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1
Stella, Martina. "Quantum embedding for molecular systems : a projection-operator approach." Thesis, University of Bristol, 2015. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.691179.
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Density functional theory (DFT) is widely used to describe the electronic structure of molecular systems and, thanks to the simplicity of its theoretical framework, it is particularly suitable for the development quantum embedding schemes. In this dissertation a novel embedding scheme, based on the employment of a projection operator, is presented. This method allows one to embed one sub-region of a given molecular system in its environment and treat these regions at different level of theory (e.g. CCSD(T)in- DFT). Thanks to the use of a projection technique that enforces the Pauli principle between subsystems, the complications associated with the appearance of non-additive kinetic energy contributions are overcome. First, I show a general software implementation of the method and the features that allow the analysis of a variety of chemical problems (e.g. organic reactions, transition metal complexes). Next, I apply the method to a wide range of benchmarking examples chosen to assess accuracy and performance. Namely, the SN2 reaction of I-propylchloride with CI- , phenol molecule deprotonation reaction, association of' iron(II) to ethylamine, Diels-Alder cycloaddition, and Stone' Vales rotation reaction are investigated. I show that , for such examples, this framework is able to reproduce the accuracy of highly correlated wave-function (WF) methods with reduced computational cost, by performing WF-in-DFT calculations. In addition, by exploring several simulation conditions, e.g. different functionals, localisation schemes, basis sets, I demonstrate the performance of the method displays a fairly independent behaviour with respect to simulation conditions. Finally, once the robustness of the code has been tested, I extend applications to more realistic chemical systems of technological and experimental interest, i.e. adsorption of cobalt on coronene. A further improvement of the method is also described. I assess a new version of the code that enables further reduction of the computational cost and the possibility of enlarging the size of the systems studied by performing an intelligent truncation of the atomic basis set used in the WF-based calculation.
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Strauss, Michael. "Spectral pollution and higher order projection methods for operator pencils." Thesis, King's College London (University of London), 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.497989.
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Doman, David Burke. "Projection Methods for Order Reduction of Optimal Human Operator Models." Diss., Virginia Tech, 1998. http://hdl.handle.net/10919/30637.
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Human operator models developed using optimal control theory
are typically complicated and over-parameterized, even for
simple controlled elements. Methods for generating less
complicated operator models that preserve the most important
characteristics of the full order model are developed so
that the essential features of the operator dynamics are
easier to determine. A new formulation of the Optimal
Control Model (OCM) of the human operator is developed
that allows order reduction techniques to be applied in
a meaningful way. This formulation preserves the critical
neuromotor dynamics and time delay characteristics of the
human operator. The Optimal Projection (OP) synthesis
technique is applied to a modified version of the OCM.
Using OP synthesis allows one to determine operator models
that minimize the quadratic performance index of the OCM
with a constraint on model order. This technique allows
analysts to formulate operator models of fixed order.
Operator model reduction methods based on variations of
balanced realization techniques are also developed since
they reduce the computational complexity associated with
OP synthesis yet maintain a reasonable level of accuracy.
Computer algorithms are developed that insure that the
reduced order models have noise to signal ratios that are
consistent with OCM theory. The OP method generates
operator models of fixed order that are consistent with
OCM theory in all respects, i.e. optimality, neuromotor
lag, time delay, and noise to signal ratios are all
preserved. The other model reduction techniques preserve
these features with the exception of optimality. Each
technique is applied to a variety of controlled elements
to illustrate how performance and frequency response
fidelity degrade when the order of the operator model is
reduced.Ph. D.
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Hickel, Tilmann. "Theory of many body effects in the Kondo lattice model projection operator method /." [S.l.] : [s.n.], 2005. http://deposit.ddb.de/cgi-bin/dokserv?idn=980739764.
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Turcu, George R. "Hypercyclic Extensions Of Bounded Linear Operators." Bowling Green State University / OhioLINK, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1386189984.
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Seidel, Markus. "On some Banach Algebra Tools in Operator Theory." Doctoral thesis, Universitätsbibliothek Chemnitz, 2012. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-83750.
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Die vorliegende Arbeit ist der Untersuchung von Operatorfolgen gewidmet, die typischerweise bei der Anwendung von Approximationsverfahren auf stetige lineare Operatoren entstehen. Dabei stehen die Stabilität der Folgen sowie das asymptotische Verhalten gewisser Charakteristika wie Normen, Konditionszahlen, Fredholmeigenschaften und Pseudospektren im Mittelpunkt.
Das Hauptaugenmerk liegt auf der Entwicklung der Theorie für Operatoren auf Banachräumen. Hierbei bildet ein dafür geeigneter Konvergenzbegriff, die sogenannte P-starke Konvergenz, den Ausgangspunkt, welcher das Studium der gewünschten Eigenschaften in einer erstaunlichen Allgemeinheit gestattet.
Die erzielten Resultate kommen, neben einer Reihe weiterer Anwendungen, insbesondere für das Projektionsverfahren für banddominierte Operatoren zum Einsatz.
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Degenfeld-Schonburg, Peter [Verfasser], Michael J. [Akademischer Betreuer] [Gutachter] Hartmann, Michael [Gutachter] Knap, and Michael [Gutachter] Fleischhauer. "Self-consistent projection operator theory / Peter Degenfeld-Schonburg ; Gutachter: Michael Knap, Michael Fleischhauer, Michael J. Hartmann ; Betreuer: Michael J. Hartmann." München : Universitätsbibliothek der TU München, 2016. http://d-nb.info/112321087X/34.
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Montero, Carlos Alberto Almendras. "Existência e unicidade da solução de um problema de plasma confinado." Universidade Federal de Juiz de Fora, 2014. https://repositorio.ufjf.br/jspui/handle/ufjf/618.
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CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
Neste trabalho, o objetivo é estudar a existência e unicidade da solução num sentido fraco para um problema não linear com valor na fronteira que é derivado de um modelo que decreve o equilibrio de um plasma confinado. Para esta finalidade se formula um problema equivalente e se estabelecem condições para este novo problema. Logo, utilizando a teoria da subdiferencial e fazendo um estudo de autovalor se consegue que este novo problema tenha solução e, além disso, seja única.
In this work, the objective is to study the existence and uniqueness of the solution in a weak sense of a nonlinear boundary value problem which it is derived from a model that describe the equilibrium of a confined plasma. For this purpose, we formulate an equivalent problem and establish conditions for this new problem. Therefore, using the theory of subdiferencial and studing an eigenvalue problem, we obtain that this new problem has a unique solution.
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Axelsson, Andreas, and kax74@yahoo se. "Transmission problems for Dirac's and Maxwell's equations with Lipschitz interfaces." The Australian National University. School of Mathematical Sciences, 2002. http://thesis.anu.edu.au./public/adt-ANU20050106.093019.
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The aim of this thesis is to give a mathematical framework for scattering of electromagnetic waves by rough surfaces. We prove that the Maxwell transmission problem with a weakly Lipschitz interface,in finite energy norms, is well posed in Fredholm sense for real frequencies. Furthermore, we give precise conditions on the material constants ε, μ and σ and the frequency ω when this transmission problem is well posed. To solve the Maxwell transmission problem, we embed Maxwells equations in an elliptic Dirac equation. We develop a new boundary integral method to solve the Dirac transmission problem. This method uses a boundary integral operator, the rotation operator, which factorises the double layer potential operator. We prove spectral estimates for this rotation operator in finite energy norms using Hodge decompositions on weakly Lipschitz domains. To ensure that solutions to the Dirac transmission problem indeed solve Maxwells equations, we introduce an exterior/interior derivative operator acting in the trace space. By showing that this operator commutes with the two basic reflection operators, we are able to prove that the Maxwell transmission problem is well posed. We also prove well-posedness for a class of oblique Dirac transmission problems with a strongly Lipschitz interface, in the L_2 space on the interface. This is shown by employing the Rellich technique, which gives angular spectral estimates on the rotation operator.
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Agniel, Vidal. "Dilatations d'opérateurs et projections L^p." Thesis, Lille, 2021. https://pepite-depot.univ-lille.fr/LIBRE/EDSPI/2021/2021LILUI001.pdf.
