Grupos topológicos

The main goal of this work is to give the reader a basic introduction into the subject of topological groups, bringing together the areas of topology and group theory.

Symmetry and optical transition rule for low-dimensional semiconductor system with spin-orbit interaction and magnetic field

Starting from effective mass Hamiltonian, we systematically investigate the symmetry of low-dimensional structures with spin-orbit interaction and transverse magnetic field. The position-dependent potentials are assumed to be space symmetric, which is ever-present in theory and experiment research. By group theory, we analyze degeneracy in different cases. Spin-orbit interaction makes the transition between Zeeman sub-levels possible, which is originally forbidden within dipole approximation. However, a transition rule given in this paper for the first time shows that the transition between some levels is forbidden for space symmetric potentials. (C) 2009 Elsevier Ltd. All rights reserved.

Pressure-induced Raman-active radial breathing mode transition in single-wall carbon nanotubes

Using classical constant-pressure molecular dynamics simulations and the force constants model, radial breathing mode (RBM) transition of single-wall carbon nanotubes under hydrostatic pressure is reported. With the pressure increased, the RBM shifts linearly toward higher frequency, and the RBM transition occurs at the same critical pressure as the structural transition. The group theory indicates that the RBMs are all Raman-active; however, due to the effect of the frequency transition and the electronic structure change for tube radial deformation, the Raman intensity of the modes becomes so weak as not to be experimentally detected, which is in agreement with a recent experiment by S. Lebedkin [Phys. Rev. B 73, 094109 (2006)]. Furthermore, the calculated RBM transition pressure is well fitted to the cube of diameter (similar to 1/d(3)).

Quantum confinement of phonon modes in GaAs quantum dots

Phonon modes in spherical GaAs quantum dots (QDs) with up to 11,855 atoms (8 nm in size) are calculated by using an empirical microscopic model. The group theory is employed to reduce the computational intensity, which further allows us to investigate the quantum confinement of phonon modes with different symmetries and reveals a phenomenon that phonon modes with different symmetries have different quantum confinement effect. For zinc-blende structure, the modes with the A(1) symmetry has the strongest quantum confinement effect and the T-1 modes the weakest. This could cause a crossover of symmetries of the highest frequency from A(1) to T-2 when the size of QDs decreases. (C) 1999 Elsevier Science Ltd, All rights reserved.

PHOTOLUMINESCENCE INVESTIGATIONS OF CD1-XMNXTE UNDER HYDROSTATIC-PRESSURE

The photoluminescence of Cd1-xMnxTe with x=0.25, 0.40, and 0.60 is investigated at 77 K and different pressures. The pressure coefficients of the photoluminescence bands Cd0.75Mn0.25Te and Cd0.6Mn0.4Te are found to be positive and the magnitudes are about 8 X 10(-3) eV/kbar, which is in good agreement with the pressure coefficients of the interband transition. The pressure coefficient of the photoluminescence bands for Cd0.4Mn0.6Te is found to be -6 X 10(-3) eV/kbar, which is quite different from the pressure coefficient of the interband transition. The possible transition mechanism is discussed in terms of group theory and crystal field theory.

The analysis of political will and its role in leadership: a study of portuguese mayors

This thesis analyses the concept of Political Will, suggests its operationalization and establishes a typological theory that provides the necessary support for the diverse strategies of action of a leader. It claims that political leadership styles articulate a choice of action that results from the Political Will of a leader, which is determined by his intention and his discerned possibilities to act. One main research question guided our research: How does a political leader select and change his leadership style? The most illustrative literature on political leadership is reviewed and the characteristics of democratic governance are analyzed. This is followed by an overview of the most noteworthy theories on the theme and a claim for the need of concept coherence, given the multiplicity of the existent standpoints. After that, we concentrate on leadership styles, with a focus on the local governance context. Human action and intentionality are addressed with particular attention, as well as the motivational drivers for action, in order to advance a conceptualization of Political Will through two dimensions: intention and possibility. This analysis led to a number of relevant propositions: (1) Political Will ‘exists’ when the agent has the intent and the possibility to act; (2) these two dimensions ‘translate’ simultaneously what the agent believes he must do and can do; (3) Intention and possibility reflect diverse but limited worldviews; (4) political leadership styles result from the agent’s Political Will; (5) different combinations of the expected and actual worldviews result in different leadership styles; and (6) political leadership styles can change accordingly to several strategies which allow conformity or reflect reaction to worldviews. We suggested the operationalization of the two dimensions of Political Will through the analytical tool of Grid-group Theory, which provided the identification of the heuristic devices that allowed further comprehension on the subjectivity of the agent’s choice. Four standard property spaces – representing four types of leadership styles – result from a preliminary approach to this process. Afterwards, and because these dimensions operate simultaneously, we advance on the analysis and suggest some plausible heuristical conflicts to happen and describe which consequences, strategies and type migrations are conceivable. An inclusive and more complete set of resulting property spaces renders fourteen different types of leadership styles and sixty different predictable causal paths that result from the expected migration strategies. Case-studies were conducted as plausibility probes designed to provide improvements to our theoretical claims and addressed the cases we selected for research purposes: Portuguese Mayors. The findings from five case studies are discussed and the probable impact and congruence of each with the theoretical claims are assessed. The communalities of the causal mechanisms related to the function of intention and possibility as the dimensions of Political Will and their role in explaining different leadership styles are, finally, addressed. To conclude, we advance some repercussions, mainly in the public policies field of research, and suggest a number of different and necessary paths for further work.

