Cette thèse porte sur le comportement en temps long de solutions d’équations de type Vlasov, principalement le modèle Vlasov-HMF. On s’intéresse en particulier au phénomène d’amortissement Landau, prouvé mathématiquement dans divers cadres, pour plusieurs équations de type Vlasov, comme l’équation de Vlasov-Poisson ou le modèle Vlasov-HMF, et présentant certaines analogies avec le phénomène d’amortissement non visqueux pour l’équation d’Euler 2D. Les résultats qui y sont décrits sont les suivants. Le premier est un théorème d’amortissement Landau pour des solutions numériques du modèle Vlasov-HMF, obtenues par discrétisation en temps de ce dernier via des méthodes de splitting. Nous prouvons en outre la convergence des schémas numériques. Le second est un théorème d’amortissment Landau pour des solutions du modéle Vlasov-HMF linéarisé autour d’états stationnaires inhomogènes. Ce théorème est accompagné de nombreuses simulations numériques destinées à étudier numériquement le cas non-linéaire, et semblant mettre en lumière de nouveaux phénomènes. Enfin, le dernier résultat porte sur la discrétisation en temps de l’équation d’Euler 2D par un intégrateur de Crouch-Grossman symplectique. Nous prouvons la convergence du schéma. / This thesis concerns the long time behavior of certain Vlasov equations, mainly the Vlasov- HMF model. We are in particular interested in the celebrated phenomenon of Landau damp- ing, proved mathematically in various frameworks, foar several Vlasov equations, such as the Vlasov-Poisson equation or the Vlasov-HMF model, and exhibiting certain analogies with the inviscid damping phenomenon for the 2D Euler equation. The results described in the document are the following.The first one is a Landau damping theorem for numerical solutions of the Vlasov-HMF model, constructed by means of time-discretizations by splitting methods. We prove more- over the convergence of the schemes. The second result is a Landau damping theorem for solutions of the Vlasov-HMF model linearized around inhomogeneous stationary states. We provide moreover a quite large amount of numerical simulations, which are designed to study numerically the nonlinear case, and which seem to show new phenomenons. The last result is the convergence of a scheme that discretizes in time the 2D Euler equation by means of a symplectic Crouch-Grossmann integrator.

Dans cette thèse, nous abordons l'estimation non paramétrique de la fonction de dépendance des distributions multivariées à valeurs extrêmes. Dans une première partie, on adopte l’hypothèse classique stipulant que les variables aléatoires sont indépendantes et identiquement distribuées (i.i.d). Plusieurs estimateurs non paramétriques sont comparés pour une fonction de dépendance trivariée de type logistique dans deux différents cas. Dans le premier cas, on suppose que les fonctions marginales sont des distributions généralisées à valeurs extrêmes. La distribution marginale est remplacée par la fonction de répartition empirique dans le deuxième cas. Les résultats des simulations Monte Carlo montrent que l'estimateur Gudendorf-Segers (Gudendorf et Segers, 2011) est plus efficient que les autres estimateurs pour différentes tailles de l’échantillon. Dans une deuxième partie, on ignore l’hypothèse i.i.d vue qu’elle n'est pas vérifiée dans l'analyse des séries temporelles. Dans le cadre univarié, on examine le comportement extrêmal d'un modèle autorégressif Gaussien stationnaire. Dans le cadre multivarié, on développe un nouveau théorème qui porte sur la convergence asymptotique de l'estimateur de Pickands vers la fonction de dépendance théorique. Ce fondement théorique est vérifié empiriquement dans les cas d’indépendance et de dépendance asymptotique. Dans la dernière partie de la thèse, l'estimateur Gudendorf-Segers est utilisé pour modéliser la structure de dépendance des concentrations extrêmes d’ozone observées dans les stations qui enregistrent des dépassements de la valeur guide et limite de la norme Tunisienne de la qualité d'air NT.106.04. / In this thesis, we investigate the nonparametric estimation of the dependence function for multivariate extreme value distributions. Firstly, we assume independent and identically distributed random variables (i.i.d). Several nonparametric estimators are compared for a trivariate dependence function of logistic type in two different cases. In a first analysis, we suppose that marginal functions are generalized extreme value distributions. In a second investigation, we substitute the marginal function by the empirical distribution function. Monte Carlo simulations show that the Gudendorf-Segers (Gudendorf and Segers, 2011) estimator outperforms the other estimators for different sample sizes. Secondly, we drop the i.i.d assumption as it’s not verified in time series analysis. Considering the univariate framework, we examine the extremal behavior of a stationary Gaussian autoregressive process. In the multivariate setting, we prove the asymptotic consistency of the Pickands dependence function estimator. This theoretical finding is confirmed by empirical investigations in the asymptotic independence case as well as the asymptotic dependence case. Finally, the Gudendorf-Segers estimator is used to model the dependence structure of extreme ozone concentrations in locations that record several exceedances for both guideline and limit values of the Tunisian air quality standard NT.106.04.