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Cette thèse porte sur l'étude de classes d'opérateurs. On étudie principalement deux familles différentes de classes d'opérateurs.- Les premières classes étudiées sont des classes d'opérateurs sur des espaces de Hilbert généralisant les classes $C_{ho}$ de Sz.Nagy et Foias.Pour $(ho_n)_n$ une suite de nombres complexes non-nuls, on définit la classe $C_{(ho_n)}(H)$ comme l'ensemble des opérateurs $T in mathcal{L}(H)$ qui possèdent une $(ho_n)$-dilatation : il existe un espace de Hilbert K et un opérateur unitaire $U in mathcal{L}(K)$ avec $H subset K$ tels que $T^n=ho_n P_H U^n|_H$ pour tout n $geq$ 1 ($P_H in mathcal{L}(K)$ étant la projection orthogonale de K sur H). Ces classes peuvent être associées à une fonction holomorphe $f_{(ho_n)}$ ainsi qu'à une quasi-norme $w_{(ho_n)}$. Nous utilisons les liens entre ces trois objets pour caractériser, décrire, et donner plusieurs propriétés spectrales sur les opérateurs contenues dans ces classes. Nous exhibons de même des relations entre plusieurs classes de cette forme, nous généralisons des résultats connus pour les classes $C_{(ho)}$, et donnons divers exemples et situations offrant des comportements différents du cas $C_{(ho)}$. Nous apportons aussi une nouvelle vision géométrique sur un résultat entre des quasi-normes $w_{ho}$, et nous étendons des calculs de $w_{ho}(T)$ pour des opérateurs T annulés par un polynôme de degré deux.- La deuxième partie principale de cette thèse concerne les classes de L^p-projections. Une L^p-projection sur un espace de Banach X, pour $1leq p leq +infty$, est une projection P qui vérifie $ |f|_X = |(|P(f)|_X, |(I-P)(f)|_X) |_{ell_{p}}$ pour tout f dans X. Cette relation est une version L^p de l'égalité $|f|^2=|Q(f)|^2 + |(I-Q)(f)|^2$, vérifiée pour les projections orthogonales dans les espaces de Hilbert.Nous nous intéressons aux relations entre les L^p-projections sur un espace de Banach X et celles sur un sous-espace F, sur un quotient X/F, ou sur un sous-espace de quotient G/F. Des caractérisations complètes sont apportées pour des espaces de Banach vérifiant quelques propriétés additionnelles, et selon la valeur de p.Nous introduisons aussi la notion de L^p-projection maximale pour X, c'est-à-dire des L^p-projections définies sur un sous-espace G de X qui ne peuvent pas être étendues comme L^p-projections sur un sous-espace plus grand, et étudions leurs propriétés, en particulier dans le cas de la dimension finie.Nous obtenons de même une caractérisation des L^{infty}-projections sur tous les espaces L^{infty}(Omega) via de nouvelles méthodes, en généralisant ainsi les résultats connus à ce sujetThis thesis focuses on the study of classes of operators. Two different families of classes of operators are mainly studied.- The first classes we study are classes of operators on Hilbert spaces that generalize the classes $C_{ho}$ of Nagy and Foias. For $(ho_n)_n$ a sequence of non-zero complex numbers, we define the class $C_{(ho_n)}(H)$ as the set of operators $T in mathcal{L}(H)$ that are said to possess a $(ho_n)$-dilation: there exists a Hilbert space K and a unitary operator $U in mathcal{L}(K)$ with $H subset K$ and $T^n=ho_n P_H U^n|_H$ for every $n geq 1$ ($P_H in mathcal{L}(K)$ being the orthogonal projection from K onto its closed subspace H). These classes can be associated with an holomorphic map $f_{(ho_n)}$ as well as a quasi-norm $w_{(ho_n)}$. These three objects are tied together and we use them to characterize, describe, and give several spectral properties of operators belonging to this class.We give multiple relationships between multiple classes of this form, generalize many results that were known for classes $C_{(ho)}$, and give several examples and cases that exhibit new behaviours. We also bring a new geometric meaning behind a relationship between quasi-norms $w_{ho}$ and extend the computations of $w_{ho}(T)$ for operators T that are zeroes of a degree two polynomial.- The second main part of our study concerns classes of L^p-projections.An L^p-projection on a Banach space X, for $1leq p leq +infty$, is an idempotent operator P satisfying $ |f|_X = |(|P(f)|_X, |(I-P)(f)|_X) |_{ell_{p}}$ for all f in X. This is anL^p version of the equality $|f|^2=|Q(f)|^2 + |(I-Q)(f)|^2$, valid for orthogonal projections on Hilbert spaces.We are interested into relationships between L^p-projections on a Banach space X and L^p-projections on a subspace F, on a quotient X/F, or on a subspace of a quotient G/F. These questions are given an answer on Banach spaces with additional properties, depending on the value of p.We also introduce a notion of maximal L^p-projections for X, that is L^p-projections defined on a subspace G of X that cannot be extended to L^p-projections on larger subspaces, and study their properties, especially on finite dimensional Banach spaces. A characterization of L^{infty}-projections on every space L^{infty}(Omega) is obtained as well using new methods, generalizing previously known results
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Hickel, Tilmann. "Theory of many-body effects in the Kondo-lattice model." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät I, 2006. http://dx.doi.org/10.18452/15500.
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Das magnetische Verhalten zahlreicher Materialien lässt sich auf eine indirekte Wechselwirkung lokalisierter magnetischer Momente, vermittelt durch die Elektronen eines Leitungsbandes, zurückführen. Das Kondo-Gitter-Modell hat sich als elegante Möglichkeit bewährt, diesen Prozess quantenmechanisch zu beschreiben. Es reduziert die Physik auf eine intraatomare Wechselwirkung der Spins von lokalisierten und itineranten Elektronen. Die vorliegende Arbeit ist den analytischen Eigenschaften dieses Modells gewidmet. Die besondere Herausforderung des Kondo-Gitter-Modells besteht dabei im Zusammenwirken zweier verschiedener Teilchensorten, beschrieben durch Fermi-Operatoren sowie quantenmechanische Spins. Bisherige Untersuchungen haben sich in der Regel nur auf eine der beiden Teilchensorten konzentriert. Mit der Projektions-Operator-Methode stellen wir eine Möglichkeit vor, beide Teilsysteme in gleicher Qualität zu behandeln. Die Auswertung des Teilsystems der itineranten Elektronen führt auf einen Ausdruck für die Selbstenergie, der lineare und quadratische Effekte in der Wechselwirkung exakt beschreibt. Die resultierenden Zustandsdichten weisen starke Korrelationseffekte auf. Deren Untersuchung dient sowohl der Bestätigung von Ergebnissen weniger systematischer Zugänge als auch dem Aufzeigen neuer Vielteilchen-Phänomene. Die Anwendung der Projektions-Operator-Methode auf das System der lokalisierten Momente führt zu einer Analyse der bereits bekannten RPA (random phase approximation). Zu diesem Zweck werden die Magnonenspektren und die Curie-Temperaturen systematisch untersucht. Dabei treten bisher unbekannte Schwachpunkte der RPA zu Tage, die auch die Kombination mit Theorien für das itinerante Teilsystem verhindern. Verbesserungen und Alternativen zur RPA werden diskutiert.The magnetic behaviour of various materials is due to an indirect interaction of localized magnetic moments, which is based on itinerant electrons in a conduction band. The Kondo-lattice model is an elegant approach for a quantum-mechanical description of this process. It reduces the relevant physics to an intra-atomic exchange interaction of the localized and the itinerant electrons. The aim of the present work is a detailed investigation of analytic properties of this model. Here, the interplay of two distinct types of particles, described by Fermi operators and quantum-mechanical spin operators respectively, is a major challenge of the considered model. Previous studies have focused on one of these subsystems only. Using the projection-operator method, we suggest an efficient way to describe both subsystems on the same level of approximation. An evaluation of the subsystem of itinerant electrons yields an expression for the self-energy, which describes linear and quadratic interaction effects exactly. The densities of states derived with this theory show strong correlation effects. We were able to assess results obtained with less systematic approaches and to predict new many-particle effects. The application of the projection-operator method to the subsystem of localized magnetic moments results in a detailed analysis of the RPA (random phase approximation). The dependence of magnon spectra and Curie temperatures on model parameters are investigated systematically. Previously unknown drawbacks of the RPA are revealed, which prevent the combination of these results with theories for the itinerant subsystem. Improvements beyond RPA and alternative approximations are discussed.
