We discuss the twist map, with a special interest in its use for the finite Frenkel–Kontorova model. We explain the meaning of the tensile force in some proposed models. We demonstrate that the application of the twist map for the finite FK model is not correct, because the procedure ignores the necessary boundary conditions.

The thesis deals with a musical aspect in Czech films directed by Miloš Forman. The topic is investigated within a wider context of musical culture of the 1960s as it is focused on analysis of cultural phenomena associated with musical expression which left their impression on Forman's films and participated, to great extent, in specificity of their soundtracks. So the films are not analyzed as separate artifacts, but they are considered as documents affected by the social climate at that time. Common social phenomena which were an integral part of Forman's films are studied such as dancing parties, twist and radio broadcasting. The Forman's cooperation with the Semafor theatre is analyzed as well as how Semafor poetics influenced his films. Jiří Suchý's lyrics and the period hits classified as the medium pop music stream are carefully analyzed as they are an important part of Forman's films. A short outline of the cinematographic context of the 1960s and comparison with films thematically similar help to specify Forman's approach to the music aspect. The collage-like structure of the work highlights a few contradictory trends in pop music of the 1960s whose variety can be seen in Forman's films.

The extracellular matrix protein Fibronectin (FN) plays an important role in cell contractility, differentiation, growth, adhesion, and migration. The 12th -14th Type III repeats of FN (FNIII 12-14), also referred to as the Heparin-II domain, comprise a highly promiscuous growth factor (GF) binding region. This binding domain aids in cellular signaling initiated from the ECM. Additionally, FN has the ability to assemble into fibrils under certain conditions, mostly observed during cell contractile processes such as those that initiate due to upregulation of Transforming Growth Factor Beta 1 (TGF-β1) [1], [2]. Previous work from our lab has shown that self-assembly of FN into insoluble fibrils is crucial for Epithelial-Mesenchymal Transition (EMT) [3]. The transition from epithelial to mesenchymal cell type has been implicated as an early event in tumor formation and breast cancer. We were previously able to find that upregulation of FN fibrils drive EMT through contractility due to the increase of the GF latent TGF-β complex concentration at the cell membrane [3]. The challenge in the current work is to exploit the role of Heparin-II binding domain and to concentrate growth factors of interest, such as those that are pro-EMT or anti-EMT at the signaling sites of the cell membrane. Initially, we investigated the localization of the fragments FNIII 12-14 delivered to cell membrane using FITC conjugated protein. We then investigated the effects of exogenous FNIII 12-14 on EMT using breast epithelial cells (MCF10A) in the presence or absence of TGF-β1 to determine whether FNIII 12-14 alters EMT signaling. Quantification of mRNA expression, for EMT markers such as Slug, Snail, Twist, and ZEB1 were analyzed. Results showed that dosage increase of FNIII 12-14 appears to inhibit EMT transcription factors. This study will develop a new understanding of disease and gene control using ECM proteins. The exploitation of ECM natural protein interactions could become a new method in turning on/off genes of interest. While we are currently investigating this as a mechanism of blocking EMT, it could also have implications in wound healing, fibrosis, and tissue engineering, where EMT is an important aspect of the physiologic progression.

This thesis presents a detailed analysis of the plane rake faced drill design, its grinding method and grinding wheel geometry. A fundamental geometrical analysis has then been carried out on the major cutting edges of the modified drills according to the national and international standards. It has been shown that this new drill design results in a significant increase in the normal rake angle at lips as well as point relieving at the chisel edge region. Geometrical models for the various drill point features have been established which uniquely define the drill point features of the modified drill design. A comprehensive experimental investigation has been carried out to study the drilling performance of the modified drills, when drilling a high tensile steel, ASSAB 4340, with TiN coated high speed steel drills over a wide range of drilling conditions. Comparing to the drilling performance with conventional twist drills under the corresponding conditions, it has been found that the modified drills can reduce the thrust force by as much as 46.9% with the average of 23.8%; the reduction of drilling torque is also significant at an average of 13.2% and the maximum of 24.9%. Similarly, the new drill design shows great superiorities over the conventional drills in terms of drill-life. In the drill-life tests, a few conventional drills were broken, but all plane rake faced drills performed very well. In order to estimate the cutting performance in process planning on a mathematical and quantitative basis when drilling with the modified drills, predictive cutting force models have been developed based on the unified-generalized mechanics of cutting approach. The models have been assessed qualitatively and quantitatively and showed good agreements with the experimental thrust, torque and power. Empirical-type force equations have also been developed to provide simple alternatives for practical applications.

