Dissertations / Theses on the topic 'Orthogonal representation'
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1
WANG, KWANG SHANG. "FINITE GROUPS FOR WHICH EVERY COMPLEX REPRESENTATION IS REALIZABLE." Diss., The University of Arizona, 1985. http://hdl.handle.net/10150/188019.
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In Chapter 2 we develop the concept of total orthogonality. A number of necessary conditions are derived. Necessary and sufficient conditions for total orthogonality are obtained for 2-groups and for split extensions of elementary abelian 2-groups. A complete description is given for totally orthogonal groups whose character degrees are bounded by 2. Brauer's problem is reduced for Frobenius groups to the corresponding problems for Frobenius kernels and complements. In Chapter 3 classes of examples are presented illustrating the concepts and results of Chapter 2. It is shown, in particular, that 2-Sylow subgroups of finite reflection groups, and of alternating groups, are totally orthogonal.
2
Segura, Bermudez Jairo Alonso [Verfasser], and Christian [Akademischer Betreuer] Franzke. "On the Empirical Orthogonal Functions representation of the ocean circulation / Jairo Alonso Segura Bermudez ; Betreuer: Christian Franzke." Hamburg : Staats- und Universitätsbibliothek Hamburg, 2020. http://d-nb.info/1214370209/34.
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Segura, Bermudez Jairo Alonso Verfasser], and Christian [Akademischer Betreuer] [Franzke. "On the Empirical Orthogonal Functions representation of the ocean circulation / Jairo Alonso Segura Bermudez ; Betreuer: Christian Franzke." Hamburg : Staats- und Universitätsbibliothek Hamburg, 2020. http://nbn-resolving.de/urn:nbn:de:gbv:18-105495.
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Dinckal, Cigdem. "Decomposition Of Elastic Constant Tensor Into Orthogonal Parts." Phd thesis, METU, 2010. http://etd.lib.metu.edu.tr/upload/12612226/index.pdf.
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All procedures in the literature for decomposing symmetric second rank (stress) tensor and symmetric fourth rank (elastic constant) tensor are elaborated and compared which have many engineering and scientific applications
for anisotropic materials. The decomposition methods for symmetric second rank tensors are orthonormal tensor basis method, complex variable representation and spectral method. For symmetric fourth rank (elastic constant)
tensor, there are four mainly decomposition methods namely as, orthonormal tensor basis, irreducible, harmonic decomposition and spectral. Those are
applied to anisotropic materials possessing various symmetry classes which are isotropic, cubic, transversely isotropic, tetragonal, trigonal and orthorhombic.
For isotropic materials, an expression for the elastic constant tensor different than the traditionally known form is given. Some misprints found in the literature are corrected.
For comparison purposes, numerical examples of each decomposition process are presented for the materials possessing different symmetry classes. Some
applications of these decomposition methods are given. Besides, norm and norm ratio concepts are introduced to measure and compare the anisotropy degree for
various materials with the same or di¤erent symmetries. For these materials,norm and norm ratios are calculated. It is suggested that the norm of a tensor may be used as a criterion for comparing the overall e¤
ect of the properties of anisotropic materials and the norm ratios may be used as a criterion to represent the anisotropy degree of the properties of materials. Finally, comparison of all methods are done in order to determine similarities and differences between them. As a result of this comparison process, it is proposed that the spectral method is a non-linear decomposition method which yields non-linear orthogonal decomposed parts. For symmetric second rank and fourth rank tensors, this case is a significant innovation in decomposition procedures in the literature.
5
Hagemann, Willem [Verfasser], and Christoph [Akademischer Betreuer] Weidenbach. "Symbolic orthogonal projections : a new polyhedral representation for reachability analysis of hybrid systems / Willem Hagemann. Betreuer: Christoph Weidenbach." Saarbrücken : Saarländische Universitäts- und Landesbibliothek, 2015. http://d-nb.info/107952388X/34.
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Smaïli, Nasser-Eddine. "Les polynômes e-semi-classiques de classe zéro." Paris 6, 1987. http://www.theses.fr/1987PA066081.
