A new maximum likelihood method for luminosity calibrations

A new statistical parallax method using the Maximum Likelihood principle is presented, allowing the simultaneous determination of a luminosity calibration, kinematic characteristics and spatial distribution of a given sample. This method has been developed for the exploitation of the Hipparcos data and presents several improvements with respect to the previous ones: the effects of the selection of the sample, the observational errors, the galactic rotation and the interstellar absorption are taken into account as an intrinsic part of the formulation (as opposed to external corrections). Furthermore, the method is able to identify and characterize physically distinct groups in inhomogeneous samples, thus avoiding biases due to unidentified components. Moreover, the implementation used by the authors is based on the extensive use of numerical methods, so avoiding the need for simplification of the equations and thus the bias they could introduce. Several examples of application using simulated samples are presented, to be followed by applications to real samples in forthcoming articles.

Validated spectrofluorometric method for determination of gemfibrozil in self nanoemulsifying drug delivery systems (SNEDDS)

A spectrofluorometric method has been developed and validated for the determination of gemfibrozil. The method is based on the excitation and emission capacities of gemfibrozil with excitation and emission wavelengths of 276 and 304 nm respectively. This method allows de determination of the drug in a self-nanoemulsifying drug delivery system (SNEDDS) for improve its intestinal absorption. Results obtained showed linear relationships with good correlation coefficients (r(2)>0.999) and low limits of detection and quantification (LOD of 0.075 μg mL(-1) and LOQ of 0.226 μg mL(-1)) in the range of 0.2-5 μg mL(-1), equally this method showed a good robustness and stability. Thus the amounts of gemfibrozil released from SNEDDS contained in gastro resistant hard gelatine capsules were analysed, and release studies could be performed satisfactorily.

Random walk radiosity with generalized absorption probabilities

The author studies random walk estimators for radiosity with generalized absorption probabilities. That is, a path will either die or survive on a patch according to an arbitrary probability. The estimators studied so far, the infinite path length estimator and finite path length one, can be considered as particular cases. Practical applications of the random walks with generalized probabilities are given. A necessary and sufficient condition for the existence of the variance is given, together with heuristics to be used in practical cases. The optimal probabilities are also found for the case when one is interested in the whole scene, and are equal to the reflectivities

On the upper bound of the number of limit cycles obtained by the second order averaging method I

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On the upper bound of the number of limit cycles obtained by the second order averaging method II

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A rotation method which gives linear Lp-Estimates for powers of the Ahlfors-Beurling operator

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Research work in Tokyo Institute of Technology

Research carried out in Tokyo Institute of Technology. The objective is to determine the influence of Interfacial Transition Zone (ITZ) around Lightweight aggregate in concrete on Chloride ion diffusivity. The ITZ of conventional concretes is the weakest point of concrete. The accumulating water on ITZ zone forms the most permeable area inside the concrete. Hence ITZ paves the way for chloride ion diffusion. The quality of ITZ depends on type and quality of aggregates used, water-cement ratio and also the method used for the production of concrete. It has been used two types of lightweight aggregates will be used, Chinese and Japanese, with different absorption capacities. The idea is to produce concrete with same effective water - cement ratio, using the same aggregates in two different conditions, dry and saturated, and compare the chloride ion diffusivity in these concretes (by diffusion test). A comparison of ITZ thickness of these concretes by SEM and EDAX-maps is also proposed. The chloride ion diffusion of concretes produced with the same effective water – cement ratio and same aggregates (dry and ssd) will depend, mainly, on ITZ.

Stability of periodic solutions obtained via the averaging method for nonsmooth Lipschitz system

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Determinació de la ubicació estructural dels ions Yb3+ i Nb3+ en Yb:RTP, Nb:RTP i (Nb,Yb):RTP

