bellaterra (Barcelona), Spain.
*Orders and Periods of
Algebraically-Finite Surface Maps,
*pp. 449-483.

ABSTRACT.
Let M be a compact, connected, orientable surface of genus g without boundary,
and let map f from M to M be a continuous map such that all the eigenvalues of
the induced action on rational homology are roots of unity. We present an
algorithm to compute as a function of g: firstly, all the algebraic orders;
secondly, the potential periods; and thirdly, the potential least periods. We
apply the algorithm up to genus 5 for degree -1 and up to genus 3 for degree +1.
Also, we give results on the algebraic orders and potential periods for
arbitrary genus. For instance, if g>2 then the map has a period less than or
equal to 2g-2. Moreover, for degree -1, the algebraic orders are always even,
and if g>1 is even then the set of algebraic orders for the surfaces of genus g
and g+1 are equal. We improve some of these results in the particular case that
f is a finite order homeomorphism.

**Loveland, L. D., **Utah State University, Logan, UT 84322-3900
(ldl@sunfs.math.use.edu), and **Loveland, S. M., **University of Alaska,
Anchorage, AK 99508
(afsml@UAA.Alaska.edu).
*Planar Sets That
Lines Hit Twice,
* pp. 485-497.

ABSTRACT.
This paper shows the relationship between two different two-point intersection
properties of sets in the plane - sets with the double midset property and sets
with a generalized Mazurkiewicz property. Many unsolved problems are stated
along with proving that path connected sets with the generalized Mazurkiewicz
property are simple closed curves. The paper closes with a proof that the simple
analogue of a Mazurkiewicz set in three-space does not exist and with results
related to such sets in three space.

**Cole, Brian J., **Brown University, Providence, RI 02912
(Brian_Cole@brown.edu), and **Wermer,
John, **Brown University, Providence, RI 02912
(John_Wermer@brown.edu).
*Boundaries of
Interpolation Bodies,
*pp. 499-527.

ABSTRACT.
Let (a_{j},b_{j}), j in [1,n], be n points in the open unit
bidisk in C^{2}. Let D be the interpolation body consisting of all
points w = (w_{1},..., w_{n}) in C^{n} such that there
exists a bounded analytic function F on the bidisk with infinity norm of F less
than or equal to 1 and F(a_{j},b_{j}) = w_{j}. We show
that there exists a real non-constant polynomial on C^{n} = R^{2n}
which vanishes on bd(D), and that bd(D) has a dense, relatively open subset
which is a real analytic manifold. In the proofs we use a result on contractive
representations of the bidisk algebra by operators on n-dimensional Hilbert
space as well as the Tarski-Seidenberg theorem on semi-algebraic sets.

**Octavio, Alfredo, **IVIC, Caracas, Venezuela
(aoctavio@ivic.ivic.ve),
**Kosiek, Marek, **Uniwersytet Jagiellonski, Krakow, Poland
(mko@@im.uj.edu.pl).
*Representations of H ^{infty}(D^{N})
and Absolute Continuity for N-tuples of Contractions, *
pp. 529-537.

ABSTRACT. In this paper we study a condition, introduced by Apostol, that implies the existence of a functional calculus for N-tuples of operators. We show that this condition can be written as the sequence of powers of each member of the N-tuple converging to 0 in a certain topology. We prove that if the N-tuple satisfies von Neumann's inequality, then this condition is equivalent to the (joint) absolute continuity of the N-tuple.

**Alpay, D., **Ben-Gurion University of the Negev, POB 653, 84105 Beer-Sheva,
Israel,
**Bolotnikov, V., **
and **Loubaton, Ph., **Unite de Formation E.E.A., Universite de
Marne-la-Vallee, 93166 Noisy-le-Grand Cedex, France.
*On Interpolation for
Hardy Functions in a Certain Class of Domains Under Moment Type Constraints, *
pp. 539-571.

ABSTRACT.
We use reproducing kernel methods to characterize H_{2} functions
satisfying certain second order conditions. As an application we get a
description of all solutions of the left--sided residue interpolation problem
under the second order constraints.

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