Integrability of a linear center perturbed by a fourth degree homogeneous polynomial

In this work we study the integrability of a two-dimensional autonomous system in the plane with linear part of center type and non-linear part given by homogeneous polynomials of fourth degree. We give sufficient conditions for integrability in polar coordinates. Finally we establish a conjecture about the independence of the two classes of parameters which appear in the system; if this conjecture is true the integrable cases found will be the only possible ones.

Integrability of a linear center perturbed by a fifth degree homogeneous polynomial

In this work we study the integrability of two-dimensional autonomous system in the plane with linear part of center type and non-linear part given by homogeneous polynomials of fifth degree. We give a simple characterisation for the integrable cases in polar coordinates. Finally we formulate a conjecture about the independence of the two classes of parameters which appear on the system; if this conjecture is true the integrable cases found will be the only possible ones.

Better-quasi-order : ideals and spaces

This thesis deals with combinatorics, order theory and descriptive set theory. The first contribution is to the theory of well-quasi-orders (wqo) and better-quasi-orders (bqo). The main result is the proof of a conjecture made by Maurice Pouzet in 1978 his thèse d'état which states that any wqo whose ideal completion remainder is bqo is actually bqo. Our proof relies on new results with both a combinatorial and a topological flavour concerning maps from a front into a compact metric space. The second contribution is of a more applied nature and deals with topological spaces. We define a quasi-order on the subsets of every second countable To topological space in a way that generalises the Wadge quasi-order on the Baire space, while extending its nice properties to virtually all these topological spaces. The Wadge quasi-order of reducibility by continuous functions is wqo on Borei subsets of the Baire space, this quasi-order is however far less satisfactory for other important topological spaces such as the real line, as Hertling, Ikegami and Schlicht notably observed. Some authors have therefore studied reducibility with respect to some classes of discontinuous functions to remedy this situation. We propose instead to keep continuity but to weaken the notion of function to that of relation. Using the notion of admissible representation studied in Type-2 theory of effectivity, we define the quasi-order of reducibility by relatively continuous relations. We show that this quasi-order both refines the classical hierarchies of complexity and is wqo on the Borei subsets of virtually every second countable To space - including every (quasi-)Polish space. -- Cette thèse se situe dans les domaines de la combinatoire, de la théorie des ordres et de la théorie descriptive. La première contribution concerne la théorie des bons quasi-ordres (wqo) et des meilleurs quasi-ordres (bqo). Le résultat principal est la preuve d'une conjecture, énoncée par Pouzet en 1978 dans sa thèse d'état, qui établit que tout wqo dont l'ensemble des idéaux non principaux ordonnés par inclusion forme un bqo est alors lui-même un bqo. La preuve repose sur de nouveaux résultats, qui allient la combinatoire et la topologie, au sujet des fonctions d'un front vers un espace métrique compact. La seconde contribution de cette thèse traite de la complexité topologique dans le cadre des espaces To à base dénombrable. Dans le cas de l'espace de Baire, le quasi-ordre de Wadge est un wqo sur les sous-ensembles Boréliens qui a suscité énormément d'intérêt. Cependant cette relation de réduction par fonctions continues s'avère bien moins satisfaisante pour d'autres espaces d'importance tels que la droite réelle, comme l'ont fait notamment remarquer Hertling, Schlicht et Ikegami. Nous proposons de conserver la continuité et d'affaiblir la notion de fonction pour celle de relation. Pour ce faire, nous utilisons la notion de représentation admissible étudiée en « Type-2 theory of effectivity » initiée par Weihrauch. Nous introduisons alors le quasi-ordre de réduction par relations relativement continues et montrons que celui-ci à la fois raffine les hiérarchies classiques de complexité topologique et forme un wqo sur les sous-ensembles Boréliens de chaque espace quasi-Polonais.

Beurling-Landau densities of weighted Fekete sets and correlation kernel estimates

Let $Q$ be a suitable real function on $C$. An $n$-Fekete set corresponding to $Q$ is a subset ${Z_{n1}},\dotsb, Z_{nn}}$ of $C$ which maximizes the expression $\Pi^n_i_{conjecture that such global results are true for a wide range of potentials.

Rotation mentale et différences sexuelles: influence des axes directionnels extraits de l'environnement

