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1
Fretwell, Paul. "Equivalence transformations in linear systems theory." Thesis, Loughborough University, 1986. https://dspace.lboro.ac.uk/2134/33259.
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There is growing interest in infinite frequency structure of linear systems, and transformations preserving this type of structure. Most work has been centred around Generalised State Space (GSS) systems. Two constant equivalence transformations for such systems are Rosenbrock's Restricted System Equivalence (RSE) and Verghese's Strong Equivalence (str.eq.). Both preserve finite and infinite frequency system structure. RSE is over restrictive in that it is constrained to act between systems of the same dimension. While overcoming this basic difficulty str.eq. on the other hand has no closed form description. In this work all these difficulties have been overcome. A constant pencil transformation termed Complete Equivalence (CE) is proposed, this preserves finite elementary divisors and non-unity infinite elementary divisors. Applied to GSS systems CE yields Complete System Equivalence (CSE) which is shown to be a closed form description of str.eq. and is more general than RSE as it relates systems of different dimensions. Equivalence can be described in terms of mappings of the solution sets of the describing differential equations together with mappings of the constrained initial conditions. This provides a conceptually pleasing definition of equivalence. The new equivalence is termed Fundamental Equivalence (FE) and CSE is shown to be a matrix characterisation of it. A polynomial system matrix transformation termed Full Equivalence (fll.e.) is proposed. This relates general matrix polynomials of different dimensions while preserving finite and infinite frequency structure. A definition of infinite zeros is also proposed along with a generalisation of the concept of infinite elementary divisors (IED) from matrix pencils to general polynomial matrices. The IED provide an additional method of dealing with infinite zeros.
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Leggetter, Christopher John. "Improved acoustic modelling for HMMs using linear transformations." Thesis, University of Cambridge, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.361709.
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Manolescu, Crina Iulia. "Lyapunov transformations and control." Thesis, Imperial College London, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.266339.
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Langworthy, Alan Marcel. "A study of some groups of projective transformations." Thesis, University of Oxford, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.365543.
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Kumar, Indra E. "Graphical Applications of Complex and Quaternionic Fractional Linear Transformations." Scholarship @ Claremont, 2016. http://scholarship.claremont.edu/scripps_theses/888.
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The geometric properties of the complex numbers and the quaternions, particularly their behavior under fractional linear transformations, make them very useful for modeling certain types of geometric objects. In this thesis, we will connect the characteristics of fractional linear transformations of both the complex numbers and quaternions to the problem of developing and modifying discrete surfaces for problems in computer graphics and engineering.
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Kinde, Haragewen Abraham. "Contraction and fixed point behavior of certain linear fractional transformations." CSUSB ScholarWorks, 1992. https://scholarworks.lib.csusb.edu/etd-project/1049.
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McInerney, Simon J. "Representations and transformations for multi-dimensional systems." Thesis, Loughborough University, 1999. https://dspace.lboro.ac.uk/2134/28237.
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Multi-dimensional (n-D) systems can be described by matrices whose elements are polynomial in more than one indeterminate. These systems arise in the study of partial differential equations and delay differential equations for example, and have attracted great interest over recent years. Many of the available results have been developed by generalising the corresponding results from the well known 1-D theory. However, this is not always the best approach since there are many differences between 1-D, 2-D and n-D (n > 2) polynomial matrices. This is due mainly to the underlying polynomial ring structure.
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Hansson, Jörgen. "Using Linear Fractional Transformations for Clearance of Flight Control Laws." Thesis, Linköping University, Department of Electrical Engineering, 2003. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-2041.
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Flight Control Systems are often designed in linearization points over a flight envelope and it must be proven to clearance authorities that the system works for different parameter variations and failures all over this envelope.
In this thesis µ-analysis is tried as a complement for linear analysis in the frequency plane. Using this method stability can be guaranteed for all static parameter combinations modelled and linear criteria such as phase and gain margins and most unstable eigenvalue can be included in the analysis. A way of including bounds on the parameter variations using parameter dependent Lyapunov functions is also tried.
To perform µ-analysis the system must be described as a Linear Fractional Transformation (LFT). This is a way of reformulating a parameter dependent system description as an interconnection of a nominal linear time invariant system and a structured parameter block.
A linear and a rational approximation of the system are used to make LFTs. These methods are compared. Four algorithms for calculation of the upper and lower bounds of µ are evaluated. The methods are tried on VEGAS, a SAAB research aircraft model.
µ-analysis works quite well for linear clearance. The rational approximation LFT gives best results and can be cleared for the criteria mentioned above. A combination of the algorithms is used for best results. When the Lyapunov based method is used the size of the problem grows quite fast and, due to numerical problems, stability can only be guaranteed for a reduced model.
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Güldenring, Daniel. "Theory and applications of linear lead transformations in computerised electrocardiology." Thesis, University of Ulster, 2013. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.603537.
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An electrocardiogram (ECG) can be used for the identification of different heart diseases. Linear lead transformations (LLTs) allow for the estimation of unrecorded ECG leads through linear combinations of a number of recorded ECG leads. This estimation relies upon statistical inter-lead correlations. Reduced lead systems (RLSs) commonly utilise LLTs for the estimation of the full 12-lead ECG from a reduced number of recorded ECG leads. The RLS used within this thesis utilised the recorded basis leads I, II, V2 and V5 for the estimation of the unrecorded target leads VI, V3, V 4 and V6. An assessment of whether the utilisation of statistical short-term autocorrelations, in addition to the commonly used inter-lead correlations, can improve the estimation performance (EP) of the above RLS has been conducted. The utilisation of statistical short-term autocorrelations was found not to improve the EP during episodes of acute myocardial ischemia (AMI). The effect of AMI on the EP of the aforementioned RLS has been investigated. It was found that AMI can reduce the EP. The inability of LLTs to fully describe the electrical volume conductor properties of the human trunk was found to be the likely source for the reduction in the EP. The EP achieved by the above RLS, has been assessed during episodes of AMI. It was found that a similar EP for target leads VI and V6 was achieved regardless of whether patient-specific or generalised transformation weights were employed. An LLT that allows for the estimation of the Frank vectorcardiogram (yCG) from the Mason-Likar (ML) 12-1ead ECG was developed. The developed LL T and the Kors matrix were used for the estimation of the Frank VCG from ML 12-lead ECG data. The developed LLT was found to allow the determination of the VCG parameters 'spatial ventricular gradient' and 'spatial QRS-T angle' with higher accuracy than when using the Kors matrix.
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Guldenring, Daniel. "Theory and applications of linear lead transformations in computerised electrocardiography." Thesis, Ulster University, 2013. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.665848.
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Almohaimeed, Amani Mohammed. "Box-Cox-type transformations for linear and logistic models with random effects." Thesis, Durham University, 2018. http://etheses.dur.ac.uk/12831/.
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Random effect models have become a mainstream statistical technique over the last decades; and the same can be said for response transformation models such as the Box-Cox transformation. The latter ensures that the assumptions of normality and of homoscedasticity of the response distribution are fulfilled, which are essential conditions for the use of a linear model or a linear mixed model. However, methodology for response transformation and simultaneous inclusion of random effects has been developed and implemented only scarcely, and is so far restricted to Gaussian random effects. The first aim of this thesis is to develop such methodology, thereby not requiring parametric assumptions on the distribution of the random effects. This is achieved by extending the “Nonparametric Maximum Likelihood” towards a “Nonparametric Profile Maximum Likelihood” (NPPML) technique. The implemented techniques allow to deal with overdispersion as well as two-level data scenarios in general linear models. The second part of this thesis considers the transformation of mixed-effects logistic models, with the aim of improving model fit. In binary data, link functions other than the logit can be used to connect predictors with the response. The Box-Cox transformation is used in mixed–effects binary regression models as an alternative link function for linearization purposes. The NPPML approach is used similarly as before, with some adjustments. The proposed approach is implemented in the R package boxcoxmix. Simulation studies and applications on real data are carried out to study the performance of this approach.