Cette thèse est essentiellement composée de deux parties traitant des problèmes de Cauchy ou des problèmes périodiques. Dans la première partie, on étudie la stabilité de solutions régulières au voisinage d'états d'équilibre non constants pour un système d'Euler-Maxwell isentropique compressible bipolaire. Par des estimations d'énergie classiques et un argument de récurrence sur l'ordre des dérivées des solutions, on montre l'existence globale et l'unicité des solutions régulières du système lorsque les données initiales sont proches des états d'équilibre. On obtient aussi le comportement asymptotique des solutions quand le temps tend vers l'infini. Dans la deuxième partie, on considère la stabilité en temps long des solutions régulières de systèmes d'Euler-Maxwell et de Navier-Stokes-Maxwell compressibles dans le cas non isentropique lorsque les états d'équilibre sont constants. Grâce à des choix convenables de symétriseurs des systèmes et à des estimations d'énergie, on montre l'existence globale et l'unicité des solutions régulières des systèmes avec données initiales petites. De plus, par le principe de Duhamel et l'outil d'analyse de Fourier, on obtient des taux de décroissance des solutions quand le temps tend vers l'infini. / This thesis is essentially composed of two parts dealing with Cauchy problems and periodic problems. In the first part, we study the stability of smooth solutions near non constant equilibrium states for a two-fluid isentropic compressible Euler-Maxwell system.By classical energy estimates together with an induction argument on the order of the derivatives of solutions, we prove the existence and uniqueness of global solutions to the system when the given initial data are near the equilibrium states. We also obtain the asymptotic behavior of solutions when the time goes to infinity. In the second part, we consider the long time stability of the global smooth solutions for compressible Euler-Maxwell and Navier-Stokes-Maxwell systems in non isentropic case when the equilibrium solutions are constants. With the help of suitable choices of symmetrizers and energy estimates, we prove the existence and uniqueness of global solutions to the systems with given small initial data. Furthermore, using the Duhamel principle and the Fourier analysis tool, we obtain the decay rates of smooth solutions as the time goes to infinity.

