Salvador Romaguera and Manuel Sanchis.

Locally Compact Topological Groups and Cofinal Completeness.

 Abstract. We prove that a Tychonoff topological group is locally compact if and only if it

is of pointwise countable type and its left uniformity is cofinally complete. From this result

 we derive a characterization of those To paratopological groups (X,T) of pointwise countable

type for which (X, TVT-1 ) is locally compact and we also deduce a characterization of locally

  pseudocompact topological gropus in terms of cofinal completeness. We also characterize the

 Tychonoff toplogical groups of pointwise countable type for which its left uniformity has

 property U. Finally, cofinal completeness of the Hausdorff-Bourbaki uniformity of a topological

 group is studied.

  Vicente Martínez and Antonio Marquina

Computacion of Travelling Wave Solutions of Scalar Conservation Laws With a Stiff Source Term.

  Abstract. In this paper we propose a non-oscillatory numerical technique to compute the

travelling wave solution of scalar conservation laws with a stiff source term. This procedure

is based on the dynamical behavior described by the associated stationary. ODE and it reduces/

avoids numerical errors usually encountered with these problems, i.e., spurious oscillations

and incorrect wave propagation speed. We combine this treatment with either the first order

Lax-Friedrichs scheme or the second order Nessyahu-Tadmor scheme. We have tested several model

problems by LeVeque and Yee for wich the sitffness coefficient can be increased.

 Gual-Arnau and J.J. Nuño-Ballesteros.

A Stereological Version of the Gauss-Bonnet Formula X.

 Vicent Palmer.

Isoperimetric Inequalities for Extrinsic Balls in Minimal Submanifolds and Their Applications

Abstract.-Y. Cheng, P. Li and S.-T. Yau proved comparison theorems for the volume of extrinsic

 balls in minimal submanifolds of space forms. These results had been extended by S. Markvoersen

 for minimal submanifolds of a riemannian manifold with just an upper bound on the sectional

curvature. We have found in this paper an isoperimetric inequality for extrinsic balls in

minimal submanifolds of a riemannian manifold N with sectional curvatures bounded from above

by a nonpositive constant. As a corollary of this result we have obtained an alterantive proof

 of the comparison for the volume of extrinsic balls stated by the preceding authors, but now

we characterize the equality case, when the upper bound for the sectional curvatures of the

ambient manifold is strictly negative. Finally, when the sectional curvaturs of N are bounded

from above for any constant (positive or negative), it is proved that the  -isoperimetric

quotient of the extrinsic balls is bounded from below by the mean curvature of the geodesic

spheres in the m-dimensional real space forms.

  Jorge Mateu and Francisco Montes.

Likelihood Inference for Gibbs Processes in the Analysis of Spatial Point Patterns

Abstract. Several authors have proposed stochastic and non-stochastic approximations to the

maximun likelihood estimate (MLE) for gibbs point processes in domelling spatial point patterns

with pairwise interactions. The approximations are necesary because of the difficulty of

evaluating the normalizing constant. In this paper, we first provide a review of methods

which yield crude appximations to the MLE. We also review methods based on Markov chain Monte

Carlo techiniques ofr which exact MLE has become feasible. We then present a comparative

simulation study of the performance of such methods of estimation based on two simulation

techniques, the Gibbs sampler and the Metropolis-Hastings algorithm, carried out for the

Strauss model.

  Jorge Galindo.

Relations Between LCA Groups with Isomorphic Group Albegras

Abstract. Let G be a LCA group and consider the group algebra L1(G) of all complex-valued

absolutely integrable functions on G. In this papaer we find some invariants that are

necessarily shared by groups with isomorphic group algebras, such as dimension, ranks or

minimal divisible extensions in the case of torsion-free groups. This sheds some light on the

question of finding out to what extent the algebra structure of L1(G) reflects the topological

group structure of G. It is shown in particular that some classes of torsion-free LCA groups

are characterized by their group algebra.

  Jorge Galindo.

Structure and Analysis on Nuclear Groups

Abstract. Closed under the most common operations which contains LCA groups and additive

groups of nuclear locally convex spaces. In this paper we attempt to clarify thNuclear groups

form a class of Abelian topological groups e structure of these groups. This is used to show

that some properties satisfied by LCA groups and nuclear locally convex spaces are also

enjoyed by nuclear groups Bounded subsets, the existence of interpolation sets, transmission

of compactness in passing to the Bohr topology and Pontryagin duality for nuclear groups are

studied.

