Lipschitz regularity for weak solutions of parabolic p-Laplacian type equations in certain subriemannian structures

The main aim of the thesis is to prove the local Lipschitz regularity of the weak solutions to a class of parabolic PDEs modeled on the parabolic p-Laplacian. This result is well known in the Euclidean case and recently has been extended in the Heisenberg group, while higher regularity results are not known in subriemannian parabolic setting. In this thesis we will consider vector fields more general than those in the Heisenberg setting, introducing some technical difficulties. To obtain our main result we will use a Moser-like iteration. Due to the non linearity of the equation, we replace the usual parabolic cylinders with new ones, whose dimension also depends on the L^p norm of the solution. In addition, we deeply simplify the iterative procedure, using the standard Sobolev inequality, instead of the parabolic one.

BAW notch filter for WiMAX applications

Als darrers anys la necessitat de connectar-se a internet des de qualsevol lloc s’ha incrementat exponencialment sobretot de manera inalàmbrica. Degut al finit espectre radioelèctric es tendeix a aprofitar totes les franges freqüencials d’aquest convivint diferents sistemes en franges properes podent induir-se interferències mútuament. Per evitar aquestes interferències es requereix de filtres a tots els dispositius els quals aïllin un sistema del adjacent. En aquest projecte es dóna una solució al cas concret de la convivència entre els sistemes Wi-Fi y WiMAX eliminant la banda Wi-Fi interferent en sistemes WiMAX. Aquesta solució consisteix en el disseny d’un filtre banda eliminada d’ordre 3 implementat mitjançant tecnologia BAW a partir de l’estructura y especificacions d’un filtre comercial. A més també es fa un petit estudi per veure si seria interessant una millora en els processos de fabricació del filtre per part del fabricant.

Théorèmes d'existence pour des systèmes d'équations différentielles et d'équations aux échelles de temps.

Nous présentons dans cette thèse des théorèmes d’existence pour des systèmes d’équations différentielles non-linéaires d’ordre trois, pour des systèmes d’équa- tions et d’inclusions aux échelles de temps non-linéaires d’ordre un et pour des systèmes d’équations aux échelles de temps non-linéaires d’ordre deux sous cer- taines conditions aux limites. Dans le chapitre trois, nous introduirons une notion de tube-solution pour obtenir des théorèmes d’existence pour des systèmes d’équations différentielles du troisième ordre. Cette nouvelle notion généralise aux systèmes les notions de sous- et sur-solutions pour le problème aux limites de l’équation différentielle du troisième ordre étudiée dans [34]. Dans la dernière section de ce chapitre, nous traitons les systèmes d’ordre trois lorsque f est soumise à une condition de crois- sance de type Wintner-Nagumo. Pour admettre l’existence de solutions d’un tel système, nous aurons recours à la théorie des inclusions différentielles. Ce résultat d’existence généralise de diverses façons un théorème de Grossinho et Minhós [34]. Le chapitre suivant porte sur l’existence de solutions pour deux types de sys- tèmes d’équations aux échelles de temps du premier ordre. Les résultats d’exis- tence pour ces deux problèmes ont été obtenus grâce à des notions de tube-solution adaptées à ces systèmes. Le premier théorème généralise entre autre aux systèmes et à une échelle de temps quelconque, un résultat obtenu pour des équations aux différences finies par Mawhin et Bereanu [9]. Ce résultat permet également d’obte- nir l’existence de solutions pour de nouveaux systèmes dont on ne pouvait obtenir l’existence en utilisant le résultat de Dai et Tisdell [17]. Le deuxième théorème de ce chapitre généralise quant à lui, sous certaines conditions, des résultats de [60]. Le chapitre cinq aborde un nouveau théorème d’existence pour un système d’in- clusions aux échelles de temps du premier ordre. Selon nos recherches, aucun résultat avant celui-ci ne traitait de l’existence de solutions pour des systèmes d’inclusions de ce type. Ainsi, ce chapitre ouvre de nouvelles possibilités dans le domaine des inclusions aux échelles de temps. Notre résultat a été obtenu encore une fois à l’aide d’une hypothèse de tube-solution adaptée au problème. Au chapitre six, nous traitons l’existence de solutions pour des systèmes d’équations aux échelles de temps d’ordre deux. Le premier théorème d’existence que nous obtenons généralise les résultats de [36] étant donné que l’hypothèse que ces auteurs utilisent pour faire la majoration a priori est un cas particulier de notre hypothèse de tube-solution pour ce type de systèmes. Notons également que notre définition de tube-solution généralise aux systèmes les notions de sous- et sur-solutions introduites pour les équations d’ordre deux par [4] et [55]. Ainsi, nous généralisons également des résultats obtenus pour des équations aux échelles de temps d’ordre deux. Finalement, nous proposons un nouveau résultat d’exis- tence pour un système dont le membre droit des équations dépend de la ∆-dérivée de la fonction.

