ElectronicEdition Vol. 23, No. 4, 1997

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)


May, Coy L., Towson University, Baltimore, Maryland 21252 (cmay@towson.edu), and Zimmerman, Jay, Towson University, Baltimore, Maryland 21252 (jzimmerman@towson.edu).
The Groups of Symmetric Genus Three, pp. 573-601.
ABSTRACT. A finite group G can be represented as a group of automorphisms of a compact Riemann surface. The symmetric genus sigma(G) is the minimum genus of any Riemann surface on which G acts (possibly reversing orientation). Here we classify the groups of symmetric genus three. There are exactly three such groups; these groups are Z2 x Z2 x S4, PSL(2,7) and PGL(2,7). We use the standard representation of a finite group G as a quotient of a non-euclidean crystallographic group by a Fuchsian surface group. We also employ the correspondence between Riemann surfaces with large automorphism groups and regular maps. The completed classification of the regular maps of genus three is quite useful here.

Lee, Jeh Gwon, Sogang University, Seoul, 121-742, Korea (ljg@ccs.sogang.ac.kr).
Lexicographic Products of Ordered Sets and Lattices, pp. 591-601.
ABSTRACT. In this paper we are concerned with lexicographic products of ordered sets, which are much more complicated than lexicographic sums of ordered sets. We show that the lexicographic product of ranked ordered sets over a finite ordered set is ranked, and we actually compute the height of every element in the lexicographic product of arbitrary ordered sets of finite length over a finite ordered set. Moreover, we give a necessary and sufficient condition for the lexicographic product of (distributive, modular) lattices over a well-founded set to be a (distributive, modular) lattice.

Azarian, Mohammad K. Mathematics Department, University of Evansville, 1800 Lincoln Avenue, Evansville IN 4772
On the Near Frattini Subgroups of Almagamated Free Products with Residual Properties. pp. 603-612.

Azarian, Mohammad K. Mathematics Department, University of Evansville, 1800 Lincoln Avenue, Evansville IN 4772
On the Near Frattini Subgroup of the Generalized Free Product of Finitely Generated Nilpotent Groups. pp. 613-615.

David F. Anderson,The University of Tennessee, Knoxville, TN 37996 (Anderson@novell.math.utk.edu), and J. Park, Inha University, Incheon, Korea (jnpark@math.inha.ac.kr).
Locally Half-Factorial Domains. pp. 617-630.
ABSTRACT. An integral domain R is a half-factorial domain (HFD) if every nonzero nonunit of R is a product of irreducibles and any two factorizations of a nonzero nonunit of R into the product of irreducibles have the same length. In this paper, we study integral domains R such that each proper localization R_S of R in an HFD. We are mainly interested in the case when R is a Dedekind domain.

Chinea, D., Departamento de Matematica Fundamental, Facultad de Matematicas, Universidad de La Laguna, 38200 La Laguna, Tenerife, Canary Islands, Spain (dchinea@ull.es), de Leon, M., Instituto de Matematicas y Fisica Fundamental, Consejo Superior de Investigaciones Cientificas, Serrano 123, 28006 Madrid, SPAIN (mdeleon@pinar1.csic.es), and Marrero, J.C., Departamento de Matematica Fundamental, Facultad de Matematicas, Universidad de La Laguna, 38200 La Laguna, Tenerife, Canary Islands, SPAIN (jcmarrer@ull.es).
Spectral Sequences on Sasakian and Cosymplectic Manifolds, pp. 631-649.
ABSTRACT. In this paper a spectral sequence {Er(M)} associated with the double complex of basic forms of a Sasakian or cosymplectic manifold M is introduced. This spectral sequence can be considered as the version for Sasakian and cosymplectic manifolds of the spectral sequence of Fr&oumllicher for complex manifolds. We prove that {Er(M)} degenerates at the first level. The relation between {E1(M)} and the space of the harmonic complex forms on M is given.

Golightly, George O. Rt. 5 Box 276, Jacksonville, TX 75766
Kernels for Spaces in which Several Operations of Differentiation are Continuous, pp. 651-667 .

Sami Baraket Faculté Des Sciences De Tunis, Départment De Mathématiques, Campus Universitaire 1060, Tunis, Tunisie and Lotfi Lassoued Laboratoire D'Analyse Numérique, Université Pierre et marie Curie, 4 Place Jussieu, 75252 paris Cedex 05
Bifurcation Analysis of Solutions to a Landau-Lifshitz Problem with External Fields. pp. 669-683.

Monica Musso and Donato Passaseo Dipartimento Di Mathematica, UniversitÀ Di Pisa, Via Buonarroti, 2, 5617 Pisa, Italy
On the Number of Positive Solutions of Some Nonlinear Elliptic Problems. pp. 685-708.

Payne, Kevin R., University of Miami, Coral Gables, FL 33124-4250 (paynek@math.miami.edu).
Boundary Geometry and Location of Singularities for Solutions to the Dirichlet Problem for Tricomi Type Equations, pp. 709-731.
ABSTRACT. For a class of mixed type partial differential equations, the effect of locating singularities at the boundary on interior regularity is analyzed for solutions to the Dirichlet problem. Singularities are always present in this problem which is overdetermined with respect to spaces of classical regularity. Necessary and sufficient conditions for interior smoothness are given in terms of microlocal regularity at the boundary. It is shown that interior singularities are detected and generated by singularities at the boundary in the hyperbolic region. A trapped gliding ray phenomenon is demonstrated at parabolic boundary points under a sharp geometric hypothesis which yields a necessary condition for the presence of isolated singularities at the boundary. The techniques involve known propagation of singularities theorems along the generalized bicharacteristic flow together with a global analysis of a relevant Hamiltonian system and a complete microlocal classification of covectors tangent to the boundary.

Almeida, Luis, Centre de Mathematiques et de Leurs Applications, Ecole Normale Superieure de Cachan, 94235 Cachan Cedex, France, and Bethuel, Fabrice, Laboratoire d'Analyse Numerique et EDP, Universite de Paris-Sud, Batiment 425, 91405 Orsay Cedex, France.
Multiplicity Results for the Ginzburg-Landau Equation in Presence of Symmetries, pp. 733-764.
ABSTRACT. We prove various multiplicity results for the Ginzburg-Landau equation, when the boundary data or the manifold on which the equation is defined, verify some equivariant conditions. These results apply in particular to the functional appearing in the theory of superconductivity. Our arguments are based on the use of an S1 index (as introduced by Fadell and Rabinowitz).

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