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Mueller, Franz Xaver. "Twistor diagrams as projection operators." Thesis, University of Oxford, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.358638.
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Rigonatto, Marcelo. "Introdução ao estudo dos vetores e aplicações no ensino médio." Universidade Federal de Goiás, 2018. http://repositorio.bc.ufg.br/tede/handle/tede/8249.
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
This work presents a proposal to introduce the study of vectors in High School, in order to oer a broader and clearer possibility for some mathematical demonstrations, applications and their use in other elds, such as Physics, for example. Make some demonstrations of trigonometry, of analytical and at geometries more playful and understandable, is the objective of this approach, besides, of course, oer conditions to work with vectors already in High School, oering pre requisites for future studies in the areas of Exact Sciences.
Esse trabalho apresenta uma proposta de introdução ao estudo dos vetores no Ensino Médio, com o intuito de oferecer uma possibilidade mais ampla e clara para algumas demonstrações matemáticas, aplicações e seu uso em outros campos, como na Física, por exemplo. Tornar algumas demonstrações da trigonometria, das geometrias analítica e plana mais lúdicas e compreensíveis é o objetivo dessa abordagem além, é claro, de oferecer condições de trabalhar com vetores já no Ensino Médio, proporcionando pré requisitos para futuros estudos nas áreas das Ciências Exatas.
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SILVA, VICTOR LOPES DA. "A PROJECTOR OPERATOR FORMALISM TO SOLVE THE ANDERSON HAMILTONIAN." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2013. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=23245@1.
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PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIROCOORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR
PROGRAMA DE SUPORTE À PÓS-GRADUAÇÃO DE INSTS. DE ENSINO
Nesta dissertação propomos um formalismo de operadores de projeção para obter a energia do estado fundamental do Hamiltoniano da Impureza de Anderson com repulsão Coulombiana U infinita. Este formalismo consiste em projetar o espaço de Hilbert em um subespaço de uma unica função correspondente ao estado fundamental do mar de Fermi, onde uma versão renormalizada do Hamiltoniano opera. A energia do estado fundamental pode ser obtida através de um processo autoconsistente. conhecendo a energia e possível calcular as propriedades fundamentais do sistema como a magnetização em função do campo magnético externo, a susceptibilidade magnética, a dependência da ocupação eletrônica como função da energia local da impureza e a temperatura Kondo, a qual caracteriza o comportamento universal do problema Kondo.
In this dissertation we propose a projector operator formalism to obtain the ground state energy of the Impurity Anderson Hamiltonian with innite Coulomb repulsion U. This formalism consists in projecting the Hilbert space into a sub-space of one function corresponding to the ground state of the free Fermi sea where a renormalized version of the Hamiltonian operates. The ground state energy can be obtained through a self-consistent process. From the knowledge of the energy, it is possible to calculate the fundamental properties of the system as it is the magnetization as a function of an external magnetic field, the magnetic susceptibility, the dependence of the electronic occupation as a function of the local energy of the impurity and the Kondo temperature, which characterizes the universal behavior of a Kondo problem.
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Schulze, Bert-Wolfgang. "Toeplitz operators, and ellipticity of boundary value problems with global projection conditions." Universität Potsdam, 2003. http://opus.kobv.de/ubp/volltexte/2008/2651/.
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Ellipticity of (pseudo-) differential operators A on a compact manifold X with boundary (or with edges) Y is connected with boundary (or edge) conditions of trace and potential type, formulated in terms of global projections on Y together with an additional symbolic structure. This gives rise to operator block matrices A with A in the upper left corner. We study an algebra of such operators, where ellipticity is equivalent to the Fredhom property in suitable scales of spaces: Sobolev spaces on X plus closed subspaces of Sobolev spaces on Y which are the range of corresponding pseudo-differential projections. Moreover, we express parametrices of elliptic elements within our algebra and discuss spectral boundary value problems for differential operators.
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Stewart, John. "Physical and analytical aspects of projection operators in non equilibrium statistical mechanics." Thesis, University of Strathclyde, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.248591.
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Moubandjo, Desiree V. "Polynomial containment in refinement spaces and wavelets based on local projection operators." Thesis, Stellenbosch : Stellenbosch University, 2007. http://hdl.handle.net/10019.1/16418.
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Schulze, Bert-Wolfgang, Boris Sternin, and Victor Shatalov. "On general boundary value problems for elliptic equations." Universität Potsdam, 1997. http://opus.kobv.de/ubp/volltexte/2008/2513/.
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We construct a theory of general boundary value problems for differential operators whose symbols do not necessarily satisfy the Atiyah-Bott condition [3] of vanishing of the corresponding obstruction. A condition for these problems to be Fredholm is introduced and the corresponding finiteness theorems
are proved.
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Weilandt, Martin. "Isospectral metrics on weighted projective spaces." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2010. http://dx.doi.org/10.18452/16169.
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Der Laplace-Operator auf kompakten Riemannschen Mannigfaltigkeiten besitzt eine natürliche Verallgemeinerung auf kompakte Riemannsche Orbifolds und das Spektrum des so gewonnenen Operators besteht ausschließlich aus Eigenwerten endlicher Vielfachheit. Die Feststellung, dass das Spektrum Informationen über die Geometrie einer Mannigfaltigkeit (oder, allgemeiner, einer Orbifold) enthält, begründete ein ganzes Teilgebiet der Mathematik. Es ist eine offene Frage der sogenannten Spektralgeometrie, ob eine Mannigfaltigkeit und eine singuläre Orbifold isospektral sein (d.h., dasselbe Spektrum mitsamt den Vielfachheiten der Eigenwerte besitzen) können. Angesichts diverser Obstruktionen zur Existenz eines solchen Beispiels für die bekannten Beispiele isospektraler guter Orbifolds, soll diese Arbeit die Spektralgeometrie schlechter Orbifolds erhellen. Zu diesem Zweck geben wir die ersten Beispiele für isospektrale Metriken auf schlechten Orbifolds an. Diese basieren auf bestimmten gewichteten projektiven Räumen, auf denen wir mittels einer Verallgemeinerung von Schüths Version der Torus-Methode nicht-trivial isospektrale Metriken konstruieren.The Laplace Operator on compact Riemannian manifolds naturally generalizes to compact Riemannian orbifolds and the spectrum of the resulting operator consists only of eigenvalues with finite multiplicities. The observation that the spectrum contains information about the geometry of a manifold (and, more generally, an orbifold) gave rise to a whole field of mathematics. It is an open question of so-called spectral geometry, whether a manifold and a singular orbifold can be isospectral (i.e., have the same spectrum with the same multiplicities of the eigenvalues). Given the various obstructions to the existence of such an example for the known examples of isospectral good orbifolds, this work is an attempt to shed light on the spectral geometry of bad orbifolds by giving the first examples of isospectral Riemannian metrics on bad orbifolds. In our case these are particular fixed weighted projective spaces equipped with non-trivially isospectral metrics obtained by a generalization of Schüth''s version of the torus method.
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Millán, Reinier Díaz. "Vários algoritmos para os problemas de desigualdade variacional e inclusão." Universidade Federal de Goiás, 2015. http://repositorio.bc.ufg.br/tede/handle/tede/4562.