Degenerate four wave mixing in some metal phthalocyanines and naphthalocyanines

Here we report measurements of third-order susceptibility χ(3), figure of merit F defined as χ(3)/α (where α is the absorption coefficient) and second hyperpolarizability 〈γ〉 of some metal substituted phthalocyanines and a naphthalocyanine in solutions of dimethyl formamide using degenerate four wave mixing at 532 nm under nanosecond excitation. It was found that among samples investigated, bis-naphthalocyanine possessed the highest value of 〈γ〉 followed by the bis-phthalocyanine. This observation is explained on the basis that bis-naphthalocyanine followed by bis-phthalocyanine has higher degree of π electron conjugation.

Variaveis da ocupacao do solo e analise multivariada

Photointerpretative and multivariate statistical techniques were applied to variants of soil use measured in 4 hydrological basins of third order ramification, belonging to Tiete basin municipal district of Botucatu, Sao Paulo State. The aim was the grouping of basins of second degree of similarity, as well as to infer spatial distribution representativeness. The hydrological basins were located in 3 physiographic regions, with peripheric depression, cuesta front and cuesta backslope, embracing the following soil units: Regosol intergrade to Red Yellow Podzolic and intergrade to Red Yellow Latosol, Red Yellow Latosol-sandy phase, Litosol basaltic substract phase and Purple Latosol. The results obtained allow the conclusion that soil use not always reflects its fertility. -after English summary

Genetic evaluation using multi-trait and random regression models in Simmental beef cattle

The Brazilian Association of Simmental and Simbrasil Cattle Farmers provided 29,510 records from 10,659 Simmental beef cattle; these were used to estimate (co)variance components and genetic parameters for weights in the growth trajectory, based on multi-trait (MTM) and random regression models (RRM). The (co)variance components and genetic parameters were estimated by restricted maximum likelihood. In the MTM analysis, the likelihood ratio test was used to determine the significance of random effects included in the model and to define the most appropriate model. All random effects were significant and included in the final model. In the RRM analysis, different adjustments of polynomial orders were compared for 5 different criteria to choose the best fit model. An RRM of third order for the direct additive genetic, direct permanent environmental, maternal additive genetic, and maternal permanent environment effects was sufficient to model variance structures in the growth trajectory of the animals. The (co)variance components were generally similar in MTM and RRM. Direct heritabilities of MTM were slightly lower than RRM and varied from 0.04 to 0.42 and 0.16 to 0.45, respectively. Additive direct correlations were mostly positive and of high magnitude, being highest at closest ages. Considering the results and that pre-adjustment of the weights to standard ages is not required, RRM is recommended for genetic evaluation of Simmental beef cattle in Brazil. ©FUNPEC-RP.