Cette thèse est consacrée à la définition d'une surface géométriquement lisse interpolant un ensemble triangulé de points de R^3. Une telle triangulation, que nous appelons "réseau surfacique", doit définir une sous-variété de dimension 2, et peut représenter des surfaces de n'importe quel genre topologique. Il fournit l'information topologique, par l'intermédiaire d'une structure de données contenant les informations d'adjacence entre les sommets, les arêtes et les faces. Nous avons développé deux méthodes pour l'interpolation des sommets du réseau surfacique. Elles sont strictement locales et produisent des surfaces polynomiales par morceaux de degré 5 et de continuité G^1. De nombreux paramètres libres sont disponibles et ajustés soit interactivement soit automatiquement afin de lisser la surface. Dans le contexte interactif, plusieurs outils de design sont développés, basés sur l'interprétation géométrique des paramètres libres. La forme voulue peut être obtenue par une modélisation temps réel, grâce à la localité des algorithmes. Dans le cas du design automatique, de nombreux algorithmes ont été developpés satisfaisant un certain nombre de caractéristiques de forme. Un grand nombre de règles heuristiques et d'optimisations locales sont utilisées pour définir les valeurs des paramètres de forme dans le but d'obtenir des formes satisfaisantes ainsi qu'un contrôle optimal de la surface.

Lead-lag dampers are present in most rotor systems to provide the desired level of damping for all flight conditions. These dampers are critical components of the rotor system, and the performance of semi-active Coulomb-friction-based lead-lag dampers is examined for the UH-60 aircraft. The concept of adaptive damping, or “damping on demand,” is discussed for both ground resonance and forward flight. The concept of selective damping is also assessed, and shown to face many challenges. In rotorcraft flight dynamics, optimized warping twist change is a potentially enabling technology to improve overall rotorcraft performance. Research efforts in recent years have led to the application of active materials for rotorcraft blade actuation. An innovative concept is proposed wherein the typically closed section blade is cut open to create a torsionally compliant structure that acts as its own amplification device; deformation of the blade is dynamically controlled by out-of-plane warping. Full-blade warping is shown to have the potential for great design flexibility. Recent advances in rotorcraft blade design have also focused on variable-camber airfoils, particularly concepts involving “truss-core” configurations. One promising concept is the use of hexagonal chiral lattice structures in continuously deformable helicopter blades. The static behavior of passive and active chiral networks using piezoelectric actuation strategies is investigated, including under typical aerodynamic load levels. The analysis is then extended to the dynamic response of active chiral networks in unsteady aerodynamic environments.

This is a report on research done in the field of mathematical physics. It is an investigation of the concept of the linking number between two simple and closed spatial curves. The linking number is a topological invariant with scientific applications ranging from DNA biology to Topological Quantum Field Theory. Our aim is to study C ̆alug ̆areanu’s theorem, also called White’s formula, which relates the linking number to the concepts of twist and writhe. We are interested in the limit of the two curves as they approach each other. To regulate this, we introduce a regularization method that utilizes a point-split. Further we explore if the result is dependent on how the regularization is introduced. Therefor we inflict an asymmetry in the regularization, with a parameter a in the point-split intervals, to check whether the result becomes dependent on a or not. We find that the result is independent of the parameter a.