  Vicente Palmer

Mean Curvature and Volume of Excentric Spheres in Hypersurfaces of Real Space Forms

Abstract. Given a hypersurface Pn-1in a real space form of constant curvature b, Ikn(b), we

have obtained a lower bound for the norm of the mean curvature normal vector field of

extrinsic shperes in Pn-1 in terms of the mean curvature of the geodesic spheres in Ikn(b),

with same radius, and the mean curvature of Pn-1. As a consecuence, and when the mean

curvature of is bounded from Pn-1 above, in absolute value, by a nonnegative constant K, the

quotient between the total mean curvature and the volume of these extrinsic spheres is bounded

 from below by one quantity given in terms of the mean curvature of the geodesic spheres with

same radius in Ikn(b) and the bound k. We have proved too that when the equality with this

bounds holds for the extrinsic spheres with same fixed center and any radius, then Pn-1 is

minimal. When, moreover, we assume that Pn-1 is a convex hypersufrface, then this equality

condition implies that the hypersufrface is totally geodesic in Ikn(b).

  Dr. Vicky McNulty, Dr. Luis M. Cruz Orive, Dr. Neil Roberts, Dr. Colin J. Holmes,
Dr. Ximo Gual-Arnau.

Estimation of Brain Compartment Volume from MR Cavalieri slices

Abstract. Recent theory has been developed to estimate volumen from a systematic sample of

tissue slices of a given thickness, and to predict the corresponding error. Our goal was to

 check the error prediction formulae by resampling, and to determine the minimum number of MRI

 slices required to estimate the volumes of the cerebrum and of the compartments of grey matter

 (GM) and white matter (WM) with prescribed errors. Materials and Methods: Our working data set

 was the average of twenty-seven coregistered 3D spoiled GRASS MRI volume scans of the human

 brain. The data were classified using a fuzzy clustering minimum distance algorithm. We thereby

 obtained an exhaustive stack of 183 coronall slices of 1 mm thickness though the cerebrum.

Empirical resampling was carried aut using the corresponding data vectors, and the theoretical

 error predictors were thereby checked for slice thicknesses of  1, 3, 9 and 27 mm, with a

distances of 45 mm between slices midplanes. Results: Irrespective of slice thickness, for GM

 and WM a minimum of three, five and ten slices provided estimates of the total volume of GM

 and  WM in the cerebrum with CE’s of 10%, 5% and 3% respectively. For the cerebrum a minimum

of two, three and four  slices were required for CE’s of the same precision. ,Conclusion: In

 combination with high signal to noise ratio and enhanced tissue contrast, Cavalieri slices

are convenient for MRI, and they supply unbiased and highly efficient volume estimates of brain

 compartments. Index Terms: Cavalieri slices, Error  prediction formulate, MRI, Stereology,

 Systematic samplig.

  Peter J. Diggle, Jorge Mateu, Helen E. Clough.

A Comparison Between Parametric and Non-parametric Approaches to the Analysis of Replicated

Spatial Point patterns

Abstract.The paper compares non-parametric (design-based) approaches to the analysis of data

in the form of replicated spatial point patterns in two or more experimental group,

and comparing the properties between groups. A non-parametric approach, building on work by

 Diggle, Lange and Benes (1991), summarises each pattern by an estimate of the reduced second

moment measure or K-function (Ripley, 1977) and compares mean K-functions between experimental

 groups using a bootstrap testing procedure. A parametric approach fits particular classes of

parametric  model to the data, uses the model parameter estimates as summaries and tests for

 differences between groups by comparing fits with and without the assumption of common

 parameter values  across groups. The paper discusses how either approach can be implemented

 in the specific context of a single-factor replicated experiment and uses simulations to show

 how the parametric approach can be more efficient when the underlying model assumptions hold,

 bur potentially misleading otherwise.

  Salvador Hernández and Sergio Macario.

Invariance of Compactness for the Bohr topology

Abstract. We define the g-extension of a topological Abelian group G as the set of all

characters on G such that the restriction to every equicontinous subset of G is continuos with

 respect to the pointwise such that its g-extension coincides with its completion. The Bohr

 topology of a topological group (G, r) is the topology that the group inherites spects a

property P if the subsets A of G that satisfy the property P are exactly the same for the Bohr

 topology and for the original topology of the group (Trigos-Arrieta, 1991). All groups here

 are assumed to be Abelian. We prove that every complete-group when endowed with its Borh

topology is a u-space. As a consequence, we obtain that for a complete g-group the properties

 of respecting functionally boundedness, pseudocompactness, countable  compactness and

compactness are all equivalent and characterisation of this property also provided. Finlally,we

 extend a theorem of Rosenthal about existence of the sequences equivalent to the l –basis. We

 prove that for a Cech-complete g-group the property of respect of respecting compactness is

 equivalent to the existence of conveniently placed sequences equivalent to the l-basis.

