The Zariski-Lefschetz principle for higher homotopy groups of nongeneric pencils

We prove a general Zariski-van Kampen-Lefschetz type theorem for higher homotopy groups of generic and nongeneric pencils on singular open complex spaces.

Mather invariants in groups of piecewise-linear homeomorphisms

We describe the relation between two characterizations of conjugacy in groups of piecewise-linear homeomorphisms, discovered by Brin and Squier in [2] and Kassabov and Matucci in [5]. Thanks to the interplay between the techniques, we produce a simplified point of view of conjugacy that allows ua to easily recover centralizers and lends itself to generalization.

The simultaneous conjugacy problem in groups of piecewise linear functions

Guba and Sapir asked, in their joint paper [8], if the simultaneous conjugacy problem was solvable in Diagram Groups or, at least, for Thompson's group F. We give an elementary proof for the solution of the latter question. This relies purely on the description of F as the group of piecewise linear orientation-preserving homeomorphisms of the unit. The techniques we develop allow us also to solve the ordinary conjugacy problem as well, and we can compute roots and centralizers. Moreover, these techniques can be generalized to solve the same questions in larger groups of piecewise-linear homeomorphisms.

The so-called 'external partners' in the groups of corporations: A model of presentation in the consolidated statements

This paper studies, on the one hand, theories set out around theconsideration of the external partners in the consolidated informationand on the other hand, financial models that discuss the convenience ofthe separation or not of the different elements that form part of theliabilities of the balance sheet of the companies. A Model is proposed,the External Partners Model, which financially argues a certain presentationand processing of such and that, in our opinion, facilitates the analysisof the consolidated financial statements. This model is based on twohypotheses: (1) the economic and financial variables are not independentand (2) the value of the company depends, among other factors, of thetype of sources that constitute their capital. These two hypotheses willimply that a separation should be included in the consolidated balance sheet between equity and liabilities as they are different sources ofcapital and then its separation will give relevant information to itsusers.

The groups of Poincaré and Galilei in arbitrary dimensional spaces

In arbitrary dimensional spaces the Lie algebra of the Poincaré group is seen to be a subalgebra of the complex Galilei algebra, while the Galilei algebra is a subalgebra of Poincar algebra. The usual contraction of the Poincar to the Galilei group is seen to be equivalent to a certain coordinate transformation.

Infinite index subgroups and finiteness properties of intersections of geometrically finite groups

We explore which types of finiteness properties are possible for intersections of geometrically finite groups of isometries in negatively curved symmetric rank one spaces. Our main tool is a twist construction which takes as input a geometrically finite group containing a normal subgroup of infinite index with given finiteness properties and infinite Abelian quotient, and produces a pair of geometrically finite groups whose intersection is isomorphic to the normal subgroup.

Elements of algebraic geometry and the positive theory of partially commutative groups

The first main result of the paper is a criterion for a partially commutative group G to be a domain. It allows us to reduce the study of algebraic sets over G to the study of irreducible algebraic sets, and reduce the elementary theory of G (of a coordinate group over G) to the elementary theories of the direct factors of G (to the elementary theory of coordinate groups of irreducible algebraic sets). Then we establish normal forms for quantifier-free formulas over a non-abelian directly indecomposable partially commutative group H. Analogously to the case of free groups, we introduce the notion of a generalised equation and prove that the positive theory of H has quantifier elimination and that arbitrary first-order formulas lift from H to H * F, where F is a free group of finite rank. As a consequence, the positive theory of an arbitrary partially commutative group is decidable.

Educational innovation in large groups. Design of an experimental study implemented at the Polytechnic University of Madrid

The present paper shows de design of an experimental study conducted with large groups using educational innovation methodologies at the Polytechnic University of Madrid. Concretely, we have chosen the course titled "History and Politics of Sports" that belongs to the Physical Activity and Sport Science Degree. The selection of this course is because the syllabus is basically theoretical and there are four large groups of freshmen students who do not have previous experiences in a teaching-learning process based on educational innovation. It is hope that the results of this research can be extrapolated to other courses with similar characteristics.

The efficiency of indicator groups for the conservation of amphibians in the Brazilian Atlantic Forest

The adequate selection of indicator groups of biodiversity is an important aspect of the systematic conservation planning. However, these assessments differ in the spatial scale, in the methods used and in the groups considered to accomplish this task, which generally produces contradictory results. The quantification of the spatial congruence between species richness and complementarity among different taxonomic groups is a fundamental step to identify potential indicator groups. Using a constructive approach, the main purposes of this study were to evaluate the performance and efficiency of eight potential indicator groups representing amphibian diversity in the Brazilian Atlantic Forest. Data on the geographic range of amphibian species that occur in the Brazilian Atlantic Forest was overlapped to the full geographic extent of the biome, which was divided into a regular equal-area grid. Optimization routines based on the concept of complementarily were applied to verify the performance of each indicator group selected in relation to the representativeness of the amphibians in the Brazilian Atlantic Forest as a whole, which were solved by the algorithm"simulated annealing", through the use of the software MARXAN. Some indicator groups were substantially more effective than others in regards to the representation of the taxonomic groups assessed, which was confirmed by the high significance of data (F = 312.76; p < 0.01). Leiuperidae was considered as the best indicator group among the families analyzed, as it showed a good performance, representing 71% of amphibian species in the Brazilian Atlantic Forest (i.e. 290 species), which may be associated with the diffuse geographic distribution of its species. This study promotes understanding of how the diversity standards of amphibians can be informative for systematic conservation planning on a regional scale.

