Dissertations / Theses on the topic 'Lagrange space'

Hadrontherapy is one of the available techniques used nowadays to treat cancer. Specifically, it employs beams of protons or heavier ions with initial energies of hundreds of MeV/u. Hadrontherapy has an advantageous energy release in the patient, allowing to irradiate the cancer volume in a more precise way and to spare the healthy tissues surrounding it. The main drawback of this kind of therapy is the nuclear interaction of the primary beam with the nuclei constituting the irradiated tissue. Target and projectile nuclear fragmentation could have a dangerous biological effect on tissues surrounding the tumor. Specifically, target fragments have a very short range and are difficultly detected. For this reason the experimental panorama is very poor, thus reducing the precision in the evaluation of success or induced risk of hadrontherapy treatments. For this purpose, the FOOT (FragmentatiOn Of Target) experiment has been designed. It aims at filling the gap both in projectile and target fragmentation experimental data, measuring the fragment production cross section by using in the latter an inverse kinematic technique. At larger energies, the FOOT measurements will be useful to evaluate the interaction of the space radiation field with materials composing the spaceship hull in a long term space mission (typically on Mars), in order to assess the radiation-induced damage on astronauts’ health and electronics on board. The FOOT apparatus allows to identify nuclear fragments by measuring their charge Z and their number of mass A. The latter is measured in three redundant ways, which need to be combined to obtain a best estimation of A. In the present thesis, the technique of Lagrange Multipliers used for the constrained minimization of functions, will be introduced and implemented in the FOOT analysis code to reconstruct the number of mass of nuclear fragments. Moreover, the results of the method will be compared to the ones already implemented in the experiment.

Le Calcul des Variations et son interprétation géométrique ont toujours joué un rôle crucial en Physique Mathématique, que ce soit par le formalisme lagrangien, ou à travers les équations hamiltoniennes.Le formalisme multisymplectique permet une description géométrique de dimension finie des théories de champ classiques (qui correspondent à des problèmes variationnels avec plusieurs variables spatio-temporelles) vues d’un point de vue hamiltonien. La géométrie multisymplectique joue un rôle similaire à celui de la géométrie symplectique dans la description de la mécanique hamiltonienne classique. De plus, l’approche multisymplectique fournit un outil pour construire une structure symplectique sur l’espace des solutions de la théorie des champs et pour l’étudier.Dans cette thèse, je m’intéresse principalement au formalisme multisymplectique pour construire des théories de champs de premier ordre et j’espère pouvoir donner deux principales contributions originales :– Je montre que, dans certaines situations, la structure symplectique de l’espace des phases covariant peut en effet dépendre du choix de la topologie du découpage de l’espace-temps en l’espace et en le temps;– Je construis une extension du formalisme multisymplectique aux théories de super-champs. En tant que «sous-produit», je présente une autre contribution que j’espère intéressante :– Je définie des formes fractionnaires sur des supervariétés avec leur calcul de Cartan. Ces formes fractionnaires se révèlent utiles pour construire le formalisme multisymplectique pour les théories de super-champs.Les ingrédients principaux du formalisme que j'utilise sont : l’espace des multimoments de dimension finie P et son extension aux théories de super-champs que je définie ; la superforme lagrangienne, le superhamiltonien et la superforme multisymplectique. Dans la thèse je montre aussi un théorème de comparaison qui permets de clarifier les relations existant entre les théories dites en composantes et les théories de superchamps. J’explique comment le formalisme supermultisymplectique peut être utilisé pour définir des super crochets de Poisson pour les superchamps. Je donne une version "super" du premier théorème de Noether valable pour l'action de supergroupes de symétrie et je propose une extension « super » de l'application multimoment. Enfin je présente quelques exemples montrant comment toute la théorie peut être mise en œuvre : en particulier j'étudie la superparticule libre et le modèle sigma 3-dimensionnel<br>The Calculus of Variations and its geometric interpretation always played a key role in Mathematical Physics, either through the Lagrangian formalism, or through the Hamiltonian equations.The multisymplectic formalism allows a finite dimensional geometric description of classical field theories seen from an Hamiltonian point of view. Multisymplectic geometry plays the same role played by symplectic geometry in the description of classical Hamiltonian mechanics. Moreover the multisymplectic approach provides a tool for building a symplectic structure on the space of solutions of the field theory and for investigating it.In this thesis I use the multisymplectic formalism to build first order field theories and I hope to give two main original contributions:– I show that, in some situations, the symplectic structure on the covariant phase space may indeed depend from the choice of splitting of spacetime in space and time;– I extend the multisymplectic formalism to superfield theories.As a "byproduct", I present another contribution:– I define fractional forms on supermanifolds with their relative Cartan Calculus. These fractional forms are useful to build the multisymplectic formalism for superfield theories.The main ingredients of the formalism I use are: the finite dimensional multimomenta phase space P and its extension to super field theories, which I give; the Lagrangian superform; the super-Hamiltonian, the multisymplectic superform.In my thesis I also prove a Comparison Theorem which allows to clarify the relations existing between the so called components theories and the so called superfield theories. I explain how the supermultisymplectic formalism can be used to define super Poisson brackets for super fields. I give a "super" version of the first Noether theorem valid for the action of supergroups of symmetry and I propose a “super” extension of the multimomentum map.Finally I present some examples showing how all the theory can be implemented: I study the free superparticle and the 3-dimensional sigma-model