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Boutahar, Jaouad. "Méthodes de réduction et de propagation d'incertitudes : application à un mùodèle de Chimie-Transport pour la modélisation et la stimulation des impacts." Marne-la-vallée, ENPC, 2004. https://pastel.archives-ouvertes.fr/tel-00007557.
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Dans une modélisation intégrée des impacts, l'objectif est de tester plusieurs scénarios d'entrées de modèle et/ ou d'identifier l'effet de l'incertitude des entrées sur les sorties de modèle. Dans les deux cas, un grand nombre de simulations de modèle sont nécessaires. Cela reste bien évidemment infaisable avec un modèle de Chimie-Transport à cause du temps CPU demandé. Pour surmonter cette difficulté, deux approches ont été étudiées dans cette thèse. La première consiste à construire un modèle réduit. Deux techniques ont été utilisées : la première est la méthode POD (Proper Orthogonal Decomposition) liée au comportement statistique du système. La seconde méthode est une méthode efficace de prétabulation fondée sur la troncature d'un développement multivariables de la relation Entrées/ sorties associé au modèle. La seconde est relative à la réduction du nombre de simulations demandé par la méthode Monte-Carlo classique de propagation d'incertitude. La technique utilisée ici est basée sur une représentation d'une sortie de modèle incertaine comme un développement de polynômes orthonormaux de variables d'entrées. Un autre point clé dans la modélisation intégrée d'impacts est de développer des stratégies de réduction des émissions en calculant des matrices de transfert sur plusieurs années de simulation. Une méthode efficace de calcul de ces matrices a été ainsi développée, notamment en définissant des scénarios "chimiquement" représentatifs. L'ensemble de ces méthodes a été appliqué au modèle POLAIR3D, modèle de Chimie-Transport développé dans le cadre de cette thèse
8
Martínez, Bayona Jonàs. "Skeletal representations of orthogonal shapes." Doctoral thesis, Universitat Politècnica de Catalunya, 2013. http://hdl.handle.net/10803/134699.
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Skeletal representations are important shape descriptors which encode topological and geometrical properties of shapes and reduce their dimension. Skeletons are used in several fields of science and attract the attention of many researchers. In the biocad field, the analysis of structural properties such as porosity of biomaterials requires the previous computation of a skeleton. As the size of three-dimensional images become larger, efficient and robust algorithms that extract simple skeletal structures are required. The most popular and prominent skeletal representation is the medial axis, defined as the shape points which have at least two closest points on the shape boundary. Unfortunately, the medial axis is highly sensitive to noise and perturbations of the shape boundary. That is, a small change of the shape boundary may involve a considerable change of its medial axis. Moreover, the exact computation of the medial axis is only possible for a few classes of shapes. For example, the medial axis of polyhedra is composed of non planar surfaces, and its accurate and robust computation is difficult. These problems led to the emergence of approximate medial axis representations. There exists two main approximation methods: the shape is approximated with another shape class or the Euclidean metric is approximated with another metric.
The main contribution of this thesis is the combination of a specific shape and metric simplification. The input shape is approximated with an orthogonal shape, which are polygons or polyhedra enclosed by axis-aligned edges or faces, respectively. In the same vein, the Euclidean metric is replaced by the L infinity or Chebyshev metric. Despite the simpler structure of orthogonal shapes, there are few works on skeletal representations applied to orthogonal shapes. Much of the efforts have been devoted to binary images and volumes, which are a subset of orthogonal shapes. Two new skeletal representations based on this paradigm are introduced: the cube skeleton and the scale cube skeleton. The cube skeleton is shown to be composed of straight line segments or planar faces and to be homotopical equivalent to the input shape. The scale cube skeleton is based upon the cube skeleton, and introduces a family of skeletons that are more stable to shape noise and perturbations. In addition, the necessary algorithms to compute the cube skeleton of polygons and polyhedra and the scale cube skeleton of polygons are presented. Several experimental results confirm the efficiency, robustness and practical use of all the presented methods.