Les tâches nécessitant des manipulations et des transformations de figures géométriques et de formes, comme les tâches de rotation mentale, donnent lieu à des différences de performance entre hommes et femmes qui restent intrigantes. Plusieurs hypothèses ont été proposées pour expliquer ces différences. La plus récurrente porte sur les différences de stratégie globale vs locale utilisées pour traiter l'information. Bien que cette conjecture soit intéressante, elle reste difficile à opérationnaliser car elle englobe tous les mécanismes cognitifs (acquisition, conservation et récupération de l'information). Ce travail prend la forme d'un retour aux sources dans la mesure où il se base sur des recherches anciennes qui ont montré que les hommes perçoivent significativement mieux que les femmes la verticale et l'horizontale. Il teste l'hypothèse selon laquelle les hommes, comparativement aux femmes, présentent une plus forte indépendance au champ perceptif visuel et sont donc plus susceptibles d'utiliser la verticalité et l'horizontalité pour résoudre une tâche de rotation mentale. Une première série d'expériences s'est penchée sur la perception spatiale pour évaluer son impact sur la résolution d'une tâche impliquant la rotation mentale. Les résultats ont montré que seuls les hommes se référaient à la verticalité et à l'horizontalité pour résoudre la tâche. Une seconde série d'expériences ont investigué l'effet de la présence, ou absence, d'axes directionnels directement liés à une tâche de rotation mentale. Elles ont été menées également en environnement réel afin d'évaluer comment le déplacement actif ou passif, correspondant à un changement de perspective en lieu et place d'une rotation mentale, module la performance des hommes et des femmes. Les résultats n'ont pas mis en évidence de différence sexuelle. Notre hypothèse est vérifiée puisque c'est uniquement lorsque la tâche ne présente pas d'axes orthogonaux évidents mais implicites que seuls les hommes, plus indépendants au champ perceptif visuel que les femmes, utilisent la perception de la verticalité et de l'horizontalité pour améliorer leur compétence en rotation mentale. -- Tasks that require manipulation and transformation of geometric shapes and forms, like tasks of mental rotation and give rise to differences in performance between men and women, remain intriguing. Several hypotheses have been proposed to explain these differences. The most recurring hypothesis addresses differences in global versus local strategies for processing information. While this conjecture is interesting, it remains difficult to study because it encompasses all the cognitive mechanisms (acquisition, retention and output). This work returns to the sources, which are based on earlier research that shows that men are significantly better than women at perceiving verticality and horizontality. It tests the hypothesis according to which men, as compared to women, exhibit a greater independence on the perceptive visual field, and therefore are more susceptible to utilizing the verticality and the horizontality to solve a mental rotation task. A first set of experiments examined spatial perception in order to assess its impact on the resolution of a task involving mental rotation. The results showed that only men referred to the verticality and the horizontality to solve the task. A second series of experiments investigated the effect of a presence, or absence of directional axes directed tied to the task of mental rotation. They were also conducted in a real world environment to evaluate how the active or passive displacement, corresponding to a change in perspective instead of a mental rotation, modulates the performance of men and women. The results did not show sex differences. Our hypothesis is verified: it is only when the task presents no obvious, but implicit orthogonal axes that men, who exhibit a greater independence on the perceptive visual field than women, use the perception of verticality and horizontality to improve their competence in mental rotation.

Radiographic adenoid evaluation: proposal of an objective parameter

Objective The objective of the present study was to evaluate current radiographic parameters designed to investigate adenoid hypertrophy and nasopharyngeal obstruction, and to present an alternative radiographic assessment method. Materials and Methods In order to do so, children (4 to14 years old) who presented with nasal obstruction or oral breathing complaints were submitted to cavum radiographic examination. One hundred and twenty records were evaluated according to quantitative radiographic parameters, and data were correlated with a gold-standard videonasopharyngoscopic study, in relation to the percentage of choanal obstruction. Subsequently, a regression analysis was performed in order to create an original model so the percentage of the choanal obstruction could be predicted. Results The quantitative parameters demonstrated moderate, if not weak correlation with the real percentage of choanal obstruction. The regression model (110.119*A/N) demonstrated a satisfactory ability to “predict” the actual percentage of choanal obstruction. Conclusion Since current adenoid quantitative radiographic parameters present limitations, the model presented by the present study might be considered as an alternative assessment method in cases where videonasopharyngoscopic evaluation is unavailable.

Alternativas quimiométricas para a resolução de problemas analíticos clássicos: determinação espectrofotométrica de misturas de zircônio e háfnio

The determination of zirconium-hafnium mixtures is one of the most critical problem of the analytical chemistry, on account of the close similarity of their chemical properties. The spectrophotometric determination proposed by Yagodin et al. show not many practical applications due to the significant spectral interference on the 200-220 nm region. In this work we propound the use of a multivariate calibration method called partial least squares ( PLS ) for colorimetric determination of these mixtures. By using PLS and 16 calibration mixtures we obtained a model which permits determination of zirconium and hafnium with accuracy of about 1-2% and 10-20%, respectively. Using conventional univariate calibration the inaccuracy of the determination is about 10-25% for zirconium and above 57% for hafnium.

Métodos matemáticos para correção de interferências espectrais e efeitos interelementos na análise quantitativa por fluorescência de raios-X

One of the main problems in quantitative analysis of complex samples by x-ray fluorescence is related to interelemental (or matrix) effects. These effects appear as a result of interactions among sample elements, affecting the x-ray emission intensity in a non-linear manner. Basically, two main effects occur; intensity absorption and enhancement. The combination of these effects can lead to serious problems. Many studies have been carried out proposing mathematical methods to correct for these effects. Basic concepts and the main correction methods are discussed here.

