Dissertations / Theses on the topic 'Discrete metric'
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Putwain, Rosemary Johanna. "Partial translation algebras for certain discrete metric spaces." Thesis, University of Southampton, 2010. https://eprints.soton.ac.uk/170227/.
Full textLopez, Marcos D. "Discrete Approximations of Metric Measure Spaces with Controlled Geometry." University of Cincinnati / OhioLINK, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1439305529.
Full textMaier, Daniela [Verfasser], and Guido [Akademischer Betreuer] Schneider. "Nonlinear phenomena on metric and discrete necklace graphs / Daniela Maier ; Betreuer: Guido Schneider." Stuttgart : Universitätsbibliothek der Universität Stuttgart, 2019. http://d-nb.info/1195529481/34.
Full textTsuchiya, Luciana Yoshie 1977. "Um estudo de reticulados q-ários com a métrica da soma." [s.n.], 2012. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306600.
Full textDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica.
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Resumo: Reticulados no 'R^n' são conjuntos discretos de pontos gerados como combinações inteiras de vetores linearmente independentes. A estrutura e as propriedades de reticulados vêm sendo exploradas em diversas áreas, dentre elas a Teoria da Informação. Neste trabalho fizemos um estudo de reticulados q-ários na métrica da soma, os quais estão relacionados aos códigos q-ários. Iniciamos com o estudo de reticulados gerais abordando questões como, densidade de empacotamento, determinação da região de Voronoi, equivalência de reticulados e processos de decodificação, fazendo um paralelo destas questões na métrica euclidiana e na métrica da soma. Em seguida, no Capitulo 2, tratamos brevemente os conceitos de códigos corretores de erros, onde os códigos q-ários estão inseridos e códigos lineares definidos sobre corpos finitos. No estudo dos códigos q-ários consideramos a distancia de Lee que e uma alternativa a usual métrica de Hamming. Por fim, no Capitulo 3, abordamos os reticulados q-ários que são obtidos a partir de códigos q-ários pelo processo conhecido como Construção A. Estudamos uma forma de se decodificar um reticulado q-ário via a Construção A, usando a decodificação do código e vice-versa e discutimos um algoritmo de decodificação (Lee Sphere Decoding) para reticulados q-ários que possuem matriz geradora de formato especial
Abstract: Lattices in 'R^n' are discrete sets of points generated as integer combinations of linearly independent vectors. The structure and properties of lattices have been explored in several areas, including Information Theory. In this work, we study q-ary lattices which are obtained from q-ary codes in the sum metric. We begin the study of general lattices, approaching topics as packing density, Voronoi regions, lattice equivalence and decoding processes, considering both the Euclidean and sum metric. In Chapter 2, we introduce some error correcting codes concepts focusing on q-ary codes and the more general class of linear codes defined over finite fields. In the study of q-ary codes, we consider the Lee distance, as an extension and alternative to the usual Hamming metric. Finally, in Chapter 3, we approach the q-ary latt ices, which are obtained from q-ary codes via the so called Construction A. We study a q-ary lattice decoding process, relate it to the associate code decoding and discuss a decoding algorithm for lattices which have special generator matrices
Mestrado
Matematica
Mestre em Matemática
Champion, Daniel James. "Mobius Structures, Einstein Metrics, and Discrete Conformal Variations on Piecewise Flat Two and Three Dimensional Manifolds." Diss., The University of Arizona, 2011. http://hdl.handle.net/10150/145313.
Full textLesser, Alice. "Optimal and Hereditarily Optimal Realizations of Metric Spaces." Doctoral thesis, Uppsala University, Department of Mathematics, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-8297.
Full textThis PhD thesis, consisting of an introduction, four papers, and some supplementary results, studies the problem of finding an optimal realization of a given finite metric space: a weighted graph which preserves the metric's distances and has minimal total edge weight. This problem is known to be NP-hard, and solutions are not necessarily unique.
It has been conjectured that extremally weighted optimal realizations may be found as subgraphs of the hereditarily optimal realization Γd, a graph which in general has a higher total edge weight than the optimal realization but has the advantages of being unique, and possible to construct explicitly via the tight span of the metric.
