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371	Contrôle optimal des équations d'évolution et ses applications / Optimal control of evolution equations and its applications Nabolsi, Hawraa 17 July 2018 (has links) Dans cette thèse, tout d’abord, nous faisons l’Analyse Mathématique du modèle exact du chauffage radiatif d’un corps semi-transparent $\Omega$ par une source radiative noire qui l’entoure. Il s’agit donc d’étudier le couplage d’un système d’Equations de Transfert Radiatif avec condition au bord de réflectivité indépendantes avec une équation de conduction de la chaleur non linéaire avec condition limite non linéaire de type Robin. Nous prouvons l’existence et l’unicité de la solution et nous démontrons des bornes uniformes sur la solution et les intensités radiatives dans chaque bande de longueurs d’ondes pour laquelle le corps est semi-transparent, en fonction de bornes sur les données, Deuxièmement, nous considérons le problème du contrôle optimal de la température absolue à l’intérieur du corps semi-transparent $\Omega$ en agissant sur la température absolue de la source radiative noire qui l’entoure. À cet égard, nous introduisons la fonctionnelle coût appropriée et l’ensemble des contrôles admissibles $T_{S}$, pour lesquels nous prouvons l’existence de contrôles optimaux. En introduisant l’espace des états et l’équation d’état, une condition nécessaire de premier ordre pour qu’un contrôle $T_{S}$ : t ! $T_{S}$ (t) soit optimal, est alors dérivée sous la forme d’une inéquation variationnelle en utilisant le théorème des fonctions implicites et le problème adjoint. Ensuite, nous considérons le problème de l’existence et de l’unicité d’une solution faible des équations de la thermoviscoélasticité dans une formulation mixte de type Hellinger- Reissner, la nouveauté par rapport au travail de M.E. Rognes et R. Winther (M3AS, 2010) étant ici l’apparition de la viscosité dans certains coefficients de l’équation constitutive, viscosité qui dépend dans ce contexte de la température absolue T(x, t) et donc en particulier du temps t. Enfin, nous considérons dans ce cadre le problème du contrôle optimal de la déformation du corps semi-transparent $\Omega$, en agissant sur la température absolue de la source radiative noire qui l’entoure. Nous prouvons l’existence d’un contrôle optimal et nous calculons la dérivée Fréchet de la fonctionnelle coût réduite. / This thesis begins with a rigorous mathematical analysis of the radiative heating of a semi-transparent body made of glass, by a black radiative source surrounding it. This requires the study of the coupling between quasi-steady radiative transfer boundary value problems with nonhomogeneous reflectivity boundary conditions (one for each wavelength band in the semi-transparent electromagnetic spectrum of the glass) and a nonlinear heat conduction evolution equation with a nonlinear Robin boundary condition which takes into account those wavelengths for which the glass behaves like an opaque body. We prove existence and uniqueness of the solution, and give also uniform bounds on the solution i.e. on the absolute temperature distribution inside the body and on the radiative intensities. Now, we consider the temperature $T_{S}$ of the black radiative source S surrounding the semi-transparent body $\Omega$ as the control variable. We adjust the absolute temperature distribution (x, t) 7! T(x, t) inside the semi-transparent body near a desired temperature distribution Td(·, ·) during the time interval of radiative heating ]0, tf [ by acting on $T_{S}$. In this respect, we introduce the appropriate cost functional and the set of admissible controls $T_{S}$, for which we prove the existence of optimal controls. Introducing the State Space and the State Equation, a first order necessary condition for a control $T_{S}$ : t 7! $T_{S}$ (t) to be optimal is then derived in the form of a Variational Inequality by using the Implicit Function Theorem and the adjoint problem. We come now to the goal problem which is the deformation of the semi-transparent body $\Omega$ by heating it with a black radiative source surrounding it. We introduce a weak mixed formulation of this thermoviscoelasticity problem and study the existence and uniqueness of its solution, the novelty here with respect to the work of M.E. Rognes et R. Winther (M3AS, 2010) being the apparition of the viscosity in some of the coefficients of the constitutive equation, viscosity which depends on the absolute temperature T(x, t) and thus in particular on the time t. Finally, we state in this setting the related optimal control problem of the deformation of the semi-transparent body $\Omega$, by acting on the absolute temperature of the