O número de contato do Rn (em inglês, kissing number) é o maior número de esferas de raio unitário e interiores dois-a-dois disjuntos que podem tocar simultaneamente uma esfera de raio unitário central. Nesta dissertação estudamos métodos que limitam o tamanho de tais configurações através de técnicas de otimização, como dualidade e programação semidefinida. O principal resultado obtido foi o cálculo de melhores limitantes para o número de contato nas dimensões 9 a 23; o que foi possível graças à exploração de simetrias dos polinômios presentes no limitante proposto por Bachoc e Vallentin (2008), levando à consideração de programas semidefinidos menores. Por fim, o limitante estudado é estendido para uma classe mais geral de problemas. / The kissing number of Rn is the maximum number of pairwise-nonoverlapping unit spheres that can simultaneously touch a central unit sphere. In this thesis we study methods to bound from above the size of such configurations using optimization techniques, like duality and semidefinite programming. The main result achieved is the computation of better bounds for the kissing number in dimensions 9 to 23; a result possible due to the exploitation of symmetries in the polynomials present in the bound proposed by Bachoc and Vallentin (2008), leading to the consideration of smaller semidefinite programs. Finally, the studied bound is extended to a bigger class of problems.

<div> <p>Guided by the continuous manufacturing paradigm shift in the pharmaceutical industry, the proposed thesis focuses on the implementation of an integrated continuous crystallization platform, the oscillatory baffled crystallizer (OBC), with real time process monitoring. First, by defining an appropriate operating regime with residence time distribution (RTD) measurements, a system can be defined that allows for plug flow operation while also maintaining solid suspension in a two-phase system. The aim of modern crystallization processes, narrow crystal size distributions (CSDs), is a direct result of narrow RTDs. Using a USB microscope camera and principal component analysis (PCA) in pulse tracer experiments, a novel non-contact RTD measurement method was developed using methylene blue. After defining an operating region, this work focuses on a specific process intensification technique, namely spherical crystallization.</p> <p>Used mainly to tailor the size of a final dosage form, spherical crystallization removes the need for downstream size-control based unit operations (grinding, milling, and granulation), while maintaining drug efficacy by tailoring the size of the primary crystals in the agglomerate. The approach for generating spherical agglomerates is evaluated for both small and large molecules, as there are major distinctions in process kinetics and mechanisms. To monitor the spherical agglomeration process, a variety of Process Analytical Technology (PAT) tools were used and the data was implemented for scale-up applications.</p> <p>Lastly, a compartmental model was designed based on the experimental RTD data with the intention of predicting OBC mixing and scale-up dynamics. Together, with validation from both the DN6 and DN15 systems, a scale independent equation was developed to predict system dispersion at different mixing conditions. Although it accurately predicts the behavior of these two OBC systems, additional OBC systems of different scale, but similar geometry should be tested for validation purposes.</p> </div> <br>

Considering the importance of combustion characteristics in combustion applications including spark ignition engines and gas turbines, both laminar and turbulent burning velocities were measured for gasoline related fuels. The first part of the present work focused on the measurements of laminar burning velocities of Fuels for Advanced Combustion Engines (FACE) gasolines and their surrogates using a spherical constant volume combustion chamber (CVCC) that can provide high-pressure high-temperature (HPHT) combustion mode up to 0.6 MPa, 395 K, and the equivalence ratios ranging 0.7-1.6. The data reduction was based on the linear and nonlinear extrapolation models considering flame stretch effect. The effect of flame instability was investigated based on critical Peclet and Karlovitz, and Markstein numbers. The sensitivity of the laminar burning velocity of the aforementioned fuels to various fuel additives being knows as octane boosters and gasoline extenders including alcohols, olfins, and SuperButol was investigated. This part of the study was further extended by examining exhaust gas re-circulation effect. Tertiary mixtures of toluene primary reference fuel (TPRF) were shown to successfully emulate the laminar burning characteristics of FACE gasolines associated with different RONs under various experimental conditions. A noticeable enhancement of laminar burning velocities was observed for blends with high ethanol content (vol ≥ 45 %). However, such enhancement effect diminished as the pressure increased. The reduction of laminar burning velocity cause by real EGR showed insensitivity to the variation of the equivalence ratio. The second part focused on turbulent burning velocities of FACE-C gasoline and its surrogates subjected to a wide range of turbulence intensities measured in a fan-stirred CVCC dedicated to turbulent combustion up to initial pressure of 1.0 MP. A Mie scattering imaging technique was applied revealing the mutual flame-turbulence interaction. Furthermore, considerable efforts were made towards designing and commissioning a new optically-accessible fan-stirred HPHT combustion vessel. A time-resolved stereoscopic particle image velocimetry (TR-PIV) technique was applied for the characterization of turbulent flow revealing homogeneous-isotropic turbulence in the central region to be utilized successfully for turbulent burning velocity measurement. Turbulent burning velocities were measured for FACE-C and TPRF surrogate fuels along with the effect of ethanol addition for a wide range of initial pressure and turbulent intensity. FACE-C gasoline was found to be more sensitive to both primarily the primary contribution of turbulence intensification and secondarily from pressure in enhancing its turbulent burning velocity. Several correlations were validated revealing a satisfactory scaling with turbulence and thermodynamic parameters. The final part focused on the turbulent burning characteristics of piloted lean methane-air jet flames subjected to a wide range of turbulence intensity by adopting TR-SPIV and OH-planar laser-induced florescence (OH-PLIF) techniques. Both of the flame front thickness and volume increased reasonably linearly as normalized turbulence intensity, u^'/ S_L^0, increased. As u^'/ S_L^0 increased, the flame front exhibited more fractalized structure and occasionally localized extinction (intermittency). Probability density functions of flame curvature exhibited a Gaussian like distribution at all u^'/ S_L^0. Two-dimensional flame surface density (2D-FSD) decreased for low and moderate u^'/ S_L^0, while it increased for high u^'/ S_L^0Turbulent burning velocity was estimated using flame area and fractal dimension methods showing a satisfactory agreement with the flamelet models by Peters and Zimont. Mean stretch factor was estimated and found to increase linearly as u^'/ S_L^0increased. Conditioned velocity statistics were obtained revealing the mutual flame-turbulence interaction.