In Paper I, we prove that the graph Γd is equivalent to the 1-skeleton of the tight span precisely when the metric considered is totally split-decomposable. For the subset of totally split-decomposable metrics known as consistent metrics this implies that Γd is isomorphic to the easily constructed Buneman graph.
In Paper II, we show that for any metric on at most five points, any optimal realization can be found as a subgraph of Γd.
In Paper III we provide a series of counterexamples; metrics for which there exist extremally weighted optimal realizations which are not subgraphs of Γd. However, for these examples there also exists at least one optimal realization which is a subgraph.
Finally, Paper IV examines a weakened conjecture suggested by the above counterexamples: can we always find some optimal realization as a subgraph in Γd? Defining extremal optimal realizations as those having the maximum possible number of shortest paths, we prove that any embedding of the vertices of an extremal optimal realization into Γd is injective. Moreover, we prove that this weakened conjecture holds for the subset of consistent metrics which have a 2-dimensional tight span
Winden, Matthew Wayne. "INTEGRATING STATED PREFERENCE CHOICE ANALYSIS AND MULTI-METRIC INDICATORS IN ENVIRONMENTAL VALUATION." The Ohio State University, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=osu1343325594.
Full textSimmer, Jan [Verfasser], Olaf [Akademischer Betreuer] Post, and Olaf [Gutachter] Post. "Approximation of energy forms on finitely ramified fractals by discrete graphs and related metric measure spaces / Jan Simmer ; Gutachter: Olaf Post ; Betreuer: Olaf Post." Trier : Universität Trier, 2021. http://d-nb.info/1230135057/34.
Full textDinh, Ngoc Thach. "Observateur par intervalles et observateur positif." Thesis, Paris 11, 2014. http://www.theses.fr/2014PA112335/document.
Full textThis thesis presents new results in the field of state estimation based on the theory of positive systems. It is composed of two separate parts. The first one studies the problem of positive observer design for positive systems. The second one which deals with robust state estimation through the design of interval observers, is at the core of our work.We begin our thesis by proposing the design of a nonlinear positive observer for discrete-time positive time-varying linear systems based on the use of generalized polar coordinates in the positive orthant. For positive systems, a natural requirement is that the observers should provide state estimates that are also non-negative so they can be given a physical meaning at all times. The idea underlying the method is that first, the direction of the true state is correctly estimated in the projective space thanks to the Hilbert metric and then very mild assumptions on the output map allow to reconstruct the norm of the state. The convergence rate can be controlled.Later, the thesis is continued by studying the so-called interval observers for different families of dynamic systems in continuous-time, in discrete-time and also in a context "continuous-discrete" (i.e. a class of continuous-time systems with discrete-time measurements). Interval observers are dynamic extensions giving estimates of the solution of a system in the presence of various type of disturbances through two outputs giving an upper and a lower bound for the solution. Thanks to interval observers, one can construct control laws which stabilize the considered systems
Siramdasu, Yaswanth. "Discrete Tire Model Application for Vehicle Dynamics Performance Enhancement." Diss., Virginia Tech, 2015. http://hdl.handle.net/10919/74394.
Full textPh. D.
Roussillon, Pierre. "Modèles de cycles normaux pour l'analyse des déformations." Thesis, Sorbonne Paris Cité, 2017. http://www.theses.fr/2017USPCB073/document.
Full textIn this thesis, we develop a second order model for the representation of shapes (curves or surfaces) using the theory of normal cycles. The normal cycle of a shape is the current associated with its normal bundle. Introducing kernel metrics on normal cycles, we obtain a dissimilarity measure between shapes which takes into account curvature. This measure is used as a data attachment term for a purpose of registration and shape analysis by deformations. Chapter 1 is a review of the field of shape analysis. We focus on the setting of the theoretical and numerical model of the Large Deformation Diffeomorphic Metric Mapping(LDDMM).Chapter 2 focuses on the representation of shapes with normal cycles in a unified framework that encompasses both the continuous and the discrete shapes. We specify to what extend this representation encodes curvature information. Finally, we show the link between the normal cycle of a shape and its varifold. In chapter 3, we introduce the kernel metrics, so that we can consider normal cycles in a Hilbert space with an explicit scalar product. We detail this scalar product for discrete curves and surfaces with some kernels, as well as the associated gradient. We show that even with simple kernels, we do not get rid of all the curvature informations. The chapter 4 introduces this new metric as a data attachment term in the framework of LDDMM. We present numerous registrations and mean shape estimation for curves and surfaces. The aim of this chapter is to illustrate the different properties of normal cycles for the deformations analysis on synthetic and real examples
Patterson, Julie A. "The Impact of Objective Quality Ratings on Patient Selection of Community Pharmacies: A Discrete Choice Experiment and Latent Class Analysis." VCU Scholars Compass, 2017. http://scholarscompass.vcu.edu/etd/4834.
