*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 Z_{2}
x Z_{2} x S_{4}, 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
**
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 {E_{r}(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 Frölicher for complex
manifolds. We prove that {E_{r}(M)} degenerates at the first level. The
relation between {E_{1}(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 S^{1} index (as introduced by Fadell and Rabinowitz).

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