In this study the breakage mechanics of brittle glass marbles was investigated. The pro-cess was to firstly investigate them in laboratory environment. The marbles or specimens was loaded until a crushing breakage occurred in a single point load test called Single Sphere Point load test in this document. From the test we could derive the crushing load, the deformation and strain, the tensile strength and other parameters needed for the second part of this work. Namely the numerical modelling, here we investigated the specimen with the Discrete Element method or DEM for shorts. The software used was an open sourced software created in MATLAB called DICE2D. Since the software was developed to only include the mathematical part of the numerical model several re-coding processes were needed, with other words the creation of add-ons to the software. The add-ons were automatic code created in Python where the user now are able to create a geometrical model for the specimen that the software can interpret. There were two add-ons created in order to generate a geometry, called the circumference method and the random generation method, i.e. different methods of creating a geometry. The first method, the circumference method creates circumferences filled with smaller particles with the same radii, then moves a step inward to the specimens center and fills another circumference until the center is reached. The second method, the random method generates particles positioned randomly inside the specimen with a random radii, created such that the radius of the particles is chosen with an interval, were the user can choose the smallest and the largest particle radius. It was found that both these add-ons were of great use with different purposes in mind. The circumference method was able to create a brittle material where the deformations were low. The random method also created a brittle material but since the particles were randomly positioned there also was empty space created such that the deformations were larger than the one found in the laboratory environment, since the empty space between the particles was closed before the plastic deformation could occur. Hence the second method of generation is more relevant for concrete and rock mechanics since in these cases this is the actual process, where the micro-cracks first closes then the elastic and plastic deformation occurs [Martin, 1993]. The first method, the circumference method is of great use when investigating the elastic deformations since here the particles are in contact. Thus creating the scenario for granular particles, In this thesis however the circumference method was used in order to create a solid specimen. For future use this add-on should be used in order such that each particle simulates an actual grain. The results found with both of these methods follows the results found in the laboratory test for the crushing load. But the incremental increase of force when the load is applied on the specimen was not able to be simulated. It is believed that the software is having difficulties to simulate brittle material due to the small deformations and the large loads.

Boron cluster compounds are substances clearly synthetic, which don't exist outdoors. This group covers boranes, heteroboranes and their derivatives. They are synthesized and examined mostly for their extraordinary structural and bonding properties. Their study also brought many remarkable findings and even allowed practical use of these compounds in science and technology. This thesis is focused on the application of mass spectrometry for the identification of boranes and heteroboranes and on the study of their fragmentation mechanisms using tandem mass spectrometry on spherical ion trap.

Diploma thesis is worked-up as a part of master’s studies of engineering technology M2I – K, analyzing the possible methods of surface treatment of spherical pin, that increase its corrosion resistance. Spherical pin is mounted into several types of chassis components such as joints, control arms, etc. The current situation is inconvenient for manufacturers, insufficient corrosion protection increases the number of complaints and this may be reflected in the number of future orders. Via of suitable surface treatment is to achieve a higher corrosion resistance while maintaining the functional properties of pins used.

This thesis deals with problem of computation of global illumination in real-time. Two methods are described. Namely Reflective Shadow Maps and Light Propagation Volumes. The first of them deals with the problem by using extended Shadow Mapping algorithm. The second one uses scene embedded into a 3D grid together with Spherical harmonics to compute light propagation in the scene. Furthermore this thesis contains results of measurement of the rendering speed of the Light Propagation Volumes algorithm with various settings on several machines. Quality of the resulting output of the algorithm is also evaluated.