Full textBen, Rabah Nourhène. "APPROCHE INTELLIGENTE À BASE DE RAISONNEMENT À PARTIR DE CAS POUR LE DIAGNOSTIC EN LIGNE DES SYSTÈMES AUTOMATISÉS DE PRODUCTION." Thesis, Reims, 2018. http://www.theses.fr/2018REIMS036/document.
Full textAutomated production systems (APS) represents an important class of industrial systems that are increasingly complex given the large number of interactions and interconnections between their different components. As a result, they are more susceptible to malfunctions, whose consequences can be significant in terms of productivity, safety and quality of production. A major challenge is to develop an intelligent approach that can be used to diagnose these systems to ensure their operational safety. In this thesis, we are only interested in the diagnosis of APS with discrete dynamics. We present in the first chapter these systems, the possible malfunctions and the used terminology for the diagnosis. Then, we present a state of the art of the existing methods for the diagnosis of this class of systems and also a synthesis of these methods. This synthesis motivated us to choose a data-based approach that relies on a machine learning technique, which is Case-Based Reasoning (CBR). For this reason, we presented in the second chapter a state of the art on machine learning and its different methods with a focus mainly on the CBR and its uses for the diagnosis of industrial systems. This study allowed us to propose in Chapter 3 a Case Based Decision Support System for the diagnosis of APS. This system is based on an online block and an offline block. The Offline block is used to define a case representation format and to build a Normal Case Base (NCB) and a Faulty Case Base (FCB) from a historical database. The online block helps human operators of monitoring to make the most appropriate diagnosis decision. The experiments results perform on a sorting system presented the pillars of this approach, which reside in the proposed case representation format and in the used case base. To solve these problems and improve the results, a new case representation format is proposed in chapter 4. According to this format and from the data acquired from the simulated system after its emulation in normal and faulty mode, cases of the initial case base are build. Then, a reasoning and incremental learning phase is presented. This phase allows the system diagnosis and the enrichment of the case base following the appearance of new unknown behaviors. The experiments presented in Chapter 5 and perform on the 'turntable' which is a subsystem of the 'sorting system” allowed to show the improvement of the results and also to evaluate and compare the performances of the proposed approach with some automatic learning approaches and with a model-based approach to turntable diagnosis
Wolford, Jane N. "Architectural contextualism in the twentieth century, with particular reference to the architects E. Fay Jones and John Carl Warnecke." Diss., Georgia Institute of Technology, 2005. http://hdl.handle.net/1853/7082.
Full textMuniz, Elaine Cristina. "Metalosupramoléculas discretas e Metal Organic Frameworks (MOFs) baseados em íons lantanídeos: design, síntese, caracterização e propriedades /." Araraquara, 2016. http://hdl.handle.net/11449/136246.