9
Braun, Oliver Verfasser], Gabriele [Akademischer Betreuer] [Nebe, and Gerhard [Akademischer Betreuer] Hiß. "Orthogonal representations of finite groups / Oliver Braun ; Gabriele Nebe, Gerhard Hiß." Aachen : Universitätsbibliothek der RWTH Aachen, 2016. http://d-nb.info/1130352382/34.
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Braun, Oliver [Verfasser], Gabriele [Akademischer Betreuer] Nebe, and Gerhard [Akademischer Betreuer] Hiß. "Orthogonal representations of finite groups / Oliver Braun ; Gabriele Nebe, Gerhard Hiß." Aachen : Universitätsbibliothek der RWTH Aachen, 2016. http://d-nb.info/1130352382/34.
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Evseeva, Elena. "Représentations du groupe pseudo-orthogonal dans les espaces des formes différentielles homogènes." Thesis, Reims, 2016. http://www.theses.fr/2016REIMS035/document.
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Dans cette thèse nous étudions des représentations du groupe de Lorentz dans les sections du fibré cotangent sur le cône isotrope. Grâce aux transformations de Fourier et de Poisson nous construisons explicitement tous les opérateurs de brisure de symétrie qui apparaissent dans les lois de branchement des produits tensoriels de telles représentationsIn this thesis we study representations of the Lorentz group acting on sectionsof the cotangent bundle over the isotropic cone. Using Fourier and Poisson transforms we construct explicitly all the symmetry breaking operators that appear in branching laws of tensor products of such representations
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Schulte, Michael [Verfasser], and Michael [Akademischer Betreuer] Dettweiler. "Galois representations of orthogonal rigid local systems / Michael Schulte. Betreuer: Michael Dettweiler." Bayreuth : Universität Bayreuth, 2012. http://d-nb.info/1059413094/34.
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Dieng, Momar. "Distribution functions for edge eigenvalues in orthogonal and symplectic ensembles : Painlevé representations /." For electronic version search Digital dissertations database. Restricted to UC campuses. Access is free to UC campus dissertations, 2005. http://uclibs.org/PID/11984.
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ISAIA, JEROME. "Espaces de modules de representations de carquois avec involution munies d'une forme orthogonale ou symplectique." Nice, 1999. http://www.theses.fr/1999NICE5346.
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Le travail expose prolonge celui realise par king sur les representations de carquois, notre but etant d'obtenir un moyen de modeliser dans le langage des representations de carquois l'action de groupes orthogonaux ou symplectiques sur des varietes algebriques. Nous introduisons une notion de representations de carquois avec involution et relations munies d'une forme orthogonale ou symplectique. Nous construisons des espaces de modules pour ce probleme et caracterisons de maniere algebrique les notions issues de la theorie geometrique des invariants : semi-stabilite, stabilite, orbites fermees. Nous etudions les proprietes de ces espaces de modules (projectivite, existence de familles universelles, lissite, modele local) et obtenons des resultats classiques proche de ceux de sorger. Desireux de mettre en exergue l'interet et l'utilite des representations de carquois en geometrie algebrique, nous montrons leur capacite a modeliser des actions de groupes orthogonaux ou symplectiques sur des produits de grassmaniennes ou de varietes de drapeaux, nous construisons des espaces de modules de faisceaux semi-stables (-semi-stables) sur p 2 et nous donnons une interpretation, en termes de representations de carquois, de la compactification des classes de jauge equivalence construite par li et homeomorphe a la compactification d'uhlenbeck.
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Zaghlool, Baher SalahElDeen Othman Ahmed. "Behaviour of three-dimensional concrete structures under concurrent orthogonal seismic excitations." Thesis, University of Canterbury. Civil Engineering, 2007. http://hdl.handle.net/10092/1177.
