This thesis deals with ranked advanced voting systems. The aim is to determine the overall winner and the ranking of candidates based on voters' preferences. The thesis utilises basic voting systems - plurality rules, lexicographical and Borda's method - as well as advanced voting systems with the application of DEA models, specifically DEA/AR model, DEA/AR exclusion model (including variations with penalties), and Llamazares-Peňa model. Compromise programming is used to obtain common vector of weights. The models and their use are demonstrated on Formula One Grand Prix results from season 2016. Formula One World Drivers' Championship and Formula One World Constructors' Championship are being investigated.

Nous nous intéressons aux cristaux liquides nématiques, qui sont une phase de la matière intermédiaire entre les liquides et les solides cristallins. Ces états sont caractérisés par la présence de défauts ponctuels ou de ligne. Le but de cette thèse est d'apporter une contribution à l'étude mathématique des défauts, dans le cadre de la théorie variationnelle de Landau-de Gennes. Dans le premier chapitre, nous étudions les minimiseurs de l'énergie dans des domaines bornés de dimension deux. Lorsque la constante élastique tend vers zéro, les minimiseurs convergent vers une application localement harmonique, avec un nombre fini de singularités ponctuelles. Au voisinage de celles-ci, les minimiseurs sont biaxes (le molécules sont alignées localement dans plusieurs directions). Le deuxième chapitre est consacré à l'analyse asymptotique des minimiseurs en dimension trois, en supposant l'énergie majorée par le logarithme de la constante élastique. Comme dans le cas bidimensionnel, nous obtenons un résultat de compacité des minimiseurs, mais cette fois l'application limite peut présenter à la fois des singularités ponctuelles et de ligne. Nous donnons aussi des conditions suffisantes pour que l'hypothèse sur l'énergie évoquée précédemment soit satisfaite. Le troisième chapitre porte sur l'existence de minimiseurs à symétrie radiale dans une couronne en dimension trois. Enfin, dans le dernier chapitre nous présentons une obstruction topologique à l'existence de champs de vecteurs unitaires de faible régularité, sur des variétés à bord. Ce résultat constitue une étape préliminaire à l'étude de modèles variationnels pour les films nématiques sur une surface. / Nematic liquid crystals are an intermediate phase of matter, sharing properties with liquids and crystalline solids. They are composed of molecules which can flow freely, but tend to align locally along some preferred directions. Nematic phases exhibit defects, which can occur at isolated points or along lines, and are one of their mean features. This thesis mainly aims at discussing some mathematical results about defects and their generation, in the framework of the Landau-de Gennes theory. In the first chapter, we study minimizers of the energy functional in a bounded, smooth domain in dimension two. We show that, as the elastic constant tends to zero, minimizers converge to a locally harmonic map with a finite number of point singularities. Minimizers are biaxial in the core of defects (that is, more than one preferred direction of molecular alignment exists at a given point). Chapter two deals with the asymptotic analysis of minimizers in dimension three. We assume that the energy is comparable to the logarithm of the elastic constant and prove a compactness result. However, the limiting map is now allowed to have line singularities as well as point singularities. We also provide sufficient conditions for the logarithmic energy estimate to be satisfied. In chapter three, we study the existence of radially symmetric minimizers on spherical shells, in dimension three. Finally, in chapter four, we discuss a topological obstruction to the existence of unit vector fields of low regularity, on a compact manifold with boundary. This result can be understood as a first step in the analysis of some variational models for a surface coated with a thin nematic film.

L'objectif principal de cette thèse est de généraliser les multizetas au cas où le corps de base Q est remplacé par un corps de nombres quelconque. La motivation derrière cette construction vient des travaux de A. Goncharov sur les corrélateurs de Hodge et de la philosophie plectique de J. Nekovar et A. Scholl. On commence par la construction des fonctions de Green plectiques supérieures. Hecke a prouvé que l'intégration d'une série d'Eisenstein appropriée sur le groupe de classes des idèles du corps de nombres donné, multipliée par un caractère du groupe des classes des idèles, est équale à la fonction L associée à ce caractère. Remplacant la série d'Eisenstein par les fonctions de Green plectiques supérieures, une intégration similaire donne des nouveaux résultats, qui généralisent les multizetas classiques et les multi-polylogarithmes. D'après le principe plectique, un sous-groupe de l'anneau des entiers du corps de nombres donné joue un rôle essentiel dans ces travaux. / The principal objective of this thesis is to generalize multiple zeta values to the case when the ground field Q is replaced by an arbitrary number field. The motivation behind the construction comes from the work of A. Goncharov on Hodge correlators and the plectic philosophy of J. Nekovar and A. Scholl. We start by constructing the higher plectic Green functions. Hecke once proved that the integral of the restriction of a suitable Eisenstein series over $\mathbb{Q}$ to the idele class group of a given number field multipled an idele class character of finite order is equal to the L-function of this charator. By replacing Eisenstein seris with our higher plectic Green functions, a similar integration gives new results, which give the generalization of classical multiple zeta values and multiple polyloarithms. According to the plectic principle, a non-trivial subgroup of the ring of integers of a given number field plays an essential role in this work.