Full textCo-orientador: Marco Aurélio Cebim
Banca: José Clayston Melo Pereira
Banca: Rogéria Rocha Gonçalves
Banca: José Maurício Almeida Caiut
Banca: Sérgio Antonio Marques de Lima
Resumo: Materiais luminescentes despertam grande interesse nas pesquisas devido à variedade de aplicações, podendo ser empregados em displays eletrônicos, lâmpadas fluorescentes e diodos emissores de luz, por exemplo. Neste contexto, os íons lantanídeos trivalentes são destaque pois apresentam propriedades luminescentes únicas como alta pureza de cor, tempo de vida de nano a milissegundos e linhas de emissão definidas e estreitas provenientes de transições intraconfiguracionais 4f-4f. No entanto, devida à natureza proibida dessas transições, os íons lantanídeos apresentam baixa absortividade molar. Para suprir essa deficiência, pode ser realizada a coordenação destes íons co m bons grupos cromóforos capazes de transferir energia para os níveis 4f dos lantanídeos. Outra estratégia para melhorar as propriedades luminescentes de materiais é através da combinação e/ou dopagem utilizando diferentes lantanídeos, o que pode resultar na emissão de ambos os íons ou na emissão preferencial de um deles por meio de processos de transferência de energia. Espécies bimetálicas heteronucleares e polímeros de coordenação porosos ( Metal Organic Frameworks, MOFs ) se destacam neste cenário. Neste trabalho foram estudadas quatro séries de compostos bimetálicos heteronucleares utilizando succinato de sódio e ácido 3,5-dicarbóxipir azolico como ligantes e variando a razão entre dois íons lantanídeos distintos, Gd 3+ :Eu 3+, Gd 3+ :Tb 3+, Dy 3+ :Eu 3+ e Eu 3+ :Tb 3+ . Os compostos obtidos foram caracterizados po r difração de raios X de monocristal e de pó, espectroscopia na região do IV, análise térmica, espectroscopia de reflectância difusa, espectroscopia de fotoluminescênc ia com excitação UV, luminescência com excitação por raios X e microscopia eletrônica de varredura associada à espectroscopia por energia dispersiva. Os complexos apresentaram interessantes propriedad...
Abstract: 12 ABSTRACT Luminescent materials attract interest in rese arch due to the diversity of applications. These materials can be used at electronic displays, fluorescent lamps and light emitting diodes, for example. In this contex t, trivalent lanthanide ions are interesting because of their unique luminescent properties like high color purity, nano to milliseconds lifetime and narrow emission lines from 4f-4f transitions. However, because of the nature of forbidden 4f-4f transitions, lanthanide ions have low molar absorptivity. To supply this deficiency, th e lanthanide ions can be coordinated to chromophore groups, capable of transfer ener gy to the 4f levels of lanthanides. It is also possible to improve the luminescent prop erties of materials by combining different lanthanides, which can result in the emission of both ions or in the preferential emission of one of them by energy transfer processes. Bimetallic heteronuclear complexes and metal organic frameworks (MOFs) are interesting in this context. In this work, four bimetallic heteronuclear compounds series with sodium succinate and 3,5- dicarboxypyrazolate ligands were prepared with different lanthanides ratio, Gd 3+ :Eu 3+, Gd 3+ :Tb 3+, Dy 3+ :Eu 3+ e Eu 3+ :Tb 3+ . The compounds were characterized by single crystal and powder X-ray diffraction, Fourier transform infrared spectroscopy, thermal analysis, UV-Vis spectroscopy, photoluminescence spectroscopy, X-ray excited optical luminescence and field emission gun-scanning electron microscopy, with energy dispersive X-ray spectroscopy. The complexes present interesting luminescent properties. In Gd 3+ compounds series, by increasing the amount of Gd 3+ ions in the sample, the intensity of the relative charge tr ansfer band also increases, indicating that the Gd 3+ ions play an important role in the energy transfer mechanism from ligands to the lanthanides. The intensity parameters, the radiat...
Doutor
Habib, Zadeh Esmaeil. "Modelling and Quantitative Analysis of Performance vs Security Trade-offs in Computer Networks: An investigation into the modelling and discrete-event simulation analysis of performance vs security trade-offs in computer networks, based on combined metrics and stochastic activity networks (SANs)." Thesis, University of Bradford, 2017. http://hdl.handle.net/10454/17412.
Full textMerendino, Edy Maicon. "Estudo de processo de reciclagem do composto de polietileno e alumínio proveniente de embalagens cartonadas assépticas através de simulação computacional usando o método dos elementos discretos (DEM)." [s.n.], 2011. http://repositorio.unicamp.br/jspui/handle/REPOSIP/266814.
