Computations in Relative Algebraic K-Groups

Let G be finite group and K a number field or a p-adic field with ring of integers O_K. In the first part of the manuscript we present an algorithm that computes the relative algebraic K-group K_0(O_K[G],K) as an abstract abelian group. We solve the discrete logarithm problem, both in K_0(O_K[G],K) and the locally free class group cl(O_K[G]). All algorithms have been implemented in MAGMA for the case K = \IQ. In the second part of the manuscript we prove formulae for the torsion subgroup of K_0(\IZ[G],\IQ) for large classes of dihedral and quaternion groups.

Computation of relativistic symmetry orbitals for finite double point groups

A program is presented for the construction of relativistic symmetry-adapted molecular basis functions. It is applicable to 36 finite double point groups. The algorithm, based on the projection operator method, automatically generates linearly independent basis sets. Time reversal invariance is included in the program, leading to additional selection rules in the non-relativistic limit.

Root parametrized differential equations

The present thesis is about the inverse problem in differential Galois Theory. Given a differential field, the inverse  problem asks which linear algebraic groups can be realized as differential Galois groups of Picard-Vessiot extensions of this field.   In this thesis we will concentrate on the realization of the classical groups as differential Galois groups. We introduce a method for a very general realization of these groups. This means that we present for the classical groups of Lie rank $l$ explicit linear differential equations where the coefficients are differential polynomials in $l$ differential indeterminates over an algebraically closed field of constants $C$, i.e. our differential ground field is purely differential transcendental over the constants.   For the groups of type $A_l$, $B_l$, $C_l$, $D_l$ and $G_2$ we managed to do these realizations at the same time in terms of Abhyankar's program 'Nice Equations for Nice Groups'. Here the choice of the defining matrix is important. We found out that an educated choice of $l$ negative roots for the parametrization together with the positive simple roots leads to a nice differential equation and at the same time defines a sufficiently general element of the Lie algebra. Unfortunately for the groups of type $F_4$ and $E_6$ the linear differential equations for such elements are of enormous length. Therefore we keep in the case of $F_4$ and $E_6$ the defining matrix differential equation which has also an easy and nice shape.   The basic idea for the realization is the application of an upper and lower bound criterion for the differential Galois group to our parameter equations and to show that both bounds coincide. An upper and lower bound criterion can be found in literature. Here we will only use the upper bound, since for the application of the lower bound criterion an important condition has to be satisfied. If the differential ground field is $C_1$, e.g., $C(z)$ with standard derivation, this condition is automatically satisfied. Since our differential ground field is purely differential transcendental over $C$, we have no information whether this condition holds or not.   The main part of this thesis is the development of an alternative lower bound criterion and its application. We introduce the specialization bound. It states that the differential Galois group of a specialization of the parameter equation is contained in the differential Galois group of the parameter equation. Thus for its application we need a differential equation over $C(z)$ with given differential Galois group. A modification of a result from Mitschi and Singer yields such an equation over $C(z)$ up to differential conjugation, i.e. up to transformation to the required shape. The transformation of their equation to a specialization of our parameter equation is done for each of the above groups in the respective transformation lemma.

Problems with large groups

A list of considerations on the problems with large groups. This material was sent to Debra Morris in 2007, by David Jaques, an educationist with many years' experience of working with groups.

L'Activité hors la classe du professeur des écoles liée à la préparation de la classe dans le domaine des mathématiques

Préparer la classe constitue une des tâches professionnelles afférentes à chaque enseignant. Cette tâche, dont l’action d’enseignement menée auprès des élèves résulte, s’effectue dans un espacetemps distinct de celui de la classe. Comment les enseignants du premier degré qui, à l’inverse des enseignants du second degré, doivent enseigner toutes les disciplines réalisent-ils cette tâche? Quelles ressources utilisent-ils? Les manuels qui représentent une grande part des supports proposés et commercialisés par les éditeurs constituent une ressource

Les activitats nàutiques i les persones amb hipoacúsia : una experiència amb focus groups.

Resumen tomado del autor

Interviews And Focus Groups: Purpose Paradigms Protocols and Pragmatics

Introduction to interview data, how it is used and how and why it might be collected

INFO2009 - Team 'DROP TABLE groups;

Edshare for INFO2009 coursework 2 - Team 'DROP TABLE groups;

W3 Working in Groups

Slides, notes and links summarising presentation, discussions, activities and further reading

Academic stress in master’s students and its modulatory variables: a between-groups design

The present investigation tries to establish the descriptive profile of the academic stress of the students of the masters in education and to identify which sociodemographic and situational variables play a modulator role. This investigation is based on the Person-Surroundings Research Program and the systemical cognitive model of academic stress. The study can be characterized as transectional, correlational and non experimental. The collection of the information was made through the SISCO inventory of Academic Stress which was applied to 152 students. The main results suggest that 95% of the master students report having felt academic stress a few times but with medium-high intensity. Variables gender, civil state, attending masters and institutional support of the attending masters act as modulators in academic stress.

Diagnostic Related Groups (drgs): Resourceful tools for financial crisis times?

This document is intended to be read by the Colombian Ministry of Social Protection (former MoH) and includes some recommendations that could be implemented on the aim to increase allocative efficiency, thus improving macroeconomic performance of the Colombian Health System (CHS). It will be conducted as follows: first it will briefly review the background and actual context of the CHS, after this, will mention some related issues that justify a policy intervention on strategic purchasing to promote long run sustainability and hopefully the future attainment of major goals such as universal coverage and quality improvement. After prioritizing the main financial threats to the system, based on findings from literature review from countries that have successfully implemented similar policies, this paper will make some policy recommendations on regards especially to inpatient health care services in Colombia.

Armed conflict and paramilitary groups in Chiapas

The armed conflict in Chiapas began in 1994 after the armed uprising of the Zapatista Army of National Liberation (EZLN). Until now the Mexican government do not recognize the existence of an armed conflict there, for what they call inter-ethnic violence that happens in different municipalities in Chiapas. This study aims at demonstrating that, first, the Mexican state of Chiapas has an armed conflict since the mid-nineties, which has intensified and transformed over sixteen years. It is in this transformation that have emerged paramilitary groups seeking to destabilize the state, generating dynamics of appropriation and control of territory through different practices such as forced displacements, selective assassinations and terror spread within populations who are the targets of their attacks (mainly community support of the Zapatista Army of National Liberation). This work studied the "Peace and Justice" paramilitary group operating in different parts of the state of Chiapas, mainly in the Northern Zone. This case-study will look at the changes it has undergone Mexican democracy, which will be analyzed at two points: first, the failure of federal and Chiapas state to allow or endorse the creation of paramilitary groups and not to punish their actions; on the other, the consequences of the actions of such actors in democratic institutions, and democracy itself. Will seek to demonstrate that indeed both the permissiveness of the Mexican state and its complicity has weakened democracy in Mexico, since they are not able to manage conflict so that they do not degenerate into violence.