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

Agências Financiadoras: FCT e MIUR

NiII, CuII and ZnII complexes with a sterically hindered scorpionate ligand (TpmsPh) and catalytic application in the diasteroselective nitroaldol (Henry) reaction

The Ni-II and Zn-II complexes [MCl(Tpms(Ph))] (Tpms(Ph) = SO3C(pz(Ph))(3), pz = pyrazolyl; M = Ni 2 or Zn 3) and the Cu-II complex [CuCl(Tpms(Ph))(H2O)] (4) have been prepared by treatment of the lithium salt of the sterically demanding and coordination flexible tris(3-phenyl-1-pyrazolyl)methanesulfonate (Tpms(Ph))(-) (1) with the respective metal chlorides. The (Tpms(Ph))(-) ligand shows the N-3 or N2O coordination modes in 2 and 3 or in 4, respectively. Upon reaction of 2 and 3 with Ag(CF3SO3) in acetonitrile the complexes [M(Tpms(Ph))-(MeCN)](CF3SO3) (M = Ni 5 or Zn 6, respectively) were formed. The compounds were obtained in good yields and characterized by analytic and spectral (IR, H-1 and C-13{H-1} NMR, ESI-MS) data, density functional theory (DFT) methods and {for 4 and [(Bu4N)-Bu-n](Tpms(Ph)) (7), the tatter obtained upon Li+ replacement by [(Bu4N)-Bu-n](+) in Li(Tpms(Ph))} by single crystal X-ray diffraction analysis. The Zn-II and Cu-II complexes (3 and 4, respectively) act as efficient catalyst precursors for the diastereoselective nitroaldol reaction of benzaldehydes and nitroethane to the corresponding beta-nitroalkanols (up to 99% yield, at room temperature) with diastereoselectivity towards the formation of the anti isomer, whereas the Ni-II complex 2 only shows a modest catalytic activity.

Percolation of colloids with distinct interaction sites

We generalize the Flory-Stockmayer theory of percolation to a model of associating (patchy) colloids, which consists of hard spherical particles, having on their surfaces f short-ranged-attractive sites of m different types. These sites can form bonds between particles and thus promote self-assembly. It is shown that the percolation threshold is given in terms of the eigenvalues of a m x m matrix, which describes the recursive relations for the number of bonded particles on the ith level of a cluster with no loops; percolation occurs when the largest of these eigenvalues equals unity. Expressions for the probability that a particle is not bonded to the giant cluster, for the average cluster size and the average size of a cluster to which a randomly chosen particle belongs, are also derived. Explicit results for these quantities are computed for the case f = 3 and m = 2. We show how these structural properties are related to the thermodynamics of the associating system by regarding bond formation as a (equilibrium) chemical reaction. This solution of the percolation problem, combined with Wertheim's thermodynamic first-order perturbation theory, allows the investigation of the interplay between phase behavior and cluster formation for general models of patchy colloids.

A new sedimentary benchmark for the Deccan Traps volcanism?

The origin of the Cretaceous-Paleogene boundary (KPB) mass extinction is still the center of acrimonious debates by opposing partisans of the bolide impact theory to those who favored a terrestrial origin linked to the Deccan Traps volcanism. Here we apply an original and high-resolution environmental magnetic study of the reference Bidart section, France. Our results show that the KPB is identified by an abrupt positive shift of the magnetic susceptibility (MS), also observed by others at the KPB elsewhere. In addition, an anomalous interval of very low MS, carried by an unknown Cl-bearing iron oxide similar to specular hematite, is depicted just below the KPB. Grain-size and morphology of the Cl-iron oxide are typically in the range of hematitic dust currently transported by winds from Sahara to Europe. This discovery is confirmed in the referenced Gubbio section (Italy) suggesting a global scale phenomenon. As a conjecture we suggest an origin by heterogeneous reaction between HCl-rich volcanic gas and liquid-solid aerosols within buoyant atmospheric plumes formed above the newly emitted Deccan flood basalts. Based on this hypothesis, our discovery provides a new benchmark for the Deccan volcanism and witnesses the nature and importance of the related atmospheric change.