A unique mechanism of protein oligomerization is domain swapping. It is a feature found in some proteins wherein a dimer or a higher oligomer is formed by the exchange of identical structural segments between protomers. Domain swapping is thought to have played a key role in the evolution of stable oligomeric proteins and in oligomerization of amyloid proteins. This thesis deals with studies to understand the significance of hinges involved in domain swapping for protein oligomerization and function. The stationary phase survival protein SurE from Salmonella typhimurium (StSurE) and Sesbania mosaic virus (SeMV) coat protein have been used as models for studies on domain swapping. This thesis has been divided into eight chapters. Chapter 1 provides a brief introduction to domain swapping, while Chapters 2 to 6 describes the studies carried out on StSurE protein, Chapter 7 deals with studies on SeMV coat protein. The final Chapter 8 provides brief descriptions of various experimental techniques employed during these investigations. Chapter 1 deals with a brief introduction to domain swapping in proteins. Examples where different domains are exchanged are cited. Then it describes physiological relevance of domain swapping in proteins and probable factors which promote swapping. Finally it also discusses the uncertainties that are inevitable in protein structure prediction and design. Chapter 2 describes the structure of Salmonella typhimurium SurE (StSurE; Pappachan et al., 2008) determined at a higher resolution. The chapter also deals with the sequence and structure based comparison of StSurE with other known SurE homolog structures. A comparative analysis of the relative conservation of N- and C-terminal halves of SurE protomer and variations observed in the quaternary structures of SurE homologs are presented. Then a brief introduction is provided on function of StSurE. The conserved active site of StSurE that might be important for its phosphatase activity is described. A plausible mechanism for the phosphatase activity as proposed by Pappachan et al. (2008) is presented. Crystal structures of StSurE bound with AMP, pNPP and pNP that was determined with the view of better understanding the mechanism of enzyme function is presented. These structures provide structural evidence for the mechanism proposed by Pappachan et al. (2008). Finally a substrate entry channel inferred from these structures is discussed. SurE from Salmonella typhimurium (StSurE) was selected for studies on domain swapping as there is at least one homologous structure (Pyrobaculum aerophilum - PaSurE) in which swapping of the C-terminal helices appears to have been avoided without leading to the loss of oligomeric structure or function. It was of interest to examine if an unswapped dimer of StSurE resembling PaSurE dimer could be constructed by mutagenesis. To achieve this objective, a crucial hydrogen bond in the hinge involved in C-terminal helix swapping was abolished by mutagenesis. These mutants were constructed with the intention of increasing the flexibility of the hinge which might bring the C-terminal helices closer to the respective protomer as in PaSurE. Chapter 3 presents a comparative analysis of the hinges involved in C-terminal helix swapping in PaSurE and StSurE. Based on the comparison of structure and sequence, crucial residues important for C-terminal helix swapping in StSurE were identified as D230 and H234. The chapter describes the construction of mutants obtained by substituting D230 and H234 by alanine and their biophysical characterization. Finally it describes structural studies carried out on these mutants. The mutation H234A and D230A/H234A resulted in highly distorted dimers, although helix swapping was not avoided. Comparative analysis of the X-ray crystal structures of native StSurE and mutants H234A and D230A/H234A reveal large structural changes in the mutants relative to the native structure. However the crystal structures do not provide information on the changes in dynamics of the protein resulting from these mutations. To gain better insights into the dynamics involved in the native and mutants H234A and D230A/H234A, MD simulations were carried on using GROMACS 4.0.7. Chapter 4 deals with a brief description of the theory of molecular dynamics, followed by results of simulation studies carried out on monomeric and dimeric forms of StSurE and dimeric forms of its mutants H234A and D230A/H234A. The conformational changes and dynamics of different swapped segments are discussed. Crystal structures of H234A and D230A/H234A mutants reveal that they form highly distorted dimers with altered dimeric interfaces. Chapter 5 focuses on comparison of dimeric interfaces of the native StSurE and hinge mutants H234A and D230A/H234A. Based on the analysis, three sets of interactions were selected to investigate the importance of the interface formed by swapped segments in StSurE mutants H234A and D230A/H234A. One of the selected sites corresponds to a novel interaction involving tetramerization loop in the hinge mutants H234A and D230A/H234A resulting in a salt bridge between E112 – R179’ and E112’ – H180 (prime denotes residue from the other chain of the dimeric protein). This salt bridge seems to stabilize the distorted dimer. It is shown by structural studies that the loss of this salt bridge due to targeted mutation restores symmetry and dimeric organization of the mutants. Loss of a crucial hydrogen bond in the hinge region involved in C-terminal helix swapping in SurE not only leads to large structural changes but also alters the conformation of a loop near the active site. It is of interest to understand functional consequences of these structural changes. StSurE is a phosphatase, and its activity could be conveniently monitored using the synthetic substrate para nitrophenyl phosphate (pNPP) at pH 7 and 25 ºC. Chapter 6 deals with the functional studies carried out with various StSurE mutants. The studies suggest that there is a drastic loss in phosphatase activity in hinge mutants D230A, H234A and D230A/H234A, while in the salt bridge mutants the function seems to have been restored. Few of these mutants also exhibit positive cooperativity, which could probably be due to altered dynamics of domains. Sesbania mosaic virus (SeMV) is a plant virus, belonging to genus sobemovirus. SeMV is a T=3 icosahedral virus (532 symmetry) made up of 180 coat protein (CP) subunits enclosing a positive-sense RNA genome. The asymmetric unit of the icosahedral capsid is composed of chemically identical A, B and C subunits occupying quasi-equivalent environments. Residues 48 – 59 of the N-terminal arms of the C subunits interact at the nearby icosahedral three-fold axes through a network of hydrogen bonds to form a structure called the “β-annulus”. Residues 60 – 73 form the “βA-arm” that connects the N-terminal β-annulus to the rest of the protomer. Various studies on SeMV-CP suggest that different lengths of the N-terminal segments affect the assembly of virus. It might be possible to exploit this flexibility of the N-terminus in SeMV-CP to introduce swapping of this segment between two 2-fold related C subunits as is found in Rice yellow mottle virus (RYMV), another sobemovirus, with which SeMV shares significant sequence similarity. Chapter 7 focuses on attempts made to examine the mutational effects planned to introduce domain swapping. The strategy used for introducing swapping in SeMV-CP was based on the sequence of the βA-arm or the hinge involved in swapping of β-annulus in RYMV. TEM images of the mutant virus like particles obtained suggest that they are heterogeneous. These mutants could not be crystallized, probably due to the heterogeneity. However, the assembly of the expressed proteins to virus like particles was profoundly influenced by the mutations. Chapter 8 discusses various crystallographic, biophysical and biochemical techniques used during these investigations. Finally the thesis concludes with Conclusions and Future perspectives of the various studies reported in the thesis. In summary, I have addressed the importance of amino acid residues and interactions of hinges involved in domain swapping for the quaternary structure and function of proteins.