This thesis deals with the design of steering holder for a race car in the category Formula Student using topology optimisation and analysis of this design. The objective of this thesis is gaining knowledge about topology optimisation and application of this knowledge to the design of a replacement of the steering gearbox and its holder.

This thesis deals with the design and production of wheel control holders for the right front wheel of the formula Dragon 4 of TU Brno Racing team. In the theoretical part, the Formula Student competition is described, including the steering holders themselves and description of their function and location. Later the analysis of aluminium and its alloy was made, including description of the CERTAL material of which the holders were made. The practical part includes the design of prototype holders in the Autodesk Inventor CAD software, the design and application of machining strategies in the PowerMILL CAM software. Further, the practical part includes production on milling machines at the MCV 754 QUICK and DECKEL MAHO DMU 50 machining centre. At the end, the dimensional analysis of the part is performed, manufactured holders were compared to the CAD model of the given components and the technical and economical evaluation of the production was made.

Diploma thesis deals with a design and manufacture of oil cooler by technology Selective Laser Melting for Formula Student. The main goal of the design is to ensure optimal oil circuit cooling at a minimal mass. The design of manufactured oil cooler is based on a plate heat exchanger concept with optimized intakes by CFD simulations and heat exchange body with fins of thickness 0.17 mm. An analytical model was created. SLM process parameters were optimized for a thin walls printing, Subsequently, a fabrication of testing parts was finished for measuring pressure drops and performances of micro heat exchangers. Results were used for an accuracy improvement of the analytical model and for consequent optimization of heat exchange surface. Afterwards optimization was executed for inlets and outlets by using flow simulations. A prototype was built and verified on a test stand. Performance of the designed oil cooler is 4.5 kW for race mode, where temperature drop of oil circuit is 22 °C. The lightweight design weighs 320 g, which reduces more than 47 % of a current oil-air cooler weight. Furthermore, a centre of gravity is decreased by designed placement of the cooler.

Master’s thesis focused on design and construction of front uprights for Formula Student racing car. Topology optimization and FEM analysis will be used to design the uprights with higher stiffness and minimal weight difference compared to the last model. In the FEM analysis loads will be applied from wheel side and from suspension side. Design of the upright then will be compared to the previous designs especially to safety factor, weight and cost.

This thesis is concerned with the mechanical stress generated in thin layers applied on a substrate. The application takes place at high temperatures and due to different coefficients of thermal expansion of materials, the sample is deformed, and thereby the stress is generated. The first part of the thesis includes the derivation of the Stoney formula for uniaxial and biaxial stress in a layer. Besides, analytical calculations of the normal stress in the layer for the simplified link model, and shear stress on the layer interface were evaluated. The main part of the work consists of solving the problem using FEM modeling. Because the actual temperature behavior during the application was not known, a fictitious temperature load was used as an input. For the samples, the coefficients of thermal expansion of the layer were then searched so that the thermal load resulting deflection corresponds to the experimental data. Three types of models were created, namely the link body model, the axisymmetric model, and the solid model. The axisymmetric model was used for the calculation of samples forming circular isolines during deformation and a volume model for samples forming elliptical isolines. The result of the FEM calculations was the normal stress in the applied layers, for which corresponding relationships were created using regression analysis.

The main goal of this thesis is to obtain lateral parameters of the Magic Formula tire model of a tire commonly used in Formula Student competition. Both the author and the supervisor of the thesis know the tire name and its specification, but the research company that did the tire testing and provided me with the date prohibits sharing this of data publicly, so the tire designation is not mentioned in this thesis. The first chapter covers main theoretical facts related to a tire, briefly describes some of the tire models and shows possibilities how to determine tire characteristics that are used in a tire model. The thesis describes how to process raw tire data measured during a laboratory experiment using scripts created in Matlab software. The inputs variables are slip angle, lateral force, normal force and inclination angle. Raw data are splitted into parts, main coefficients of the Magic formula model (B, C, D, E, Sh, Sv) are calculated and subsequently the lateral parameters are obtained using least square method to fit parameters into the measured data. The works gives two main outcomes. The first output is a set of Matlab scripts that can be used to determine lateral parameters of any tire that has the same input data format as presented. A TIR file of the Formula Student tire in case of lateral slip is the second result of the work. This can be used for vehicle dynamics simulation of Formula Student racing car. The thesis also offers a comparison between parameters, which I calculated, and those gained thanks to Optimum Tire software by Calspan research company. Additionally the work shows the effect of load and inclination angle on lateral force.

My thesis will be aimed at front axle design. I am going to design the assembly of the front axle in the program ADAMS by MSC. I am going to observe and record most of cinematic changes of the car such as change of position of vehicle roll centre ,wheel camber, geometry adjustment , wheel toe-in measuring and other necessary data. The final report is going to include strength calculation of particular axle parts. I am also going to solve the axle stabilizer including strength calculation.