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Souza, Vitor Rodrigues Braga de. "Cônicas, álgebra linear e geogebra, uma combinação que deu certo." Universidade Federal de Goiás, 2014. http://repositorio.bc.ufg.br/tede/handle/tede/4530.
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In the rst part of this work, we present all conical with their cartesian equations and their graphs. Then, we made an approach to concepts of linear algebra, vector spaces, linear transformations, eigenvalues and eigenvectors in order to build matrices of linear transformations able to rotate, translate or even make these conical shear. Constructed matrices, GeoGebra software for constructing graphs obtained by transformation matrices were used. Besides this geometric part, we discuss the quadratic forms in order to identify a conic analyzing only the coe cients of its quadratic form and the eigenvalues. The end result was an excellent visual material built from software GeoGebra applying the concepts of Linear Algebra. We can not fail to mention that the construction of the taper in GeoGebra techniques that replace the ruler, compass and the string used by the ancient Greeks were implemented.
Na primeira parte desse trabalho, apresentamos todas as cônicas com suas respectivas equações cartesianas e seus respectivos grá cos. Em seguida, zemos uma abordagem de conceitos de Álgebra Linear, espaços vetoriais, transformações lineares, autovalores e autovetores a m de, construir as matrizes de transformações lineares capazes de rotacionar, transladar ou até fazer o cisalhamento destas cônicas. Construídas as matrizes, foi utilizado o software GeoGebra para a construção dos grá cos obtidos pelas matrizes de transformação. Além dessa parte geométrica, abordamos as formas quadráticas no intuito de identi car uma cônica analisando apenas os coe cientes da sua forma quadrática e os autovalores associados. O resultado nal foi um excelente material visual construído a partir do software GeoGebra aplicando os conceitos de Álgebra Linear. Não podemos deixar de citar que foram implementadas técnicas de construção das cônicas no GeoGebra que substituem a régua, o compasso e o barbante utilizados pelos gregos antigos.
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Zhou, Yahong. "Estimation of transformation models, generalized bivariate probit models, and box-cox partially linear models : three essays in microeconomics /." View abstract or full-text, 2005. http://library.ust.hk/cgi/db/thesis.pl?ECON%202005%20ZHOU.
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Wong, Ming Lai. "Q-Fourier transform, q-Heisenberg algebra and quantum group actions /." View Abstract or Full-Text, 2003. http://library.ust.hk/cgi/db/thesis.pl?MATH%202003%20WONG.
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Boucard, Pierre-Alain. "Approche à grand incrément de temps en grandes transformations." Cachan, Ecole normale supérieure, 1996. http://www.theses.fr/1996DENS0006.
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L'étude des problèmes statiques en grandes transformations suppose la résolution d'équations non linéaires ou les non linéarités sont d'origine physique et géométrique. Les méthodes usuelles de calcul sont basées sur la méthode incrémentale en sollicitation et nécessitent l'utilisation de techniques de type Riks ou Crisfield pour franchir les points d'instabilité. L'approche utilisée dans ce travail s'en différencie sur deux points. Tout d'abord nous exploitons une reformulation matérielle du problème en grandes transformations qui, utilisant des grandeurs tournées par la rotation locale, permet d'écrire le comportement et l'équilibre dans un espace unique de représentation. La formulation ainsi obtenue est formellement très proche d'un problème de type petites perturbations. Sur cette formulation, une approche a grand incrément de temps est développée: c'est une méthode non incrémentale qui traite de façon itérative l'ensemble de l'intervalle d'étude sans hypothèse a priori et qui ne nécessite pas le recours a des méthodes de type Riks ou Crisfield lorsque celui-ci inclut un point critique. Les premiers développements donnes dans cette étude ont été menés sur les arcs plans élastiques. La reformulation matérielle en théorie des poutres et l'approche à grand incrément de temps qui lui est associée y sont détaillées. Ce cadre nous sert de banc d'essai pour mettre en évidence et résoudre les problèmes informatiques et numériques poses par cette nouvelle approche. Sur quelques exemples de la littérature traitant du calcul du post flambement, nous illustrons le fonctionnement de la méthode, et nous la comparons avec les démarches classiques. Pour ces exemples, la réponse post critique est guidée par l'introduction d'une imperfection. Le problème est résolu globalement sur tout l'intervalle d'étude, ou sur deux sous-intervalles séparés par le point critique, ne nécessitant chacun que peu d'itérations donc peu de problèmes globaux à résoudre. Cette première étude est donc une étude de faisabilité qui montre les performances de la méthode dans un cadre simplifie et permet d'envisager des extensions au cadre tridimensionnel et à des modèles de matériaux en grandes transformations
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Leung, Chi Ho. "Necessary and Sufficient Conditions on State Transformations That Preserve the Causal Structure of LTI Dynamical Networks." BYU ScholarsArchive, 2019. https://scholarsarchive.byu.edu/etd/7413.
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Linear time-invariant (LTI) dynamic networks are described by their dynamical structure function, and generally, they have many possible state space realizations. This work characterizes the necessary and sufficient conditions on a state transformation that preserves the dynamical structure function, thereby generating the entire set of realizations of a given order for a specific dynamic network.
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Tahir, Muhammad Ali Verfasser], Hermann [Akademischer Betreuer] [Ney, and Reinhold [Akademischer Betreuer] Häb-Umbach. "Discriminative training of linear transformations and mixture density splitting for speech recognition / Muhammad Ali Tahir ; Hermann Ney, Reinhold Häb-Umbach." Aachen : Universitätsbibliothek der RWTH Aachen, 2015. http://d-nb.info/113065950X/34.
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Tahir, Muhammad Ali [Verfasser], Hermann [Akademischer Betreuer] Ney, and Reinhold [Akademischer Betreuer] Häb-Umbach. "Discriminative training of linear transformations and mixture density splitting for speech recognition / Muhammad Ali Tahir ; Hermann Ney, Reinhold Häb-Umbach." Aachen : Universitätsbibliothek der RWTH Aachen, 2015. http://d-nb.info/113065950X/34.
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Grande, André Lúcio. "O conceito de independência e dependência linear e os registros de representação semiótica nos livros didáticos de Álgebra Linear." Pontifícia Universidade Católica de São Paulo, 2006. https://tede2.pucsp.br/handle/handle/11123.