black radiative source surrounding it. We prove the existence of an optimal control and we compute the Fréchet derivative of the associated reduced cost functional. Fonction de Planck Fonctionnelle coût Fonctionnelle coût réduite Existence de contrôles optimaux Espace des états Continuité des états Différentiabilité Fréchet Problème adjoint Équation parabolique rétrograde Inéquation variationnelle Thermoviscoélasticité Existence et unicité de la solution Contrôle du champ de déplacements Planck function Cost functional Reduced cost functional Existence of optimal controls State space Continuity of the states State equation Fréchet differentiability Implicit Function Theorem Adjoint Problem Backward parabolic equation Variational inequality Thermoviscoelasticity Maxwell model in thermoviscoelasticity Existence and uniqueness of the solution Control of the field of displacements
372	On completeness of partial metric spaces, symmetric spaces and some fixed point results 10 1900 (has links) The purpose of the thesis is to study completeness of abstract spaces. In particular, we study completeness in partial metric spaces, partial metric type spaces, dislocated metric spaces, dislocated metric type spaces and symmetric spaces that are generalizations of metric spaces. It is well known that complete metric spaces have a wide range of applications. For instance, the classical Banach contraction principle is phrased in the context of complete metric spaces. Analogously, the Banach's xed point theorem and xed point results for Lipschitzian maps are discussed in this context, namely in, partial metric spaces and metric type spaces. Finally, xed point results are presented for symmetric spaces / Mathematical Sciences / Ph. D. (Mathematics) Metric space Quasi metric space Dislocated metric space Partial metric space TV S-cone metric space TV S-partial cone metric space Dislocated cone metric space Convergent sequence Cauchy sequence Convergence complete Cauchy complete 0-Cauchy complete Contraction constant Contraction map Lipschitzian constant Lipschitzian map Fixed point Metric type space Dislocated metric type space Partial metric type space Symmetric space 516.1 Metric spaces Symmetric spaces
373	Demography of Birch Populations across Scandinavia Sendrowski, Janek January 2022 (has links) Boreal forests are particularly vulnerable to climate change, experiencing a much more drastic increase in temperatures and having a limited amount of more northern refugia. The trees making up these vast and important ecosystems already had to adapt previously to environmental pressures brought about by the repeated glaciations during past ice ages. Studying the patterns of adaption of these trees can thus provide valuable insights on how to mitigate future damage. This thesis presents and analyses population structure, demo- graphic history and the distribution of fitness effects (DFE) of the diploid Betula pendula and tetraploid B. pubescens across Scandinavia. Birches–being widespread in boreal forests as well as having great economical importance–constitute superb model species. The analyses of this work confirm the expectations on postglacial population expansion and diploid-tetraploid introgression. They furthermore ascertain the presence of two genetic clusters and a remarkably similar DFE for the species. This work also contributes with a transparent, reproducible and reusable pipeline which facilitates running similar analyses for related species. birch betula pubescens pendula betula pubescens betula pendula silver birch downy birch demography population structure distribution of fitness effects DFE dadi UMAP PCA ADMIXTURE polyDFE ice age glaciation tree boreal forest climate change adaption tetraploid diploid-tetraploid introgression Scandinavia genetic cluster pipeline snakemake bioinformatics reproducible population genetics postglacial population expansion demographic history FEEMS site-frequency spectrum SFS last glacial maximum LGM workflow python population expansion population growth EST-SFS 0-fold degenerate 4-fold degenerate maximum likelihood estimation MLE variant call format VCF single-nucleotide polymorphism SNP Bioinformatics (Computational Biology) Bioinformatik (beräkningsbiologi)