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
Nesta tese apresentamos v arios algoritmos para resolver os problemas de Desigualdade Variacional e Inclus~ao. Para o problema de desigualdade variacional propomos, no Cap tulo 2 uma generaliza c~ao do algoritmo cl assico extragradiente, utilizando vetores normais n~ao nulos do conjunto vi avel. Em particular, dois algoritmos conceituais s~ao propostos e cada um deles cont^em tr^es variantes diferentes de proje c~ao que est~ao relacionadas com algoritmos extragradientes modi cados. Duas buscas diferentes s~ao propostas, uma sobre a borda do conjunto vi avel e a outra ao longo das dire c~oes vi aveis. Cada algoritmo conceitual tem uma estrat egia diferente de busca e tr^es formas de proje c~ao especiais, gerando tr^es sequ^encias com diferente e interessantes propriedades. E feito a an alise da converg^encia de ambos os algoritmos conceituais, pressupondo a exist^encia de solu c~oes, continuidade do operador e uma condi c~ao mais fraca do que pseudomonotonia. No Cap tulo 4, n os introduzimos um algoritmo direto de divis~ao para o problema variacional em espa cos de Hilbert. J a no Cap tulo 5, propomos um algoritmo de proje c~ao relaxada em Espa cos de Hilbert para a soma de m operadores mon otonos maximais ponto-conjunto, onde o conjunto vi avel do problema de desigualdade variacional e dado por uma fun c~ao n~ao suave e convexa. Neste caso, as proje c~oes ortogonais ao conjunto vi avel s~ao substitu das por proje c~oes em hiperplanos que separam a solu c~ao da itera c~ao atual. Cada itera c~ao do m etodo proposto consiste em proje c~oes simples de tipo subgradientes, que n~ao exige a solu c~ao de subproblemas n~ao triviais, utilizando apenas os operadores individuais, explorando assim a estrutura do problema. Para o problema de Inclus~ao, propomos variantes do m etodo de divis~ao de forward-backward para achar um zero da soma de dois operadores, a qual e a modi ca c~ao cl assica do forwardbackward proposta por Tseng. Um algoritmo conceitual e proposto para melhorar o apresentado por Tseng em alguns pontos. Nossa abordagem cont em, primeramente, uma busca linear tipo Armijo expl cita no esp rito dos m etodos tipo extragradientes para desigualdades variacionais. Durante o processo iterativo, a busca linear realiza apenas um c alculo do operador forward-backward em cada tentativa de achar o tamanho do passo. Isto proporciona uma consider avel vantagem computacional pois o operador forward-backward e computacionalmente caro. A segunda parte do esquema consiste em diferentes tipos de proje c~oes, gerando sequ^encias com caracter sticas diferentes.
In this thesis we present various algorithms to solve the Variational Inequality and Inclusion Problems. For the variational inequality problem we propose, in Chapter 2, a generalization of the classical extragradient algorithm by utilizing non-null normal vectors of the feasible set. In particular, two conceptual algorithms are proposed and each of them has three di erent projection variants which are related to modi ed extragradient algorithms. Two di erent linesearches, one on the boundary of the feasible set and the other one along the feasible direction, are proposed. Each conceptual algorithm has a di erent linesearch strategy and three special projection steps, generating sequences with di erent and interesting features. Convergence analysis of both conceptual algorithms are established, assuming existence of solutions, continuity and a weaker condition than pseudomonotonicity on the operator. In Chapter 4 we introduce a direct splitting method for solving the variational inequality problem for the sum of two maximal monotone operators in Hilbert space. In Chapter 5, for the same problem, a relaxed-projection splitting algorithm in Hilbert spaces for the sum of m nonsmooth maximal monotone operators is proposed, where the feasible set of the variational inequality problem is de ned by a nonlinear and nonsmooth continuous convex function inequality. In this case, the orthogonal projections onto the feasible set are replaced by projections onto separating hyperplanes. Furthermore, each iteration of the proposed method consists of simple subgradient-like steps, which does not demand the solution of a nontrivial subproblem, using only individual operators, which explores the structure of the problem. For the Inclusion Problem, in Chapter 3, we propose variants of forward-backward splitting method for nding a zero of the sum of two operators, which is a modi cation of the classical forward-backward method proposed by Tseng. The conceptual algorithm proposed here improves Tseng's method in many instances. Our approach contains rstly an explicit Armijo-type line search in the spirit of the extragradient-like methods for variational inequalities. During the iterative process, the line search performs only one calculation of the forward-backward operator in each tentative for nding the step size. This achieves a considerable computational saving when the forward-backward operator is computationally expensive. The second part of the scheme consists of special projection steps bringing several variants.
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Goerl, Lee W. "Sheaves of differential operators and D-modules over non-commutative projective spaces." Diss., Kansas State University, 2016. http://hdl.handle.net/2097/34515.
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Doctor of PhilosophyDepartment of Mathematics
Zongzhu Lin
For a scheme, let D be the sheaf of differential operators, assigning to any open subscheme it’s ring of differential operators. The study of D-modules advances their theory independently, but pervades many other areas of modern mathematics as well. Most notably, the theory provided a framework to solve Hilbert’s 21-st problem, and to develop the Riemann-Hilbert correspondence, and eventually led to the resolution of the Kazhdan-Lustig conjecture in representation theory. For an affine patch of the scheme having dimension n, the sheaf will assign the n-th Weyl algebra. In [1], Hayashi develops the quantized Weyl algebra, a deformation of this algebra, and in [2] Lunts and Rosenberg develop versions of β and quantum differential operators for a graded non-commutative algebra. Iyer and McCune compute in [3] the ring of these quantum differential operators of Lunts and Rosenberg over the polynomial algebra in n-variables, or, over affine n-space. In [4], Bischof examines how a reconciliation of the β deformation in [2] and a 2-cocycle deformation of the graded algebra influence the category of these quantum D-modules, and considers some localizations. One naturally wonders about the category of modules for these quantum differential operators on a non-commutative space; about it’s objects and it’s structure. With the aim of future study in non-commutative grassmannians and flag varieties, of U[subscript]q(sl[subscript]n), for example, we consider a non-commutative projective space glued together from a covering of 2-cocycle deformed polynomial rings, as proposed in [5] and [4]. We determine when there exists a deformed polynomial ring from which we can obtain this covering, and the category of quasi-coherent sheaves can be realized via the categorical Proj construction. With a guiding hand from Rosenberg’s [5] we develop a general ring structure for containing these quantum differential operators on polynomial algebras. Finally, towards the goal of defining holonomic quantum D-modules, we consider the GK-dimension of the corresponding associated graded algebra for the purpose of determining the dimension of what might be considered the singular support for a quantum D-module.
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Srithharan, T. "Theory and applications of Hilbert's and Thompson's metrics to positive operators in ordered spaces." Thesis, University of Sussex, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.262302.
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Rolon, Soto Juan Enrique. "Coherent Exciton Phenomena in Quantum Dot Molecules." Ohio University / OhioLINK, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1314742055.
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Eveson, S. P. "Theory and application of Hilbert's projective metric to linear and nonlinear problems in positive operator thoery." Thesis, University of Sussex, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.316513.
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Meo, Michel. "Transformations intégrales pour les courants positifs fermés et théorie de l'intersection." Grenoble 1, 1996. http://www.theses.fr/1996GRE10015.
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On etudie tout d'abord la transformation integrale qui permet d'etendre aux courants positifs fermes la definition des coordonnees de chow des cycles effectifs de l'espace projectif. A un courant de bidegre (q,q) est associe un courant de bidegre (1,1), obtenu par integration sur les sous-espaces projectifs de dimension q-1 et dont les potentiels jouent le role des formes de chow. On verifie que cette transformation est elle aussi injective. La demonstration repose, apres utilisation d'un tranchage, sur une formule classique d'inversion de la transformation de radon des fonctions. Dans la seconde partie on etablit, pour un courant positif ferme defini sur une varite projective, des inegalites auto-intersection qui permettent de borner le degre des strates ou la multiplicite est constante. La demonstration consiste d'abord a se ramener par plongement au cas de l'espace projectif. On applique alors la theorie des operateurs de monge-ampere pour effectuer l'intersection du courant avec les regularises d'un courant auxiliaire de bidegre (1,1) qui a le meme degre et les memes nombres de lelong. Pour definir ce dernier, plusieurs constructions differentes sont etudiees. Dans la derniere partie, on etudie l'existence de l'image inverse d'un courant positif ferme quelconque par une application analytique surjective. Sauf dans le cas de la codimension 1, cette image inverse n'existe pas en general: le cas d'un eclatement donne un contre-exemple. Dans le cas d'une application ouverte, on peut en revanche definir l'image inverse. On se ramene grace a un tranchage au cas d'un morphisme fini et on utilise alors un potentiel local associe au courant. On donne ensuite des inegalites entre les nombres de lelong du courant et ceux de son image inverse
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Hendrich, Christopher. "Proximal Splitting Methods in Nonsmooth Convex Optimization." Doctoral thesis, Universitätsbibliothek Chemnitz, 2014. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-149548.