Nous étudions le problème d'unicité, de l'interpolation faible et de la convergence de la série d'interpolation de Lagrange dans les espaces de Fock pondérés par des poids radiaux. Nous étudions aussi les suites d'échatillonnage, d'interpolation et les bases de Riesz dans les petit espaces de Fock<br>We study the uniqueness sets, the weak interpolation sets, and convergence of the Lagrange interpolation series in radial weighted Fock spaces. We study also sampling, interpolation and Riesz bases in small radial weighted Fock spaces

À travers les exemples de Lagrasse, Alet-les-Bains et Caunes-Minervois, cette thèse propose de déterminer les mécanismes et le rôle des acteurs du développement des bourgs monastiques du VIIIe au milieu du XVIe siècle en pays d’Aude. Les modalités du peuplement des sites sont appréhendées, ainsi que les relations entre la communauté des religieux et celle des habitants. La construction de l’espace urbain de ces villes moyennes du Moyen Âge est un des thèmes principaux, abordé à travers l’inventaire des maisons, l’analyse des plans anciens et les sources écrites médiévales et modernes. L’espace périurbain est envisagé comme un secteur permettant aux deux communautés d’assurer une partie de leur approvisionnement et, en ce sens, comme un espace qu’elles devaient se partager et qui devenait essentiel dans les relations qu’elles entretenaient<br>Through the examples of Lagrasse, Alet-les-Bains and Caunes-Minervois, this thesis intends to determine the mechanisms and the stakeholders’ role in the development of monastic towns in the Aude department from the 8th century to the mid-16th century. The modes of settlement on these sites are examined, as well as the relations between the religious community and the inhabitants. The construction of urban space in these medium-sized medieval towns is one of the main topics addressed through the inventory of houses, the analysis of historic plans and of medieval or modern written sources. The peri-urban space is regarded as an area allowing both communities to secure a part of their supplies and, in this sense, as a space they had to share and that was essential to the relations between them