Modelos de dimensão finita e infinita para avaliação da produção de ovos em aves de postura

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Modelos de regressão aleatória para a estimação de parâmetros genéticos da produção e constituintes do leite de búfalas

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

Verificação de terceira ordem de estruturas de concreto armado de edíficios

The change in design of a building can occur during its construction process, especially when this change involves greater amount of profit for the building company, as it is the case of adding extra floors. However, there must be an analysis of the structure of the building in order to see if it is possible to increase the number of floors without the need of reinforcement, as this need would result in higher costs for the building company. This graduation report presents this analysis by using the methods of third order verification of reinforced concrete structures

Temporal and spectral nonlinear pulse shaping methods in optical fibers

The combination of the third-order optical nonlinearity with chromatic dispersion in optical fibers offers an extremely rich variety of possibilities for tailoring the temporal and spectral content of a light signal, depending on the regime of dispersion that is used. Here, we review recent progress on the use of third-order nonlinear processes in optical fibers for pulse shaping in the temporal and spectral domains. Various examples of practical significance will be discussed, spanning fields from the generation of specialized temporal waveforms to the generation of ultrashort pulses, and to stable continuum generation.

Nonlinear Waves: An Introduction

This book deals with equations of mathematical physics as the different modifications of the KdV equation, the Camassa-Holm type equations, several modifications of Burger's equation, the Hunter-Saxton equation, conservation laws equations and others. The equations originate from physics but are proposed here for their investigation via purely mathematical methods in the frames of university courses. More precisely, we propose classification theorems for the traveling wave solutions for a sufficiently large class of third order nonlinear PDE when the corresponding profiles develop different kind of singularities (cusps, peaks), existence and uniqueness results, etc. The orbital stability of the periodic solutions of traveling type for mKdV equations are also studied. Of great interest too is the interaction of peakon type solutions of the Camassa-Holm equation and the solvability of the classical and generalized Cauchy problem for the Hunter-Saxton equation. The Riemann problem for special systems of conservation laws and the corresponding -shocks are also considered. As it concerns numerical methods we apply the CNN approach. The book is addressed to a broader audience including graduate students, Ph.D. students, mathematicians, physicist, engineers and specialists in the domain of PDE.

First-principles electronic theory of non-collinear magnetic order in transition-metal nanowires

The structural, electronic and magnetic properties of one-dimensional 3d transition-metal (TM) monoatomic chains having linear, zigzag and ladder geometries are investigated in the frame-work of first-principles density-functional theory. The stability of long-range magnetic order along the nanowires is determined by computing the corresponding frozen-magnon dispersion relations as a function of the 'spin-wave' vector q. First, we show that the ground-state magnetic orders of V, Mn and Fe linear chains at the equilibrium interatomic distances are non-collinear (NC) spin-density waves (SDWs) with characteristic equilibrium wave vectors q that depend on the composition and interatomic distance. The electronic and magnetic properties of these novel spin-spiral structures are discussed from a local perspective by analyzing the spin-polarized electronic densities of states, the local magnetic moments and the spin-density distributions for representative values q. Second, we investigate the stability of NC spin arrangements in Fe zigzag chains and ladders. We find that the non-collinear SDWs are remarkably stable in the biatomic chains (square ladder), whereas ferromagnetic order (q =0) dominates in zigzag chains (triangular ladders). The different magnetic structures are interpreted in terms of the corresponding effective exchange interactions J(ij) between the local magnetic moments μ(i) and μ(j) at atoms i and j. The effective couplings are derived by fitting a classical Heisenberg model to the ab initio magnon dispersion relations. In addition they are analyzed in the framework of general magnetic phase diagrams having arbitrary first, second, and third nearest-neighbor (NN) interactions J(ij). The effect of external electric fields (EFs) on the stability of NC magnetic order has been quantified for representative monoatomic free-standing and deposited chains. We find that an external EF, which is applied perpendicular to the chains, favors non-collinear order in V chains, whereas it stabilizes the ferromagnetic (FM) order in Fe chains. Moreover, our calculations reveal a change in the magnetic order of V chains deposited on the Cu(110) surface in the presence of external EFs. In this case the NC spiral order, which was unstable in the absence of EF, becomes the most favorable one when perpendicular fields of the order of 0.1 V/Å are applied. As a final application of the theory we study the magnetic interactions within monoatomic TM chains deposited on graphene sheets. One observes that even weak chain substrate hybridizations can modify the magnetic order. Mn and Fe chains show incommensurable NC spin configurations. Remarkably, V chains show a transition from a spiral magnetic order in the freestanding geometry to FM order when they are deposited on a graphene sheet. Some TM-terminated zigzag graphene-nanoribbons, for example V and Fe terminated nanoribbons, also show NC spin configurations. Finally, the magnetic anisotropy energies (MAEs) of TM chains on graphene are investigated. It is shown that Co and Fe chains exhibit significant MAEs and orbital magnetic moments with in-plane easy magnetization axis. The remarkable changes in the magnetic properties of chains on graphene are correlated to charge transfers from the TMs to NN carbon atoms. Goals and limitations of this study and the resulting perspectives of future investigations are discussed.