Utilização de regressão multivariada para avaliação espectrofotométrica da demanda química de oxigênio em amostras de relevância ambiental

In this work, a partial least squares regression routine was used to develop a multivariate calibration model to predict the chemical oxygen demand (COD) in substrates of environmental relevance (paper effluents and landfill leachates) from UV-Vis spectral data. The calibration models permit the fast determination of the COD with typical relative errors lower by 10% with respect to the conventional methodology.

Determinação de misturas de sulfametoxazol e trimetoprima por espectroscopia eletrônica multivariada

In this work a multivariate spectroscopic methodology is proposed for quantitative determination of sulfamethoxazole and trimethoprim in pharmaceutical associations. The multivariate model was developed by partial least-squares regression, using twenty synthetic mixtures and the spectral region between 190 and 350 nm. In the validation stage, which involved the analysis of five synthetic mixtures, prediction errors lower that 3% were observed. The predictive capacity of the multivariate models is seriously affected by spectral changes induced by pH variations, a fact that acquires a great significance in the analysis of real samples (pharmaceuticals) that contain chemical additives.

Rescatando a Baiter: a propósito de la origo de Marco Celio Rufo (CIC. CAEL. 5)

El objetivo del texto es recuperar la intuición de Johan Georg Baiter (1801-­‐‑1877) que propuso Tusculum (Lacio, Italia) como patria de origen de Marco Celio Rufo enmendando una corruptela en la edición orelliana del Pro Caelio ciceroniano. Esta conjetura, desestimada en todas las ediciones posteriores del texto, ha sido recientemente confirmada gracias al hallazgo de un epígrafe que documenta por vez primera en la ciudad lacial un magistrado M. Caelius de época tardorepublicana.

Otimizaçâo das condições de preparação de eletrodos à base de carbono cerâmico utilizando-se planejamento fatorial

Different parameters of carbon ceramic electrodes (CCE) preparation, such as type of precursor, carbon material, catalyst amount, among others, significantly influence the morphological properties and consequently their electrochemical responses. This paper describes a 2³ factorial design (2 factors and 3 levels with central point replicates), which the factors analyzed were catalyst amount (HCl 12 mol L-1), graphite/precursor ratio, and precursor type (TEOS - tetraethoxysilane and MTMOS - methyltrimetoxysilane). The design resulted in a significant third order interaction for peak current values (Ipa) and a second order interaction for potential difference (ΔE), between thefactors studied, which could not be observed when using an univariated study.

Determinação de sibutramina em formas farmacêuticas através de espectroscopia no infravermelho com refletância difusa e métodos de calibração multivariada

The goal of this work is the development and validation of an analytical method for fast quantification of sibutramine in pharmaceutical formulations, using diffuse reflectance infrared spectroscopy and partial least square regression. The multivariate model was elaborated from 22 mixtures containing sibutramine and excipients (lactose, microcrystalline cellulose, colloidal silicon dioxide and magnesium stearate) and using fragmented (750-1150/ 1350-1500/ 1850-1950/ 2600-2900 cm-1) and smoothing spectral data. Using 10 latent variables, excellent predictive capacity were observed in the calibration (n=20, RMSEC=0.004, R= 0.999) and external validation (n=5, RMSEC= 9.36, R=0.999) phases. In the analysis of synthetic mixtures the precision (SD=3,47%) was compatible with the rules of the Agencia Nacional de Vigilância Sanitária (ANVISA-Brazil). In the analysis of commercial drugs good agreement was observed between spectroscopic and chromatographic methods.

Determinação simultânea de ácido kójico e hidroquinona por espectrofotometria visível e calibração multivariada

A multivariate spectrophotometric method was developed for analysis of kojic acid/hydroquinone associations in skin whitening cosmetics. The method is based on the reaction between kojic acid and Fe3+ and on the reduction of Fe3+ by hydroquinone and further complexation of Fe2+ with 1,10-phenanthroline. The multivariate model was developed by Partial Least Squares Regression (PLSR), using 25 synthetic mixtures and mean-centered spectral data (350-380 nm). The use of 3 (kojic acid) and 2 (hydroquinone) latent variables permits the observation of mean errors of about 5% in the external validation phase.

Avaliação do perfil de dissolução de medicamentos utilizando-se espectroscopia eletrônica multivariada

In this work the evaluation of the dissolution profile of captopril-hydrochlorothiazide and zidovudine-lamivudine associations were carried out by multivariate spectroscopic method. The models were developed by partial least square regression from 20 synthetic mixtures using mean-centered spectral data. The external validation was accomplished with 5 synthetic mixtures shown mean prevision error of about 1%. Good agreement was observed in the analyses of commercial drugs (content uniformity and dissolution profile), considering the results obtained by the standard chromatographic method, with prevision error lower than 10%.