À travers les exemples de Lagrasse, Alet-les-Bains et Caunes-Minervois, cette thèse propose de déterminer les mécanismes et le rôle des acteurs du développement des bourgs monastiques du VIIIe au milieu du XVIe siècle en pays d’Aude. Les modalités du peuplement des sites sont appréhendées, ainsi que les relations entre la communauté des religieux et celle des habitants. La construction de l’espace urbain de ces villes moyennes du Moyen Âge est un des thèmes principaux, abordé à travers l’inventaire des maisons, l’analyse des plans anciens et les sources écrites médiévales et modernes. L’espace périurbain est envisagé comme un secteur permettant aux deux communautés d’assurer une partie de leur approvisionnement et, en ce sens, comme un espace qu’elles devaient se partager et qui devenait essentiel dans les relations qu’elles entretenaient<br>Through the examples of Lagrasse, Alet-les-Bains and Caunes-Minervois, this thesis intends to determine the mechanisms and the stakeholders’ role in the development of monastic towns in the Aude department from the 8th century to the mid-16th century. The modes of settlement on these sites are examined, as well as the relations between the religious community and the inhabitants. The construction of urban space in these medium-sized medieval towns is one of the main topics addressed through the inventory of houses, the analysis of historic plans and of medieval or modern written sources. The peri-urban space is regarded as an area allowing both communities to secure a part of their supplies and, in this sense, as a space they had to share and that was essential to the relations between them

The research topic of this PhD thesis is a comparative analysis of classical specic&nbsp;geometric frameworks and of their anisotropic extensions; the construction of three different&nbsp;types of Finsler frameworks, which are suitable for the analysis of the cancer cells population&nbsp;dynamical system; the development of the anisotropic Beltrami framework theory with the&nbsp;derivation of the evolution&nbsp;ow equations corresponding to different classes of anisotropic&nbsp;metrics, and tentative applications in image processing.<br>Predmet istraživanja doktorske disertacije je uporedna analiza klasičnih i specifičnih&nbsp;geometrijskih radnih okruženja i njihovih anizotropnih pro&scaron;irenja; konstrukcija &nbsp;tri Finslerova&nbsp;radna okruženja različitog tipa koja su pogodna za analizu dinamičkog &nbsp;sistema populacije&nbsp;kanceroznih ćelija; razvoj teorije anizotropnog Beltramijevog radnog okruženja i formiranje&nbsp;jednačina evolutivnog toka za različite klase anizotropnih metrika, kao i mogućnost primene&nbsp;dobijenih teorijskih rezultata u digitalnoj obradi slika.

Pose au debut des annees 80 par a. Katok et m. Gromov, le probleme riemannien de l'entropie minimale a recu une reponse positive en 1994 grace aux resultats de g. Besson, g. Courtois et s. Gallot. Comme un prolongement de ce travail, l'objet de cette these est l'etude du minimum des entropies volumique et topologique pour les metriques de finsler qui constituent la plus petite extension de la geometrie de riemann. Les trois premiers chapitres conduisent a la construction explicite d'un contre-exemple general a la conjecture finslerienne de l'entropie volumique minimale sur les espaces riemanniens compacts, localement symetriques, de type non-compact et de rang au moins egal a deux. De plus, ce contre-exemple est l'unique minimum de l'entropie volumique parmi les metriques de finsler g-invariantes normalisees par le volume finslerien de la variete. Dans une deuxieme partie, relative au cas du rang un et regroupant les chapitres iv et v, on prouve, avec la meme normalisation que precedemment, le caractere critique des metriques riemanniennes hyperboliques pour l'entropie topologique sur l'ensemble de toutes les metriques de finsler d'une variete compacte de dimension quelconque. Par ailleurs, nous obtenons un resultat identique pour les surfaces compactes en normalisant par le volume de liouville des fibres spheriques, et ce, apres avoir montre que les deux manieres de normaliser ne sont pas equivalentes dans le cadre de la geometrie finslerienne

In this thesis we present a slight generalisation of the Pearl complex or relative quantum homology to some non monotone Lagrangian submanifolds. First we develop the theory for the so called almost monotone Lagrangian submanifolds, We apply it to uniruling problems as well as estimates for the relative Gromov width. In the second part we develop the theory for toric fiber in toric Fano manifolds, recovering previous computaional results of Floer homology .<br>Doctorat en Sciences<br>info:eu-repo/semantics/nonPublished