Full textDissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Química
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Resumo: As embalagens cartonadas assépticas para alimentos são comuns em nosso dia-a-dia. Tais embalagens são compostas por três materiais: papel, polietileno de baixa densidade e alumínio. Seu processo de reciclagem se dá em duas etapas sucessivas: a reciclagem do papel e a posterior reciclagem do composto de polietileno e alumínio. Durante a primeira etapa de reciclagem, um percentual das fibras de papel não é retirado do composto de polietileno e alumínio o que pode comprometer a qualidade de produtos feitos a partir da reciclagem deste composto. Para a extração do papel residual foi desenvolvido de maneira empírica um equipamento centrífugo em escala industrial. Visando o estudo do funcionamento deste equipamento fez-se a simulação deste usando o método dos elementos discretos (DEM). O primeiro passo foi a determinação de parâmetros físicos e de interação através de experimentos práticos e respectivas simulações computacionais para a calibração de um modelo, o qual foi conseguido de maneira satisfatória. Uma vez tendo o modelo calibrado, foram realizadas simulações com diferentes geometrias para o rotor e parte estática deste equipamento buscando levantar hipóteses para o entendimento do funcionamento do equipamento. Os resultados para diferentes especificações foram comparados e discutidos
Abstract: Milk and beverages carton packages are very common in our lives. These packages are made of three different materials: paper, low density polyethylene and aluminium. The recycling process of these packages takes place in two successive stages: the recycling of paper and the subsequent recycling of polyethylene and aluminium composite. During the first stage of recycling a percentage of the paper is not removed from the composite of polyethylene and aluminium which can compromise the quality of products made from recycling of this composite. An industrial-scale centrifuge equipment was developed empirically for extraction of residual paper. In order to study the operation of this equipment, it was made its simulation using the discrete element method (DEM). The first step was set-up of physical and interaction parameters through practical experiments and computer simulations to calibrate a model, which was achieved satisfactorily. Once the model was calibrated, simulations were performed with different geometries for rotor and static body of this equipment seeking hypotheses in order to understand equipment operation. The results for different specifications were compared and discussed
Mestrado
Processos em Tecnologia Química
Mestre em Engenharia Química
Wilkins, Leonard Duane. "Discrete Geometric Homotopy Theory and Critical Values of Metric Spaces." 2011. http://trace.tennessee.edu/utk_graddiss/1039.
Full textIsmail, Anas. "Computing the Gromov hyperbolicity constant of a discrete metric space." Thesis, 2012. http://hdl.handle.net/10754/244575.
Full textMarado, Luís Miguel. "Análise dos caracteres discretos da dentição inferior e do osso mandibular numa série do Museu de História Natural (FCUP)." Master's thesis, 2010. http://hdl.handle.net/10316/20825.
Full textO estudo da dentição surge na Antiguidade Clássica, desenvolvendo-se para a análise da anatomia (formação e estudo histológico dentário) nos séculos XVIII e XIX (Alt et al., 1998). Os caracteres discretos começam a considerar-se na pesquisa de relações biológicas entre populações a partir do século XIX (Silva, 2002), surgindo a apreciação dos caracteres fenotípicos dentários a partir do trabalho de Lasker (1950, in Irish e Nelson, 2008). A consideração por graus da variação discreta dos caracteres identificados surge sistematicamente com o método ASUDAS (Turner et al., 1991). O presente trabalho teve como objectivos estudar os caracteres discretos de 163 mandíbulas e da dentição presente em 104 destas, caracterizando uma população de origem portuguesa, alojada no Museu de História Natural da FC-UP. Além disso, pretendeu-se caracterizar biologicamente essa amostra através do padrão estabelecido, quando comparado com o de outras populações mundiais e ibéricas. O sistema ASUDAS (Tuner et al., 1991), a que se acresceu um carácter sugerido por Weets (2009), foi usado para a caracterização morfológica dentária. Hauser e De Stefano (1989), Movsesjan et al. (1975 in Galera et al., 1995) e Albuquerque (1952) sugeriram metodologias de observação dos caracteres anatómicos mandibulares, aqui adoptadas. A diagnose sexual mandibular recorreu, ainda, a vários métodos complementares (Loth e Henneberg [1996], adaptado por Balci et al. [2005]; Buikstra et al., 1994; Ferenbach et al., 1980; Giles, 1964). As frequências de caracteres não-métricos dentários permitiram denotar a proximidade da população estudada com as populações europeias e, em menor grau, norte-africanas. A comparação com amostras ibéricas mostrou uma semelhança entre estas e o presente material, indiciando alguma proximidade com populações de território português. Os dados referentes a caracteres mandibulares corroboram a ligação biológica a populações europeias, o que era esperado. Este trabalho contribuiu assim para a caracterização de uma amostra que se presumia portuguesa , através da dentição inferior e da morfologia mandibular. O autor sugere investimento da investigação na caracterização da morfologia dentária das amostras portuguesas, recentes e de passados mais remotos, que contribuam para a interpretação da história ibérica, sublinhando a necessidade de garantir resultados completos e inequívocos.