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Previous issue date: 2006-08-14Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
This research aims to investigate which semiotic representation registers are most used in Linear Algebra textbooks in the presentation and study of the topic linear independence. The mathematics textbook is a resource much used by the teachers in its work. They present many representation registers, which can to be analyzed qualitatively to assess their potential contribution to the teaching-learning process. To this end, five Linear Algebra textbooks were selected for an analysis which involved the diagnosis of the representation registers used in the definition of linear independence, as well as the examples and exercises proposed for its study. The theory used in the analysis of these textbooks was Raymond Duval´s theory of Registers of Semiotic Representation, which highlights the importance of changes between registers in the learning of mathematical objects. In each textbooks, the registers present were classified and analyzed, along with the possible transformations of registers as carried out in the resolution of the examples and considered exercises. As result, scarcity of the use of some registers of representation it was evidenced in the chapters that approach the slight knowledge of independence and linear dependence, as for example, the geometric one to determine if a set of vectors is linearly independent or not, and the register of the natural language, in the resolution of examples and considered exercises that involve demonstrations. The analysis also indicated a lack of attention to conversions between registers in the examples and proposed exercises of analyzed textbooks
Esta pesquisa tem como objetivo investigar nos livros didáticos de Álgebra Linear quais são os registros de representação semiótica mais utilizados no estudo das noções e atividades propostas sobre independência linear. O livro didático é um recurso muito utilizado pelos professores no seu trabalho, o qual apresenta muitos registros de representação que podem ser analisados qualitativamente para a contribuição no processo de ensino-aprendizagem. Para isso, foram selecionados cinco livros didáticos de Álgebra Linear que se diagnosticou os registros de representação utilizados na definição, exemplos e exercícios propostos a respeito de independência linear. A teoria utilizada na análise dos livros didáticos foi a dos Registros de Representação Semiótica de Raymond Duval, que destaca a importância da mudança de registros na aprendizagem dos objetos matemáticos. Em cada obra, os registros foram classificados e analisados, bem como as possíveis transformações de registros realizadas na resolução dos exemplos e exercícios propostos. Como resultado, constatou-se nos capítulos que abordam as noções de independência e dependência linear uma escassez da utilização de alguns registros de representação, como por exemplo, o geométrico para determinar se um conjunto de vetores é linearmente independente ou não, e o registro da língua natural, na resolução de exemplos e exercícios propostos que envolvem demonstrações. Além disso, verificou-se a falta de conversão de registros nas definições, exemplos e exercícios propostos dos livros didáticos analisados
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Karrer, Monica. "Articulação entre Álgebra Linear e Geometria - Um Estudo sobre as Transformações Lineares na Perspectiva dos Registros de Representação Semiótica." Pontifícia Universidade Católica de São Paulo, 2006. https://tede2.pucsp.br/handle/handle/11068.
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Previous issue date: 2006-06-08Pontificia Universidade de São Paulo
This study addressed questions related to the teaching and learning of Linear Algebra in Higher Education. More precisely, it involved the design of activities which concerned the mathematical object linear transformations and which engaged learners in exploring the conversion of registers in a dynamic geometry environment. The aim was to investigate the learning trajectories of university students and the impact of the didactical choices which characterized the teaching approach. The study was organized into two phases. In the first, preliminary studies along with theoretical considerations led to the formulation of hypotheses and to the identification of the conceptual tools to be used in the analysis of the learning trajectories. Using as a theoretical framework Duval s theory of semiotic representation registers (1995, 2000, 2003), during this phase the registers and conversions present in sections on linear transformations in both Linear Algebra and Computational Graphics textbooks were analyzed. In addition, eighty-six students of Computer Science completed a questionnaire about linear transformation. These studies highlighted difficulties in relation to the exploration of different semiotic registers on the part of the students, particularly as concerned matrixial and graphical registers. In the second phase, which employed the methodology of Design Experiments (COBB et al., 2003), activities were developed to explore the diverse representation of planar linear transformations using Cabri-Géomètre and paper&pencil environments. Six students of Computational Engineering at a private university in the city of São Paulo participated in the experiment. The results indicated evolutions in the subjects understandings of the conditions for determinating linear transformations and of the particularities of their graphs, as well as a more comprehensive mastery of diverse representations and conversions. Analysis of students trajectories also revealed how students strategies were mediated by characteristics of the tasks and the computational environment.
Este estudo trata de questões relativas ao ensino e à aprendizagem de conceitos da Álgebra Linear no ensino superior. Mais precisamente, esta pesquisa envolveu o design de atividades sobre o objeto matemático transformação linear , explorando a conversão de registros em um ambiente de geometria dinâmica. Com isso buscou-se investigar as trajetórias de aprendizagem de estudantes universitários e o impacto dessas escolhas na abordagem de ensino. O trabalho foi organizado em duas fases. Na primeira, realizaram-se estudos preliminares e desenvolvimentos teóricos para a formulação de hipóteses de trabalho e identificação de ferramentas conceituais para a análise das trajetórias. Com base na teoria dos registros de representação semiótica de DUVAL (1995, 2000, 2003), analisou-se a exploração dos registros e conversões presentes no conteúdo das transformações, tanto nos livros didáticos de Álgebra Linear quanto nos de Computação Gráfica. Ainda, aplicou-se um questionário sobre transformações lineares a oitenta e seis (86) estudantes da área de Computação. Estes estudos apontaram deficiências e dificuldades com relação à exploração de diferentes registros por parte dos estudantes, principalmente os registros matricial e gráfico. Na segunda fase, com base na metodologia de Design Experiments (COBB et al., 2003), foram concebidas atividades de exploração das diversas representações de transformações lineares planas, nos ambientes Cabri-Géomètre e papel&lápis. Seis (6) estudantes do curso de Engenharia da Computação de uma instituição particular de ensino superior da cidade de São Paulo participaram do experimento. Os resultados revelaram evoluções dos sujeitos na compreensão das condições de determinação de transformações lineares e de particularidades gráficas inerentes a estas, além de um domínio mais amplo das diversas representações e de suas conversões. Por fim, foram observados efeitos específicos nas estratégias dos estudantes relacionados às características das tarefas e do ambiente computacional.
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Djerfi, Kheireddine. "Non-linear magnetoconductivity of the two-dimensional electron fluid and solid on liquid helium." Thesis, Royal Holloway, University of London, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.325526.
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Muehlemann, Anton. "Variational models in martensitic phase transformations with applications to steels." Thesis, University of Oxford, 2016. https://ora.ox.ac.uk/objects/uuid:bb7f4ff4-0911-4dad-bb23-ada904839d73.
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This thesis concerns the mathematical modelling of phase transformations with a special emphasis on martensitic phase transformations and their application to the modelling of steels. In Chapter 1, we develop a framework that determines the optimal transformation strain between any two Bravais lattices and use it to give a rigorous proof of a conjecture by E.C. Bain in 1924 on the optimality of the so-called Bain strain. In Chapter 2, we review the Ball-James model and related concepts. We present some simplification of existing results. In Chapter 3, we pose a conjecture for the explicit form of the quasiconvex hull of the three tetragonal wells, known as the three-well problem. We present a new approach to finding inner and outer bounds. In Chapter 4, we focus on highly compatible, so called self-accommodating, martensitic structures and present new results on their fine properties such as estimates on their minimum complexity and bounds on the relative proportion of each martensitic variant in them. In Chapter 5, we investigate the contrary situation when self-accommodating microstructures do not exist. We determine, whether in this situation, it is still energetically favourable to nucleate martensite within austenite. By constructing different types of inclusions, we find that the optimal shape of an inclusion is flat and thin which is in agreement with experimental observation. In Chapter 6, we introduce a mechanism that identifies transformation strains with orientation relationships. This mechanism allows us to develop a simpler, strain-based approach to phase transformation models in steels. One novelty of this approach is the derivation of an explicit dependence of the orientation relationships on the ratio of tetragonality of the product phase. In Chapter 7, we establish a correspondence between common phenomenological models for steels and the Ball-James model. This correspondence is then used to develop a new theory for the (5 5 7) lath transformation in low-carbon steels. Compared to existing theories, this new approach requires a significantly smaller number of input parameters. Furthermore, it predicts a microstructure morphology which differs from what is conventionally believed.
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Chetty, Vasu Nephi. "Theory and Applications of Network Structure of Complex Dynamical Systems." BYU ScholarsArchive, 2017. https://scholarsarchive.byu.edu/etd/6270.