Dans cette thèse, nous nous proposons d'étudier et de traiter conjointement plusieurs problèmes phares en traitement d'images incluant le recalage d'images qui vise à apparier deux images via une transformation, la segmentation d'images dont le but est de délimiter les contours des objets présents au sein d'une image, et la décomposition d'images intimement liée au débruitage, partitionnant une image en une version plus régulière de celle-ci et sa partie complémentaire oscillante appelée texture, par des approches variationnelles locales et non locales. Les relations étroites existant entre ces différents problèmes motivent l'introduction de modèles conjoints dans lesquels chaque tâche aide les autres, surmontant ainsi certaines difficultés inhérentes au problème isolé. Le premier modèle proposé aborde la problématique de recalage d'images guidé par des résultats intermédiaires de segmentation préservant la topologie, dans un cadre variationnel. Un second modèle de segmentation et de recalage conjoint est introduit, étudié théoriquement et numériquement puis mis à l'épreuve à travers plusieurs simulations numériques. Le dernier modèle présenté tente de répondre à un besoin précis du CEREMA (Centre d'Études et d'Expertise sur les Risques, l'Environnement, la Mobilité et l'Aménagement) à savoir la détection automatique de fissures sur des images d'enrobés bitumineux. De part la complexité des images à traiter, une méthode conjointe de décomposition et de segmentation de structures fines est mise en place, puis justifiée théoriquement et numériquement, et enfin validée sur les images fournies<br>In this thesis, we study and jointly address several important image processing problems including registration that aims at aligning images through a deformation, image segmentation whose goal consists in finding the edges delineating the objects inside an image, and image decomposition closely related to image denoising, and attempting to partition an image into a smoother version of it named cartoon and its complementary oscillatory part called texture, with both local and nonlocal variational approaches. The first proposed model addresses the topology-preserving segmentation-guided registration problem in a variational framework. A second joint segmentation and registration model is introduced, theoretically and numerically studied, then tested on various numerical simulations. The last model presented in this work tries to answer a more specific need expressed by the CEREMA (Centre of analysis and expertise on risks, environment, mobility and planning), namely automatic crack recovery detection on bituminous surface images. Due to the image complexity, a joint fine structure decomposition and segmentation model is proposed to deal with this problem. It is then theoretically and numerically justified and validated on the provided images

Dans cette thèse sont montrés des développements de l'approximation de la phase aléatoire (RPA) dans le contexte de théories à séparation de portée. On présente des travaux sur le formalisme de la RPA en général, et en particulier sur le formalisme "matrice diélectrique" qui est exploré de manière systématique. On montre un résumé d'un travail sur les équations RPA dans le contexte d'orbitales localisées, notamment des développements des orbitales virtuelles localisées que sont les "orbitales oscillantes projetées" (POO). Un programme a été écrit pour calculer des fonctions telles que le trou de d'échange, la fonction de réponse, etc... sur des grilles de l'espace réel (grilles parallélépipédiques ou de type "DFT"). On montre certaines de ces visualisations. Dans l'espace réel, on expose une adaptation de l'approximation du dénominateur effectif (EED), développée originellement dans l'espace réciproque en physique du solide. Également, les gradients analytiques des énergies de corrélation RPA dans le contexte de la séparation de portée sont dérivés. Le formalisme développé ici à l'aide d'un lagrangien permet une dérivation tout-en-un des termes courte- et longue-portée qui émergent dans les expressions du gradient, et qui montrent un parallèle intéressant. Des applications sont montrées, telles que des optimisations de géométries aux niveaux RSH-dRPA-I et RSH-SOSEX d'un ensemble de 16 petites molécules, ou encore le calcul et la visualisation des densités corrélées au niveau RSH-dRPA-I<br>In this thesis are shown developments in the random phase approximation (RPA) in the context of range-separated theories. We present advances in the formalism of the RPA in general, and particularly in the "dielectric matrix" formulation of RPA, which is explored in details. We show a summary of a work on the RPA equations with localized orbitals, especially developments of the virtual localized orbitals that are the "projected oscillatory orbitals" (POO). A program has been written to calculate functions such as the exchange hole, the response function, etc... on real space grid (parallelepipedic or of the "DFT" type) ; some of those visualizations are shown here. In the real space, we offer an adaptation of the effective energy denominator approximation (EED), originally developed in the reciprocal space in solid physics. The analytical gradients of the RPA correlation energies in the context of range separation has been derived. The formalism developed here with a Lagrangian allows an all-in-one derivation of the short- and long-range terms that emerge in the expressions of the gradient. These terms show interesting parallels. Geometry optimizations at the RSH-dRPA-I and RSH-SOSEX levels on a set of 16 molecules are shown, as well as calculations and visualizations of correlated densities at the RSH-dRPA-I level