  Jorge Mateu, Carmen Antolin and Luis Roca.

Spatial Modelling of Post-fire Natural Mediterranean Shrubs in View to Analyze Induced

Abstract. Soil PropertiesEnvironmental heterogeneity has had an important influence on the

development of the spatial statistical methodology. These methods are concerned with modelling

 data as a partial realization of a random spatial process. Within this context, soil

 propertiesan spatial locations of shrubs con be regarded as spatial processes and connections

 between them are scarcely unknown. In this paper we attempt to investigate the relationship

 among spatial locations of shrubs and local soil environment by means of geostatistics and

 point processes. We analyze Ulex parviflours, an important mediterranean shrub species,

particularly after a forest fire. The results confirm that mediterranean shrubs prevent the

 soil from erosion promoting better soil properties.

  J. Martinez Alfaro and C. Chiralt Monleón.

Keplerian Periodic Orbits in the Isosceles Problem

Abstract. The planar isosceles three-body problem where the two symmetric bodies have small

masses is considered as a perturbation of the Kepler Problem.We proves that the circular orbits

 con be continued to saddle orbits of the isosceles problem. This continuation is not possible

 in the elliptic case. Their perturbed orbits tend to a continued circular one or approach a

triple collision. The basic tool used is the study of the Poincaré maps associated to the

 periodic solutions.

  Jorge Mateu and Francisco Montes.

Approximate Maximum Likelihood Estimation for a Spatial Point Pattern

Abstract. Several authors have proposed non-stochastic and non-stochastic approximations to

the maximum likelihood estimate for a spatial point pattern. This approximation is necessary

 because of the difficulty of evaluating the normalising constant. However, it appears to be

 neither a general theory which provides groups for preferring a particular method, nor any

extensive empirical comparisons, In this paper, we review five general methods based on

 approximations to the maximum likelihood estimate which have been proposed in the literature.

 We also present the results of a comparative simulation study developed for the Strauss model.

  X. Gual Arnau.

Total Absolute Curvatures in Spheres Via Integral Geometry

Abstract. We define total absolute curvatures of compact submanifolds immersed in a sphere

from the integral geometry viewpoint. Afterwards we relate these curvatures to the "Gauss"

maps and level functions defined on the submanifold and we obtain the three different

definitions of total absolute curvatures of immersed submanifolds of spheres which appear in

the literature.

  Jorge Mateu and Francisco Montes.

Pseudolikelihood A Inference for Gibss Processes with Exponential Families Through Generalized

 Linear Models

Abstract. Parameter estimation for two-dimensional point pattern data is difficult, because

 most of the available stochastic models have intractable likelihoods, which usually depend on

an unknown scaling factor. However, the problem of the scaling factor can be bypassed using the

 pseudolikelihood estimation method. In this paper we develop and analyse a method to evaluate

the integral term in the pseudolikelihood function for a Gibbs point process using Generalized

 Linear Models. Several techniques based on Voronoi polygons to evaluate the quadrature points

 will be presented. A comparative simulation study is performed using the Strauss process.

  A. Campillo and C. Galindo.

Syzygies of the Graded Algebra Relative to a Valuation

  J. Mateu, J. M. Albert, J.C. Pernias.

Limiting Stochastic Processes to Detect Spatial Structure

Abstract. Spatial point processes that can be obtained from the limit of a suitable sequence

of auto-Poisson stochastic lattice processes can be regarded as a useful tool to analyze

 spatial  patterns exhibiting random and ordered structures. In this paper, we present a

 theoretical  framework and develop some practical issues in terms of a simulation study and

 real-dada analysis.

  Sergey Antonyan and Manuel Sanchis.

Extension of locally pseudocompact group actions

Abstract. It is shown that: (1) any action of an arbitrary product G of locally pseudocompact

topological groups on a metrizable space X can uniquely be extended to an action of the

Dieudonné completion G on a bf—space (in particular, on a first countable space) X can uniquely

 be extended to an action of the Wel completioon G on the Dieudonné completion X of X. As a

consequence, we obtain that, for each pseodocompact topological group G , every G-space with

the bf—property admits an equivariant embedding into a compact Hausdorff G-space. Furthermore,

for each pseudocompact group G, every metrizable G-space has a G-invariant metric compatible

with its topology. We also give a direct construction of such an invariant metric.

