Dualidade de Poincaré e invariantes cohomológicos

Pós-graduação em Matemática - IBILCE

Fractal scaling exponents of heart rate variability association with linear indices and Poincaré Plot

The literature indicated that the fractal analysis of heart rate variability (HRV) is related to the chaos theory. However, it is not clear if the both short and long-term fractal scaling exponents of HRV are reliable for short period analysis in women. We evaluated the association of the fractal exponents of HRV with the time and frequency domain and geometric indices of HRV. We evaluated 65 healthy women between 18 and 30 years old. HRV was analyzed with a minimal number of 256 RR intervals in the time (SDNN, RMSSD, NN50 and pNN50) and frequency (LF, HF and LF/HF ratio) domains, the geometric index were also analyzed (triangular indexRRtri, triangular interpolation of RR intervals-TINN and Poincaré plot-SD1, SD2 and SD1/SD2) as well as short and long-term fractal exponents (alpha-1 and alpha-2) of the detrended fluctuation analysis (DFA). No significant correlation was observed for alpha-2 exponent with all indices. There was significant correlation of the alpha-1 exponent with RMSSD, pNN50, SDNN/RMSSD, LF (nu), HF (nu and ms2 ), LF/HF ratio, SD1 and SD1/SD2 ratio. Our data does not indicate the alpha-2 exponent to be used for 256 RR intervals and we support the alpha-1 exponent to be used for HRV analysis in this condition.

COINCIDENCES OF FIBREWISE MAPS BETWEEN SPHERE BUNDLES OVER THE CIRCLE

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Flattening of the resonance spectrum of hadrons from κ-deformed Poincaré algebra

Recently Lukierski et al. [1] defined a κ-deformed Poincaré algebra which is characterized by having the energy-momentum and angular momentum sub-algebras not deformed. Further Biedenharn et al. [2] showed that on gauging the κ-deformed electron with the electromagnetic field, one can set a limit on the allowed value of the deformation parameter ∈ ≡ 1/κ < 1 fm. We show that one gets Regge like angular excitations, J, of the mesons, non-strange and strange baryons, with a value of ∈ ∼ 0.082 fm and predict a flattening with J of the corresponding trajectories. The Regge fit improves on including deformation, particularly for the baryon spectrum.

Introdução à teoria de Poincaré-Bendixson para campos de vetores planares

O Teorema de Poincaré-Bendixson é um resultado muito importante no estudo de Sistemas Dinâmicos, pois ele estabelece para quais tipos de conjunto limite as trajetórias de um campo de vetores em IR2 deve convergir. Neste trabalho vamos abordar a Funç˜ao do primeiro Retorno de Poincaré, além de discutir a estabilidade de Ciclos Limites e provar o Teorema de Poincaré-Bendixson.

Contesting Sphere Boundaries Online: Private/Technical/Public Discourses in Polycystic Ovarian Syndrome Discussion Groups

The internet is fast becoming a means for people to obtain information, creating a unique forum for the intersection of the public, technical, and private spheres. To ground my research theoretically, I used Jürgen Habermas’s sphere theory. Habermas (1987) explains that the technical sphere colonizes the private sphere, which decreases democratic potential. In particular, the internet is a place for altering technical colonization of the private and public spheres. My research focuses on women’s health because it is a particularly useful case study for examining sphere tensions. Historically, the biomedical health establishment has been a powerful agent of colonization, resulting in detrimental effects for women and their health. The purpose of this study is to examine how the internet encourages expert and female patient deliberation, which empowers women to challenge the experts and, thus, make conversations between the private/technical spheres more democratic. I used PCOS (Polycystic Ovarian Syndrome) as a case to observe the changing sphere boundaries by studying the discourse that took place on multiple patient and doctor websites over a four-year period. Through my research, I found that the PCOS women challenge the biomedical model by appropriating medical language. By understanding the medical talk, the women are able to feel confident when discussing their health conditions with the doctor and with each other. The PCOS women also become lay-experts who have personal and medical experience with PCOS, reducing private sphere colonization. This case study exemplifies how female empowerment can influence expert culture, challenging our conventional understanding of democracy.

