Cette thèse consiste en trois parties que j'ai faites pendant ces trois ans.La première partie va être constituée de l'étude de la distribution de la longueur de corde sur le plan hyperbolique. Nous montrons l'identité de Pleijel pour le plan hyperbolique. En utilisant cette identité, nous remontrons l'identité de formule de Crofton et l'inégalité isopérimétrique pour le plan hyperbolique, et puis nous calculons la distribution de la longueur de corde associée à un triangle idéal et celle associée à un quadrilatère idéal. Ensuit, nous montons les résultats analogues pour les surfaces riemannienne simplement connexes avec la courbure constante. La seconde partie va contribuer aux études de la métrique de pression sur l'espace de Teichmüller d'un tore privé d'un disque. En étudiant la dégénération du tore quand la longueur du bord va à l'infini, nous trouvons la relation de cette métrique avec la métrique de pression sur l'espace modulaires des graphes métriques. Nous montrons ensuite que la fonction de l'entropie n'est pas constante sur les feuilles symplectique de l'espace Teichmüller d'une surface à bord.Finalement, la troisième partie concerne la quantification de l'espace de Teichmüller d'une surface avec les piqûres. nous montrons. Dans ce chapitre, nous étudions l'extension centrale du groupe modulaire via la quantification de Chekhov-Fock et calculons sa classe de cohomologie qui est 12 fois la classe de Meyer plus les classes d'Euler associées aux piqûres. / This thesis consists of three parts corresponding to the three subjects that I have studied during the last three years.The first part contains the study of the chord length distribution associated to a compact (or non-compact) domain in the hyperbolic plane. We prove the hyperbolic Pleijel identity. By using this identity, we find new approaches to the Crofton's formula and the isoperimetric inequality, and then compute the chord length distribution associated to an ideal triangle and that associated to an ideal quadrilateral. Then we prove the analogue results for the simply connected Riemannian surface with constant curvature.The second part of this thesis (Chapter 5) consists of the study of the pressuremetric on the Teichmüller space of one-holed torus. By studying the degeneration of the torus when the boundary length goes to infinity, we find the relation of this metric to the pressure metric on the moduli space of metric graphs. Then we study the entropy function and prove that it is not constant on the symplectic leaf of the Teichmüller space of a bordered surface.Finally, the third part concerns the quantization of the Teichmüller space of a punctured surface. In this chapter, we study the central extension of the mapping class group coming from the quantization and compute its cohomology class which is 12 times the Meyer class plus the Euler classes associated to punctures.

Este estudo se dedica a uma parte pouco conhecida dos trabalhos de Leonhard Euler (1707 - 1783) relacionado à música enquanto uma ciência matemática. Tais trabalhos mostram, em certo sentido, um lado pitagórico do pensador e também algumas contribuições do mesmo à teoria musical. O interesse deste matemático pelo assunto permeia várias obras e épocas de sua vida, mas neste trabalho focamos em três delas: um conjunto de nove cartas que compõem a obra Lettres a une princesse dAllemagne sur divers sujets de physique e de philosophie (1768) e dois artigos, Conjecture sur la raison de quelques dissonances generalement reçues dans la musique (1766) e De harmoniae veris principiis per speculum musicum repraesentatis (1774). Para possibilitar uma melhor compreensão desses textos, faremos uma revisão histórica do tratamento aritmético dado à música desde os tempos clássicos até o Renascimento com enfoque nas principais contribuições que levam à construção da escala da entonação pura ou justa, trabalhada por Euler nos originais estudados. Após a apresentação e análise desses trabalhos eulerianos, especialmente seus diagramas para representar sons e acordes e do seu expoente de um acorde para medir consonâncias, terminaremos essa dissertação refletindo sobre as implicações pedagógicas e históricas, bem como as potencialidades e limitações do uso de fontes originais de determinados mestres do pensamento matemático ocidental, nomeadamente o próprio Euler, na formação de matemáticos, professores e licenciados. / This present research takes a journey into a little know part of Leonhard Eulers works about music as a mathematical science. Those works show, at certain level, his Pythagorean thoughts and also his contributions to music theory. Eulers interest for this subject permeates many of his works through his lifetime (1707 - 1783), but here we focus on three of them: a set of nine letters from the book Lettres a une princesse dAllemagne sur divers sujets de physique e de philosophie (1768), and two articles, Conjecture sur la raison de quelques dissonances generalement reçues dans la musique (1766) and De harmoniae veris principiis per speculum musicum repraesentatis (1774). To allow a better understanding of his ideas, first we put on a historical review of the arithmetic treatment of music since the ancient Greece to the Renaissance Era pointing out the main contributions to the development of the pure just intonation scale, the one used by Euler on the works just mentioned. After presenting and analyzing these Eulers contributions, specially his diagrams to represent sounds and chords to the eyes and the concept of exponent of a chord to measure consonances, we conclude this dissertation thinking about the pedagogical and historical impact, and also the potential and limitations concerning the use of historical sources of the masters of mathematics, to the training of future mathematics and teachers.