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One of the most powerful properties of mathematical systems theory is the fact that interconnecting systems yields composites that are themselves systems. This property allows for the engineering of complex systems by aggregating simpler systems into intricate patterns. We call these interconnection patterns the "structure" of the system. Similarly, this property also enables the understanding of complex systems by decomposing them into simpler parts. We likewise call the relationship between these parts the "structure" of the system. At first glance, these may appear to represent identical views of structure of a system. However, further investigation invites the question: are these two notions of structure of a system the same? This dissertation answers this question by developing a theory of dynamical structure. The work begins be distinguishing notions of structure from their associated mathematical representations, or models, of a system. Focusing on linear time invariant (LTI) systems, the key technical contributions begin by extending the definition of the dynamical structure function to all LTI systems and proving essential invariance properties as well as extending necessary and sufficient conditions for the reconstruction of the dynamical structure function from data. Given these extensions, we then develop a framework for analyzing the structures associated with different representations of the same system and use this framework to show that interconnection (or subsystem) structures are not necessarily the same as decomposition (or signal) structures. We also show necessary and sufficient conditions for the reconstruction of the interconnection (or subsystem) structure for a class of systems. In addition to theoretical contributions, this work also makes key contributions to specific applications. In particular, network reconstruction algorithms are developed that extend the applicability of existing methods to general LTI systems while improving the computational complexity. Also, a passive reconstruction method was developed that enables reconstruction without actively probing the system. Finally, the structural theory developed here is used to analyze the vulnerability of a system to simultaneous attacks (coordinated or uncoordinated), enabling a novel approach to the security of cyber-physical-human systems.
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Dressler, Bernhard. "Modélisation numérique des coques en grandes transformations : mise en oeuvre dans un environnement orienté objet." Châtenay-Malabry, Ecole centrale de Paris, 1997. http://www.theses.fr/1997ECAP0522.
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Ce mémoire est consacré à la dynamique des coques en grandes rotations. La théorie bidimensionnelle des coques est déduite du principe des travaux virtuels d'un milieu continu tridimensionnel en introduisant la cinématique de Mindlin. On obtient un système d'équations non-linéaires qui est linéarise par rapport aux déplacements de la surface moyenne ainsi que par rapport aux paramètres de rotation. La paramétrisation des grandes rotations par le vecteur de rotation est comparée à la paramétrisation directe par la matrice de rotation. En vue d'une discrétisation en éléments finis isoparamétriques on utilise des objets tensoriels intrinsèques qui sont ramenés a une configuration de référence aplatie. Cette configuration aplatie est identifiée à l'élément de référence. En dehors d'une loi de comportement hyper élastique on présente deux lois élastoplastiques en grandes transformations supposant que les déformations locales restent petites. Les efforts résultants sont obtenus ou par une intégration numérique dans l'épaisseur ou a partir d'une loi de comportement globale qui est directement formulée en efforts résultants. L’implémentation numérique est effectuée dans un environnement de programmation orientée objet qui a été développe pour l'analyse non-linéaire par la méthode des éléments finis. En particulier, on regarde le rôle des grandes rotations dans le calcul de la matrice de rigidité tangente. Des résultats numériques confirment l'efficacité de cette approche.
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Housková, Markéta. "Užití transformací v regresní analýze." Master's thesis, Vysoká škola ekonomická v Praze, 2014. http://www.nusl.cz/ntk/nusl-193579.
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This Thesis deals with the using of transformations in model of regression analysis. The first part of the Thesis summarizes the theoretical findings of the regression models, assumption of these models and the possibility of using different types of transformations in the event non-compliance of regression models. The practical part of this Thesis deals with regression analysis of real dataset on school readiness of children from the district of Kolín in 2013 and using transformations in the selected regression model.
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Silva, Eliza Souza da. "Transformações lineares em um curso de Licenciatura em Matemática: uma estratégia didática com uso de tecnologias digitais." Pontifícia Universidade Católica de São Paulo, 2015. https://tede2.pucsp.br/handle/handle/11034.
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Previous issue date: 2015-04-13Universidade do Estado do Pará
This research has as object of study the learning of linear transformations by undergraduates in mathematics and was held having as subjects eight students in a class of second year of the Licentiateship Degree in Mathematics from the State University of Pará. The theoretical framework of the investigation rests on the theory of didactic situations, used in order to produce a didactic sequence to investigate how Mathematics Degree students are able to solve conceptual problems related to the topic "linear transformations" in the context of didactic situations using digital technologies. The employed activities are based on a didactic situation architected in order to give to subjects conditions to develop, with autonomy, their own strategies, counting with the computer program GeoGebra 5 as mediating element. The theoretical review pointed to the existence of difficulties on the part of college students in learning linear algebra contents, which were confirmed in this study. The research results showed also that the development of activities based on the conceptual framework presented through a didactic sequence properly planned and with mediation by digital technologies can help students develop autonomy in learning and considerable cognitive gains, despite remaining difficulties related to the conceptual construction
Esta pesquisa tem como objeto de estudo a aprendizagem das transformações lineares por licenciandos em Matemática e foi realizada tendo como sujeitos oito alunos de uma turma do segundo ano do curso de Licenciatura em Matemática da Universidade Estadual do Pará. O referencial teórico da investigação repousa sobre a teoria das situações didáticas, utilizada com o intuito de produzir uma sequência didática com o propósito de investigar de que forma estudantes de Licenciatura em Matemática resolvem problemas conceituais em relação ao tema transformações lineares no âmbito de situações didáticas e com o uso de tecnologias digitais. As atividades empregadas têm por base uma situação didática arquitetada para dar aos sujeitos condições de desenvolverem, com autonomia, suas próprias estratégias, contando, para este fim, com o uso do programa computacional GeoGebra 5 como elemento mediador. A revisão bibliográfica realizada apontou para a existência de dificuldades, por parte dos estudantes universitários, na aprendizagem de conteúdos de álgebra linear, as quais foram confirmadas ao longo deste estudo. Os resultados da pesquisa apontaram, também, que o desenvolvimento de atividades baseadas nos pressupostos teóricos apresentados, por meio de uma sequência didática adequadamente planejada e com mediação por tecnologias digitais pode auxiliar os estudantes a desenvolver autonomia na aprendizagem e ganhos cognitivos consideráveis, ainda que permaneçam dificuldades relacionadas à construção conceitual
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Adams, Lynn I. "Classifying Triply-Invariant Subspaces." University of Akron / OhioLINK, 2007. http://rave.ohiolink.edu/etdc/view?acc_num=akron1185565121.
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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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Ramos, Marco Aurélio David. "Transformações lineares, autovalores e autovetores." Universidade Federal de Goiás, 2013. http://repositorio.bc.ufg.br/tede/handle/tede/3505.
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In this thesis we study linear transformations, eigenvalues and eigenvectors with the objective of solve a system of linear ordinary differential equations with constant coefficients.
Nesta dissertação estudamos transformações lineares, autovalores e autovetores com o intuito de resolvermos um sistema de equações diferenciais ordinárias lineares com coeficientes constantes.
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Lainé, Christian. "Étude numérique et expérimentale du comportement mécanique de plaques et coques sandwich : développement d'un élément non-linéaire, grandes transformations et application au flambement de plaques raidies en construction navale." Université Joseph Fourier (Grenoble ; 1971-2015), 1998. http://www.theses.fr/1998GRE10037.