Les performances des antennes Ultra Large Bande (ULB) les rendent appropriées pour de nombreuses applications. En radar à pénétration de surface (SPR), application visée de cette thèse, une telle bande passante offre un excellent compromis entre capacité de pénétration et résolution spatiale en imagerie micro-ondes. De plus, il a été démontré que la prise en compte du champ rayonné par l'antenne en présence de la surface améliore considérablement la qualité des images obtenues. Cette thèse aborde la problématique de la quantité de données représentant les antennes ULB. En effet, les descripteurs classiques d'antenne ne suffisent pas à caractériser l’évolution en fréquence de leurs performances. Le développement en harmoniques ou vecteurs sphériques est utilisé pour modéliser le diagramme de rayonnement d’antennes tout en réduisant le volume de données. D'autre part, les méthodes d'expansion en singularités modélisent la réponse en fréquence (ou impulsionnelle) de l'antenne par un ensemble de pôles de résonance. Le but de ce travail de thèse est d'établir un modèle compact qui représente avec précision le rayonnement d'antenne, et permette la connaissance du champ à différentes distances. A cette fin, plusieurs combinaisons des méthodes de caractérisation ont été étudiées. L'approche proposée est validée par la modélisation du diagramme de rayonnement simulé et mesuré d'une antenne Vivaldi (ETSA). Le modèle établi fournit le champ rayonné à différentes distances de l'antenne avec une erreur inférieure à 3% avec un taux de compression de 99%. La dernière partie de cette thèse présente une application de l'approche proposée au rayonnement d’antennes en présence d’interfaces / UWB antennas bandwidth makes them highly suitable for a number of applications. In surface penetrating radar (SPR) applications, which is the focus of our research, such a bandwidth range allows good signal penetration ability and fine space resolution for microwave imaging. In addition, it has been shown that the knowledge of the radiated field by the antenna enhances drastically the quality of the resulting images. The work reported in this thesis deals with the problematic of the huge amount of data representing UWB antennas. Indeed, due to the frequency dependence, the classical antenna parameters are not sufficient to characterize this type of antenna. The scalar or vector spherical wave expansion is widely used to expand the radiation pattern of a radiating antenna and permit a high compression data rate. On the other hand, the Singularity Expansion Methods are used in frequency/time domain to model the antenna response by a set of resonant poles. The purpose of this thesis is to establish a compact model representing accurately the antenna radiation characteristics, which also allows to find the field at various distances. To this end, several ways of combining the aforementioned methods have been investigated. The proposed approach is validated by modeling the simulated and measured radiation pattern of an Exponential Tapered Slot Antenna (ETSA) in free space. Furthermore, we verify that the established compact model provide radiated field at different distances from the antenna with a compression of the initial pattern up to 99% and an error below 3%. The last part of this thesis, present an application of the proposed methodology to SPR context

Every year a higher life expectancy is reported for people living in industrial countries. With increasing age, the risk of getting Alzheimer's Disease increases as well. Alzheimer's Disease is a neurodegenerative disease that is characterised by progressive deterioration of brain tissue. One of the first regions in the brain to be affected is the hippocampus. A common method to quantify the deterioration of the hippocampus is to measure its volume. However, decreasing volume is no specific marker of Alzheimer's Disease, but can be caused by other diseases as well. Thus, the deformation has to be observed in more detail, which can be done using shape analysis. A powerful shape analysis technique is the approximation of the surface by means of spherical harmonics. A process chain computing such an approximation is explained in this thesis. Therefore, the data is triangulated, forming a closed manifold. Afterwards, a homogeneous mapping of the surface to the unit sphere is computed in two steps. First an initial spherical parametrisation is computed, which is optimised afterwards to resemble the properties of the initial surface. The optimisation is mandatory, to allow for inter-subject comparability. The optimised parametrisation defines a function on the sphere, that can be approximated by spherical harmonics, a set of basis functions on the unit sphere. This procedure results in a mathematical description of the surface that can be analysed statistically. The method is applied to data of Alzheimer's Disease patients.

The Pilsen region suffers the highest incidence of kidney tumours worldwide. Approximately 240 new cases diagnosed as C64 (malignant renal tumours outside the pelvis) were recorded in this region of about 580,000 inhabitants in 2015. Clear renal cell carcinoma has long held first place as the most common tumour, with papillary renal cell carcinoma (pRCC) being the second most frequently operated kidney tumour at the Urology Department of the University Hospital in Pilsen. The 2016 WHO classification of kidney tumours recognizes officially only the stratification of pRCC to type 1 (pRCC1) and type 2 (pRCC2). Unfortunately, the current division does not correspond with knowledge derived from everyday practice. Most clinical trials involving pRCC do not differentiate between the subtypes, adhering only to the official type 1 and 2 divisions and the atypical papillary forms being excluded from their studies. We therefore have to face the question of whether the histological pRCC subtype affects the risk of recurrence, or death, in surgically treated patients. The aim of this dissertation work is to take into consideration also all other papillary types which differ from characterization of pRCC1 and pRCC2. The analyses of a group of patients with surgically treated and histologically verified pRCC at...