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This thesis is concerned with the development of novel numerical methods for solving nondifferentiable convex optimization problems in real Hilbert spaces and with the investigation of their asymptotic behavior. To this end, we are also making use of monotone operator theory as some of the provided algorithms are originally designed to solve monotone inclusion problems.
After introducing basic notations and preliminary results in convex analysis, we derive two numerical methods based on different smoothing strategies for solving nondifferentiable convex optimization problems. The first approach, known as the double smoothing technique, solves the optimization problem with some given a priori accuracy by applying two regularizations to its conjugate dual problem. A special fast gradient method then solves the regularized dual problem such that an approximate primal solution can be reconstructed from it. The second approach affects the primal optimization problem directly by applying a single regularization to it and is capable of using variable smoothing parameters which lead to a more accurate approximation of the original problem as the iteration counter increases. We then derive and investigate different primal-dual methods in real Hilbert spaces. In general, one considerable advantage of primal-dual algorithms is that they are providing a complete splitting philosophy in that the resolvents, which arise in the iterative process, are only taken separately from each maximally monotone operator occurring in the problem description. We firstly analyze the forward-backward-forward algorithm of Combettes and Pesquet in terms of its convergence rate for the objective of a nondifferentiable convex optimization problem. Additionally, we propose accelerations of this method under the additional assumption that certain monotone operators occurring in the problem formulation are strongly monotone. Subsequently, we derive two Douglas–Rachford type primal-dual methods for solving monotone inclusion problems involving finite sums of linearly composed parallel sum type monotone operators. To prove their asymptotic convergence, we use a common product Hilbert space strategy by reformulating the corresponding inclusion problem reasonably such that the Douglas–Rachford algorithm can be applied to it. Finally, we propose two primal-dual algorithms relying on forward-backward and forward-backward-forward approaches for solving monotone inclusion problems involving parallel sums of linearly composed monotone operators.
The last part of this thesis deals with different numerical experiments where we intend to compare our methods against algorithms from the literature. The problems which arise in this part are manifold and they reflect the importance of this field of research as convex optimization problems appear in lots of applications of interest.
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Dragan, Catalin. "Norms Associated to Weights in von Neumann Algebras and Decompositions of Positive Operators." University of Cincinnati / OhioLINK, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1470741341.
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Bittencourt, Raphael Schimidt. "Unitariedade de modelos de spin-3 /." Guaratinguetá, 2019. http://hdl.handle.net/11449/190789.
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Orientador: Elias Leite MendonçaResumo: Neste trabalho propomos uma base de operadores de projeção e transição de spin para tensores de rank-3. Utilizaremos essa base para determinar os coeficientes da densidade de lagrangiana do modelo de Singh-Hagen (SH). Forneceremos uma expressão geral para obtenção do propagador para teorias de rank-3 via tensor totalmente simétrico sem quebra de paridade. Além disso, realizaremos o processo de Imersão de Calibre de Noether (ICN) no modelo SH em D dimensões e verificaremos seu conteúdo físico. Por fim iremos verificar o conteúdo físico de um novo modelo de dubleto de spin-3 de sexta ordem obtido pelo processo de solda dos modelos auto-duais de quinta e sexta ordem que não necessitam de campos auxiliares.
Abstract: In this work we suggest a basis of spin projection and transition operators for rank-3 tensors. We use it in order to determine the coefficients of the Singh-Hagen model. We also provide a general expression for obtaining the propagator for rank-3 theories via full symmetric tensor without parity breaking. In addition, we perform the Noether Gauge Embendment (NGE) procedure on the SH model in D dimensions and verify its particle content. Finally we analyze the unitarity of a new sixth-order spin-3 doublet model obtained through the soldering approach of the fifth and sixth order self-dual models which do not require auxiliary fields.
Mestre
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Lima, Camila de. "Cálculo rápido do operador de retroprojeção com aplicações em reconstrução tomográfica de imagens." Universidade de São Paulo, 2017. http://www.teses.usp.br/teses/disponiveis/55/55134/tde-10112017-101543/.
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Os métodos incrementais pertencem a uma classe de métodos iterativos que divide o conjunto de dados em subconjuntos ordenados, e que atualiza a imagem ao processar cada subconjunto (sub-iterações). Isso acelera a convergência das reconstruções, e imagens de qualidade são obtidas em menos iterações. No entanto, a cada sub-iteração é necessário calcular os operadores de projeção e retroprojeção, resultando no custo computacional de ordem O(n3) para a reconstrução de imagens de dimensão × . Por outro lado, algumas alternativas baseadas na interpolação em uma grade regular no espaço de Fourier ou em transformadas rápidas não-uniformes, dentre outras ideias, foram desenvolvidas a fim de aliviar esse custo computacional. Além disso, diversas abordagens foram bem sucedidas em acelerar o cálculo das iterações de algoritmos clássicos, mas nenhuma havia sido utilizada em conjunto com os métodos incrementais. Neste trabalho é proposta uma nova abordagem em que a técnica de transformada rápida de Fourier não uniforme (NFFT) é utilizada nas sub-iterações de métodos incrementais com o objetivo de efetuar de forma eficiente os cálculos numericamente mais intensos: a projeção e a retroprojeção, resultando em métodos incrementais com complexidade O(n2 log n ). Os métodos propostos são aplicados à tomografia por radiação síncrotron e os resultados da pesquisa mostram um bom desempenho.Incremental methods belong to a class of iterative methods that divide the data set into ordered subsets, and which update the image when processing each subset (sub-iterations). It accelerates the reconstruction convergence and quality images are obtained in fewer iterations. However, it is necessary to compute the projection and backprojection operators in each sub-iteration, resulting in the computational cost of O(n3) flops for × images. On the other hand, some alternatives based on interpolation over a regular grid on the Fourier space or on nonequispaced fast transforms, among other ideas, were developed in order to alleviate the computational cost. In addition, several approaches substantially speed up the computation of the iterations of classical algorithms, but the incremental methods had not been benefited from these techniques. In this work, a new approach is proposed in which the nonequispaced fast Fourier transform (NFTT) is used in each subiteration of incremental methods in order to perform the numerically intensive calculations efficiently: the projection and backprojection, resulting in incremental methods with complexity O(n2 log n ). The proposed methods are applied to the synchrotron radiation tomography and the results show a good performance.
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Procházka, Jiří. "Databázový systém pro výrobu desek plošných spojů." Master's thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2009. http://www.nusl.cz/ntk/nusl-218033.
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Analysis of problems during designing web database and their structure for requirement of manufacturer of PCBs. Study of using applications intended for creation, administration and protection of database system. Systems for operation of web server. Principles of projection tabels in databases. Design of database's structure for production system of PCBs.
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Barber, IV John Letherman. "Application of optimal prediction to molecular dynamics." Berkeley, Calif. : Oak Ridge, Tenn. : Lawrence Berkeley National Laboratory ; distributed by the Office of Scientific and Technical Information, U.S. Dept. of Energy, 2004. http://www.osti.gov/servlets/purl/838987-xpCsPP/native/.
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Thesis (Ph.D.); Submitted to the University of California at Berkeley, Berkeley, CA 94720 (US); 1 Dec 2004.Published through the Information Bridge: DOE Scientific and Technical Information. "LBNL--56842" Barber IV, John Letherman. USDOE Director. Office of Science. Advanced Scientific Computing Research (US) 12/01/2004. Report is also available in paper and microfiche from NTIS.
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Le, Van An. "Petits espaces de Fock, petits espaces de Bergman et leurs opérateurs." Thesis, Aix-Marseille, 2019. http://theses.univ-amu.fr.lama.univ-amu.fr/191210_LE_604try554eejyoj865ovdfq987fxy_TH.pdf.