  Vicente Martínez.

An artificial compression procedure via flux correction

Abstract. We present a new procedure to sharpen contact discontinuities. Our procedure corrects

 the linear flux to obtain a consistent dynamical behaviour. The equivalence between the

original equation and the modified equation is proved. Numerical examples are provided to test

the performance of the procedure.

  Steen Markvorsen and Vicente Palmer.

Generalized isoperimetric inequalities for extrinsic  balls in minimal submanifolds

Abstract. The volumne of an extrinsic ball in a minimal submanifold has a well defined

lower bound when the ambient manifold has as an upper bound on its sectional curvatures, see

eg. (3) and (10). On the other hand, when this upper bound on the sectional curvatures of the

ambient manifold is non-positive, the second named author has obtained an isoperimetric

 inequality for the extrinsic balls, see (11). From this result follows again the volume

 comparison result alluded to above together with a characterization of the totally geodesic

 submanifolds of hyperbolic space forms. In the present paper we extend this isoperimetric

inequality to hold for extrinsic balls in minimal submanifolds of a riemannian manifold with

sectional curvatures bounded from above by any constant. In parjticular we obtain as a

 corollary the characterization of the totally geodesic submanifolds of spherical space forms.

  B. Campos, J. Martinez Alfaro, P. Vindel.

Bifurcations of Links of Periodic Orbits in  Non-Singular Morse-Smale Systems with a

Rotational Symmetry on S3

Abstract. In this paper we consider a rotational symmetry on a NMS systems analyzing the

restrictions this symmetry imposes on the links defined by the set of its periodic orbits

and to the appearance of local generic codimension one biurcations in the set of NMS flows on

S3. The topological characterization is obtained by writing the involved links in terms o

Wada operations. It is also obtained that symmetry implies that, in general, bifurcations have

to be multiple. On the other hand, we also see that there exists a set of links that cannot be

related to any other by sequences of this kind of bifurcation.

  J. M. Albert, J. Mateu & J. C. Pernías.

Spatial structure analysis using planar indices

Abstract. Spatial planar indices have become a useful tool to analyze patterns of points.

Despite that, no simulation study has been reported in literature in order to analyze the

 behaviour of these quantities under different patterns structures. We present here an

extensive Monte Carlo simultation study focused on two important indices: the Index of

Dispersion and the Index of Cluster Size, usually used to detect lack of homogeneity in

a spatial point model. finally, an application is also presented.

  C. Galindo.

On the structure of the value semigroup of a valuation

  Keming Yu & Jorge Mateu.

Nearest-Neighbour variogram analysis

Abstract. Empirical variogram estimation plays an important role in many areas of spatial

statistics. Traditional estimators do not account for all spatial information and may have

some draw in highly correlated patterns. In this paper we present an alternative distribution-

free estimator based on nearest-neighbour estimation with non-constant smoothing parameter

resulting in a stronger spatial adaptation. The simulation study confirms the goodness-of-fit

of our estimator compared to a nearest-neighbour estimator built with a constant smoothing

parameter. We also re-analyze well known data sets.

  W.W. Comfort, Salvador Hernández and F. Javier Trigos-Arrieta.

Cross sections and homeomorphism classes of abelian groups equipped with the Bohr topology

Abstract. A closed subgroup H of a topological group G is a ccs-subgroup if there is a

continuous crosssection from G/H to G - that is, a continuous function \Gamma such that \pi

o \Gamma = id|G/H (with \pi:G -- G/Hthe natural homomorphism). The symbol G# denotes G with

its Bohr topology, i.e., the topology induced by Hom(G, T). A topological group H is an

absolute ccs-group(#) [resp., an absolute retract(#)] if H is a ccs-subgroup [resp., is a

retract] in every group of the form G# containing H as a (necessarily closed) subgroup. One

then writes H \in ACCS(#)[resp., H \in AR(#)]. Theorem 1. Every ccs-subgroup H of a group of

the form G# is a retract of G# (and G# is homeomorphic to (G/H)# ×H#); hence ACCS(#)

'subset or equal' AR(#). Theorem 2. H# \in ACCS(#) [resp., H# \in AR(#)] iff H# is a

ccs-subgroup of its divisible hull (div(H))# [resp., H# is aretract of (div(H))#]. Theorem 3.

