A class of singular first order differential equations with applications in reaction-diffusion

Agências Financiadoras: FCT e MIUR

Synthesis and Coordination Chemistry of a New N-4-Polydentate Class of Pyridyl-Functionalized Scorpionate Ligands: Complexes of Fe-II, Zn-II, V-IV, Pd-II and Use for Heterobimetallic Systems

The new potentially N-4-multidentate pyridyl-functionalized scorpionates 4-((tris-2,2,2-(pyrazol-1-ypethoxy)methyl)pyridine (TpmPy, (1)) and 4-((tris-2,2,2-(3-phenylpyrazol-1-yl)ethoxy)methyl)pyridine (TpmPy(Ph), (2)) have been synthesized and their coordination behavior toward Fe-II, Ni-II, Zn-II, Cu-II, Pd-II, and V-III centers has been studied. Reaction of (1) with Fe(BF4)(2)center dot 6H(2)O yields [Fe(TpmPy)(2)](BF4)(2) (3), that, in the solid state, shows the sandwich structure with trihapto ligand coordination via the pyrazolyl arms, and is completely low spin (LS) until 400 K. Reactions of 2 equiv of (1) or (2) with Zn-II or Ni-II chlorides give the corresponding metal complexes with general formula [MCl2(TpmPy*)(2)] (M = Zn, Ni; TpmPy* = TpmPy, TpmPy(Ph)) (4-7) where the ligand is able to coordinate through either the pyrazolyl rings (in case of [Ni(TpmPy)(2)Cl-2 (5)) or the pyridyl-side (for [ZnCl2(TpmPy)(2)] (4), [ZnCl2(TpmPy(Ph))(2)] (6) and [NiCl2(TpmPy(Ph))(2)] (7)). The reaction of (1) with VCl3 gives [VOCl2(TpmPy)] (8) that shows the N-3-pyrazolyl coordination-mode. Moreover, (1) and react with cis-[PdCl2(CH3CN)(2)] to give the disubstituted complexes [PdCl2(TprnPy)(2)] (9) and [PdCl2(TpmPy(Ph))(2)] (10), respectively, bearing the scorpionate coordinated via the pyridyl group. Compounds (9) and (10) react with Fe(BF4)(2) to give the heterobimetallic Pd/Fe systems [PdCl2(mu-TpmPy)(2)-Fe](BF4)(2) (11) and [PdCl2(mu-TpmPy(Ph))(2)Fe-2(H2O)(6)]BF4)(4) (13), respectively. Compound (11) can also be formed from reaction of (3) with cis-[PdCl2(CH3CN)(2)], while reaction of (3) with Cu(NO3)(2).2.5H(2)O generates [Fe(mu-TpmPy)(2)-Cu(NO3)(2)](BF4)(2) (12), confirming the multidentate ability of the new chelating ligands. The X-ray diffraction analyses of compounds (1), (3), (4), (5), and (9) are also reported.

Basis invariant conditions for supersymmetry in the two-Higgs-doublet model

The minimal supersymmetric standard model involves a rather restrictive Higgs potential with two Higgs fields. Recently, the full set of classes of symmetries allowed in the most general two-Higgs-doublet model was identified; these classes do not include the supersymmetric limit as a particular class. Thus, a physically meaningful definition of the supersymmetric limit must involve the interaction of the Higgs sector with other sectors of the theory. Here we show how one can construct basis invariant probes of supersymmetry involving both the Higgs sector and the gaugino-Higgsino-Higgs interactions.

Extreme Value Theory versus traditional GARCH approaches applied to financial data: a comparative evaluation

Although stock prices fluctuate, the variations are relatively small and are frequently assumed to be normal distributed on a large time scale. But sometimes these fluctuations can become determinant, especially when unforeseen large drops in asset prices are observed that could result in huge losses or even in market crashes. The evidence shows that these events happen far more often than would be expected under the generalized assumption of normal distributed financial returns. Thus it is crucial to properly model the distribution tails so as to be able to predict the frequency and magnitude of extreme stock price returns. In this paper we follow the approach suggested by McNeil and Frey (2000) and combine the GARCH-type models with the Extreme Value Theory (EVT) to estimate the tails of three financial index returns DJI,FTSE 100 and NIKKEI 225 representing three important financial areas in the world. Our results indicate that EVT-based conditional quantile estimates are much more accurate than those from conventional AR-GARCH models assuming normal or Student’s t-distribution innovations when doing out-of-sample estimation (within the insample estimation, this is so for the right tail of the distribution of returns).