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Cette etude s'interesse au comportement mecanique des structures en materiaux composites epais, utilisees en construction navale (monolithiques epais et sandwichs). Une attention particuliere est apportee au comportement en flambement. La premiere etape consiste a identifier les caracteristiques materiaux. Des essais permettant de determiner la contrainte de compression, les modules de cisaillement transverse ainsi que le comportement non-lineaires sont examines. Une procedure de caracterisation en vue du calcul est proposee. La seconde etape aboutit au developpement de deux elements coques, non lineaires, grands deplacements et grandes deformations. Le champs de cisaillement transverse est decrit soit par une formulation variationnelle, soit par une evolution quadratique dans l'epaisseur. Une ecriture de la loi de comportement en reperage materiel est proposee. Lors de la troisieme etape deux essais sont proposes : plaque sous pression hydrostatique pour la validation du logiciel, flambement de plaques raidies par cisaillement afin de mettre au point une procedure de calcul.
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Ziegler, Rudolph F. "Character animation using transformation based linear dynamics." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape11/PQDD_0022/MQ51590.pdf.
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Shah, Aditya Arunkumar. "Combining mathematical programming and SysML for component sizing as applied to hydraulic systems." Thesis, Georgia Institute of Technology, 2010. http://hdl.handle.net/1853/33890.
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In this research, the focus is on improving a designer's capability to determine near-optimal sizes of components for a given system architecture. Component sizing is a hard problem to solve because of the presence of competing objectives, requirements from multiple disciplines, and the need for finding a solution quickly for the architecture being considered. In current approaches, designers rely on heuristics and iterate over the multiple objectives and requirements until a satisfactory solution is found. To improve on this state of practice, this research introduces advances in the following two areas: a.) Formulating a component sizing problem in a manner that is convenient to designers and b.) Solving the component sizing problem in an efficient manner so that all of the imposed requirements are satisfied simultaneously and the solution obtained is mathematically optimal.
In particular, an acausal, algebraic, equation-based, declarative modeling approach is taken to solve component sizing problems efficiently. This is because global optimization algorithms exist for algebraic models and the computation time is considerably less as compared to the optimization of dynamic simulations. In this thesis, the mathematical programming language known as GAMS (General Algebraic Modeling System) and its associated global optimization solvers are used to solve component sizing problems efficiently.
Mathematical programming languages such as GAMS are not convenient for formulating component sizing problems and therefore the Systems Modeling Language developed by the Object Management Group (OMG SysML ) is used to formally capture and organize models related to component sizing into libraries that can be reused to compose new models quickly by connecting them together. Model-transformations are then used to generate low-level mathematical programming models in GAMS that can be solved using commercial off-the-shelf solvers such as BARON (Branch and Reduce Optimization Navigator) to determine the component sizes that satisfy the requirements and objectives imposed on the system. This framework is illustrated by applying it to an example application for sizing a hydraulic log splitter.
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Ye, Hui. "Voice morphing using a sinusoidal model and linear transformation." Thesis, University of Cambridge, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.615315.
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Perkins, Jonathan Hale. "Some applications of linear algebra to quantitative spectroscopy /." Thesis, Connect to this title online; UW restricted, 1988. http://hdl.handle.net/1773/11534.
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Jowett, Simon. "A novel photogrammetric technique using DLT to measure golf shaft dynamics." Thesis, University of Nottingham, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.272754.
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Goubault, de Brugière Timothée. "Methods for optimizing the synthesis of quantum circuits Quantum CNOT Circuits Synthesis for NISQ Architectures Using the Syndrome Decoding Problem Quantum circuits synthesis using Householder transformations Synthesizing quantum circuits via numerical optimization Reuse method for quantum circuit synthesis." Thesis, université Paris-Saclay, 2020. http://www.theses.fr/2020UPASG018.
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Pour exécuter un algorithme abstrait sur un ordinateur quantique il faut compiler l'algorithme en une séquence d'instructions bas niveau exécutables par le processeur. L'étape de compilation est cruciale car elle détermine la quantité de ressources nécessaire pour l'exécution d'un algorithme ; par conséquent elle se doit d'être optimisée. Dans cette thèse nous nous intéressons à une brique de la compilation~: la synthèse de circuits quantiques à partir d'une spécification abstraite d'un opérateur. Dans un premier temps nous étudions le cas où la matrice unitaire d'un opérateur quantique nous est donnée et nous explorons la minimisation des ressources quantiques et la minimisation des ressources classiques. Même si l'optimisation simultanée de ces deux types de ressources semble difficile, nous proposons de meilleurs compromis améliorant la littérature.Dans un second temps nous nous intéressons à la classe des opérateurs dits linéaires réversibles. Nous nous intéressons cette fois-ci exclusivement à l'optimisation des ressources quantiques et nous améliorons l'état de l'art dans diverses cas de métriques (taille et profondeur du circuit) et de processeurs quantiques (processeurs NISQ, ou à connectivité complète)To run an abstract algorithm on a quantum computer, the algorithm must be compiled into a sequence of low-level instructions that can be executed by the processor. The compilation step is crucial because it determines the quantity of resources necessary for the execution of an algorithm. Therefore, the compilation stage must be optimized. In this thesis, we are interested in a brick of compilation: the synthesis of quantum circuits from an abstract specification of an operator.First, we study the case where the unitary matrix of a quantum operator is given to us and we explore the minimization of both quantum resources and classical resources. Even if the simultaneous optimization of these two types of resources seems difficult, we propose better compromises improving the literature.Secondly, we are interested in the class of so-called reversible linear operators. This time we are exclusively interested in the optimization of quantum resources and we improve the state of the art in various cases of quantum metrics (circuit size, circuit depth) and processors (NISQ, fully-connected processors)
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Ngounda, Edgard. "Numerical Laplace transformation methods for integrating linear parabolic partial differential equations." Thesis, Stellenbosch : University of Stellenbosch, 2009. http://hdl.handle.net/10019.1/2735.
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Thesis (MSc (Applied Mathematics))--University of Stellenbosch, 2009.ENGLISH ABSTRACT: In recent years the Laplace inversion method has emerged as a viable alternative method for the numerical solution of PDEs. Effective methods for the numerical inversion are based on the approximation of the Bromwich integral. In this thesis, a numerical study is undertaken to compare the efficiency of the Laplace inversion method with more conventional time integrator methods. Particularly, we consider the method-of-lines based on MATLAB’s ODE15s and the Crank-Nicolson method. Our studies include an introductory chapter on the Laplace inversion method. Then we proceed with spectral methods for the space discretization where we introduce the interpolation polynomial and the concept of a differentiation matrix to approximate derivatives of a function. Next, formulas of the numerical differentiation formulas (NDFs) implemented in ODE15s, as well as the well-known second order Crank-Nicolson method, are derived. In the Laplace method, to compute the Bromwich integral, we use the trapezoidal rule over a hyperbolic contour. Enhancement to the computational efficiency of these methods include the LU as well as the Hessenberg decompositions. In order to compare the three methods, we consider two criteria: The number of linear system solves per unit of accuracy and the CPU time per unit of accuracy. The numerical results demonstrate that the new method, i.e., the Laplace inversion method, is accurate to an exponential order of convergence compared to the linear convergence rate of the ODE15s and the Crank-Nicolson methods. This exponential convergence leads to high accuracy with only a few linear system solves. Similarly, in terms of computational cost, the Laplace inversion method is more efficient than ODE15s and the Crank-Nicolson method as the results show. Finally, we apply with satisfactory results the inversion method to the axial dispersion model and the heat equation in two dimensions.