Estudi elaborat a partir d’una estada al Stony Brook University al juliol del 2006. El RbTiOPO4 (RTP) monocristal•lí és un material d' òptica no lineal molt rellevant i utilitzat en la tecnologia làser actual, químicament molt estable i amb unes propietats físiques molt destacades, entre elles destaquen els alts coeficients electro-òptics i l'alt llindar de dany òptic que presenta. En els últims anys s’està utilitzant tecnològicament en aplicacions d'òptica no lineal en general i electro-òptiques en particular. En alguns casos ja ha substituït, millorant prestacions, a materials tals com el KTP o el LNB(1). Dopant RTP amb ions lantànids (Ln3+) (2-4), el material es converteix en un material làser auto-doblador de freqüència, combinant les seves propietats no lineals amb les de matriu làser. El RTP genera radiació de segon harmònic (SHG) a partir d’un feix fonamental amb longituds d’ona inferiors a 990 nm, que és el límit que presenta el KTP.La determinació de la ubicació estructural i l’estudi de l'entorn local del ions actius làser és de fonamental importància per a la correcta interpretació de les propietats espectroscòpiques d’aquest material. Mesures de difracció de neutrons sobre mostra de pols cristal•lí mostren que els ions Nb5+ i Ln3+ només substitueixin posicions de Ti4+ (8-9). Estudis molt recents d'EPR (electron paramagnetic resonance) semblen indicar que quan la concentració d'ió Ln3+ es baixa, aquest ió presenta la tendència a substituir l'ió alcalí present a l'estructura (10).Després dels resultats obtinguts en el present treball a partir de la tècnica EXAFS a la instal•lació sincrotò del Brookhaven National Laboratory/State University of New York (Stony Brook) es pot concloure definitivament que els ions Nb s’ubiquen en la posició Ti (1) i que els ions Yb3+ es distribueixen paritariament en les dues posicions del Ti (1 i 2). Aquests resultats aporten una valuosa informació per a la correcta interpretació dels espectres, tant d’absorció com d’emissió, del material i per la avaluació dels paràmetres del seu comportament durant l'acció làser.

Hopf bifurcation in higher dimensional differential systems via the averaging method

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Simulación de fluidos inmiscibles con el Particle Finite Element Method (PFEM)

Proyecto de investigación realizado a partir de una estancia en el Centro Internacional de Métodos Computacionales en Ingeniería (CIMEC), Argentina, entre febrero y abril del 2007. La simulación numérica de problemas de mezclas mediante el Particle Finite Element Method (PFEM) es el marco de estudio de una futura tesis doctoral. Éste es un método desarrollado conjuntamente por el CIMEC y el Centre Internacional de Mètodos Numèrics en l'Enginyeria (CIMNE-UPC), basado en la resolución de las ecuaciones de Navier-Stokes en formulación Lagrangiana. El mallador ha sido implementado y desarrollado por Dr. Nestor Calvo, investigador del CIMEC. El desarrollo del módulo de cálculo corresponde al trabajo de tesis de la beneficiaria. La correcta interacción entre ambas partes es fundamental para obtener resultados válidos. En esta memoria se explican los principales aspectos del mallador que fueron modificados (criterios de refinamiento geométrico) y los cambios introducidos en el módulo de cálculo (librería PETSc, algoritmo predictor-corrector) durante la estancia en el CIMEC. Por último, se muestran los resultados obtenidos en un problema de dos fluidos inmiscibles con transferencia de calor.

A mixed finite element method for nonlinear diffusion equations

We propose a mixed finite element method for a class of nonlinear diffusion equations, which is based on their interpretation as gradient flows in optimal transportation metrics. We introduce an appropriate linearization of the optimal transport problem, which leads to a mixed symmetric formulation. This formulation preserves the maximum principle in case of the semi-discrete scheme as well as the fully discrete scheme for a certain class of problems. In addition solutions of the mixed formulation maintain exponential convergence in the relative entropy towards the steady state in case of a nonlinear Fokker-Planck equation with uniformly convex potential. We demonstrate the behavior of the proposed scheme with 2D simulations of the porous medium equations and blow-up questions in the Patlak-Keller-Segel model.

Giacomo Becattini and the Marshall's method. A Schumpeterian approach

The studies of Giacomo Becattini concerning the notion of the "Marshallian industrial district" have led a revolution in the field of economic development around the world. The paper offers an interpretation of the methodology adopted by Becattini. The roots are clearly Marshallian. Becattini proposes a return to the economy as a complex social science that operates in historical time. We adopt a Schumpeterian approach to the method in economic analysis in order to highlight the similarities between the Marshall and Becattini's approach. Finally the paper uses the distinction between logical time, real time and historical time which enable us to study the "localized" economic process in a Becattinian way.