374	Investigations into cyclopropanation and ethylene polymerization via salicylaldiminato copper (II) complexes Boyd, Ramon Cornell 23 January 2007 Two distinct overall research objectives are in this Masters thesis. Very little relates the two chapters apart from the ligands. The first chapter addresses diastereoselective homogeneous copper catalyzed cyclopropanation reactions. Cyclopropanation of styrene and ethyl diazoacetate (EDA) is a standard test reaction for homogeneous catalysts. Sterically bulky salicylaldimine (SAL) ligands should select for the ethyl trans-2-phenylcyclopropanecarboxylate diastereomer. Steric bulk poorly influences trans:cis ratios. Salicylaldiminine ligands do not posses the correct symmetry to affect diastereoselectivity. The SAL ligand belongs to the Cs point group in the solid state. Other ligand motifs are more effective at altering the trans:cis ratios. The second chapter addresses the general route toward successful copper(II) ethylene polymerization catalysts. Catalytic activity of the copper(II) complexes is very low. Polymer chain growth from a copper catalyst is very unlikely. Copper-carbon bonds decompose by homolytic cleavage or C-H activation. Copper-alkyls and aryls readily decompose into brown colored oils and salts with different colors. Ligand transfer to trimethylaluminum (TMA) appears to explain low yield ethylene polymerization. bulky migratory insertion mechanism coordination/insertion methodology d-block metal late transition metal phenolic ring coordination number ketimine precatalysts ketimine nitrogen bis(salicylaldiminato)copper(II) ratio cyclopropane steric bulk salicylaldiminato TMA salt trimethylaluminum aryl oil alkyl copper-aryls copper-alkyls C-H activation homolytic homolytic cleavage copper(II) polymerization ethylene cis trans symmetry diastereomer salicylaldimine SAL EDA ethyl diazoacetate styrene cyclopropanation copper diastereoselective steric protection stable CH(SiMe3)2 intermediate catalytic activity associated TMA free TMA vacant coordination site hydrolysis Lewis acid halogen anionic anionic ligand donor ligand monodentate anionic ligand aluminum(III) monodentate polymer chain polymer chain aluminum-carbon bond bulky SAL ligand open coordination site first row transition metal PE paramagnetic high molecular weight polyethylene alkylate methylaluminoxane MAO anionic ligands arylate aluminum carbon aluminum carbon bond beta-hydrogen elimination beta hydrogen elimination Aufbau reaction Aufbau neutral dialkyl aluminum aluminum-alkyl aluminum alkyl copper(0)
375	Investigations into cyclopropanation and ethylene polymerization via salicylaldiminato copper (II) complexes Boyd, Ramon Cornell 23 January 2007 (has links) Two distinct overall research objectives are in this Masters thesis. Very little relates the two chapters apart from the ligands. The first chapter addresses diastereoselective homogeneous copper catalyzed cyclopropanation reactions. Cyclopropanation of styrene and ethyl diazoacetate (EDA) is a standard test reaction for homogeneous catalysts. Sterically bulky salicylaldimine (SAL) ligands should select for the ethyl trans-2-phenylcyclopropanecarboxylate diastereomer. Steric bulk poorly influences trans:cis ratios. Salicylaldiminine ligands do not posses the correct symmetry to affect diastereoselectivity. The SAL ligand belongs to the Cs point group in the solid state. Other ligand motifs are more effective at altering the trans:cis ratios. The second chapter addresses the general route toward successful copper(II) ethylene polymerization catalysts. Catalytic activity of the copper(II) complexes is very low. Polymer chain growth from a copper catalyst is very unlikely. Copper-carbon bonds decompose by homolytic cleavage or C-H activation. Copper-alkyls and aryls readily decompose into brown colored oils and salts with different colors. Ligand transfer to trimethylaluminum (TMA) appears to explain low yield ethylene polymerization. bulky migratory insertion mechanism coordination/insertion methodology d-block metal late transition metal phenolic ring coordination number ketimine precatalysts ketimine nitrogen bis(salicylaldiminato)copper(II) ratio cyclopropane steric bulk salicylaldiminato TMA salt trimethylaluminum aryl oil alkyl copper-aryls copper-alkyls C-H activation homolytic homolytic cleavage copper(II) polymerization ethylene cis trans symmetry diastereomer salicylaldimine SAL EDA ethyl diazoacetate styrene cyclopropanation copper diastereoselective steric protection stable CH(SiMe3)2 intermediate catalytic activity associated TMA free TMA vacant coordination site hydrolysis Lewis acid halogen anionic anionic ligand donor ligand monodentate anionic ligand aluminum(III) monodentate polymer chain polymer chain aluminum-carbon bond bulky SAL ligand open coordination site first row transition metal PE paramagnetic high molecular weight polyethylene alkylate methylaluminoxane MAO anionic ligands arylate aluminum carbon aluminum carbon bond beta-hydrogen elimination beta hydrogen elimination Aufbau reaction Aufbau neutral dialkyl aluminum aluminum-alkyl aluminum alkyl copper(0)

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