The condensation and ordering of models of empty liquids

We consider a simple model consisting of particles with four bonding sites ("patches"), two of type A and two of type B, on the square lattice, and investigate its global phase behavior by simulations and theory. We set the interaction between B patches to zero and calculate the phase diagram as the ratio between the AB and the AA interactions, epsilon(AB)*, varies. In line with previous work, on three-dimensional off-lattice models, we show that the liquid-vapor phase diagram exhibits a re-entrant or "pinched" shape for the same range of epsilon(AB)*, suggesting that the ratio of the energy scales - and the corresponding empty fluid regime - is independent of the dimensionality of the system and of the lattice structure. In addition, the model exhibits an order-disorder transition that is ferromagnetic in the re-entrant regime. The use of low-dimensional lattice models allows the simulation of sufficiently large systems to establish the nature of the liquid-vapor critical points and to describe the structure of the liquid phase in the empty fluid regime, where the size of the "voids" increases as the temperature decreases. We have found that the liquid-vapor critical point is in the 2D Ising universality class, with a scaling region that decreases rapidly as the temperature decreases. The results of simulations and theoretical analysis suggest that the line of order-disorder transitions intersects the condensation line at a multi-critical point at zero temperature and density, for patchy particle models with a re-entrant, empty fluid, regime. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3657406]

A educação do corpo na formação do actor conectar-se com o corpo

Projecto de Intervenção apresentado à Escola Superior de Educação de Lisboa para obtenção de grau de mestre em Educação Artística, na especialização de Teatro na Educação

Atividades de investigação em Geometria: uma experiência no 2º ano de escolaridade

Dissertação apresentada à Escola Superior de Educação de Lisboa para obtenção de grau de mestre em Ciências da Educação, especialidade Educação Matemática na Educação Pré-Escolar e nos 1.º e 2.º Ciclos do Ensino Básico

Between theory and practice – teaching maths to elementary school students in Poland

The development of children's school achievements in mathematics is one of the most important aims of education in Poland. The results of research concerning monitoring of school achievements in maths is not optimistic. We can observe low levels of children’s understanding of the merits of maths, self-developed strategies in solving problems and practical usage of maths skills. This article frames the discussion of this problem in its psychological and didactic context and analyses the causes as they relate to school practice in teaching maths

Microscopic Theory of Anchoring Transitions at the Surfaces of Pure Liquid-Crystals and their Mixtures .1. The Fowler Approximation

We have generalized earlier work on anchoring of nematic liquid crystals by Sullivan, and Sluckin and Poniewierski, in order to study transitions which may occur in binary mixtures of nematic liquid crystals as a function of composition. Microscopic expressions have been obtained for the anchoring energy of (i) a liquid crystal in contact with a solid aligning surface; (ii) a liquid crystal in contact with an immiscible isotropic medium; (iii) a liquid crystal mixture in contact with a solid aligning surface. For (iii), possible phase diagrams of anchoring angle versus dopant concentration have been calculated using a simple liquid crystal model. These exhibit some interesting features including re-entrant conical anchoring, for what are believed to be realistic values of the molecular parameters. A way of relaxing the most drastic approximation implicit in the above approach is also briefly discussed.

Simulation and theory of hybrid aligned liquid crystal films

We present a study of the effects of nanoconfinement on a system of hard Gaussian overlap particles interacting with planar substrates through the hard-needle-wall potential, extending earlier work by two of us [D. J. Cleaver and P. I. C. Teixeira, Chem. Phys. Lett. 338, 1 (2001)]. Here, we consider the case of hybrid films, where one of the substrates induces strongly homeotropic anchoring, while the other favors either weakly homeotropic or planar anchoring. These systems are investigated using both Monte Carlo simulation and density-functional theory, the latter implemented at the level of Onsager's second-virial approximation with Parsons-Lee rescaling. The orientational structure is found to change either continuously or discontinuously depending on substrate separation, in agreement with earlier predictions by others. The theory is seen to perform well in spite of its simplicity, predicting the positional and orientational structure seen in simulations even for small particle elongations.

A metáfora e a imagem : estratégias pedagógicas no processo de ensino-aprendizagem na aula de Técnica de Dança Moderna com os alunos dos 2º e 3º anos do ensino vocacional na Academia de Dança Contemporânea de Setúbal

Relatório Final de Estágio apresentado à Escola Superior de Dança, com vista à obtenção do grau de Mestre emMetodologias do Ensino da Dança.

A construção da versatilidade e da motivação nas aulas de Técnica de Dança Moderna com os alunos do 8º ano da Academia de Dança Contemporânea de Setúbal

Relatório Final de Estágio apresentado à Escola Superior de Dança, com vista à obtenção do grau de Mestre em Ensino de Dança.

A composição coreográfica na Academia de Dança Contemporânea de Setúbal dirigida ao ensino secundário

Relatório Final de Estágio apresentado à Escola Superior de Dança, com vista à obtenção do grau de Mestre em Ensino de Dança.

As emoções e o desenvolvimento da criatividade dos alunos de 3º ciclo, no âmbito da Composição Coreográfica, na Escola Vocacional de Dança das Caldas da Rainha

Relatório Final de Estágio apresentado à Escola Superior de Dança, com vista à obtenção do grau de Mestre em Ensino de Dança.