(a) Every cyclic group is in ACCS(#).(b) The classes ACCS(#) and AR(#) are closed under finite

 products. Theorem 4. Not every Abelian group is in ACCS(#). 

Question [ van Douwen, 1990]. Is every Abelian group in AR(#)?

  W.W.Comfort, Salvador Hernández and F. Javier Trigos-Arrieta.

Epi-reflective properties of the Bohr compactification

Abstract. We find explicit intrinsc conditions on a locally compact Abelian group G necessary

and sufficient that G+, the group G int the topology inherited from its Bohr compactification,

is topologically complete; when these are satisfied the gropu G+ is in addition realcompact.

Responding to additional questions of E.K. van Douwen (Topology and Its Applications 34 (1990),

69-91), we show for G discrete Abelian and for X E ((0.1), N, (0.1), R) that every continuous

function from a subgroup of G+ to X extends continuously over G+.

  B. Campos, J. Martínez Alfaro.

Bifurcations of links of periodic orbits in Mathieu systems

Abstract. We consider the nonlinear dissiative Mathieu equation.

We prove that orbits space from infinity, therefore the shpere S3 can be considered as its

phase space. If the parameter is large enough the system is non singular Morse-Smale and its

periodic orbits define a Hopf Lins. As decreases, the system suffers some bifurcations that

we describe geometrically. We relate the bifurcation orbits with periodic orbits continued

from the linear Mathieu equation.

  Steen Markvorsen and Vicente Palmer.

On the isoperimetric rigidity of extrinsic minimal balls.

Abstract.  We consider a minimal submanifold P and a metric R-sphere in an ambient space N.

If the sphere has its center p on P, then it will cut aout a well defined connected component of

P which contains this center point. We call this connected component an extrinsic minimal R-ball

of P. The quotient between the volume of the extrinsic ball and the volume of its boundary, also

known in the literature as the -isoperimetric quotient, has previously been compared with the

corresponding quotient obtained in the space form standard situation, where the minimal submanifold

is totally geodesic and the ambient space has constant curvature, see (Pa), (MP). When the

ambient space N has a non-zero upper bound on its sectional curvatures (this bound being also

the constant curvature of the comparison space), then the isoperimetric comparison inequality

is rigid and optimal in the sense than equality characterizes the totally geodesic submanifolds

in space forms of non-zero curvature. In this paper we address the remaining question of obtaining

a similar rigidity result in the zero curvature case, i.e. for minimal submanifolds of Euclidean

spaces. We show that if the minimal submanifold has dimension larger than 3, if the extrinsic

minimal R-ball gives equality in the corresponding isoperimetric comparison inequality and if P

is not too curved along the boundary of this extrinsic minimal R-ball, then indeed the minimal

submanifold is totally geodesic.

  G. Ayala and A. Simó.

Interaction in spatial point patterns

Abstract. Some correlation measures are proposed for bivariate point processes. Their

estimators and their expressions are considered for the hypotheses of independence and random

labelling. They are compared with the produc intensity and its integrated version, the cross K

function. A randomization test for testing the random labelling hypothesis is proposed, based

on the emperical distribution of the estimators. These functions and the test are applied to

two different bivariate examples where the usual K functions cannot discriminate the type

of dependence: the location of maples and oaks in Lasing Woods (Diggle (7)) and the location

of normal and degenered fibres in a vertical cross-section of a nerve from a rat (Ruiz (20)).

  Steen Markvorsen and Vicente Palmer.

The relative volume growth of minimal submanifolds

Abstract. The volumme growth of certain well-defined subsets of minimal submanifols in

riemannian spaces are compared with the volume growth of balls and spheres in spaces forms

of constant curvature.

  Antonio Beltrán.

The invariant degree graph of a solvable group

Abstract. Let A and G be finite groups and suppose that A acts coprimely on G. We define the

A-invariant degree graph of G to be the graph having as vertices those primes dividing some

A-invariant irreducible character degree of G and with two primes being adjacent if there

exists some A-invariant irreducible character of G whose degree is divisible by both primes. We

prove that when G is solvable then this graph has at most two connected components.

   Juan J. Font and Manuel Sanchis.