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).

Coordination Chemistry of the (eta(6)-p-Cymene)ruthenium(II) Fragment with Bis-, Tris-, andTetrakis(pyrazol-1-yl)borate Ligands: Synthesis, Structural, Electrochemical, and CatalyticDiastereoselective Nitroaldol Reaction Studies

Novel [Ru(eta(6)-p-cymene)(kappa(2)-L)X] and [Ru(eta(6)-p-cymene)(kappa(3)-L)]X center dot nH(2)O complexes (L = bis-, tris-, or tetrakis-pyrazolylborate; X = Cl, N-3, PF6, or CF3SO3) are prepared by treatment of [Ru(eta(6)-p-cymene)Cl-2](2) with poly-(pyrazolyl)borate derivatives [M(L)] (L in general; in detail L = Ph(2)Bp = diphenylbis-(pyrazol-1-yl)borate; L = Tp = hydrotris(pyrazol-1-yl)borate; L = pzTp = tetrakis(pyrazol-1-yl)borate; L = Tp(4Bo) = hydrotris(indazol-1-yl)borate, L = T-p4Bo,T-5Me = (5-methylindazol-1-yl)borate; L = Tp(Bn,4Ph) = hydrotris(3-benzyl-4-phenylpyrazol-1-yl)borate; M = Na, K, or TI) and characterized by analytical and spectral data (IR, ESIMS, H-1 and C-13 NMR). The structures of [Ru(eta(6)-p-cymene)(Ph(2)Bp)Cl] (1) and [Ru(eta(6)-p-cymene)(Tp)Cl] (3) have been established by single-crystal X-ray diffraction analysis. Electrochemical studies allowed comparing the electron-donor characters of Tp and related ligands and estimating the corresponding values of the Lever E-L ligand parameter. The complexes [Ru(eta(6)-p-cymene)-(kappa(2)-L)X] and [Ru(eta(6)-p-cymene)(kappa(3)-L)]X center dot nH(2)O act as catalyst precursors for the diastereoselective nitroaldol reaction of benzaldehyde and nitroethane to the corresponding beta-nitroalkanol (up to 82% yield, at room temperature) with diastereoselectivity toward the formation of the threo isomer.

Study on the glycerolysis reaction of high free fatty acid oils for use as biodiesel feedstock

Biodiesel is the main alternative to fossil diesel and it may be produced from different feedstocks such as semi-refined vegetable oils, waste frying oils or animal fats. However, these feedstocks usually contain significant amounts of free fatty acids (FFA) that make them inadequate for the direct base catalyzed transesterification reaction (where the FFA content should be lower than 4%). The present work describes a possible method for the pre-treatment of oils with a high content of FFA (20 to 50%) by esterification with glycerol. In order to reduce the FFA content, the reaction between these FFA and an esterification agent is carried out before the transesterification reaction. The reaction kinetics was studied in terms of its main factors such astemperature, % of glycerin excess, % of catalyst used, stirring velocity and type of catalyst used. The results showed that glycerolysis is a promising pretreatment to acidic oils or fats (> 20%) as they led to the production of an intermediary material with a low content of FFA that can be used directly in thetransesterification reaction for the production of biodiesel. (C) 2011 Elsevier B.V. All rights reserved.

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

Enlarging the window for radiative leptogenesis

We investigate the scenario of resonant thermal leptogenesis, in which the leptonic asymmetries are generated through renormalization group corrections induced at the leptogenesis scale. In the framework of the standard model extended by three heavy Majorana neutrinos with masses M(1) = M(2) << M(3) at some high scale, we show that the mass splitting and CP-violating effects induced by renormalization group corrections can lead to values of the CP asymmetries large enough for a successful leptogenesis. In this scenario, the low-energy neutrino oscillation data can also be easily accommodated. The possibility of having an underlying symmetry behind the degeneracy in the right-handed neutrino mass spectrum is also discussed. (c) 2005 Elsevier B.V. All rights reserved.

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.

