Orientador: Celso Pascoli Bottura / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de Computação / Made available in DSpace on 2018-07-22T22:47:58Z (GMT). No. of bitstreams: 1 Richter_CarlosMendes_M.pdf: 42112569 bytes, checksum: 2229a8747e522a3dd137578102cfd11a (MD5) Previous issue date: 1997 / Resumo: Este trabalho trata da análise de sistemas de controle monovariável e multivariável através das superficies de Riemann. É mostrado que a representação total destas superfícies abrange quatro dimensões, e novas representações são apresentadas em gráficos bidimensionais e tridimensionais. São propostas generalizações das representações já existentes, como lugar das raízes, diagramas de ganho, diagramas de Nyquist, de Bode e de Nichols, bem como dos respectivos diagramas complementares. São propostas novas formas de determinação de margens de fase e margens de ganho dos sistemas de controle monovariável, sendo estendidos os conceitos para o caso multivariável com base no critério generalizado de estabilidade de Nyquist. Para os casos monovariável e multivariável é mostrado que as margens de estabilidade podem ser determinadas diretamente sobre diversas representações de superficies de Riemann, e para diversos valores de ganho de realimentação negativa ou positiva, com tratamento único. São estabelecidos para os casos monovariável e multivariável novos gráficos de margens de estabilidade em função do ganho de realimentação negativa ou positiva, que são novas ferramentas de auxílio para análise e projeto de sistemas de controle realimentados / Abstract: This work deals with monovariable and multivariablecontrol systems analysisthrough Riemann surfaces. It is shown that a complete Riemann surface representation has dimension four, and new representations are presented in two-dimensional and three-dimensional plots. Generalizations ofthe existing representations, like root-Iocus, gain plots, Nyquist, Bode and Nichols diagrams, are proposed. New phase and gain margin determination methods are proposed for monovariable systems, and the concepts are extended to the multivariable case using the generalized Nyquist stability criterion. For both monovariable and multivariable cases, it is shown that gain and phase margins can be determined directly over several Riemann surface representations for several values of negative or positive feedback gains using an unique approach. New stability margin plots, functions of negative or positive feedback gain, are established, which are new aiding tools for analysis and synthesis of feedback control systems / Mestrado / Mestre em Engenharia Elétrica

The aim of this thesis is to examine the connection between the Riemannhypothesis and the distribution of prime numbers. We first derive theanalytic continuation of the zeta function and prove some of its propertiesusing a functional equation. Results from complex analysis such asJensen’s formula and Hadamard factorization are introduced to facilitatea deeper investigation of the zeros of the zeta function. Subsequently, therelation between these zeros and the asymptotic distribution of primesis rendered explicit: they determine the error term when the prime-counting function π(x) is approximated by the logarithmic integral li(x).We show that this absolute error is O(x exp(−c√log x) ) and that the Riemannhypothesis implies the significantly improved upper bound O(√x log x).

The object of this paper is to define, to establish necessary and sufficient conditions for the existence of, and to consider the elementary properties of the Riemann definite integral of a bounded function.