A characterization of locally compact spaces with homeomorphic one-point compactifications

Abstract. Let x and Y be locally compact noncompact spaces. For a large class of closed linear

subspaces, A and B, of Co(X,R) and Co (Y, R) resp., we show that there exist basically two types

of diameter-preserving linear bijections "formula" is a homeomorphism which can be extended to

the one-point compactifications of Y and X. All these facts are proved as a consequence of a full

descrption of the extreme points of the closed unit ball of the dual of Co(X) and such subspaces

endowed all with the diameter norm. Finally, we characterize the locally compact spaces with

homeomorphic one-point compactifications as those which admit diameter-preserving linear

bijections like the ones described above.

 Antonio Beltrán and Gabriel Navarro.

Sylow normalizers and brauer character degrees

  Salvador Hernández.

Pontryagin duality for topological abelian groups

Abstract. A topological Abelian group G is Pontryagin reflexive, or P- reflexive for short, if

the natural homomorphism of G to its bidual group is a topological isomorphism. We look at the

question, set by Kaplan in 1948, of characterizing the topological Abelian groups that are

P-reflexive. Thus, we find some conditions on an arbitrary group G that are equivalent to the

P- reflexivity of G and give an example that corrects a wrong statement appearing in previously

existent characterizations of P-reflexive groups.

  W. W. Comfort and Jorge Galindo Pastor.

Pseudocompact topological group refinements ofmaximal weight

Abstract. It is known that a compact metrizable group admits no proper pseudocompact topological

group refinement. The authors show, in contrats, that every (Hausdorff) pseudocompact Abelian

gropu G= (G,T) of uncountable weight a, satisfying any of the following conditions, admits a

pseudocompact group refinement of maximal weight (that is, of weight 2 (g)):

(i) G is compact; (ii) G is torsion-free with "formula"; (iii) (GCH) G is torsion-free.

Remark. (i) answers a question posed by Comfort and Remus (Math. Zeitschrift 215 (1994), 337-346).

AMS Classification Numbers: 22A05, 54H11. Key Words and Pharses: topological group, pseudocompact,

refinement topology, maximal weight.

  A. Cordero, J. Martinez Alfaro, P. Vindel.

Topology of the Two Fixed Centers Problem

Abstract. In this paper we give a complete topological characterization of the Two Fixed

Centers Problem flow. This characterization is based on the link formed by some basic

periodic orbits. The Restricted Circular Three-Body Problem is considered as a perturbation

of the Two Fixed Centers in the case of two primaries with equal masses. The basic periodic

orbits of the integrable problem can be continued in the non integrable one.

  Salvador Romaguera, Manuel Sanchis.

Applications of utility functions defined on quasi-metric spaces

Abstract. A quasi-metric space (X,d) is called sup-separable if (X,ds) is a separable metric

space, where ds(x,y)= max (d(x,y), d(y,x)) for all x,y E X. We characterize those preferences,

defined on a supseparable quasi-metric space, for which there is a semi-Lipschitz utility

function. We deduce from our results that several interesting examples of quasi-metric spaces

which appear in different fields of Theoretical Computer Science admit semi-Lipschitz utility

functions. We also aply our methods to the study of certain kinds of dynamical systems defined

on quasi-metric spaces.

  B. Campos,J. Martinez, P. Vindel.

Phase Portraits and Canonical Regions of NMS Flows on S3

Abstract.  In this paper we obtain a global picture of the flow and construct associated graphs

for the NMS systems on S3 corresponding to Wada operations applied on Hopf links.

  B. Campos, A. Cordero, J. Martínez, P.Vindel.

NMS Flows on Three-Dimensional Manifolds with One Saddle Periodic Orbit

Abstract. In S3 and S2 x S1 the simplest NMS flow is a polar flow formed by an attractive

and a repulsive periodic orbits as limit sets. In this paper we enlarge this known result

showing that the only orientable, simple, compact, 3-dimensional manifolds without boundary

that admit a NMS flow with none or one saddle periodic orbit are S3 and S2 x S1. We also see

that when a fattened round handle is the connected sum of tori the corresponding flow is also

a trivial connected sum of flows.

  A. Beltran

On a Graph Associated to Invariant Conjugacy Classes of Finite Groups

Abstract. Let A and G be finite groups such that A acts by automorphisms on G. We define

the A-invariant conjugacy class graph of G to be the graph having as vertices the noncentral

A-invariant conjugacy classes of G, and two vertices are connected by an edge if their cardinalities

are not coprime. We prove that the number of connected components of this graph is at most 2.

When the graph is connected then its diameter is at most 4. When the graph is disconnected the

diameter of ecah component is at most 2 and in addition, if (/A/,/G/)= 1, then G is solvable.