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Nous étudions les mesures de Carleson et les opérateurs de Toeplitz sur la classe des espaces de Bergman dite de petite taille, introduits récemment par Seip. On obtient une caractérisation des mesures de Carleson qui étend les résultats de Seip à partir du disque unité de mathbb C à la boule unité mathbb Bn de mathbb Cn. Nous utilisons cette caractérisation pour donner les conditions nécessaires et suffisantes à la continuité et à la compacité des opérateurs de Toeplitz. Enfin, nous étudions l’appartenance des opérateurs Toeplitz aux classes de Schatten d'ordre p pour 1We study the Carleson measures and the Toeplitz operators on the class of the so-called small weighted Bergman spaces, introduced recently by Seip. A characterization of Carleson measures is obtained which extends Seip's results from the unit disk of mathbb C to the unit ball mathbb Bn of mathbb Cn. We use this characterization to give necessary and sufficient conditions for the boundedness and compactness of Toeplitz operators. Finally, we study the Schatten p classes membership of Toeplitz operators for 1
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Engh, Cameron Howard. "A See-ability Metric to Improve Mini Unmanned Aerial Vehicle Operator Awareness Using Video Georegistered to Terrain Models." Diss., CLICK HERE for online access, 2008. http://contentdm.lib.byu.edu/ETD/image/etd2664.pdf.
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Wilfer, Oleg. "Duality investigations for multi-composed optimization problems with applications in location theory." Doctoral thesis, Universitätsbibliothek Chemnitz, 2017. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-222660.
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The goal of this thesis is two-fold. On the one hand, it pursues to provide a contribution to the conjugate duality by proposing a new duality concept, which can be understood as an umbrella for different meaningful perturbation methods. On the other hand, this thesis aims to investigate minimax location problems by means of the duality concept introduced in the first part of this work, followed by a numerical approach using epigraphical splitting methods.
After summarizing some elements of the convex analysis as well as introducing important results needed later, we consider an optimization problem with geometric and cone constraints, whose objective function is a composition of n+1 functions. For this problem we propose a conjugate dual problem, where the functions involved in the objective function of the primal problem are
decomposed. Furthermore, we formulate generalized interior point regularity conditions for strong duality and give necessary and sufficient optimality conditions. As applications of this approach we determine the formulae of the conjugate as well as the biconjugate of the objective function of the primal problem and analyze an optimization problem having as objective function the sum of reciprocals of concave functions.
In the second part of this thesis we discuss in the sense of the introduced duality concept three classes of minimax location problems. The first one consists of nonlinear and linear single minimax location problems with geometric constraints, where the maximum of nonlinear or linear functions composed with gauges between pairs of a new and existing points will be minimized. The version of the nonlinear location problem is additionally considered with set-up costs. The second class of minimax location problems deals with multifacility location problems as suggested by Drezner (1991), where for each given point the sum of weighted distances to all facilities plus set-up costs is determined and the maximal value of these sums is to be minimized. As the last and third class the classical multifacility location problem with geometrical constraints is considered in a generalized form where the maximum of gauges between pairs of new facilities and the maximum of gauges between pairs of new and existing facilities will be minimized. To each of these location problems associated dual problems will be formulated as well as corresponding duality statements and necessary and sufficient optimality conditions. To illustrate the results of the duality approach and to give a more detailed characterization of the relations between the location problems and their corresponding duals, we consider examples in the Euclidean space.
This thesis ends with a numerical approach for solving minimax location problems by epigraphical splitting methods. In this framework, we give formulae for the projections onto the epigraphs of several sums of powers of weighted norms as well as formulae for the projection onto the epigraphs of gauges. Numerical experiments document the usefulness of our approach for the
discussed location problems.
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Henry, Raphaël. "Spectre et pseudospectre d'opérateurs non-autoadjoints." Phd thesis, Université Paris Sud - Paris XI, 2013. http://tel.archives-ouvertes.fr/tel-00924425.
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L'instabilité du spectre des opérateurs non-autoadjoints constitue la thématique centrale de cette thèse. Notre premier objectif est de mettre en évidence ce phénomène dans le cas de certains modèles naturels tels que l'opérateur d'Airy, l'oscillateur harmonique ou l'oscillateur cubique complexes. Dans ce but, nous nous intéressons au comportement des projecteurs spectraux associés aux valeurs propres de ces opérateurs, poursuivant une démarche initiée par E. B. Davies. Le second objectif de notre travail consiste à montrer de quelle manière ces modèles peuvent contribuer à la compréhension de certains problèmes issus de domaines mathématiques et physiques aussi variés que la mécanique quantique, la supraconductivité ou la théorie du contrôle. Nos résultats sur l'instabilité spectrale de l'oscillateur cubique complexe viennent ainsi corroborer un travail de B. Krejcirik et P. Siegl, soulignant l'impossibilité de fournir une justification rigoureuse aux théories actuelles de la mécanique quantique non-hermitienne. Par ailleurs, nous nous appuyons sur les propriétés des modèles mentionnés ci-dessus pour obtenir des résultats sur le spectre et la résolvante d'opérateurs de Schrödinger à potentiels imaginaires purs dans des ouverts bornés. Ces résultats peuvent en particulier être appliqués à l'étude du système de Ginzburg-Landau dépendant du temps en supraconductivité. Enfin, nous présentons des résultats sur la contrôlabilité d'équations paraboliques dégénérées qui reposent sur une étude spectrale et pseudospectrale de l'opérateur d'Airy et de l'oscillateur harmonique complexes. Ce dernier travail est le fruit d'une collaboration avec K. Beauchard, B. Helffer et L. Robbiano.
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Silva, Alessandra Ribeiro da. "Linearização de aplicações multilineares contínuas entre espaços de Banach e multi-ideais de composição." Universidade Federal de Uberlândia, 2010. https://repositorio.ufu.br/handle/123456789/16777.
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Coordenação de Aperfeiçoamento de Pessoal de Nível SuperiorThe rst aim of this dissertation is to construct the tensor product of nitely many linear spaces from elementary tensors and to show that this is the space through which multilinear mappings can be linearized. Next continuous multilinear mappings between Banach spaces are studied. The projective norm is introduced in the tensor product in order to perform the linearization of continuous multilinear mappings. The last chapter is devoted to the study of operator ideals and their generalization to the multilinear setting. The interplay between the theory of multi-ideals and the projective tensor product is established by the theory of composition multi-ideals.
O primeiro objetivo desta dissertação é construir o produto tensorial de um número finito de espaços vetoriais a partir dos tensores elementares e mostrar que e atraves desse espaco que aplicações multilineares podem ser linearizadas. Em seguida são estudadas as aplicações multilineares contnuas entre espacos de Banach. A norma projetiva e introduzida no produto tensorial para realizar a linearização das aplicações multilineares contnuas. No ultimo captulo os ideais de operadores lineares são estudados e generalizados para o contexto de ideais de aplicações multilineares. A conexão da teoria de multi-ideais com o produto tensorial projetivo e feita atraves dos multi-ideais de composição.
Mestre em Matemática
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Pina, Hugo Rafael Matos. "Metodologia BIM na gestão da manutenção de uma estação elevatória." Master's thesis, Universidade de Aveiro, 2015. http://hdl.handle.net/10773/14955.
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Mestrado em Engenharia CivilA complexidade crescente dos projetos de construção, leva à correspondente multiplicidade e exigência de todo o processo, quer durante a fase de conceção e construção, quer durante a fase de exploração das edificações/instalações. A importância da fase de operação e manutenção para o aumento da durabilidade e para a redução de custos das instalações, associada à potencialidade da metodologia Building Information Modeling (BIM), conduz ao desenvolvimento de novas formas de gestão integrada do edificado. Esta metodologia possui os requisitos necessários para ser integrada na gestão de qualquer edifício ou instalação, não só pela sua capacidade gráfica e de visualização, mas sobretudo pelas potencialidades que a base de dados criada oferece, contendo informação parametrizada de cada um dos componentes presentes na mesma. O estudo desenvolvido pretende contribuir para a implementação do conceito do Facility Management (FM) em Portugal, associado ao Building Information Modeling, integrando a gestão das instalações com o modelo tridimensional da instalação. Para o caso de estudo, foi escolhida uma estação elevatória de águas residuais, que engloba equipamentos que necessitam de manutenção ao longo da sua vida de serviço, sendo a sua estrutura constituída por anéis de betão armado, betonados in situ. Foi desenvolvido um modelo tridimensional da instalação, utilizando o software de modelação Autodesk Revit 2014, com todas as especialidades e equipamentos, no qual se introduziram todas as informações relativas a cada elemento do modelo. De seguida, criou-se uma base de dados, onde é possível alojar estas informações. A partir do próprio software de modelação, utilizando o Construction Operation Building information exchange (COBie), foi possível criar bases de dados que, posteriormente, na fase de operação e manutenção, possam ser utilizadas pelos responsáveis destas fases. Por fim, a informação inserida na fase de modelação da instalação é exportada para o software utilizado na gestão e manutenção da instalação. No presente caso de estudo utilizou-se o IBM Maximo, através do qual se efetuou a simulação da gestão dos ativos após a qual se fez a comparação entre esta metodologia e a usualmente utilizada pelas empresas.