The study of human dentition began in the Classical Era, developing towards the analysis of anatomy (dental formation and histology) in the 18th and 19th centuries (Alt et al., 1998). Discrete trais were used in the search for biological relationships between populations from the 19th century onwards (Silva, 2002), and the consideration of fenotypical dental traits was brought on by Lasker.s work (Lasker, 1950, in Irish e Nelson, 2008). The recording by degrees of expression was systematized by the ASUDAS method (Turner et al., 1991). The present work has the objective of studying the discrete traits of 163 mandibles and the dentition present in 104 of these, to characterize a population of portuguese origin, located at the Museu de Historia Natural da FC-UP. As well as this, there was the intention of biologically characterizing such sample, by comparing the established pattern with the ones found in world and iberian samples. The ASUDAS system, to which a trait suggested by Weets (2009) was added, was used to characterize the dental morphology. Hauser and De Stefano (1989), Movsesjan et al. (1975 in Galera et al., 1995) and Albuquerque (1952) suggested methods of recording mandibular non-metric traits, adopted herein. The mandibular sexual diagnosis was established through a multiplicity of complementary methodologies (Loth and Henneberg [1996], adapted by Balci et al. [2005]; Buikstra et al., 1994; Ferenbach et al., 1980; Giles, 1964). The frequencies of non-metric dental traits allowed the identification of the proximity of european samples and, to a lesser degree, of north African samples, to the present population. The comparison of iberian samples showed likeness between these and the present material, underlining some proximity with the populations in the current xv portuguese territory. The data referring to mandibular traits corroborate the biological link to european populations, which was expected. This work thus contributes to characterize a sample that was assumed to be Portuguese and natural of Oporto, through the inferior dentition and the mandibular traits. The author suggests that future researchers should invest in characterizing the portuguese samples, recent and otherwise, contributing to a greater knowledge of iberian history, also emphasizing the need to acquire complete and unequivocal results.
Origlia, Marcos Miguel. "Estructuras localmente conformes Kähler y localmente conformes simplécticas en solvariedades compacta." Doctoral thesis, 2017. http://hdl.handle.net/11086/5837.
Full textEn esta tesis estudiamos las estructuras localmente conformes Kähler (LCK) y localmente conformes simplécticas (LCS) invariantes a izquierda en grupos de Lie, o equivalentemente tales estructuras en álgebras de Lie. Luego se buscan retículos (subgrupos discretos co-compactos) en dichos grupos. De esta manera obtenemos estructuras LCK o LCS en las solvariedades compactas (cociente de un grupo de Lie por un retículo). Específicamente estudiamos las estructuras LCK en solvariedades con estructuras complejas abelianas. Luego describimos explícitamente la estructura de las álgebras de Lie que admiten estructuras de Vaisman. También determinamos los grupos de Lie casi abelianos que admiten estructuras LCK o LCS y además analizamos la existencia de retículos en ellos. Finalmente desarrollamos un método para construir de manera sistemática ejemplos de álgebras de Lie equipadas con estructuras LCK o LCS a partir de un álgebra de Lie que ya admite tales estructuras y una representación compatible.
In this thesis we study left invariant locally conformal Kähler (LCK) structures and locally conformal symplectic structures (LCS) on Lie groups, or equivalently such structures on Lie algebras. Then we analize the existence of lattices (co-compact discrete subgroups) on these Lie groups. Therefore, we obtain LCK or LCS structures on compact solvmanifolds (quotients of a Lie group by a lattice). Specifically we study LCK structures on solvmanifold where the complex structure is abelian. Then we describe the structure of a Lie algebra admitting a Vaisman structure. On the other hand we determine the almost abelian Lie groups equipped with a LCK or LCS structures, and we also analize the existence of lattices on these groups. Finally we construct a method to produce examples of Lie algebras admitting LCK or LCS structures beginning with a Lie algebra with these structures and a compatible representation.