碩士<br>國立中央大學<br>數學系<br>105<br>The trajectory optimization is a commonly-used technique of applications in aerospace engineering, such as find the optimal trajectory to maximize the weight of the payload or minimize the time for satellite insertion the target orbit, etc. This type of problem can be modeled mathematically as some form of continuous time optimal control problems. This thesis focuses on the study of the full-space quasi Lagrange-Newton-Krylov method as our numerical solver. First, we introduce the Lagrangian multiplier to convert the constrained optimization problem into unconstrained optimization problem, and solve the first-order necessary condition(KKT condition). By the Newton method combined with the backtrack technique, in each Newton iteration, all KKT system variables (state variables, control variables, design variables, Lagrangian multipliers) will be solved at the same time by Krylov-subspace method with the precondition technology. In this thesis, we improve the computational efficiency of Hessian matrix constructor in KKT system, and solve the problem of inequality constraint by introducing slack variable. The three-dimensional case of the three stage rocket problems and two-dimensional case of Taurus rocket as a numerical example, the relevant physical background and numerical results will be presented in the thesis.

碩士<br>國立中央大學<br>數學系<br>107<br>The trajectory optimization problem with a wide range of applications in physics and engineering can be modeled mathematically in some form of continuous time optimal control problems. After discretizing the optimal control problem we solve the resulting parameter constrained optimization problem by using the Lagrange-Newton method. In this method, we introduce the Lagrange multiplier to the objective function and then solve the constrained optimization problem by finding the critical solution of the first-order necessary condition (KKT condition). We consider two classes of Lagrange-Newton method: one is the full space algorithm and the other is the reduced space algorithm. The full space algorithm updates the control, state, and Lagrange multipliers at the same time. On the other hand, the reduced space algorithm updates those variables sequentially. In this study, we show numerically that for the construction of the Hessian matrix, the computing time for the analytical method is less than that for the finite difference method and the BFGS method. Remarkably, the full space Lagrange-Newton algorithm is faster than the reduced space Lagrange-Newton algorithm, especially for refined mesh cases.

碩士<br>國立中央大學<br>數學研究所<br>100<br>Trajectory optimization problem is concerned with the design of an optimal trajectory that maximizes or minimizes some measurement and satisfies prescribed conditions. Because of this characteristic, it is in general formulated as an optimal control problem and hence is related to the optimal control theory, a branch of mathematics as an application of the calculus of variations. Recently, with an improvement of computer powers, computational techniques become more widely used in solving optimal control problems. Two main approaches, namely direct and indirect methods, reformulated an optimal control problem as a boundary value problem and a nonlinear programming problem respectively and then numerical methods can be employed. In this work, we focus on a class of direct methods and purposed a full space Lagrange-Newton-Krylov algorithm for the nonlinear programming problems. This algorithm is based on the full space sequential quadratic programming framework and associated with particular globalization strategy and process to generate the initial guess. With the implementation of this algorithm, we try to solve several minimum time trajectory optimization problems and the numerical results exhibit the practicability and potentiality of this algorithm.