The construction project’s complexity leads to the multiplicity and demanding of the entire process. Whether in the concept and construction phase, or in phase of exploration of an infrastructure, the importance of the operation and maintenance for the increase of the durability and cost reduction of the infrastructure, can be associated to the potential of the Building Information Modeling (BIM) methodology, leading to the development of new management procedures, integrated in the buildings. The BIM methodology has the necessary requirements to be integrated in the management of any building, infrastructure or installation, not only due to the graphical capacity and visualization but above all for the possibilities introduced by the defined database that includes the parameterized information of each components. The study developed aims to contribute to the implementation of the concept of Facility Management (FM) in Portugal, associated with Building Information Modeling, integrating the management of installations with three-dimensional model of the installation. For the case study, a wastewater pumping station was selected, which includes equipment that needs maintenance during its service life. The structure was defined by rings of reinforced concrete, casted in situ. A three-dimensional model of the installation was developed using Autodesk Revit 2014, a modeling software with all specialties and equipment, in which were introduced all the information for each model element. Then, a database where it is possible to accommodate this information was created. It was possible, from the own modeling software, using the Construction Operation Building information exchange (COBie), to export databases that later, in the operation and maintenance phase, can be used by those responsible for these phases. Finally, the information included in the installation modeling phase was exported to the software used in the management and maintenance of the facility, which in the case study was the IBM Maximo. Finally was carried out the management of the assets and was performed a simplified comparison between the methodology developed and the commonly used by the companies.
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Searle, Deane. "Low Intensity Conflict: Contemporary Approaches and Strategic Thinking." The University of Waikato, 2007. http://hdl.handle.net/10289/2591.
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Low Intensity Conflict (LIC) is a significant feature of the contemporary world and it is a particular challenge to the armed forces of many states which are involved is such conflict, or are likely to become so. This thesis is not concerned with how such difficult conflict situations arise. Rather it is concerned with how, from the point of view of the state, they may be contained and ultimately brought to a satisfactory resolution. The work is thus concerned with the practicalities of ending LIC. More specifically, the purpose of this research is to establish a framework of doctrinal and military principles applicable to the prevention and resolution of LIC. The principles of this thesis are based in numerous historical examples of LIC and six in depth case studies. These distilled principles are analysed in two central chapters, and are then applied in two latter defence force chapters so as to ensure there practicality and resilience. Numerous defence academics and military practitioners have been consulted in the production of this thesis; their contribution has further reinforced the functionality of the principles examined in this research. The research illustrates the criticality of a holistic approach to LIC. The function of this approach is to guarantee the stability of the sovereign state, by unifying civil, police, intelligence and military services. The effectiveness of the military elements must also be ensured, as military force is central to the suppression of LIC. Consequently, the research makes strategic and operational prescriptions, so as to improve the capability of defence forces that are concerned with preventing or resolving LIC.
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Séméria, Marie-Noëlle. "Etude de circuits submicroniques implantés pour mémoire à bulles magnétiques." Grenoble 1, 1987. http://www.theses.fr/1987GRE10137.
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La technologie necessaire a la realisation de memoires a bulles magnetiques implantees de haute densite (au moins 16 mb/cm**(2)) est etudiee sous differents aspects: le report de motifs submicroniques (0. 3-0. 8 mu m) necessite d'optimiser les moyens classiques de lithographie optique par contact ou projection. A cette fin, une modelisation est utilisee et des experiences comparatives realisees; la realisation des circuits comporte des implantations ioniques: differents materiaux de masque sont proposes (or, silice, polymere). Dans chacun des cas, des realisations concretes de masques graves sont effectuees et analysees; enfin des implantations hydrogene sont realisees. Le fonctionnement des dispositifs est correle aux parametres de l'implantation et au dessin des motifs. Des conclusions pratiques sont tirees sur l'implantation et la technologie compatibles avec un bon fonctionnement des dispositifs
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Sharir, Yacov. "Beyond the electronic connection : the technologically manufactured cyber-human and its physical human counterpart in performance : a theory related to convergence identities." Thesis, University of Plymouth, 2013. http://hdl.handle.net/10026.1/1498.
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This thesis is an investigation of the complex processes and relationships between the physical human performer and the technologically manufactured cyber-human counterpart. I acted as both researcher and the physical human performer, deeply engaged in the moment-to-moment creation of events unfolding within a shared virtual reality environment. As the primary instigator and activator of the cyber-human partner, I maintained a balance between the live and technological performance elements, prioritizing the production of content and meaning. By way of using practice as research, this thesis argues that in considering interactions between cyber-human and human performers, it is crucial to move beyond discussions of technology when considering interactions between cyber-humans and human performers to an analysis of emotional content, the powers of poetic imagery, the trust that is developed through sensory perception and the evocation of complex relationships. A theoretical model is constructed to describe the relationship between a cyber-human and a human performer in the five works created specifically for this thesis, which is not substantially different from that between human performers. Technological exploration allows for the observation and analysis of various relationships, furthering an expanded understanding of ‘movement as content’ beyond the electronic connection. Each of the works created for this research used new and innovative technologies, including virtual reality, multiple interactive systems, six generations of wearable computers, motion capture technology, high-end digital lighting projectors, various projection screens, smart electronically charged fabrics, multiple sensory sensitive devices and intelligent sensory charged alternative performance spaces. They were most often collaboratively created in order to augment all aspects of the performance and create the sense of community found in digital live dance performances/events. These works are identified as one continuous line of energy and discovery, each representing a slight variation on the premise that a working, caring, visceral and poetic content occurs beyond the technological tools. Consequently, a shift in the physical human’s psyche overwhelms the act of performance. Scholarship and reflection on the works have been integral to my creative process throughout. The goals of this thesis, the works created and the resulting methodologies are to investigate performance to heighten the multiple ways we experience and interact with the world. This maximizes connection and results in a highly interactive, improvisational, dynamic, non-linear, immediate, accessible, agential, reciprocal, emotional, visceral and transformative experience without boundaries between the virtual and physical for physical humans, cyborgs and cyber-humans alike.
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Sun, Yi-Jen, and 孫乙任. "Fusion of Wavelet Transform, Sobel Operator and Orthogonal Projection for Face Recognition." Thesis, 2008. http://ndltd.ncl.edu.tw/handle/71356573211761515910.
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碩士國立成功大學
電機工程學系碩博士班
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Study of human face recognition system has grown vigorously for last decades. The biometrics of human face is an important feature in the identity authentication. The traditional principal component analysis (PCA), Eigenface, and linear decision algorithm (LDA) operate directly on a whole pattern represented as a vector and acquire a set of projection vectors to extract global features from given training patterns. The computation loads in these methods are heavy. In this thesis, a novel fusion algorithm of the wavelet transform, Sobel operator and orthogonal projection is proposed for human face recognition, where the Haar wavelet transform is utilized to reduce the dimension of images, the Sobel operator is adopted to extract facial features, and the orthogonal projection is presented to perform feature transformation and face recognition. The Olivetti Research Lab (ORL) face database is adopted to demonstrate the feasibility and effectiveness of the proposed face recognition system.