Un formalisme pour la traçabilité des transformations

Dans le développement logiciel en industrie, les documents de spécification jouent un rôle important pour la communication entre les analystes et les développeurs. Cependant, avec le temps, les changements de personel et les échéances toujours plus courtes, ces documents sont souvent obsolètes ou incohérents avec l'état effectif du système, i.e., son code source. Pourtant, il est nécessaire que les composants du système logiciel soient conservés à jour et cohérents avec leurs documents de spécifications pour faciliter leur développement et maintenance et, ainsi, pour en réduire les coûts. Maintenir la cohérence entre spécification et code source nécessite de pouvoir représenter les changements sur les uns et les autres et de pouvoir appliquer ces changements de manière cohérente et automatique. Nous proposons une solution permettant de décrire une représentation d'un logiciel ainsi qu'un formalisme mathématique permettant de décrire et de manipuler l'évolution des composants de ces représentations. Le formalisme est basé sur les triplets de Hoare pour représenter les transformations et sur la théorie des groupes et des homomorphismes de groupes pour manipuler ces transformations et permettrent leur application sur les différentes représentations du système. Nous illustrons notre formalisme sur deux représentations d'un système logiciel : PADL, une représentation architecturale de haut niveau (semblable à UML), et JCT, un arbre de syntaxe abstrait basé sur Java. Nous définissons également des transformations représentant l'évolution de ces représentations et la transposition permettant de reporter les transformations d'une représentation sur l'autre. Enfin, nous avons développé et décrivons brièvement une implémentation de notre illustration, un plugiciel pour l'IDE Eclipse détectant les transformations effectuées sur le code par les développeurs et un générateur de code pour l'intégration de nouvelles représentations dans l'implémentation.

On infinite graphs and related matrices

This thesis Entitled On Infinite graphs and related matrices.ln the last two decades (iraph theory has captured wide attraction as a Mathematical model for any system involving a binary relation. The theory is intimately related to many other branches of Mathematics including Matrix Theory Group theory. Probability. Topology and Combinatorics . and has applications in many other disciplines..Any sort of study on infinite graphs naturally involves an attempt to extend the well known results on the much familiar finite graphs. A graph is completely determined by either its adjacencies or its incidences. A matrix can convey this information completely. This makes a proper labelling of the vertices. edges and any other elements considered, an inevitable process. Many types of labelling of finite graphs as Cordial labelling, Egyptian labelling, Arithmetic labeling and Magical labelling are available in the literature. The number of matrices associated with a finite graph are too many For a study ofthis type to be exhaustive. A large number of theorems have been established by various authors for finite matrices. The extension of these results to infinite matrices associated with infinite graphs is neither obvious nor always possible due to convergence problems. In this thesis our attempt is to obtain theorems of a similar nature on infinite graphs and infinite matrices. We consider the three most commonly used matrices or operators, namely, the adjacency matrix

A computer-algebraic approach to the study of the symmetry properties of molecules and clusters

This thesis work is dedicated to use the computer-algebraic approach for dealing with the group symmetries and studying the symmetry properties of molecules and clusters. The Maple package Bethe, created to extract and manipulate the group-theoretical data and to simplify some of the symmetry applications, is introduced. First of all the advantages of using Bethe to generate the group theoretical data are demonstrated. In the current version, the data of 72 frequently applied point groups can be used, together with the data for all of the corresponding double groups. The emphasize of this work is placed to the applications of this package in physics of molecules and clusters. Apart from the analysis of the spectral activity of molecules with point-group symmetry, it is demonstrated how Bethe can be used to understand the field splitting in crystals or to construct the corresponding wave functions. Several examples are worked out to display (some of) the present features of the Bethe program. While we cannot show all the details explicitly, these examples certainly demonstrate the great potential in applying computer algebraic techniques to study the symmetry properties of molecules and clusters. A special attention is placed in this thesis work on the flexibility of the Bethe package, which makes it possible to implement another applications of symmetry. This implementation is very reasonable, because some of the most complicated steps of the possible future applications are already realized within the Bethe. For instance, the vibrational coordinates in terms of the internal displacement vectors for the Wilson's method and the same coordinates in terms of cartesian displacement vectors as well as the Clebsch-Gordan coefficients for the Jahn-Teller problem are generated in the present version of the program. For the Jahn-Teller problem, moreover, use of the computer-algebraic tool seems to be even inevitable, because this problem demands an analytical access to the adiabatic potential and, therefore, can not be realized by the numerical algorithm. However, the ability of the Bethe package is not exhausted by applications, mentioned in this thesis work. There are various directions in which the Bethe program could be developed in the future. Apart from (i) studying of the magnetic properties of materials and (ii) optical transitions, interest can be pointed out for (iii) the vibronic spectroscopy, and many others. Implementation of these applications into the package can make Bethe a much more powerful tool.

Exam 1999 pdf

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Exam 1999

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Exam 2000 pdf

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Exam 2000

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Exam 2001 pdf

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Exam 1998

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