Titre de l'écran-titre (visionné le 2 octobre 2023) / Dans cette thèse, le problème de Steklov est étudié. Tout d'abord, ce problème est étudié sur des variétés riemanniennes fermées soumises à des excisions tubulaires. Étant données $\varepsilon > 0$, une variété riemannienne fermée $M$ de dimension $m \geq 2$ et une sous-variété fermée $N \subset M$ de dimension $0 \leq n \leq m - 2$, une excision tubulaire consiste à enlever le voisinage tubulaire $N^{\varepsilon} := \{ p \in M : d_{g}(p, N) \leq \varepsilon \}$ de taille $\varepsilon$ autour de $N$ afin d'obtenir le domaine $\Omega_{\varepsilon} := M \setminus N^{\varepsilon}$. Le résultat principal de cette thèse concerne le comportement des valeurs propres de Steklov d'une variété riemannienne fermée $M$ soumise à un nombre fini $b \geq 1$ d'excisions tubulaires. Plus précisément, il est montré que les valeurs propres divergent lorsque la taille des voisinages tubulaires tend vers $0$. Cette construction donne un nouvel exemple de variétés ayant une grande première valeur propre et permet d'étudier des problèmes de type isopérimétrique, comme étudier la pertinence de certaines quantités géométriques présentes dans des bornes supérieures connues. On utilise la quasi-isométrie et la comparaison des valeurs propres de Steklov à des valeurs propres de problèmes mixtes -- le problème de Steklov-Neumann et le problème de Steklov-Dirichlet. La séparation de variables est ensuite utilisée pour calculer les valeurs propres de ces problèmes mixtes. Grâce à cette méthode, on obtient l'ordre et le taux de divergence des valeurs propres ordonnées d'indice supérieur à $b$. Finalement, les fonctions propres et les valeurs propres de Steklov pour des boules géodésiques des sphères et des espcaes hyperboliques sont calculées. Elles sont trouvées à l'aide de la méthode de séparation de variables. / In this thesis, the Steklov problem is studied. This problem is first studied on closed Riemannian manifolds subject to tubular excisions. Given $\varepsilon > 0$, a closed Riemannian manifold $M$ of dimension $m \geq 2$ and a closed submanifold $N \subset M$ of dimension $0 \leq n \leq m - 2$, a tubular excision consists of removing the tubular neighbourhood $N^{\varepsilon} := \{ p \in M : d_{g}(p, N) \leq \varepsilon \}$ of size $\varepsilon$ around $N$ to obtain the domain $\Omega_{\varepsilon} := M \setminus N^{\varepsilon}$. The principal result of this thesis concerns the behaviour of the Stekov eigenvalues of a closed Riemannian manifold $M$ subject to a finite number $b \geq 1$ of tubular excisions. More precisely, it is proven that the eigenvalues diverge to infinity when the size of the tubular neighbourhood tends to $0$. This construction gives a new example of manifolds with a large first eigenvalue and allows to study isoperimetric type problems, as well as study the importance of certain geometric quantities present in known upper bounds. We use quasi-isometry and the bracketing of Steklov eigenvalues which compares the Steklov eigenvalues with eigenvalues of mixed problems -- the Steklov-Neumann and the Steklov-Dirichlet problems. Then, the eigenvalues of those mixed problems are computed via the method of separation of variables. This method gives us the order and the rate of divergence of the ordered eigenvalues of index superior to "b". In a second part, the eigenfunctions and eigenvalues of geodesic balls in spheres and hyperbolic spaces are computed via the method of separation of variables.

No description available.

This paper is a study of the Stieltjes integral, a generalization of the Riemann integral normally studied in introductory calculus courses. The purpose of the paper is to investigate many of the basic manipulative properties of the integral.

In the first part of this thesis, we proved a pseudo-locality theorem for a coupled Ricci flow, extending Perelman’s work on Ricci flow to the Ricci flow coupled with heat equation. By use of the reduced distance and the pseudo-locality theorem, we showed that the parabolic rescaling of a Type I coupled Ricci flow with respect to a Type I singular point converges to a non-trivial Ricci soliton. In the second part of the thesis, we prove the existence of infinitely many solutions to the Hull- Strominger system on generalized Calabi-Gray manifolds, more specifically compact non-K \"ahler Calabi-Yau 3-folds with infinitely many distinct topological types and sets of Hodge numbers. We also studied the behavior of the anomaly flow on the generalized Calabi-Gray manifolds, and reduced it to a scalar flow on a Riemann surface. We obtained the long-time existence and convergence after rescaling in the case when the curvature of initial metric is small.

In this thesis, we explore the restrictions imposed on the genus of a smooth curve $X$ which possesses at least three independent gonal morphisms to $\Pp^1$. We will prove a sharp lower bound on the dimension of global sections given by the sum of the divisors for the gonal morphisms. This inequality will provide an upper bound on the genus of a curve with the described properties. By considering the birational image of $X$ in $\Pp^1 \times \Pp^1 \times \Pp^1$ under the product of three pairwise independent morphisms, we observe that the boundary case for the previously mentioned inequality is closely related to the case where the image of $X$ is contained in a type 1-1-1 surface. Motivated by this phenomenon, we examine the constraints on the arithmetic genus of an irreducible curve in $\Pp^1 \times \Pp^1 \times \Pp^1$ whose natural projections are pairwise independent and all have degree 7.

Reproduction de : Habilitation à diriger des recherches : Informatique : Université de Nice-Sophia Antipolis : 2005. / Titre provenant de l'écran-titre. 30 p. Bibliogr. p. 27-30.

Thesis (Ph.D.)--City University of Hong Kong, 2009. / "Submitted to Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy." Includes bibliographical references (leaves [95]-100)