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This thesis is a study into the response and seismic safety of three-dimensional multi-storey concrete structures under concurrent orthogonal seismic excitations. It employs the nonlinear time-history method as its analysis tools. Time-history analyses rely heavily on their utilised earthquake records. Accordingly, this study examines the different approaches of selecting earthquake suites and develops a methodology of selecting representative earthquake scenarios. This methodology is credibly implemented in selecting a far- and a near field suites representative of the New Zealand seismic hazard. The study investigates the response of 6-, 9- and 12-storey concrete structures of different n-X-bays × m-Y-bays. Bidirectional responses of these considered structures are examined and consequently the current combination rules are scrutinised. Consequently this study strongly recommends the use of the 40-percent combination rule in lieu of the widely used 30-percent rule; and the use of time-history analysis in lieu of quasi/equivalent static and response modal analysis methods to avoid their strong dependence on combination rules. An intensive study is conducted employing the incremental dynamic analysis (IDA) technique to investigate structural demands of interstorey drifts, lateral storey drifts and storey accelerations. The study utilises the developed far-field suite and identifies the 50th and 90th percentile demands. Hence it provides easy-to-use expressions to facilitate rapid calculation of the structural demands and the effects of biaxial interactions. An implementation into the Demand and Capacity Factor Design (DCFD) format is presented that infers confidence in the performance levels of the considered structures. The study also draws attention to the importance of considering storey accelerations as their storey values reach as high as 10 × PGA. A sensitivity study is conducted by repeating the IDA investigation while using the developed near-field suite. Subsequently a comparison between the near- and the far-field results is conducted. The results were markedly similar albeit of less magnitudes until the (seismic hazard) intensity measure IM = Sa(T₁) = 0.4g when the near-field results show sudden flat large increase in demands suggesting a brittle collapse. This is attributed to the higher content of the higher mode frequencies contained in near-field ground motions. Finally, the study examines the (vectorial) radial horizontal shear demands in columns and beam-column joints of the previous far- and near-field studies. The combined radial shear demands in corner, edge and internal columns and joints are evaluated that roughly show a square-root proportional relationship with IM that exhibit somewhat brittle failure at IM ≥ 0.35g. Shears demands in the (4-way) internal columns and the (2-way) corner joints show highest magnitude in their respective class. The results suggest transverse joint shear reinforcement of 1.5, 1.0 and 0.5 of the longitudinal reinforcement of the neighbouring beam respectively for corner, edge and internal joints. An implementation of a proposed practical (and simpler) DCFD format shows satisfactory confidence in columns performance in shear up to IM = 0.35g, conversely to joints unsatisfactory performance in shear at the onset of inelastic behaviour (IM > 0.05g).
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Saturnino, Artur Bicalho. "Curvatura extrínseca de órbitas de representações." Universidade de São Paulo, 2017. http://www.teses.usp.br/teses/disponiveis/45/45131/tde-05122017-104145/.
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Seja K um grupo de Lie compacto agindo na esfera unitária Sⁿ por isometrias. Mostramos como uma cota superior para as curvaturas principais de uma órbita dessa ação pode ser usada (mas não é suficiente) para encontrar uma cota inferior para o diâmetro do espaço de órbitas Sⁿ/K. Em seguida mostramos que existe uma órbita Kp com curvaturas principais majoradas por 4√ 14.Let K be a compact Lie group acting on the unit sphere Sⁿ by isometries. We show how an upper bound on the principal curvatures of one orbit can be used (but is not sufficient) to obtain a lower bound for the diameter of the orbit space Sⁿ/K. Then we show that there is an orbit Kp with principal curvatures bounded from above by 4√ 14.
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Abdesselam, Boucif. "Representations d'algebres et des super-algebres pour les racines de l'unite, relations dans le centre, algebre de hecke, symetries orthogonales, algebres non-lineaires." Paris 11, 1996. http://www.theses.fr/1996PA112102.