This thesis presents a detailed analysis of the plane rake faced drill design, its grinding method and grinding wheel geometry. A fundamental geometrical analysis has then been carried out on the major cutting edges of the modified drills according to the national and international standards. It has been shown that this new drill design results in a significant increase in the normal rake angle at lips as well as point relieving at the chisel edge region. Geometrical models for the various drill point features have been established which uniquely define the drill point features of the modified drill design. A comprehensive experimental investigation has been carried out to study the drilling performance of the modified drills, when drilling a high tensile steel, ASSAB 4340, with TiN coated high speed steel drills over a wide range of drilling conditions. Comparing to the drilling performance with conventional twist drills under the corresponding conditions, it has been found that the modified drills can reduce the thrust force by as much as 46.9% with the average of 23.8%; the reduction of drilling torque is also significant at an average of 13.2% and the maximum of 24.9%. Similarly, the new drill design shows great superiorities over the conventional drills in terms of drill-life. In the drill-life tests, a few conventional drills were broken, but all plane rake faced drills performed very well. In order to estimate the cutting performance in process planning on a mathematical and quantitative basis when drilling with the modified drills, predictive cutting force models have been developed based on the unified-generalized mechanics of cutting approach. The models have been assessed qualitatively and quantitatively and showed good agreements with the experimental thrust, torque and power. Empirical-type force equations have also been developed to provide simple alternatives for practical applications.

Cette thèse traite de plusieurs aspects algorithmiques des courbes algébriques. La première partie décrit et implémente en Magma un algorithme de calcul des tordues pour les courbes sur les corps finis et en étudie la complexité. Dans le cas hyperellitptique, il s’agit du premier algorithme complet pour faire cela en tout genre. La deuxième partie construit des familles représentatives pour les courbes non hyperelliptiques de genre 3 afin de permettre leur énumération efficace en lien avec le problème de l’obstruction de Serre. Cette partie a fait l’objet d’une publication dans ANTS et une annexe de la thèse est constituée d’un préprint étudiant un modèle statistique pour l’interprétation des données obtenues. La dernière partie de la thèse étudie les invariants et covariants des formes binaires en lien avec la description de l’espace de modules des courbes de genre 2. On y décrit en particulier une nouvelle opération pour engendrer des covariants en petite caractéristique. On étudie aussi l’application d’une nouvelle stratégie (dite de Geyer-Sturmfels) pour obtenir les algèbres de séparants et on l’applique au cas du degré 4 et du degré 6. Enfin, un dernier chapitre montre la validité d’un algorithme de reconstruction pour les courbes de genre 2 à partir de leurs invariants en toute caractéristique différente de 2 et l’implémente en SAGE. / This thesis addresses several algorithmic aspects of algebraic curves.The first part describe and plug in Magma a computational algorithm of twists for the curves over finite fields and study it's complexity. In the hyperelliptic case, it is the first complete algorithm to do this in all genus. The second part builts representatives family for the non hyperelliptic curves of genus 3 to enable them effective enumeration in connection with the Serre obstruction problem. This part has been published in ANTS and an annex of this thesis is made up of a preprint studing a statistic model for interpreting the data obtained.The last part of the thesis studies the invariants and covariants of binary forms in connexion with the description of the moduli space of curves of genus 2. A new operation in particular is described to generate covariants in small characteristic. We study to the implementation of a new strategy (called Geyer-Sturmfels) to get the algebras of separants and we apply it of the case of degree 4 ans 6. Finally, the last chapter shows the validity of a reconstruction algorithm for genus 2 curves from their invariants in all characteristic diferent from 2 and implements it in SAGE .

This master’s thesis is devoted to rifling technologies of the barrel bore of fire and gas arms. In cooperation with the company Winston Production, s.r.o. also enters into operation issues of selected manufacturing machine Zs 151 for barrel rifling. It contains an analysis of legislative demands on the technical documentation, description of the construction and function of machinery and materials for the creation of local operating safety rules for its operation. The part of work is also 3D model of the machine created in software SolidWorks.