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In this thesis, we study the Stieltjes transforms of the probability distribution functions and compare them with the characteristic functions of the probability distribution functions simultaneously. In section 1 and section 2, we introduce briefly the Stieltjes transforms. In section 3, we conclude that the Stieltjes transform is similar to the complexion of symmetry under the condition of symmetric probability distribution functions. In section 4, we discuss the relation between Stieltjes transforms of probability distribution functions and the density of probability distribution functions. We also show that the nth derivative of Stieltjes transform is uniformly continuous on the upper complex plane.

We study the semiclassical and quantum transport properties of the two-dimensional electron system in GaAs/AlGaAs semiconductor heterostructures under a perpendicular magnetic field. We studied two different samples, A and B under different experimental frameworks. For sample A, we mainly probe the applicable range of the Shubnikov-de Haas (SdH) theory when the thermal damping is reduced with decreasing temperature. We found the applicable range of the SdH theory can be extended, and the positive magneto-resistance and the disorder-induced damping play important roles. In the experiment of sample B, we removed the influence of thermal resistance by measuring forward and backward currents. We found the semiclassical Lifshitz-Kosevich formula in the SdH theory is more robust in describing the magneto-oscillations. Surprisingly, we found the existence of the mobility gap, which indicates the quantum Hall effect. The semiclassical behavior is attributed to the electrons away from the tails of Landau bands. Our study hints that we shall consider the quantum diffusion model to modify the Dingle term.

Esta pesquisa aborda o Turismo e o Automobilismo e os efeitos da Fórmula 1 em São Paulo. Embora existam referências pontuais, poucos estudos existem sobre esses temas que ainda não despertaram o interesse dos estudiosos de Turismo. Este estudo, fundamentado em obras relacionadas ao esporte em geral, aos eventos esportivos, em informações da internet, em jornais e revistas e, principalmente, em pesquisa de campo partiu da investigação do esporte através dos tempos, da estrutura e organização do automobilismo para chegar ao Autódromo Municipal José Carlos Pace e à análise dos efeitos da Fórmula 1 em São Paulo. Com base nas abordagens, na literatura, nas análises elaboradas e discussões apresentadas, concluiu-se que a Fórmula 1 em São Paulo gera efeitos que, em parte, podem ser explicados pela visibilidade do Grande Prêmio na mídia. / This research examines Tourism and Automobilism and impacts of Formule 1 Grand Prix in São Paulo. Althought it has been indications, few studies about the subject have not been emerge yet topic of expertise of Tourism. This research, based on works about sport, sport events, internet datas, papers and, mainly, field survey begun investigations sports through times, its structure and organization of Automobilism in order to work Autódromo Municipal José Carlos Pace and analyses of effects of Formule 1 in São Paulo. Considering approaches, literature, analyses made and discussions showed, the conclusion is that Formule 1 in São Paulo generates effects that, partly, can be explained by visibility of Grand Prix in media.

Esta pesquisa aborda o Turismo e o Automobilismo e os efeitos da Fórmula 1 em São Paulo. Embora existam referências pontuais, poucos estudos existem sobre esses temas que ainda não despertaram o interesse dos estudiosos de Turismo. Este estudo, fundamentado em obras relacionadas ao esporte em geral, aos eventos esportivos, em informações da internet, em jornais e revistas e, principalmente, em pesquisa de campo partiu da investigação do esporte através dos tempos, da estrutura e organização do automobilismo para chegar ao Autódromo Municipal José Carlos Pace e à análise dos efeitos da Fórmula 1 em São Paulo. Com base nas abordagens, na literatura, nas análises elaboradas e discussões apresentadas, concluiu-se que a Fórmula 1 em São Paulo gera efeitos que, em parte, podem ser explicados pela visibilidade do Grande Prêmio na mídia. / This research examines Tourism and Automobilism and impacts of Formule 1 Grand Prix in São Paulo. Althought it has been indications, few studies about the subject have not been emerge yet topic of expertise of Tourism. This research, based on works about sport, sport events, internet datas, papers and, mainly, field survey begun investigations sports through times, its structure and organization of Automobilism in order to work Autódromo Municipal José Carlos Pace and analyses of effects of Formule 1 in São Paulo. Considering approaches, literature, analyses made and discussions showed, the conclusion is that Formule 1 in São Paulo generates effects that, partly, can be explained by visibility of Grand Prix in media.

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No description available.

Consider the Sturm-Liouville system : 8 > > > > > < > > > > > : − y00 + q(x)y = y y(0) cos + y0(0) sin = 0 y(1) cos + y0(1) sin = 0 , where q 2 L 1 (0, 1) and , 2 [0, £¾). Let 0 < x(n)1 < x(n)2 < ... < x(n)n − 1 < 1 be the nodal points of n-th eigenfunction in (0,1). The inverse nodal problem involves the determination of the parameters (q, , ) in the system by the knowledge of the nodal points . This problem was first proposed and studied by McLaughlin. Hald-McLaughlin gave a reconstruc- tion formula of q(x) when q 2 C 1 . In 1999, Law-Shen-Yang improved a result of X. F. Yang to show that the same formula converges to q pointwisely for a.e. x 2 (0, 1), when q 2 L 1 . We found that there are some mistakes in the proof of the asymptotic formulas for sn and l(n)j in Law-Shen-Yang¡¦s paper. So, in this thesis, we correct the mistakes and prove the reconstruction formula for q 2 L 1 again. Fortunately, the mistakes do not affect this result.Furthermore, we show that this reconstruction formula converges to q in L 1 (0, 1) . Our method is similar to that in the proof of pointwise convergence.