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Cette these est consacree a l'etude des groupes quantiques. Ces nouvelles structures apparaissent naturellement dans les modeles integrables et dans les theories des champs conformes. Dans partie i, nous introduisons le formalisme de la partie fractionnaire qui permet d'unifier la description des representations irreductibles de dimension finie pour q generique, et pour q racine de l'unite. Nous demontrons que l'application de ce formalisme a la representation de gelfand-zetlin de u#q(sl(n)) permet de decrire la totalite des representations existantes. Dans la partie ii, nous classifions les representations irreductibles de dimension finie du groupe quantique u#q(sl(2|1)). Nous discutons la notion d'ensemble complet de representations pour etablir les relations dans le centre de u#q(sl(2|1)). Nous demontrons dans la partie iii que les invariants fondamentaux de h#n(q) et u#q(sl(n)) caracterisent les representations irreductibles de dimension finie (propriete de memoire), et nous developpons un nouvel algorithme pour extraire les caracteres des representations irreductibles de dimension finie de h#n(q) base sur cette propriete de l'invariant fondamental et sur la notion d'operateur de murphy. Nous discutons dans la partie iv la construction des representations irreductibles de dimension finie du groupe quantique u#q(so(5)), et nous introduisons la notion de deformation non-minimale. Nous utilisons la propriete de memoire du casimir quadratique de u#q(so(5)) et la notion de contraction des representations pour demontrer la dependance du spin et la masse dans le groupe euclidien u#q(e(4)) et le groupe de poincare quantique u#q(p#4). Finalement dans la partie v, nous etudions la realisation de l'algebre de lie sl(2) non-lineaire en fonction des generateurs de sl(2) habituels et les possibilites d'y definir une structure de hopf. Nous classifions les representations irreductibles de l'algebre sl(2) non-lineaire en deux types, la deuxieme est specifique a la deformation non-lineaire
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Lachaussée, Guillaume. "Autour de l'énumération des représentations automorphes cuspidales algébriques de GLₙ sur Q en conducteur > 1." Thesis, université Paris-Saclay, 2020. http://www.theses.fr/2020UPASM018.
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Les représentations automorphes cuspidales du groupe linéaire sur le corps des rationnels sont, en un certain sens, "les objets finaux" de la théorie des formes automorphes. On s’intéresse ici à une sous-classe, celle des représentations algébriques. La complexité d'une telle représentation est mesurée par deux entiers, son poids motivique w et son conducteur N. Il est alors naturel d'essayer d’établir une liste de représentations automorphes cuspidales algébriques de petit conducteur et de petit poids. Chenevier et ses coauteurs ont réussi à établir une telle liste en poids motivique inférieur à 23 et en conducteur N=1. Le cas suivant à considérer est celui du conducteur N=p, où p est un nombre premier. Le premier résultat principal de cette thèse est une liste explicite de toutes les représentations de ce type, en poids motivique inférieur à 17 et en conducteur N=2 (il y en a 10). Sous l'hypothèse supplémentaire d'autodualité, le résultat peut être étendu jusqu'au poids motivique 19. On obtient des résultats similaires pour des conducteurs premiers jusqu’à 17 (la borne de poids diminuant à mesure que le conducteur augmente). Ces listes exhaustives de représentations automorphes sont obtenues en deux étapes : il faut trouver "l'empreinte" des représentations en question puis prouver que la liste ainsi obtenue est complète. Pour la première étape, nous utilisons la théorie d'Arthur, qui permet de construire de nombreuses représentations pertinentes à partir de formes modulaires classiques : l'objet classique conduit à une représentation d'un groupe orthogonal ou symplectique, qui peut ensuite être transférée à un groupe linéaire général. Pour la deuxième étape, nous utilisons une méthode analytique à savoir la formule explicite de Riemann-Weil-Mestre. Pour les petits poids et petits conducteurs, la limite inférieure fournie par la méthode constructive coïncide avec la limite supérieure fournie par la formule explicite, et on obtient ainsi une liste exhaustive des représentations automorphes. Le transfert qui nous intéresse ici, selon la théorie d'Arthur, est celui des groupes orthogonaux déployés SO₂ₙ₊₁ vers GL₂ₙ. Puisque le but est de construire des représentations de GL₂ₙ de conducteur premier, il s’agit de comprendre les représentations de SO₂ₙ₊₁ de conducteur premier. C'est là qu'intervient la partie locale de la thèse. Nous sommes en mesure de classifier les représentations irréductibles, admissibles et tempérées de SO₂ₙ₊₁(F) de conducteur premier, où