Morphology and topography analysis of mesoporous titania templated by micrometric latex sphere arrays

In this work, mesoporous titania is prepared by templating latex sphere arrays with four different sphere diameters at the micrometric scale (phi > 1 mu m). The mesoporous titania homogeneously covers the latex spheres and substrate, forming a thin coating characterized by N-2 adsorption isotherm, small angle X-rays scattering, atomic force, field emission and transmission electronic microscopies. Mesoporous titania has been templated into different shapes such as hollow particles and monoliths according to the amount of sol used to fill the voids of the close packed latex spheres. Titania topography strongly depends on the adsorption of polymeric segments over latex spheres surface, which could be decreased by changing the dimensions of latex spheres (phi = 9.5 mu m) generating a lamellar architecture. Thus, micrometric latex sphere arrays can be used to achieve new surface patterns for mesoporous materials via a fast and inexpensive chemical route for construction of functional devices in different technological fields such as energy conversion, inclusion chemistry and biomaterials. (C) 2011 Elsevier Inc. All rights reserved.

Weighted Fourier–Laplace transforms in reproducing kernel Hilbert spaces on the sphere

We study the action of a weighted Fourier–Laplace transform on the functions in the reproducing kernel Hilbert space (RKHS) associated with a positive definite kernel on the sphere. After defining a notion of smoothness implied by the transform, we show that smoothness of the kernel implies the same smoothness for the generating elements (spherical harmonics) in the Mercer expansion of the kernel. We prove a reproducing property for the weighted Fourier–Laplace transform of the functions in the RKHS and embed the RKHS into spaces of smooth functions. Some relevant properties of the embedding are considered, including compactness and boundedness. The approach taken in the paper includes two important notions of differentiability characterized by weighted Fourier–Laplace transforms: fractional derivatives and Laplace–Beltrami derivatives.

Sharp estimates for eigenvalues of integral operators generated by dot product kernels on the sphere

We obtain explicit formulas for the eigenvalues of integral operators generated by continuous dot product kernels defined on the sphere via the usual gamma function. Using them, we present both, a procedure to describe sharp bounds for the eigenvalues and their asymptotic behavior near 0. We illustrate our results with examples, among them the integral operator generated by a Gaussian kernel. Finally, we sketch complex versions of our results to cover the cases when the sphere sits in a Hermitian space.