Transitional justice in the judiciary: lessons from the portuguese democratisation

The nature of the Portuguese transition to democracy and the following state crises (1974-1975) created a ‘window of opportunity’ in which the ‘reaction to the past’ was much stronger than in the other Southern or even of Central and Eastern European transitions. In Portugal, initiatives of symbolic rupture with the past began soon after the April 25, 1974, coup d’état and transitional justice policies assumed mainly three formulas. First, the institutional reforms directed primarily to abusive state institutions such as the political police (PIDE-DGS) and political courts (Plenary courts) in order to dismantle the repressive apparatus and prevent further human rights abuses and impunity. Secondly, the criminal prosecutions addressed to perpetrators considered as being the most responsible for repression and abuses. Finally, lustration or political purges (saneamentos, the term used in Portugal to designate political purges) which were, in fact, the most common form of political justice in Portuguese transition to democracy. This paper deals with the peculiarities of transitional justice in Portugal devoting a particular attention to the judicial, a key sector to understand the way the Portuguese dealt with their authoritarian past.

Action, reaction and protest by publishers in 1960s Portugal: books and other publications in the Catholic opposition

The authoritarian regime of the Portuguese Estado Novo (New State), the longest dictatorship in twentieth-century Western Europe, suffered one of its most serious threats during the late 1950s and the whole of the following decade. An array of events and dynamics of opposition to the regime and condemnation of the political and social situation in Portugal appeared at that time. One of the core groups that displayed their dissidence in the 1960s, with the awakening of their critical conscience, originated in Catholic sectors that rallied the laity and the clergy to express their disagreement or even break with the government of Salazar (and, later, Marcelo Caetano). This article aims to establish the role of print culture and, in particular, publishing in the opposition’s mobilisation of Catholics who criticised the Estado Novo. It will also closely examine the contribution of certain publishers to the formulation of the terms of this mobilisation, in publishing new authors and topics and creating new printed forums (e.g. periodicals) for discussion and reflection. The most detailed case will be that of the publishing house Livraria Moraes Editora, under the command of the publisher António Alçada Baptista.

Cobalt complexes with pyrazole ligands as catalyst precursors for the peroxidative oxidation of cyclohexane: Z-ray absorption spectroscopy studies and biological applications

[CoCl(-Cl)(Hpz(Ph))(3)](2) (1) and [CoCl2(Hpz(Ph))(4)] (2) were obtained by reaction of CoCl2 with HC(pz(Ph))(3) and Hpz(Ph), respectively (Hpz(Ph)=3-phenylpyrazole). The compounds were isolated as air-stable solids and fully characterized by IR and far-IR spectroscopy, MS(ESI+/-), elemental analysis, cyclic voltammetry (CV), controlled potential electrolysis, and single-crystal X-ray diffraction. Electrochemical studies showed that 1 and 2 undergo single-electron irreversible (CoCoIII)-Co-II oxidations and (CoCoI)-Co-II reductions at potentials measured by CV, which also allowed, in the case of dinuclear complex 1, the detection of electronic communication between the Co centers through the chloride bridging ligands. The electrochemical behavior of models of 1 and 2 were also investigated by density functional theory (DFT) methods, which indicated that the vertical oxidation of 1 and 2 (that before structural relaxation) affects mostly the chloride and pyrazolyl ligands, whereas adiabatic oxidation (that after the geometry relaxation) and reduction are mostly metal centered. Compounds 1 and 2 and, for comparative purposes, other related scorpionate and pyrazole cobalt complexes, exhibit catalytic activity for the peroxidative oxidation of cyclohexane to cyclohexanol and cyclohexanone under mild conditions (room temperature, aqueous H2O2). Insitu X-ray absorption spectroscopy studies indicated that the species derived from complexes 1 and 2 during the oxidation of cyclohexane (i.e., Ox-1 and Ox-2, respectively) are analogous and contain a Co-III site. Complex 2 showed low invitro cytotoxicity toward the HCT116 colorectal carcinoma and MCF7 breast adenocarcinoma cell lines.