碩士<br>國立中央大學<br>數學系<br>106<br>In the planning stage of space missions, trajectory optimization plays an important role in planning the flight path that maximum or minimum some quanitities before the mission begins. This type of mathematically problem can be expressed as a continuous time optimal control problem. In recent years, more space missions choose to use electric propulsion for orbital operations. However, this propulsion system is classified into the low thrust propulsion system. The problem of low thrust orbit transition is a difficult problem. Compared with the high thrust spacecraft, the low thrust engine takes more time to complete the mission, and this is the reason that it is difficult to accurately calculate the state of the spacecraft at each time point in mathematical. This thesis is to study how to parallelize the full-space Lagrange-Newton method, to make this algorithm can compute faster for solving the problem of low thrust trajectory problem. When computing KKT systems, different from most methods that dividing the dense matrix evenly, we store the data in a sparse matrix and reduce it by respectively dividing the state variables and the Lagrange multipliers into each computational cores. Reducing the number of data transfers for this algorithm allows the numerical solver to significantly reduce computational time. We take a few two-dimensional low-thrust orbit transfer trajectory optimization problems like the examples to test the feasibility of this algorithm in the application of low thrust transfer.

碩士<br>國立中央大學<br>數學系<br>107<br>In space missions, the low-thrust propulsion system is another name for the electrically-powered spacecraft propulsion system. Recently, traditional chemical propulsion system change to the electrically-powered spacecraft propulsion system in the most space missions, so the low-thrust problems become more common. The optimization and design of low-thrust orbit transfer always have been a difficult problem in space exploration missions. For these problems, we propose a nonlinearly preconditioned Full-space Lagrange-Newton Method. The method is kind of the right nonlinear preconditioning techniques deals with nonlinearities by changing unknowns or replacing nonlinear functions, respectively. Owing to it needs inner iterations working on subsets of the original system, which lead to additional cost per step. Therefore, for the purpose of effectively improve efficiency nonlinear preconditioner require not to be invoked on every Newton iteration, especially when the approximate solution close to the typical solution. The numerical result verifies the effectiveness of the method.

This thesis is concerned with a class of general-purpose algorithms for constrained minimization problems, variational inequalities, and quasi-variational inequalities in Banach spaces. A substantial amount of background material from Banach space theory, convex analysis, variational analysis, and optimization theory is presented, including some results which are refinements of those existing in the literature. This basis is used to formulate an augmented Lagrangian algorithm with multiplier safeguarding for the solution of constrained optimization problems in Banach spaces. The method is analyzed in terms of local and global convergence, and many popular problem classes such as nonlinear programming, semidefinite programming, and function space optimization are shown to be included as special cases of the general setting. The algorithmic framework is then extended to variational and quasi-variational inequalities, which include, by extension, Nash and generalized Nash equilibrium problems. For these problem classes, the convergence is analyzed in detail. The thesis then presents a rich collection of application examples for all problem classes, including implementation details and numerical results<br>Die vorliegende Arbeit handelt von einer Klasse allgemein anwendbarer Verfahren zur Lösung restringierter Optimierungsprobleme, Variations- und Quasi-Variationsungleichungen in Banach-Räumen. Zur Vorbereitung wird eine erhebliche Menge an Grundmaterial präsentiert. Dies beinhaltet die Theorie von Banach-Räumen, konvexe und variationelle Analysis sowie Optimierungstheorie. Manche der angegebenen Resultate sind hierbei Verfeinerungen der entsprechenden Ergebnisse aus der Literatur. Im Anschluss wird ein Augmented-Lagrange-Verfahren für restingierte Optimierungsprobleme in Banach-Räumen präsentiert. Der Algorithmus wird hinsichtlich lokaler und globaler Konvergenz untersucht, und viele typische Problemklassen wie nichtlineare Programme, semidefinite Programme oder Optimierungsprobleme in Funktionenräumen werden als Spezialfälle aufgezeigt. Der Algorithmus wird dann auf Variations- und Quasi-Variationsungleichungen verallgemeinert, wodurch implizit auch (verallgemeinerte) Nash-Gleichgewichtsprobleme abgehandelt werden. Für diese Problemklassen werden eigene Konvergenzanalysen betrieben. Die Dissertation beinhaltet zudem eine umfangreiche Sammlung von Anwendungsbeispielen und zugehörigen numerischen Ergebnissen