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Steinigeweg, Robin. "Application of Projection Operator Techniques to Transport Investigations in Closed Quantum Systems." Doctoral thesis, 2008. https://repositorium.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-2008082910.
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The work at hand presents a novel approach to transport in closed quantum systems. To this end a method is introduced which is essentially based on projection operator techniques, in particular on the time-convolutionless (TCL) technique. The projection onto local densities of quantities such as energy, magnetization, particles, etc. yields the reduced dynamics of the respective quantities in terms of a systematic perturbation expansion. Especially, the lowest order contribution of this expansion is used as a strategy for the analysis of transport in "modular" quantum systems. The term modular basically corresponds to (quasi-) one-dimensional structures consisting of identical or at least similar many-level subunits. Modular quantum systems are demonstrated to represent many physical situations and several examples are given. In the context of these quantum systems lowest order TCL is shown as an efficient tool which also allows to investigate the dependence of transport on the considered length scale. In addition an estimation for the validity range of lowest order TCL is derived. As a first application a "design" model is considered for which a complete characterization of all available transport types as well as the transitions to each other is possible. For this model the relationship to quantum chaos and the validity of the Kubo formula is further discussed. As an example for a "real" system the Anderson model is finally analyzed. The results are partially verified by the numerical solution of the full time-dependent Schroedinger equation which is obtained by exact diagonalization or approximative integrators.
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Hickel, Tilmann [Verfasser]. "Theory of many body effects in the Kondo lattice model : projection operator method / von Tilmann Hickel." 2005. http://d-nb.info/980739764/34.
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Steinigeweg, Robin [Verfasser]. "Application of projection operator techniques to transport investigations in closed quantum systems / vorgelegt von Robin Steinigeweg." 2008. http://d-nb.info/990213633/34.
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Seidel, Markus. "On some Banach Algebra Tools in Operator Theory." Doctoral thesis, 2011. https://monarch.qucosa.de/id/qucosa%3A19670.
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Die vorliegende Arbeit ist der Untersuchung von Operatorfolgen gewidmet, die typischerweise bei der Anwendung von Approximationsverfahren auf stetige lineare Operatoren entstehen. Dabei stehen die Stabilität der Folgen sowie das asymptotische Verhalten gewisser Charakteristika wie Normen, Konditionszahlen, Fredholmeigenschaften und Pseudospektren im Mittelpunkt.
Das Hauptaugenmerk liegt auf der Entwicklung der Theorie für Operatoren auf Banachräumen. Hierbei bildet ein dafür geeigneter Konvergenzbegriff, die sogenannte P-starke Konvergenz, den Ausgangspunkt, welcher das Studium der gewünschten Eigenschaften in einer erstaunlichen Allgemeinheit gestattet.
Die erzielten Resultate kommen, neben einer Reihe weiterer Anwendungen, insbesondere für das Projektionsverfahren für banddominierte Operatoren zum Einsatz.
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Axelsson, Andreas. "Transmission problems for Dirac's and Maxwell's equations with Lipschitz interfaces." Phd thesis, 2002. http://hdl.handle.net/1885/46056.
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The aim of this thesis is to give a mathematical framework for scattering of electromagnetic waves by rough surfaces. We prove that the Maxwell transmission problem with a weakly Lipschitz interface, in finite energy norms, is well posed in Fredholm sense for real frequencies. Furthermore, we give precise conditions on the material constants ε, μ and σ and the frequency ω when this transmission problem is well posed. To solve the Maxwell transmission problem, we embed Maxwell’s equations in an elliptic Dirac equation. We develop a new boundary integral method to solve the Dirac transmission problem. This method uses a boundary integral operator, the rotation operator, which factorises the double layer potential operator. We prove spectral estimates for this rotation operator in finite energy norms using Hodge decompositions on weakly Lipschitz domains. To ensure that solutions to the Dirac transmission problem indeed solve Maxwell’s equations, we introduce an exterior/interior derivative operator acting in the trace space. By showing that this operator commutes with the two basic reflection operators, we are able to prove that the Maxwell transmission problem is well posed. We also prove well-posedness for a class of oblique Dirac transmission problems with a strongly Lipschitz interface, in the L_2 space on the interface. This is shown by employing the Rellich technique, which gives angular spectral estimates on the rotation operator.
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Hennig, Paul. "Adaptive Isogeometric Analysis of Phase-Field Models." 2020. https://tud.qucosa.de/id/qucosa%3A73811.
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In this thesis, a robust, reliable and efficient isogeometric analysis framework is presented that allows for an adaptive spatial discretization of non-linear and time-dependent multi-field problems. In detail, B\'ezier extraction of truncated hierarchical B-splines is proposed that allows for a strict element viewpoint, and in this way, for the application of standard finite element procedures. Furthermore, local mesh refinement and coarsening strategies are introduced to generate graded meshes that meet given minimum quality requirements. The different strategies are classified in two groups and compared in the adaptive isogeometric analysis of two- and three-dimensional, singular and non-singular problems of elasticity and the Poisson equation. Since a large class of boundary value problems is non-linear or time-dependent in nature and requires incremental solution schemes, projection and transfer operators are needed to transfer all state variables to the new locally refined or coarsened mesh. For field variables, two novel projection methods are proposed and compared to existing global and semi-local versions. For internal variables, two different transfer operators are discussed and compared in numerical examples.
The developed analysis framework is than combined with the phase-field method. Numerous phase-field models are discussed including the simulation of structural evolution processes to verify the stability and efficiency of the whole adaptive framework and to compare the projection and transfer operators for the state variables. Furthermore, the phase-field method is used to develop an unified modelling approach for weak and strong discontinuities in solid mechanics as they arise in the numerical analysis of heterogeneous materials due to rapidly changing mechanical properties at material interfaces or due to propagation of cracks if a specific failure load is exceeded. To avoid the time consuming mesh generation, a diffuse representation of the material interface is proposed by introducing a static phase-field. The material in the resulting transition region is recomputed by a homogenization of the adjacent material parameters. The extension of this approach by a phase-field model for crack propagation that also accounts for interface failure allows for the computation of brittle fracture in heterogeneous materials using non-conforming meshes.
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"Projection operators in correlated noise fields." Massachusetts Institute of Technology, Laboratory for Information and Decision Systems], 1995. http://hdl.handle.net/1721.1/3399.
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Bartsch, Christian. "General Projective Approach to Transport Coefficients of Condensed Matter Systems and Application to an Atomic Wire." Doctoral thesis, 2010. https://repositorium.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-201003165677.
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We present a novel approach to the investigation of transport coefficients in condensed matter systems, which is based on a pertinent time-convolutionless (TCL) projection operator technique. In this context we analyze in advance the convergence of the corresponding perturbation expansion and the influence of the occurring inhomogeneity.
The TCL method is used to establish a formalism for a consistent derivation of a Boltzmann equation from the underlying quantum dynamics, which is meant to apply to non-ideal quantum gases. We obtain a linear(ized) collision term that results as a finite non-singular rate matrix and is thus adequate for further considerations, e.g., the calculation of transport coefficients. In the work at hand we apply the provided scheme to numerically compute the diffusion coefficient of an atomic wire and especially analyze its dependence on certain model properties, in particular on the width of the wire.
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Krčmář, Jindřich. "Teorie elektron-fononové interakce v modelovém otevřeném kvantovém systému." Master's thesis, 2011. http://www.nusl.cz/ntk/nusl-300533.
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The aim of this work is to investigate projection operator method of deriva- tion of equations of motion for reduced density matrix and apply it to a model open quantum system. We gradually pass from quantum mechanical model of a molecule with one vibrational degree of freedom to an example of open quantum system relevant in the theory of nonlinear spectroscopy. In the thesis we present results of numerical simulations of the time evolution of the open quantum system performed with a program written for this purpose. We are specially concerned with simulations of the solution of the time-convolutionless generalized master equation up to the a second order of the perturbation expan- sion, and we show that under certain conditions it provides an exact solution of the problem. The text also contains derivation of the recurrence relations for the Franck-Condon factors for the most general case of two quantum harmonic oscillators in one space dimension, i. e. transformation matrix between two bases of the L2 (R) space determined by the solutions of the time-independent Schrödinger equation appropriate for these oscillators. 1