F est un corps p-adique. Nous sommes en outre capable de caractériser de telles représentations selon une conjecture de Gross (qui est donc prouvée dans le cas donné). Cela constitue le deuxième résultat principal de cette thèseThe cuspidal automorphic representations of the linear group over the rationals are, in a certain sense, "the final objects" in the theory of automorphic forms. Among these, a distinguished subclass are the algebraic representations. The complexity of such a representation is measured by two numbers, its motivic weight w and its conductor N. It is then natural to try to make lists of automorphic algebraic representations with small conductor and small weight. Chenevier and his coauthors succeeded in making such lists for motivic weight up to 23 and conductor N=1. The next logical case to consider is that of conductor N=p, a single prime. The first main result of this thesis is an explicit list of all such representations with motivic weight up to 17 and conductor N=2; there are 10 of them. This result can be extended under the additional hypothesis of self-duality up to motivic weight 19. There are similar results for prime conductor up to 17 (in which the weight bound becomes lower as the conductor becomes higher). Making exhaustive lists of automorphic representations (up to a certain motivic weight and conductor) involves two steps: firstly find the "footprints" of the representations in question; secondly, prove that the list is complete. For the first step, we use the theory of Arthur, which allows for the construction of many relevant representations from classical modular forms. (First the classical object leads to a representation of an orthogonal or symplectic group, which can then be transferred to a general linear group.) For the second step, we use an analytic method known as the explicit formula of Riemann-Weil-Mestre. For small weight and conductor, the lower bound provided by the constructive method coincides with the upper bound provided by the explicit formula, and hence one has obtained a complete list of automorphic representations. Along Arthur's theory, the relevant transfer for this thesis is that of split orthogonal groups SO₂ₙ₊₁ to GL₂ₙ. Since the goal is to construct representations of GL₂ₙ with prime conductor, a precise understanding of the representations of SO₂ₙ₊₁ with prime conductor is required. This is where the local part of the thesis comes in. We are able to classify the irreducible, admissible, tempered representations of SO₂ₙ₊₁(F) of prime conductor, where F is a p-adic field. We are furthermore able to characterize such representations according to a conjecture of Gross (which is then proven in the given case). This is the second main result of this thesis
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Boutahar, Jaouad. "Méthodes de réduction et de propagation d'incertitudes : application à un modèle de chimie-transport pour la modélisation et la simulation des impacts." Phd thesis, Ecole des Ponts ParisTech, 2004. http://tel.archives-ouvertes.fr/tel-00007557.
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Dans une modélisation intégrée des impacts, l'objectif est de tester plusieurs scénarios d'entrées de modèle et/ ou d'identifier l'effet de l'incertitude des entrées sur les sorties de modèle. Dans les deux cas, un grand nombre de simulations de modèle sont nécessaires. Cela reste bien évidemment infaisable avec un modèle de Chimie-Transport à cause du temps CPU demandé. Pour surmonter cette difficulté, deux approches ont été étudiées dans cette thèse : La première consiste à construire un modèle réduit. Deux techniques ont été utilisées : la première est la méthode POD (Proper Orthogonal Decomposition) liée au comportement statistique du système. La seconde méthode est une méthode efficace de prétabulation fondée sur la troncature d'un développement multivariables de la relation Entrées/ sorties associé au modèle.La seconde est relative à la réduction du nombre de simulations demandé par la méthode Monte-Carlo classique de propagation d'incertitude. La technique utilisée ici est basée sur une représentation d'une sortie de modèle incertaine comme un développement de polynômes orthonormaux de variables d'entrées. Un autre point clé dans la modélisation intégrée d'impacts est de développer des stratégies de réduction des émissions en calculant des matrices de transfert sur plusieurs années de simulation. Une méthode efficace de calcul de ces matrices a été ainsi développée, notamment en définissant des scénarios "chimiquement" représentatifs.
L'ensemble de ces méthodes a été appliqué au modèle POLAIR3D, modèle de Chimie-Transport développé dans le cadre de cette thèse.
20
Su, Kuo-Jui, and 蘇國瑞. "Image Retrieval Using Orthogonal Wavelet Representation." Thesis, 2004. http://ndltd.ncl.edu.tw/handle/58289452018669766252.