AFRIKAANSE OPSOMMING: In die afgelope paar jaar het die Laplace omkeringsmetode na vore getree as ’n lewensvatbare alternatiewe metode vir die numeriese oplossing van PDVs. Effektiewe metodes vir die numeriese omkering word gebasseer op die benadering van die Bromwich integraal. In hierdie tesis word ’n numeriese studie onderneem om die effektiwiteit van die Laplace omkeringsmetode te vergelyk met meer konvensionele tydintegrasie metodes. Ons ondersoek spesifiek die metode-van-lyne, gebasseer op MATLAB se ODE15s en die Crank-Nicolson metode. Ons studies sluit in ’n inleidende hoofstuk oor die Laplace omkeringsmetode. Dan gaan ons voort met spektraalmetodes vir die ruimtelike diskretisasie, waar ons die interpolasie polinoom invoer sowel as die konsep van ’n differensiasie-matriks waarmee afgeleides van ’n funksie benader kan word. Daarna word formules vir die numeriese differensiasie formules (NDFs) ingebou in ODE15s herlei, sowel as die welbekende tweede orde Crank-Nicolson metode. Om die Bromwich integraal te benader in die Laplace metode, gebruik ons die trapesiumreël oor ’n hiperboliese kontoer. Die berekeningskoste van al hierdie metodes word verbeter met die LU sowel as die Hessenberg ontbindings. Ten einde die drie metodes te vergelyk beskou ons twee kriteria: Die aantal lineêre stelsels wat moet opgelos word per eenheid van akkuraatheid, en die sentrale prosesseringstyd per eenheid van akkuraatheid. Die numeriese resultate demonstreer dat die nuwe metode, d.i. die Laplace omkeringsmetode, akkuraat is tot ’n eksponensiële orde van konvergensie in vergelyking tot die lineêre konvergensie van ODE15s en die Crank-Nicolson metodes. Die eksponensiële konvergensie lei na hoë akkuraatheid met slegs ’n klein aantal oplossings van die lineêre stelsel. Netso, in terme van berekeningskoste is die Laplace omkeringsmetode meer effektief as ODE15s en die Crank-Nicolson metode. Laastens pas ons die omkeringsmetode toe op die aksiale dispersiemodel sowel as die hittevergelyking in twee dimensies, met bevredigende resultate.
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Fotinopoulos, Ioannis. "Root moments : a non-linear transformation technique with applications in signal processing." Thesis, Imperial College London, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.396276.
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Sundberg, Jesper. "Anomaly Detection in Diagnostics Data with Natural Fluctuations." Thesis, KTH, Optimeringslära och systemteori, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-170237.
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In this thesis, the red hot topic anomaly detection is studied, which is a subtopic in machine learning. The company, Procera Networks, supports several broadband companies with IT-solutions and would like to detected errors in these systems automatically. This thesis investigates and devises methods and algorithms for detecting interesting events in diagnostics data. Events of interest include: short-term deviations (a deviating point), long-term deviations (a distinct trend) and other unexpected deviations. Three models are analyzed, namely Linear Predictive Coding, Sparse Linear Prediction and Wavelet Transformation. The final outcome is determined by the gap to certain thresholds. These thresholds are customized to fit the model as well as possible.I den här rapporten kommer det glödheta området anomalidetektering studeras, vilket tillhör ämnet Machine Learning. Företaget där arbetet utfördes på heter Procera Networks och jobbar med IT-lösningar inom bredband till andra företag. Procera önskar att kunna upptäcka fel hos kunderna i dessa system automatiskt. I det här projektet kommer olika metoder för att hitta intressanta företeelser i datatraffiken att genomföras och forskas kring. De mest intressanta företeelserna är framfärallt snabba avvikelser (avvikande punkt) och färändringar äver tid (trender) men också andra oväntade mänster. Tre modeller har analyserats, nämligen Linear Predictive Coding, Sparse Linear Prediction och Wavelet Transform. Det slutgiltiga resultatet från modellerna är grundat på en speciell träskel som är skapad fär att ge ett så bra resultat som mäjligt till den undersäkta modellen..
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Figueiredo, Orlando de Andrade [UNESP]. "Sentidos de percepção e educação matemática: geometria dinâmica e ensino de funções com auxílio de representações dinâmicas." Universidade Estadual Paulista (UNESP), 2010. http://hdl.handle.net/11449/102162.
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figueiredo_oa_dr_rcla.pdf: 599343 bytes, checksum: 2107a2036f27ecde0dcfdbff1f4a2bf3 (MD5)Os processos perceptivos que fundamentam a experiência humana podem nos parecer absolutamente naturais. Devido a isso, costumamos não tematizá-los. Este trabalho é um esforço de evidenciação da percepção na educação matemática, mais especificamente na geometria dinâmica e no ensino de funções com auxílio de representações dinâmicas. Percepção é entendida em uma concepção fenomenológica. Sustenta-se que: (a) é da natureza humana certa capacidade de perceber comportamentos de dependências entre eventos do mundo físico, isto é, existe um sentido de percepção de dependência; (b) as representações dinâmicas de funções, como os Dynagraphs (conhecidos na literatura) e os funcionetes (propostos no trabalho), são depreendidas pelo sentido de percepção de dependência; (c) o emprego de representações dinâmicas no auxílio ao ensino de funções abre novos sentidos para funções matemáticas, conceitos, propriedades e teoremas correlatos, justificando o interesse em sua aplicação; além disso, os sentidos abertos são perceptivos e, por isso, diretos, imediatos e evidentes (conforme a fundamentação fenomenológica); (d) existe um sentido de percepção de restrições ou impedimentos; (e) na resolução interativa (geometria dinâmica) de sistemas de restrições geométricas, o sentido de percepção de restrições apresenta, ao trazer perceptivamente as restrições para primeiro plano, as construções geométricas como uma combinação de restrições. No desenvolvimento dessas ideias: apresentam-se os funcionetes planos e sua aplicação na construção de uma abordagem pedagógica para o conceito (da álgebra linear) transformação linear, que é um tipo de função; abordam-se os tópicos: autovetores de um operador linear, propriedade de linearidade e núcleo de uma transformação linear, inclusive o teorema do núcleo e da imagem...
The perceptive processes that provide the basis for human experience can seem absolutely natural. Therefore we do not have the habit of focusing on them as the object of study. The present theoretical study aimed to make perception evident in the context of mathematics education, specifically dynamic geometry and teaching of functions using dynamic representations. Perception is understood as a phenomenological conception. It is maintained that: (a) it is of human nature to be able to perceive dependent behaviors among events in the physical world, i.e. a sense of perception of dependence; (b) dynamic representations of functions, such as Dynagraphs (known in the literature) and “funcionetes” (proposed here), are ascertained through the sense of perception of dependence; (c) the use of dynamic representations to aid in the teaching of functions opens up new senses for mathematical functions, concepts, properties and correlated theorems, justifying interest in its application; in addition, these newly-opened senses are perceptive in nature, and therefore direct, immediate and evident (according to foundations of phenomenology); (d) there exists a sense of perception of constraints or impediments; (e) in the interactive resolution (dynamic geometry) of constraint systems for geometric domain, the sense of perception of constraints presents geometric constructions as a combination of constraints as it perceptively brings the constraints to the foreground. The concept of “funcionetes planos” is presented and their use proposed as part of an approach for teaching the concept (from linear algebra) of linear transformation, which is a type of function. Topics addressed include: eigenvectors of a linear operator, the property of linearity and nucleus of a linear transformation, including the theorem of nucleus and of image, presented in a perceptive sense... (Complete abstract click electronic access below)
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Hernandez, Lopezomoza Mario Andres. "Cadre de travail généralisé de compensation non-linéaire robuste : application à la rentrée atmosphérique." Thesis, Toulouse, ISAE, 2012. http://www.theses.fr/2012ESAE0022/document.