On Hyperbolic once-punctured-torus bundles II. Fractal tessellations of the plane

We describe fractal tessellations of the complex plane that arise naturally from Cannon-Thurston maps associated to complete, hyperbolic, once-punctured-torus bundles. We determine the symmetry groups of these tessellations.

Regional decomposition of CO2 emissions in the world: a cluster analysis

The purpose of this paper is to study the possible differences among countries as CO2 emitters and to examine the underlying causes of these differences. The starting point of the analysis is the Kaya identity, which allows us to break down per capita emissions in four components: an index of carbon intensity, transformation efficiency, energy intensity and social wealth. Through a cluster analysis we have identified five groups of countries with different behavior according to these four factors. One significant finding is that these groups are stable for the period analyzed. This suggests that a study based on these components can characterize quite accurately the polluting behavior of individual countries, that is to say, the classification found in the analysis could be used in other studies which look to study the behavior of countries in terms of CO2 emissions in homogeneous groups. In this sense, it supposes an advance over the traditional regional or rich-poor countries classifications .

Shellability of noncrossing partition lattices

We give a case-free proof that the lattice of noncrossing partitions associated to any finite real reflection group is EL-shellable. Shellability of these lattices was open for the groups of type Dn and those of exceptional type and rank at least three.

Contraction groups in complete Kac-Moody groups

Let G be an abstract Kac-Moody group over a finite field and G the closure of the image of G in the automorphism group of its positive building. We show that if the Dynkin diagram associated to G is irreducible and neither of spherical nor of affine type, then the contraction groups of elements in G which are not topologically periodic are not closed. (In those groups there always exist elements which are not topologically periodic.)

Occurrence and bioaccumulation study of PCDD and PCDF from mineral feed additives

Occurrence of polychlorinated dibenzo-p-dioxins (PCDDs) and polychlorinated dibenzofurans (PCDFs) was evaluated in sepiolite as a widely employed binder and anti-caking agent for animal feed. Also, naturally contaminated kaolinitic clay was used for comparative purposes. Since sepiolite shows remarkable adsorption properties, particular interest was paid to the extraction steps as they become critical for the final determination of these pollutants in such matrixes. Furthermore, classical Soxhlet extraction using different extracting strategies as well as acid treatment were carried out with simultaneous liquid-liquid extraction. Results obtained depended on the extraction procedure applied. Acid treatment or Soxhlet extraction using a mixture of toluene:ethanol as solvent allowed to reach the minimum requirements of recovery rates. However, Soxhlet extraction using a mixture cyclohexane:toluene as extracting solvent did not allow to comply with minimum specifications for recovery. Significant differences were obtained in TEQ units when acid treatment was applied in comparison to Soxhlet extraction. This fact can be explained because the use of drastic acid conditions allows removing strongly adsorbed analytes which can be uniquely extracted after a total destruction of the crystalline structure of sepiolite. On the contrary, Soxhlet extraction was not able to destroy the structure of sepiolite and as a consequence the PCDDs/Fs were strongly adsorbed in the internal structure of the mineral. From biological point of view the availability of these toxicants constitutes a critical aspect playing an important role in the final decision choosing particular analytical procedures. Then, acid conditions in the digestive tract should be taken into account. In this scenario, a bioaccumulation study was conducted to evaluate the transference of PCDDs/PCDFs from the sepiolite into the animal tissues when fed with feed containing sepiolite. To this end, chickens were used as a model to examine the bioavailability of PCDDs/PCDFs. Four groups of chickens were exposed through their diet to a control feed, feed with 3% w/w sepiolite as additive, feed contaminated with PCDDs/PCDFs at concentration around 2.8 pg WHO-TEQ/g and feed with 2% of a contaminated kaolinitic clay (460 pg TEQ/g mineral). Livers of the four studied groups were analyzed throughout the exposure period. Results of this trial showed that the performance of broilers was not affected by the presence of dioxins at levels tested, and chickens did not show any abnormal behaviour. Dioxins intentionally added to the diet were absorbed and accumulated in the liver in a significant manner, whereas the PCDDs/Fs from sepiolite were not available for chickens since livers from broilers fed 3% sepiolite presented similar WHO-TEQ values than those from broilers fed control diet.

Tree automorphisms and quasi-isometries of Thompson's group F

We prove that automorphisms of the infinite binary rooted tree T2 do not yield quasi-isometries of Thompson's group F, except for the map which reverses orientation on the unit interval, a natural outer automorphism of F. This map, together with the identity map, forms a subgroup of Aut(T2) consisting of 2-adic automorphisms, following standard terminology used in the study of branch groups. However, for more general p, we show that the analgous groups of p-adic tree automorphisms do not give rise to quasiisometries of F(p).