  A. Beltran, Mª José Felipe

On the Diameter of A p-Regular Conjugacy Class Graph of Finite Groups

Abstract. Let G be a finite p-solvable group. Attach to G the following graph p(G): its vertices

are the non-central conjugacy classes of p-regular elements of G, and two vertices are connected by

an edge if their cardinalities are not coprime. We prove that the number of connected components

of p(G) is at most 2. When p(G) is connnected, then the diameter of the graph is at most 3, and

when p(G) is disconneted, then each of the two components is a complete graph.

  J. Galindo

Dense Pseudocompact Subgroups and Finer Pseudocompact Group Topologies

Abstract. Compact Abelian groups have long been known to have (1) a proper dense pseudocompact

group and (2) a strictly finer pseudocompact group tolology, but the corresponding questions

for arbitrary pseudocompact Abelian groups are still open. The purpose of this paper is to report

on the status of these problems provinding at the same time a unified approach to the different

techniques which have proved to be useful in finding dense pseudocompact subgroups and

pseudocompact refinements.

  J. Galindo, P. de la Harpe y T. Vust

Two Observations on Irreducible Representations of Groups

Abstract. For an irreducible representation of a connected affine algebraic group G in a

vector space V of dimension at least 2, it is shown that the intersection of any orbit (G) x (with

X E V) and any huyperplane of V is non-empaty. The question is raised to decide whether and

analogous fact holds for irreducible continuous representations of connected compact groups,

for example of SU (2).

 A. Campillo y C. Galindo

The Poincaré Series Associated With Finitely Many Monomial Valuations

  C. Galindo

On The Structure of the Value Semigroup of a Valuation

  Steen Markvorsen y V. Palmer

Transience and Capacity of Minimal Submanifolds

Abstract.We prove explicit lower bounds for the capacity of angular domains of minimal submanifolds Pm

in ambient Riemannian spaces N with sectional curvatures bounded from above. We characterize

the situations in which the lower bounds for the capacity are actually attained. Furthermore

we give two different proofs of the result that Brownian motion defined on a complete minimal

submanifold is transient when the ambient space is a negatively curved Hadamard-Cartan manifold.

The firs proof uses a previously established comparison theorem for the Dirichlet heat kernels

on minimal submanifolds, whereas the second proof stems directly from the capacity bounds that

we establish in the present paper. Moreover, this latter proof also covers minimal submanifolds

of dimension m>2 in Euclidean spaces.

  B. Campos, J. Martínez and P. Vindel

Graphs of Nms Flows on S3 With Unknotted Saddle Periodic Orbits

Abstract.In this paper we build dual graphs for the NMS systems on S3 characterized by I, II and III Wada

operations and with no heteroclinic trayectories connecting two saddles orbits. Moreover, we

show that these kind of NMS flows can be reproduced from these dual graphs. AMS classification numbers:

58F09, 58F14, 58F22. Keywords: NMS systems, Wada operations, Peixoto graphs.

 A. Beltrán and Mª José Felipe

On Th Diameter of A p-Regular Conjugacy Class Graph Of Finite Groups II 

Abstract. Let G be a finite p-solvable group. Let us consider the graph (G) whose vertices are the primes which 

occur as the divisors of the conjugacy classes of p-regular elements of G and two primer are joined by an edge if

there exists such a class whose size is divisible by both primes. Suppose thet (G) is a connected graph, then we

prove that the diameter of this graph is at most 3 and this is the best bound.

 Jorge Galindo and Manuel Sanchis

A Topological Approach To Stone-Weierstrass-Type Theorems For Group-Valued Functions

Abstract. The existence of Stone-Weierstrass theorems for group-valued functions is studied with the aid of 

the concept of constructive group. Constructive groups were introduced by Sternfeld in (5) as metrizable groups

G whose group of G-valued functions satisfies a (suitably defined) sort of Stone-Weirestrass theorem. We

address here the question raised in (5) as to which groups are constructive and prove that a metrizable

locally compact grup with more than two elements is constructive if and only if it is either totally

disconnected or topologically isomorphic to some vector group R. In particular no compact Lie group is

constructive. In the case of connected locally compact groups the homotopy theory of compact groups

(essentially applied to simple compact Lie groups and compact connected Abelian groups) and the structure 

theory of locally compact groups turn to be appropriate tools. A relevant feature in the case of a non-Abelian

group G is the existence of a locally euclidean group H1 with nondivisible homotopy group (H1) for some n and

a covering mapping that factorizes throug G. The scheme for totally disconected groups is more related to 

set-theoretic topology and the great liberty to construct continuous functions that exhibit zero-dimensional 

spaces.