Entre 1750 et 1800, l’émergence et l’adoption de nouveaux genres musicaux et modèles stylistiques, bouleversent la pratique de l’accompagnement au clavier en France. La basse chiffrée se raréfie dans les œuvres gravées et cède progressivement le pas à des parties de clavier entièrement écrites dans la musique vocale. La première partie de cette thèse définit la place de l’accompagnateur et l’évolution de la notation. La seconde est consacrée à l’enseignement dispensé par les méthodes et traités, et établit des passerelles avec les écoles étrangères et le siècle suivant. Enfin, la troisième partie reconsidère la question de l’accompagnement dans les sonates pour clavier et violon. La confrontation des écrits théoriques et des partitions trouve une application directe dans la pratique de la basse continue et de l’accompagnement au clavier, et permet de proposer des modèles de réalisation conformes aux caractéristiques observées dans les œuvres de cette période. / Between 1750 and 1800, the emergence and adoption of new musical genres and stylistic models radically change the accompaniment practice on keyboard instruments in France. Figured bass becomes scarce and is gradually replaced by written-out keyboard parts in vocal music. The first part of this thesis defines the role of the accompanist and the evolution of the notation. The second part is devoted to the instructions given in methods and treatises and establishes links with foreign schools and the following century. Finally, the third part reconsiders the question of the accompaniment in the sonatas for keyboard and violin. The comparison between theoretical writings and scores finds a direct application in the continuo and keyboard accompaniment practice, and leads to the proposition of realisation models in accordance with the characteristics observed in the musical works of that period.

The subject of this thesis is the recalculation and alternative construction design of roofing winter stadium in Znojmo. The building has a rectangular plan with dimensions of 84 x 63 m. The existing roof structure consists of truss purlins and main truss with parabolic chord, which are carried out by a pair of steel arch with a span of 84 m. The new design is processed in two options. The first option is the structure formed by triangular arch truss girder with truss purlins. The second option is a steel lamellar vault formed by vierendeel beams. After evaluating the design options was for a detailed solution chosen the first option.

Title: Cover Song Identification using Music Harmony Features, Model and Complexity Analysis Author: Ladislav Maršík Department: Department of Software Engineering Supervisor: Prof. RNDr. Jaroslav Pokorný, CSc., Department of Software Engineering Abstract: Analysis of digital music and its retrieval based on the audio fe- atures is one of the popular topics within the music information retrieval (MIR) field. Every musical piece has its characteristic harmony structure, but harmony analysis is seldom used for retrieval. Retrieval systems that do not focus on similarities in harmony progressions may consider two versions of the same song different, even though they differ only in instrumentation or a singing voice. This thesis takes various paths in exploring, how music harmony can be used in MIR, and in particular, the cover song identification (CSI) task. We first create a music harmony model based on the knowledge of music theory. We define novel concepts: a harmonic complexity of a mu- sical piece, as well as the chord and chroma distance features. We show how these concepts can be used for retrieval, complexity analysis, and how they compare with the state-of-the-art of music harmony modeling. An extensive comparison of harmony features is then performed, using both the novel fe- atures and the...

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This thesis describes a novel new method, termed the Tangent-Line-Chord (TLC) method, that can be used to more efficiently model creep deformation dominated by the tertiary regime. Creep deformation is a widespread mechanical mode of failure found in high-stress and temperature mechanical systems. To accurately simulate creep and its effect on structures, researchers utilize finite element analysis (FEA). General purpose FEA packages require extensive amounts of time and computer resources to simulate creep softening in components because of the large deformation rates that continuously evolve. The goal of this research is to employ multi-regime creep models, such as the Kachanov-Rabotnov model, to determine a set of equations that will allow creep to be simulated using as few iterations as possible. The key outcome is the freeing up of computational resources and the saving of time. Because both the number of equations and the value of material constants within the model change depending on the approach used, programming software will be utilized to automate this analytical process. The materials being considered in this research are mainly generic Ni-based superalloys, as they exhibit creep responses that are dominated by secondary and tertiary creep.