Une nouvelle famille de complexes de difluorure de bore photosensibles est développée. Elle est basée sur des structures moléculaires contenant une unité β-dicétone à conjugaison électronique π.La grande variété de groupements aromatiques et la nature donneur ou accepteur d'électrons des différents substituants permet l'élaboration de systèmes électroniques donneur-accepteur-donneur d'électrons (D1-A-D1) et donneur-accepteur (D2-A).L'absorption électronique de cette famille de molécule se situe dans la partie visible du spectre électromagnétique et une partie du spectre ultraviolet, et est caractérisée par une bande d'absorption π-π* intense avec des coefficients d'absorption molaire supérieurs à 50 000 M-1cm-1.L'émission de fluorescence couvre une plage spectrale qui va du visible au proche infrarouge avec des rendements quantiques de fluorescence en solution relativement élevés pouvant atteindre 62 %.En fin, cette famille de molécule est photochimiquement stable et est, contrairement à d'autres familles de complexes de difluorure de bore, chimiquement très stable en solution.Mots-clés : Difluorure de bore, β-dicétone, matériaux π-conjugués, luminescence, fluorescence stationnaire et résolue dans le temps (TRES), synthèse organique, RMN-19F dynamique, complexes & colorants fluorescents, curcumine & curcuminoide, complexe BF2, photophysique. / A new photosensitive family of boron difluoride complex is developed. It is based on π-conjugated molecular structures containing β-diketonates unit.The wide variety of aromatic groups and the nature of donor or electron acceptor of the different substituents allow the development of electron donor-acceptor-donor (DAD) and donor-acceptor (DA) electronic systems.The electronic absorption of this family of molecules is in the visible part of the electromagnetic spectrum and a portion of the ultraviolet spectrum, and is characterized by an intense π-π* absorption band with molar absorption coefficient greater than 50 000 M-1.cm-1.The fluorescence emission covers a spectral range going from visible to near infrared, with relatively high fluorescence quantum yields of up to 62 % in solution.This new material family is photochemically stable and, unlike some other families of boron difluoride complexes, chemically very stable in solution.