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Ce travail de thèse est consacré à l'extension de l'Inversion Dynamique non-linéaire (NDI-Nonlinear Dynamic Inversion) pour un ensemble plus grand de systèmes non-linéaires, tout en garantissant des conditions de stabilité suffisantes. La NDI a été étudiée dans le cas de diverses applications, y compris en aéronautique et en aérospatiale. Elle permet de calculer des lois de contrôle capables de linéariser et de découpler un modèle non-linéaire à tout point de fonctionnement de son enveloppe d'état. Cependant cette méthode est intrinsèquement non-robuste aux erreurs de modélisation et aux saturations en entrée. En outre, dans un contexte non-linéaire, l'obtention d'une garantie quantifiable du domaine de stabilité atteint reste à l'heure actuelle complexe. Contrairement aux approches classiques de la NDI, notre méthodologie peut être considérée comme un cadre de compensation non-linéaire généralisé qui permet d'intégrer les incertitudes et les saturations en entrée dans le processus de conception. En utilisant des stratégies de contrôle antiwindup, la loi de pilotage peut être calculée grâce à un simple processus en deux phases. Dans ce cadre de travail généralisé des transformations linéaires fractionnaires (LFT - Linear Fractional Transformations) de la boucle fermée non-linéaire peuvent être facilement déduites pour l'analyse de la stabilité robuste en utilisant des outils standards pour de systèmes linéaires. La méthode proposée est testée pour le pilotage d'un véhicule de rentrée atmosphérique de type aile delta lors de ses phases hypersonique, transsonique et subsonique. Pour cette thèse, un simulateur du vol incluant divers facteurs externes ainsi que des erreurs de modélisation a été développé dans SimulinkThis thesis work is devoted to extending Nonlinear Dynamic Inversion (NDI) for a large scale of nonlinear systems while guaranteeing sufficient stability conditions. NDI has been studied in a wide range of applications, including aeronautics and aerospace. It allows to compute nonlinear control laws able to decouple and linearize a model at any operating point of its state envelope. However, this method is inherently non-robust to modelling errors and input saturations. Moreover, obtaining a quantifiable guarantee of the attained stability domain in a nonlinear control context is not a very straightforward task. Unlike standard NDI approaches, our methodology can be viewed as a generalized nonlinear compensation framework which allows to incorporate uncertainties and input saturations in the design process. Paralleling anti-windup strategies, the controller can be computed through a single multichannel optimization problem or through a simple two-step process. Within this framework, linear fractional transformations of the nonlinear closed-loop can be easily derived for robust stability analysis using standard tools for linear systems. The proposed method is tested for the flight control of a delta wing type reentry vehicle at hypersonic, transonic and subsonic phases of the atmospheric reentry. For this thesis work, a Flight Mechanics simulator including diverse external factors and modelling errors was developed in Simulink
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Porto, Victor Monteiro Ferreira. "Criptografia: Da origem aos dias atuais." Universidade do Estado do Rio de Janeiro, 2015. http://www.bdtd.uerj.br/tde_busca/arquivo.php?codArquivo=9182.
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Esta pesquisa foi realizada com a intenção de motivar o estudo da criptografia, mostrando que a matemática e a comunicação estão presentes em diversos momentos, tanto no passado quanto no presente. Este trabalho mostra a origem da criptoanálise e toda a sua evolução dando ênfase nos mecanismos de codificação e decodificação através de exemplos práticos. Além disso, alguns métodos criptográficos são destacados como a cifra de substituição monoalfabética, a cifra de Vigenère, a criptografia RSA que é o método mais conhecido de criptografia de chave pública, as cifras de Hill, o método das transformações lineares e o método de Rabin, devido a sua grande importância para a evolução de sistemas computacionais e assinaturas digitais entre outros. Por fim, mostra-se a importância e a necessidade dos recursos criptográficos nos dias de hoje, na tentativa de impedir que hackers e pessoas que fazem mau uso do conhecimento matemático possam causar danos a sociedade, seja por uma simples mensagem ou até mesmo através de situações mais imprudentes como as transações bancárias indevidasThis research was conducted with the intention of motivating the study of cryptography, showing that mathematics and the communication are present at various times, both past and present. This work shows the origin of cryptanalysis and all its evolution giving emphasis on coding and decoding mechanisms through practical examples. In addition, some methods cryptographic are highlighted as the monoalphabetic substitution cipher, the Vigenere cipher, RSA encryption that is the best known method of public key cryptography , ciphers Hill, the method of linear transformations and the Rabin method, due to its great importance for the evolution of computer systems and signatures digital among others. Finally, we show the importance and the need for cryptographic resources these days, in an attempt to prevent hackers and people who make bad use of mathematical knowledge can cause damage to society, whether by a simple message or through more situations reckless as improper banking transactions
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Bell, Simon J. G. "Numerical techniques for smooth transformation and regularisation of time-varying linear descriptor systems." Thesis, University of Reading, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.284311.
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Slye, Jeffrey. "UNDERGRADUATE MATHEMATICS STUDENTS’ CONNECTIONS BETWEEN THEIR GROUP HOMOMORPHISM AND LINEAR TRANSFORMATION CONCEPT IMAGES." UKnowledge, 2019. https://uknowledge.uky.edu/math_etds/65.
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It is well documented that undergraduate students struggle with the more formal and abstract concepts of vector space theory in a first course on linear algebra. Some of these students continue on to classes in abstract algebra, where they learn about algebraic structures such as groups. It is clear to the seasoned mathematician that vector spaces are in fact groups, and so linear transformations are group homomorphisms with extra restrictions. This study explores the question of whether or not students see this connection as well. In addition, I probe the ways in which students’ stated understandings are the same or different across contexts, and how these differences may help or hinder connection making across domains. Students’ understandings are also briefly compared to those of mathematics professors in order to highlight similarities and discrepancies between reality and idealistic expectations.
The data for this study primarily comes from clinical interviews with ten undergraduates and three professors. The clinical interviews contained multiple card sorts in which students expressed the connections they saw within and across the domains of linear algebra and abstract algebra, with an emphasis specifically on linear transformations and group homomorphisms. Qualitative data was analyzed using abductive reasoning through multiple rounds of coding and generating themes.
Overall, I found that students ranged from having very few connections, to beginning to form connections once placed in the interview setting, to already having a well-integrated morphism schema across domains. A considerable portion of this paper explores the many and varied ways in which students succeeded and failed in making mathematically correct connections, using the language of research on analogical reasoning to frame the discussion. Of particular interest were the ways in which isomorphisms did or did not play a role in understanding both morphisms, how students did not regularly connect the concepts of matrices and linear transformations, and how vector spaces were not fully aligned with groups as algebraic structures.
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Golcher, Felix. "Wiederholungen in Texten." Doctoral thesis, Humboldt-Universität zu Berlin, Philosophische Fakultät II, 2013. http://dx.doi.org/10.18452/16867.