Optical resonances of sphere-on-plane geometries

The optical resonances of metallic nanoparticles placed at nanometer distances from a metal plane were investigated. At certain wavelengths, these “sphere-on-plane” systems become resonant with the incident electromagnetic field and huge enhancements of the field are predicted localized in the small gaps created between the nanoparticle and the plane. An experimental architecture to fabricate sphere-on-plane systems was successfully achieved in which in addition to the commonly used alkanethiols, polyphenylene dendrimers were used as molecular spacers to separate the metallic nanoparticles from the metal planes. They allow for a defined nanoparticle-plane separation and some often are functionalized with a chromophore core which is therefore positioned exactly in the gap. The metal planes used in the system architecture consisted of evaporated thin films of gold or silver. Evaporated gold or silver films have a smooth interface with their substrate and a rougher top surface. To investigate the influence of surface roughness on the optical response of such a film, two gold films were prepared with a smooth and a rough side which were as similar as possible. Surface plasmons were excited in Kretschmann configuration both on the rough and on the smooth side. Their reflectivity could be well modeled by a single gold film for each individual measurement. The film has to be modeled as two layers with significantly different optical constants. The smooth side, although polycrystalline, had an optical response that was very similar to a monocrystalline surface while for the rough side the standard response of evaporated gold is retrieved. For investigations on thin non-absorbing dielectric films though, this heterogeneity introduces only a negligible error. To determine the resonant wavelength of the sphere-on-plane systems a strategy was developed which is based on multi-wavelength surface plasmon spectroscopy experiments in Kretschmann-configuration. The resonant behavior of the system lead to characteristic changes in the surface plasmon dispersion. A quantitative analysis was performed by calculating the polarisability per unit area /A treating the sphere-on-plane systems as an effective layer. This approach completely avoids the ambiguity in the determination of thickness and optical response of thin films in surface plasmon spectroscopy. Equal area densities of polarisable units yielded identical response irrespective of the thickness of the layer they are distributed in. The parameter range where the evaluation of surface plasmon data in terms of /A is applicable was determined for a typical experimental situation. It was shown that this analysis yields reasonable quantitative agreement with a simple theoretical model of the sphere-on-plane resonators and reproduces the results from standard extinction experiments having a higher information content and significantly increased signal-to-noise ratio. With the objective to acquire a better quantitative understanding of the dependence of the resonance wavelength on the geometry of the sphere-on-plane systems, different systems were fabricated in which the gold nanoparticle size, type of spacer and ambient medium were varied and the resonance wavelength of the system was determined. The gold nanoparticle radius was varied in the range from 10 nm to 80 nm. It could be shown that the polyphenylene dendrimers can be used as molecular spacers to fabricate systems which support gap resonances. The resonance wavelength of the systems could be tuned in the optical region between 550 nm and 800 nm. Based on a simple analytical model, a quantitative analysis was developed to relate the systems’ geometry with the resonant wavelength and surprisingly good agreement of this simple model with the experiment without any adjustable parameters was found. The key feature ascribed to sphere-on-plane systems is a very large electromagnetic field localized in volumes in the nanometer range. Experiments towards a quantitative understanding of the field enhancements taking place in the gap of the sphere-on-plane systems were done by monitoring the increase in fluorescence of a metal-supported monolayer of a dye-loaded dendrimer upon decoration of the surface with nanoparticles. The metal used (gold and silver), the colloid mean size and the surface roughness were varied. Large silver crystallites on evaporated silver surfaces lead to the most pronounced fluorescence enhancements in the order of 104. They constitute a very promising sample architecture for the study of field enhancements.

La PCA per la riduzione dei dati di SPHERE IFS

Nel primo capitolo di questa tesi viene presentata una panoramica dei principali metodi di rivelazione degli esopianeti: il metodo della Velocità Radiale, il metodo Astrometrico, il metodo del Pulsar Timing, il metodo del Transito, il metodo del Microlensing ed infine il metodo del Direct Imaging che verrà approfondito nei capitoli successivi. Nel secondo capitolo vengono presentati i principi della diffrazione, viene mostrato come attenuare la luce stellare con l'uso del coronografo; vengono descritti i fenomeni di aberrazione della luce provocati dalla strumentazione e dagli effetti distorsivi dell'atmosfera che originano le cosiddette speckle; vengono poi presentate le moderne soluzioni tecniche come l'ottica attiva e adattiva, che hanno permesso un considerevole miglioramento della qualità delle osservazioni. Nel terzo capitolo sono illustrate le tecniche di Differential Imaging che permettono di rimuovere efficacemente le speckle e di migliorare il contrasto delle immagini. Nel quarto viene presentata una descrizione matematica della Principal Component Analysis (Analisi delle Componenti Principali), il metodo statistico utilizzato per la riduzione dei dati astronomici. Il quinto capitolo è dedicato a SPHERE, lo strumento progettato per il Very Large Telescope (VLT), in particolare viene descritto il suo spettrografo IFS con il quale sono stati ottenuti, nella fase di test, i dati analizzati nel lavoro di tesi. Nel sesto capitolo vengono mostrate le procedure di riduzione dati e l'applicazione dell'algoritmo di IDL LA_SVD che applica la Principal Component Analysis e ha permesso, analogamente ai metodi di Differenzial Imaging visti in precedenza, di rimuovere le speckle e migliorare il contrasto delle immagini. Nella parte conclusiva, vengono discussi i risultati.

The Poincaré polynomial for the Hilbert scheme of points of C^2

Questo lavoro prende in esame lo schema di Hilbert di punti di C^2, il quale viene descritto assieme ad alcune sue proprietà, ad esempio la sua struttura hyper-kahleriana. Lo scopo della tesi è lo studio del polinomio di Poincaré di tale schema di Hilbert: ciò che si ottiene è una espressione del tipo serie di potenze, la quale è un caso particolare di una formula molto più generale, nota con il nome di formula di Goettsche.