Conjugacy problem for braid groups and Garside groups

We present a new algorithm to solve the conjugacy problem in Artin braid groups, which is faster than the one presented by Birman, Ko and Lee. This algorithm can be applied not only to braid groups, but to all Garside groups (which include finite type Artin groups and torus knot groups among others).Comment: New version, with substantial modifications. 21 pages, 2 figure

Partial Classification of Lorenz Knots: Syllable Permutations of Torus Knots Words

We define families of aperiodic words associated to Lorenz knots that arise naturally as syllable permutations of symbolic words corresponding to torus knots. An algorithm to construct symbolic words of satellite Lorenz knots is defined. We prove, subject to the validity of a previous conjecture, that Lorenz knots coded by some of these families of words are hyperbolic, by showing that they are neither satellites nor torus knots and making use of Thurston's theorem. Infinite families of hyperbolic Lorenz knots are generated in this way, to our knowledge, for the first time. The techniques used can be generalized to study other families of Lorenz knots

Genus and Braid Index Associated to Sequences of Renormalizable Lorenz Maps

We describe the Lorenz links generated by renormalizable Lorenz maps with reducible kneading invariant (K(f)(-), = K(f)(+)) = (X, Y) * (S, W) in terms of the links corresponding to each factor. This gives one new kind of operation that permits us to generate new knots and links from the ones corresponding to the factors of the *-product. Using this result we obtain explicit formulas for the genus and the braid index of this renormalizable Lorenz knots and links. Then we obtain explicit formulas for sequences of these invariants, associated to sequences of renormalizable Lorenz maps with kneading invariant (X, Y) * (S,W)*(n), concluding that both grow exponentially. This is specially relevant, since it is known that topological entropy is constant on the archipelagoes of renormalization

IN-SITU XRD STUDIES OF THERMAL STABILITY OF PURE SILICA AND Ti-MCM-41 MATERIALS

In this work we present a study on the thermal stability of siliceous and titanium containing ordered mesoporous materials with MCM-41 structure, prepared by direct synthesis at ambient temperature and pressure, as previously described [1]. Grades with different pore diameter and Si/Ti molar ratios were analyzed, in the form of compacted powder, to assess its influence on the order-disorder transition temperature

Desenvolvimento de fósforos à base de β-Ga2O3 e c-ZnGa2O4

Mestrado em Engenharia FísicaNeste trabalho foram produzidas e caracterizadas amostras de matrizes óxidas de gália (β-Ga2O3) e de galato de zinco (c-ZnGa2O4), materiais com reconhecido interesse para aplicações em fósforos. Foram crescidas fibras de β-Ga2O3 e c-ZnGa2O4 pela técnica de fusão de zona com laser, e produzidos filmes finos de ZnO:Ga2O3 pela técnica de deposição de fluxo assistida por laser. As amostras foram caracterizadas quanto à sua morfologia, composição elementar, estrutura cristalina e propriedades óticas, com o objetivo de correlacionar os centros oticamente ativos, de origem intrínseca ou por via de dopagem, com as características estruturais das fibras. Para as fibras de gália, não obstante a boa qualidade estrutural e ótica das amostras não dopadas, a incorporação de dopantes promove a policristalinidade da fibra e a emissão intraiónica característica do ião Eu3+ é apenas detetada para temperaturas criogénicas. É promovida uma fase secundária rica em iões de európio, o Eu3Ga5O12, onde se encontra inserida a maioria dos centros emissores detetados, em simetrias locais diferentes consoante a concentração de dopante e a velocidade de crescimento usada. Para as fibras de galato de zinco, foi detetada uma contaminação com iões Mn2+ que dá lugar a uma emissão verde com tempo de vida de ~ms, com os iões incorporados na fase c-ZnGa2O4 em ambientes de simetria local Td e em ambientes de mais baixa simetria, o que é explicado pela natureza policristalina da fibra. Com o intuito de identificar os processos de extinção térmica da luminescência foram realizados estudos da evolução da intensidade de emissão em função da temperatura, que revelaram uma energia de ativação de ~20 meV para os dois centros, o que sugere um baixo grau de competição dos processos não radiativos com a emissão do Mn2+. Este material revela grandes potencialidades para aplicações em fósforos, sendo que a otimização no que concerne às variáveis de crescimento está já a ser efetuada, de modo a serem produzidas fibras monocristalinas de c- ZnGa2O4 para aumentar a eficiência de emissão do Mn2+ e outros fósforos.In this work potential phosphors based on gallium oxide (β-Ga2O3) and zinc gallate (c-ZnGa2O4) hosts were produced and characterized. The β-Ga2O3 and c-ZnGa2O4 fibres were grown by laser floating zone technique and ZnO:Ga2O3 films were produced by laser assisted flow deposition. The samples’ morphology, elementary composition, crystalline structure and optical properties, were analyzed aiming to correlate their optically active defects with the samples structural characteristics. For the europium doped gallium oxide fibres a polycrystalline nature is promoted. The characteristic fingerprint lines of Eu3+ ion is observed in all the grown samples at cryogenic temperatures. A secondary europium ion rich phase develops, the Eu3Ga5O12, where the majority of the detected lines of europium ions indicate that the lanthanide ions should be placed at different local symmetries depending on the dopant concentration and growth velocity used. For the zinc gallate fibres, a contamination with Mn2+ ions was detected which gives rise to an intense green emission at room temperature, with a lifetime of ~ms. The ions were incorporated both at environments with Td and with lower symmetry in the c-ZnGa2O4 phase, which is explained by the fibres’ polycrystalline nature. The evolution of the luminescence intensity as a function of temperature indicate an activation energy of ~20 meV for both optical centres, suggesting a low degree of competition between the nonradiative processes and the Mn2+ emission. This material exhibit high potentiality for phosphor applications, being the growth optimization process currently undergoing, aiming to grow c-ZnGa2O4 monocrystalline fibres to increase the Mn2+ and other phosphors emission’s efficiency

How reporting and controlling systems can be effectively designed to support the decision-making process: the case of a software SME

A Work Project, presented as part of the requirements for the Award of a Masters Degree in Management from the NOVA – School of Business and EconomicsThis Work Project (WP) addresses the challenges faced by companies, particularly software houses, in reporting, decision making and controlling project performance activities. It focuses on issues regarding design and implementation of management control systems to support those activities and help achieve strategic goals. The WP suggests courses of action to be followed to improve the quality of information provided by such systems for budgeting and costing projects, and evaluate their performance. A case study approach (Ryan et al. 2002) was followed, applying Pinheiro’s (2007) control plan to a real company. The findings may apply to other companies facing similar constraints