Cette thèse est centrée autour de l’étude théorique et de l’analyse numérique des équations paraboliques non linéaires avec divers conditions aux limites. La première partie est consacrée aux équations paraboliques dégénérées mêlant des phénomènes non-linéaires de diffusion et de transport. Nous définissons des notions de solutions entropiques adaptées pour chacune des conditions aux limites (flux nul, Robin, Dirichlet). La difficulté principale dans l’étude de ces problèmes est due au manque de régularité du flux pariétal pour traiter les termes de bords. Ceci pose un problème pour la preuve d’unicité. Pour y remédier, nous tirons profit du fait que ces résultats de régularités sur le bord sont plus faciles à obtenir pour le problème stationnaire et particulièrement en dimension un d’espace. Ainsi par la méthode de comparaison "fort-faible" nous arrivons à déduire l’unicité avec le choix d’une fonction test non symétrique et en utilisant la théorie des semi-groupes non linéaires.L’existence de solution se démontre en deux étapes, combinant la méthode de régularisation parabolique et les approximations de Galerkin. Nous développons ensuite une approche directe en construisant des solutions approchées par un schéma de volumes finis implicite en temps. Dans les deux cas, on combine les estimations dans les espaces fonctionnels bien choisis avec des arguments de compacité faible ou forte et diverses astuces permettant de passer à la limite dans des termes non linéaires. Notamment, nous introduisons une nouvelle notion de solution appelée solution processus intégrale dont l’objectif, dans le cadre de notre étude, est de pallier à la difficulté de prouver la convergence vers une solution entropique d’un schéma volumes finis pour le problème de flux nul au bord.La deuxième partie de cette thèse traite d’un problème à frontière libre décrivant la propagation d’un front de combustion et l’évolution de la température dans un milieu hétérogène. Il s’agit d’un système d’équations couplées constitué de l’équation de la chaleur bidimensionnelle et d’une équation de type Hamilton-Jacobi. L’objectif de cette partie est de construire un schéma numérique pour ce problème en combinant des discrétisations du type éléments finis avec les différences finies. Ceci nous permet notamment de vérifier la convergence de la solution numérique vers une solution onde pour un temps long. Dans un premier temps, nous nous intéressons à l’étude d’un problème unidimensionnel. Très vite,nous nous heurtons à un problème de stabilité du schéma. Cela est dû au problème de prise en compte de la condition de Neumann au bord. Par une technique de changement d’inconnue et d’approximation nous remédions à ce problème. Ensuite, nous adaptons cette technique pour la résolution du problème bidimensionnel. A l’aide d’un changement de variables, nous obtenons un domaine fixe facile pour la discrétisation. La monotonie du schéma obtenu est prouvée sous une hypothèse supplémentaire de propagation monotone qui exige que la frontière libre se déplace dans les directions d’un cône prescrit à l’avance. / This thesis focuses on the theoretical study and numerical analysis of parabolic equations with boundary conditions.The first part is devoted to degenerate parabolic equation which combines features of a hyperbolic conser-vation law with those of a porous medium equation. We define suitable notions of entropy solutions foreach of the boundary conditions (zero-flux, Robin, Dirichlet). The main difficulty in these studies residesin the formulation of the adequate notion of entropy solution and in the proof of uniqueness. There isa technical difficulty due to the lack of regularity required to treat the boundaries terms. We take ad-vantage of the fact that boundary regularity results are easier to obtain for the stationary problem, inparticular in one space dimension. Thus, using strong-weak uniqueness approach we get the uniquenesswith the choice of a non-symmetric test function and using the nonlinear semigroup theory. The exis-tence of solution is proved in two steps, combining the method of parabolic regularization and Galerkinapproximations. Next, we develop a direct approach to construct approximate solutions by an implicitfinite volume scheme. In both cases, the estimates in the appropriately chosen functional spaces are com-bined with arguments of weak or strong compactness and various tricks to pass to the limit in nonlinearterms. In the appendix, we propose a result of existence of strong trace of a solution for the degenerateparabolic problem. In another appendix of independent interest, we introduce a new concept of solutioncalled integral process solution. We exploit it to overcome the difficulty of proving the convergence ofour finite volume scheme to an entropy solution for the zero-flux boundary problem.The second part of this thesis deals with a free boundary problem describing the propagation of a com-bustion front and the evolution of the temperature in a heterogeneous medium. So we have a coupledproblem consisting of the heat equation of bidimensional space and a Hamilton-Jacobi equation. The ob-jective is to construct a numerical scheme and to verify that the numerical solution converges to a wavesolution for a long time. Recall that an existence of wave solution for this problem was already proven inan analytical framework. At first, we focus on the study of a one-dimensional problem. Here, we face aproblem of stability of the scheme. This is due to a difficulty of taking into account the Neumann boun-dary condition. Through a technique of change of unknown, we can propose a monotone scheme. Wealso adapt this technique for solving two-dimensional problem. Using a change of variables, we obtaina fixed domain where the discretization becomes easy. The monotony of the scheme is proved under anadditional assumption of monotone propagation that requires the free boundary moves in the directionsof a cone given beforehand.

The subject of this diploma thesis is the construction and technological solution of the construction of the campus building Bohunice - object C. This building is a new building located on several unfinished parcels. The diploma thesis contains technical reports, technological regulations of the selected works, control and test plans for these works, design of the machine group, the transport relations in the narrower and wider surroundings of the construction, the budget budget, the timetable, the design and realization of the tower cranes.

This work deals with the possibilities of filtering the ECG signal, representing the first part, which is the basis for successful delineation and follow diagnosis of the ECG signal. Filtration in this case is mean to suppress interference from electrical grid, noise of electrical grid. The content of the work is description of filters realized trough wavelet transform and linear filtering as a means to successful filtration of interference. There are method of stationary wavelet transform - dyadic wavelet transform, wavelet packet transform and wavelet wiener filtering method. Linear filtering includes two narrow-band FIR filters. The objective of this work is to propose different methods of wavelet and linear filters in Matlab, filtering of ECG signals and compare the success of filtration methods. ECG signals used in this work are from the CSE database.

This master´s thesis is dealing with selected part of the construction technology project of the high-rise building AZ Tower. The main content becomes the realization of supporting gross upper structure. It compiles in detail the most optimal proposal of technological processes, working machines, schedule, control and test plan, occupational safety, environment protection, construction site equipment and last but not least, the coordination of four tower cranes. Apart from the architectural and technically impressive draft of the Czech Republic tallest building it will be interesting to deal with progress of the whole construction. New technologies and elementary construction activities adapting to work at extreme altitudes will be used.

The thesis contains analysis earthworks, foundations, carcass substructure of residential house on the street Kopečná 9 in Brno. The work also includes gradual changes in site equipment, detailed schedule of work for selected works, rough schedule of the whole building, construction budget, site equipment budget and details of construction. Specialization in the work addresses the specific use of roads and traffic signs.