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Diese Arbeit untersucht vollständige Zeichenkettenfrequenzverteilungen natürlichsprachiger Texte auf ihren linguistischen und anwendungsbezogenen Gehalt. Im ersten Teil wird auf dieser Datengrundlage ein unüberwachtes Lernverfahren entwickelt, das Texte in Morpheme zerlegt. Die Zerlegung geht von der Satzebene aus und verwendet jegliche vorhandene Kontextinformation. Es ergibt sich ein sprachunabhängiger Algorithmus, der die gefundenen Morpheme teilweise zu Baumstrukturen zusammenordnet. Die Evaluation der Ergebnisse mit Hilfe statistischer Modelle ermöglicht die Identifizierung auch kleiner Performanzunterschiede. Diese sind einer linguistischen Interpretation zugänglich. Der zweite Teil der Arbeit besteht aus stilometrischen Untersuchungen anhand eines Textähnlichkeitsmaßes, das ebenfalls auf vollständigen Zeichenkettenfrequenzen beruht. Das Textähnlichkeitsmaß wird in verschiedenen Varianten definiert und anhand vielfältiger stilometrischer Fragestellungen und auf Grundlage unterschiedlicher Korpora ausgewertet. Dabei ist ein wiederholter Vergleich mit der Performanz bisheriger Forschungsansäzte möglich. Die Performanz moderner Maschinenlernverfahren kann mit dem hier vorgestellten konzeptuell einfacheren Verfahren reproduziert werden. Während die Segmentierung in Morpheme ein lokaler Vorgang ist, besteht Stilometrie im globalen Vergleich von Texten. Daher bietet die Untersuchung dieser zwei unverbunden scheinenden Fragestellungen sich gegenseitig ergänzende Perspektiven auf die untersuchten Häufigkeitsdaten. Darüber hinaus zeigt die Diskussion der rezipierten Literatur zu beiden Themen ihre Verbindungen durch verwandte Konzepte und Denkansätze auf. Aus der Gesamtheit der empirischen Untersuchungen zu beiden Fragestellungen kann abgeleitet werden, dass den längeren und damit selteneren Zeichenketten wesentlich mehr Informationsgehalt innewohnt, als in der bisherigen Forschung gemeinhin angenommen wird.This thesis investigates the linguistic and application specific content of complete character substring frequency distributions of natural language texts. The first part develops on this basis an unsupervised learning algorithm for segmenting text into morphemes. The segmentation starts from the sentence level and uses all available context information. The result is a language independent algorithm which arranges the found morphemes partly into tree like structures. The evaluation of the output using advanced statistical modelling allows for identifying even very small performance differences. These are accessible to linguistic interpretation. The second part of the thesis consists of stylometric investigations by means of a text similarity measure also rooted in complete substring frequency statistics. The similarity measure is defined in different variants and evaluated for various stylometric tasks and on the basis of diverse corpora. In most of the case studies the presented method can be compared with publicly available performance figures of previous research. The high performance of modern machine learning methods is reproduced by the considerably simpler algorithm developed in this thesis. While the segmentation into morphemes is a local process, stylometry consists in the global comparison of texts. For this reason investigating of these two seemingly unconnected problems offers complementary perspectives on the explored frequency data. The discussion of the recieved litarature concerning both subjects additionally shows their connectedness by related concepts and approaches. It can be deduced from the totality of the empirical studies on text segmentation and stylometry conducted in this thesis that the long and rare character sequences contain considerably more information then assumed in previous research.
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Shirke, Abhijit R. "Transformation from Linear Development Model to Iterative Development within a Waterfall Environment : A Case Study." The Ohio State University, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=osu1345447033.
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Sousa, Francisco Josà Calixto de. "CombinaÃÃes afins." Universidade Federal do CearÃ, 2013. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=10039.
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CoordenaÃÃo de AperfeiÃoamento de Pessoal de NÃvel SuperiorNeste trabalho, consideramos combinaÃÃes afins de vetores de um espaÃo vetorial com especiais aplicaÃÃes no ensino mÃdio atravÃs da mÃdia aritmÃtica ponderada e da desigualdade de Jensen. Verificamos caracterÃsticas de transformaÃÃes lineares de conjuntos especÃficos nos espaÃos vetoriais como conjuntos convexos e variedades afins, atravÃs do nÃcleo e da imagem das transformaÃÃes. Estabelecemos relaÃÃes entre transformaÃÃes afins, combinaÃÃes afins e transformaÃÃes lineares. Discutimos a dimensÃo do hiperplano relacionando-o como variedade afim. Vemos que todo subespaÃo vetorial de Rn com dimensÃo n - 1 Ã um hiperplano, assim como o nÃcleo de um funcional linear.
In this paper, we consider combinations of related vectors of a vector space with special applications in high school through the weighted arithmetic mean and the Jensen inequality. We observed characteristics of specific sets of linear transformations in the vector spaces as convex sets and related varieties through the core and image transformations. Established relations between affine transformations, combinations thereof and linear transformations. We discuss the size of the hyperplane relating it as affine variety. We see that all of Rn vector subspace with dimension n - 1 is a hyperplane, as the core of a linear functional.
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Panchapagesan, Sankaran. "Frequency warping by linear transformation, and vocal tract inversion for speaker normalization in automatic speech recognition." Diss., Restricted to subscribing institutions, 2008. http://proquest.umi.com/pqdweb?did=1610480121&sid=1&Fmt=2&clientId=1564&RQT=309&VName=PQD.
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Silva, Maria Eliana Santana da Cruz. "Concepção de transformação linear por estudantes de licenciatura em matemática." Pontifícia Universidade Católica de São Paulo, 2016. https://tede2.pucsp.br/handle/handle/19025.
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This doctoral dissertation reports an investigation of the conceptions of linear transformation held by teaching certification students in mathematics following a course of linear algebra devised to involve students in the search for elements to build the concept of this mathematical object. The analysis of these conceptions was carried out according to the APOS theory by Dubinsky and Lewin (1986) and Asiala et al. (1996), in articulation with premises of didactic engineering (MACHADO, 2010). The investigation was a qualitative, case-study type, which, according to Bogdan and Biklen (1994) and Lüdke and André (1986), enables the context studied to be investigated and interpreted, given that all qualitative studies seek to portray reality in a more dense fashion and represent the different perspectives present in a given social situation. Centered on this understanding of qualitative research, classes were organized with the aim of actively involving the study participants to facilitate data collection, which was carried out three semesters after the linear algebra course. Premises of didactic engineering were employed to prepare and conduct the activities, which were discussed and solved by paired students. Their interactions were audio recorded and also noted by an observer. The analysis revealed that the subjects paired for the activities experienced different stages in terms of conception (action, process, and object) in most of the activities. We concluded that the students investigated did not always show a conception of object during the activities, but were all able to demonstrate a conception of process for the notion of linear transformation
Esta tese apresenta uma pesquisa que busca investigar as concepções de transformação linear de alunos de uma licenciatura em matemática ao vivenciarem um curso de álgebra linear elaborado com a intenção de envolvê-los na busca de elementos para a construção desse objeto matemático. A análise das concepções se embasou principalmente em partes da teoria APOS, de Dubinsky e Lewin (1986) e Asiala et al. (1996), articulada com alguns pressupostos da engenharia didática (MACHADO, 2010). A pesquisa se caracteriza como qualitativa, abordagem que, segundo Bogdan e Biklen (1994) e Lüdke e André (1986), possibilita investigar e interpretar o contexto investigado, uma vez que todo estudo qualitativo visa retratar a realidade de forma densa, procurando representar as diferentes perspectivas presentes em dada situação social. A partir dessa compreensão de pesquisa qualitativa, foi possível organizar aulas com o objetivo de envolver ativamente os participantes da pesquisa, de forma a facilitar a coleta de dados, que foi realizada após três semestres do curso em questão. Utilizamos pressupostos da engenharia didática na preparação e execução das atividades, discutidas e resolvidas em duplas, atividades essas audiogravadas e descritas por um observador. As análises revelaram que os sujeitos que compuseram as duplas durante a realização das atividades vivenciaram diferentes etapas em termos de concepção (ação, processo e objeto) na maioria das atividades propostas. Concluímos que os sujeitos da pesquisa nem sempre demonstraram uma concepção de objeto no desenvolvimento das atividades, mas todos foram capazes de demonstrar uma concepção de processo da noção de transformação linear
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Egner, Sebastian [Verfasser]. "Zur algorithmischen Zerlegungstheorie linearer Transformationen mit Symmetrie / Sebastian Egner." Karlsruhe : KIT-Bibliothek, 1997. http://d-nb.info/1014060621/34.
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