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碩士國立中正大學
資訊工程研究所
92
Multimedia database systems are becoming increasingly important with the advent of broadband networks, high-power PC’s, audio/video compression standards, and many applications, such as digital libraries and trademark and copyright databases. In this study, an image retrieval system using orthogonal wavelet representation is proposed. In the proposed system, a color image is represented in the RGB color coordinate system so that three component images can be extracted from the color image. Based on the frequency coefficients, each component image is segmented into 10 bands, i.e., one low frequency band and nine high frequency bands, by 3-level orthogonal wavelet representation first, and the coefficients of the low frequency band are extracted as the image feature and the coefficients of the nine high frequency bands are extracted as the image texture features. In the image retrieval stage, the distance measure between a query image and a target image in the image database system will be the weighted sum of squared errors of two sets of coefficients of the image texture features extracted from nine high frequency bands. To obtain the better retrieval precision, different high frequency coefficients with different importances in orthogonal wavelet representation will receive different weights. Based on the experimental results obtained in this study, the performance of the proposed system is better than that of two comparison systems. This shows the feasibility of the proposed system.
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HONG, RUI-CUN, and 洪瑞村. "Application of orthogonal polynomials with tensor representation to optimal control systems." Thesis, 1991. http://ndltd.ncl.edu.tw/handle/55932559922458755632.
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Weniger, Edward L. "Tropical cyclone intensity prediction based on empirical orthogonal function representation of wind and shear fields." Thesis, 1987. http://hdl.handle.net/10945/22562.
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Penk, Tomáš. "Integrální reprezentace operátorových algeber." Master's thesis, 2013. http://www.nusl.cz/ntk/nusl-321357.
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By a representation of a C*-algebra A on a Hilbert space H we mean a morphism : A → L(H). After summing up neccessary knowledge from the theory of Banach and Hilbert spaces and C*-al- gebras we show that for every C*-algebra a representation exists. We describe its structure detiledly and we focus on examining cyclic representations. We find out that cyclic representations relate to the state space. Because every state can be expressed as an integral with respect to an appropriate measure on the states, in is possible to assign a measure on the state space to each cyclic represen- tation. Therefore, we investigate connexion of a representation with this measure as same as with the corresponding state. This leads us to the definition of an orthogonal measure. We find out that its properties relate with certain subalgebras of L(H). At the end we show that for a separable C*-algebra it is possible to express a representation fulfilling suitable assumptions in the form of a direct integral. 1
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Degni, Christopher Edward. "Positive orthogonal sets for Sp(4) /." 2002. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&res_dat=xri:pqdiss&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&rft_dat=xri:pqdiss:3048374.
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Берегун, Віктор Сергійович. "Дослідження щільностей імовірностей акустичних сигналів методом ортогональних подань." Doctoral thesis, 2010. https://ela.kpi.ua/handle/123456789/1066.
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Lekala, Mantile Leslie. "Dynamics of few-cluster systems." Thesis, 2004. http://hdl.handle.net/10500/1145.
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The three-body bound state problem is considered using configuration-space Faddeev equations within the framework of the total-angular-momentum representation. Different
three-body systems are considered, the main concern of the investigation being the
i) calculation of binding energies for weakly bounded trimers, ii) handling of systems
with a plethora of states, iii) importance of three-body forces in trimers, and iv) the
development of a numerical technique for reliably handling three-dimensional integrodifferential
equations. In this respect we considered the three-body nuclear problem, the
4He trimer, and the Ozone (16 0 3 3) system.
In practice, we solve the three-dimensional equations using the orthogonal collocation
method with triquintic Hermite splines. The resulting eigenvalue equation is handled
using the explicitly Restarted Arnoldi Method in conjunction with the Chebyshev polynomials to improve convergence. To further facilitate convergence, the grid knots are distributed quadratically, such that there are more grid points in regions where the potential is stronger. The so-called tensor-trick technique is also employed to handle
the large matrices involved. The computation of the many and dense states for the Ozone case is best implemented using the global minimization program PANMIN based
on the well known MERLIN optimization program. Stable results comparable to those of other methods were obtained for both nucleonic and molecular systems considered.Physics
D.Phil. (Physics)