 Jorge Galindo and Salvador Hernández

Interpolation Sets And The Bohr Topology Of Locally Compact Groups

Abstract. Rosenthal's theorem describing those Bana h spaces containing no copy of l1 is extended to topological

groups replacin l1-basis by interpolation sets in the sense of Hartman and Ryll-Nardzewsky (15). This extension 

provides a characterization of those locally compact groups containing no interpolation sets and of those locally

compact gorups which respect compactness, i.e, such that every Bohr compact subset is compact. The approach followed

in this paper sheds some light on other questions related to the duality theory of non-Abelian locally compact groups.

 J. Martinez Alfaro and Cristina Chiralt

Regularization of The Isosceles Problem

Abstract. In this paper we regularize the Isosceles Three-Body Problem. We make use of several methods to deal 

with collisions: blow-up of singularities, Levi-Civita ransformations and topological regularization. We define

a triple collison manifold so that the flow on it is the limit of the flow on the pahse space.

 Antonio Beltran and Mª José Felipe

Finite Groups With Two p-Regular Conjugacy Class Lengths

Abstract. Let G a finite p-solvable gorup for a fixed prime p. We determine the structure of G when the set of 

p-regular conjugacy class sizes of G is (1,m) for an arbitrary integer m>1.

 Antonio Beltran and Mª José Felipe

Certain Relations Between p-Regular Class Sizes and the p-Structure of p-Solvable Groups

Abstract. Let G a finite p-solvable group for a fixed prime p. We study how certain arithmetical conditions on

the set of p-regular conjugacy class sizes of G influence the p-structure of G. In particular, the structure of

the p-complements of G is described when this set is {1,m,n} for arbitrary coprime integers m,n> 1. The structure

of G is determined when the noncentral p-regular class lengths are consecutive numbers and when all of them are

prime powers.

 Mª Victoria Ibañez and Amelia Simó

Spatio-Temporal Modelling Of Perimetric Test Data

Abstract. This work describes a spatio-temporal modelization motivated by the study of glaucoma, a very serious

and widespred ocular illness which may in time result in damage to the optic nerve, loss of peripheral vision, and

finally blindness. In order to ascertain whether a patient suffers from glaucoma, a perimetry (also called 

perimetric test) is perfomred. The output of a perimetry is called a visual field (VF) and consists of a map with

52 numerical values sited on a regular grid. In this work we propose a first step of this study. In order to 

understand how a glaucomatous eye works, firstly we need to know how a healthly eye works. So the aim of the

paper is to analyse a data set of healthy patines visual fields, and to modelize their spatio-temporal distribution.

We begin with an exploratory spatial data analysis. A semi-parametric approach is used to model the mean, and the 

variogram is fitted using a Matern function. Once the spatial structure has been studied, the temporal analysis

begins with the calculation of variograms and cross-variograms. We fit several correlation functions and we study

the differences between them. Finally, we combien the previous results into a single space-time model. We built

the joint spatio-temporal model form two different points of view: assuming a separable and a non-separable 

correlation structure. We compare both models. The parameters are estimated by maximum likelihood, and different

methods are used to check the goodness of the fit.

Keywords: Geostatistics, spatio-temporal modelling, perimetry, corss validation, spatio-temporal covariance models

 M. Victoria Ibañez and Amelia Simó 

Conditional and Unconditional Simulation of Healthy Patients' Visual Fields

Abstract. This paper describes a simulation problem, motivated by the study of glaucoma, a very seriuos and

widespread ocular illness. To ascertain whether a patient suffers from glaucoma, a perimetric test is done,

but hte evolution of the disease is very slow, and large longitudinal sets of tests taken on the same patient

are needed to study its evolution, to analyze the efficiency of existing methods to detect the progression

of glaucoma and to develop new ones. Simulation can be a very useful procedure to get appropriate data sets

to work with. Our aim in this work is to simulate several VFs in a healthy patient to reflect his evolution

in time. We use a spatio-temporal model to simulate from, taking into account the correlation existing between

the observed (or simulated) values in space and time. Two different simulation procedures (unconditional and

conditional) are studied, and applied to obtain the simulations we are interest in.

Keywords: Conditioanl and Unconditional simulation, spatio-temporal modellin, perimetry.

 W.W. Comfort and Jorge Galindo

Extremal Pseudocompact Topological Groups