Nonmesonic weak decay dynamics from proton spectra of Lambda-hypernuclei

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

Solutions to common issues in widefield microscopy: vignetting, mosaicing and depth of focus

In this thesis we have developed solutions to common issues regarding widefield microscopes, facing the problem of the intensity inhomogeneity of an image and dealing with two strong limitations: the impossibility of acquiring either high detailed images representative of whole samples or deep 3D objects. First, we cope with the problem of the non-uniform distribution of the light signal inside a single image, named vignetting. In particular we proposed, for both light and fluorescent microscopy, non-parametric multi-image based methods, where the vignetting function is estimated directly from the sample without requiring any prior information. After getting flat-field corrected images, we studied how to fix the problem related to the limitation of the field of view of the camera, so to be able to acquire large areas at high magnification. To this purpose, we developed mosaicing techniques capable to work on-line. Starting from a set of overlapping images manually acquired, we validated a fast registration approach to accurately stitch together the images. Finally, we worked to virtually extend the field of view of the camera in the third dimension, with the purpose of reconstructing a single image completely in focus, stemming from objects having a relevant depth or being displaced in different focus planes. After studying the existing approaches for extending the depth of focus of the microscope, we proposed a general method that does not require any prior information. In order to compare the outcome of existing methods, different standard metrics are commonly used in literature. However, no metric is available to compare different methods in real cases. First, we validated a metric able to rank the methods as the Universal Quality Index does, but without needing any reference ground truth. Second, we proved that the approach we developed performs better in both synthetic and real cases.

The making of an ideology of the third way:the evolution of christian democracy in Germany (with special reference to 1945-49)

This study investigates the search for the third way in the history of German Christian Democracy. Today, in the United Kingdom, the 'third way' is seen as a new phenomenon, a synthesis of post-war belief in the welfare state and neo-liberal conservatism. Yet it insufficiently acknowledges that the origins of third way thinking, the marriage of social justice with free market economics, of individualism with collective responsibility, are found in the early philosophies of Catholic Social Theory and Protestant Social Ethical Teaching in Germany. This study shows that in the hundred years from the 1840s to the end of the 1940s, there were Catholic and Protestant socio-ethical thinkers and political reformists in Germany who attempted to bridge the philosophical differences between liberalism and socialism, to develop a socio-economic order based on Christian moral values. It will focus on the period 1945-1949, when the CDU was founded as the first interdenominational, Christian party. The study provides the first comprehensive account of the political debates in Christian democratic groups in the Soviet, British, French and American allied occupied zones, also giving equal attention to the contribution from the Protestant wing, alongside the more widely acknowledged role of Catholics in the birth of the CDU. It examines how Christian Democrats envisaged correcting the aberrations of German history, by uniting all social classes and Christian religions in one all-embracing Volkspartei, and transforming party politics from its earlier obsession with sectarian and ideological interests towards a more pragmatic 'third way' programme. The study argues that through the making of its ideology, the CDU modified the nation's understanding of its history, re-interpreted its traditions, and redefined the meaning and perception of established political philosophies. This reveals how the ambiguity of political terminology, and the flexible practice of 'third way' politics, were an invaluable political resource in the CDU's campaign for unity, ideological legitimisation and political power.