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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
401

[pt] PROBLEMAS DE RIEMANN HILBERT NA TEORIA DE MATRIZES ALEATÓRIAS / [en] RIEMANN HILBERT PROBLEMS IN RANDOM MATRIX THEORY

PERCY ALEXANDER CACERES TINTAYA 19 May 2016 (has links)
[pt] Estudamos as noções básicas da Teoria das Matrizes Aleatórias e em particular discutimos o Emsemble Unitário Gaussiano. A continuação descrevemos o gaz de Dyson em equilíbrio e fora do equilíbrio que permite interpretar a informação estatística dos autovalores das matrizes aleatórias. Além desso mostramos descrições alternativas dessa informação estatística. Em seguida discutimos aspectos diferentes dos polinômios ortogonais. Uma dessas caracterizações é dada pelos problemas de Riemann-Hilbert. As técnicas dos problemas de Riemann-Hilbert são uma ferramenta eficaz e potente na Teoria das Matrizes Aleatórias a qual discutimos com mais cuidado. Finalmente usamos o método de máxima gradiente na análise assintótico dos polinômios ortogonais. / [en] We review the basic notions of the Random Matrix Theory and in particular the Gaussian Unitary Ensemble. In what follows we describe the Dyson gas in equilibrium and nonequilibrium that allows one to interpret the statistical information of the eigenvalues of random matrices. Furthermore we show alternative descriptions of this statistical information. In the following we discuss different aspects of orthogonal polynomials. One of these caracterizations is given by a Riemann Hilbert problem. Riemann Hilbert problem techniques are an efficient and powerfull tool for Random Matrix Theory which we discuss in more detail. In the final part we use the steepest descent method in the asymptotic analysis of orthogonal polynomials.
402

Delta udarni talasi i metod praćenja talasa / Delta shock waves and wave front tracking method

Dedović Nebojša 24 April 2014 (has links)
<p>U doktorskoj disertaciji posmatrani su Rimanovi problemi kod strogo i slabo hiperboličnih&nbsp;nelinearnih sistema PDJ. U uvodu je predstavljena jednačina zakona održanja u jednoj prostornoj&nbsp;dimenziji i definisani su Ko&scaron;ijevi i Rimanovi problemi. U drugoj glavi, date su osnovne osobine&nbsp;nelinearnih hiperboličnih zakona održanja, uvedeni supojmovi stroge hiperboličnosti i slabog re&scaron;enja&nbsp;zakona održanja. Definisani su Rankin-Igono i entropijski uslovi kao i op&scaron;te re&scaron;enje Rimanovog problema&nbsp;(za dovoljno male početne uslove). U trećoj glavi detaljno je obja&scaron;njena Glimova diferencna &nbsp;&scaron;ema. Metod&nbsp;praćenja talasa predstavljen je u četvrtoj glavi. Pokazano je da se ovom metodom, za dovoljno male&nbsp;početne uslove, dobija stabilno i jedinstveno re&scaron;enje koje u svakom vremenu ima ograničenu totalnu&nbsp;varijaciju. U petoj glavi, posmatrana je jednačina protoka izentropnog gasa u Lagranžovim koordinatama.&nbsp;Uz pretpostavku da je početni uslov ograničen i da ima ograničenu totalnu varijaciju, pokazano je da&nbsp;Ko&scaron;ijev problem ima jedinstveno slabo re&scaron;enje ako je totalna varijacija početnog uslova pomnožena sa &nbsp;0&lt;&epsilon;&lt;&lt; 1 dovoljno mala. Slabo re&scaron;enjedobijeno je metodom praćenja talasa. U glavi &scaron;est ispitana je&nbsp;interakcija dva delta talasa koji su posmatrani kao specijalna vrsta shadowtalasa. U glavi sedam,&nbsp;pokazano je da za proizvoljno velike početne uslove, re&scaron;enje Rimanovog problema jednodimenzionalnog&nbsp;Ojlerovog zakona održanja gasne dinamikepostoji, daje jedinstveno i entropijski dopustivo, uz drugačiju<br />ocenu snaga elementarnih talasa. Data je numerička verifikacija interakcije dva delta talasa kori&scaron;ćenjem&nbsp;metode praćenja talasa.</p> / <p>In this doctoral thesis, Riemann problems for strictly and weakly nonlinear hyperbolic PDE&nbsp;systems were observed. In the introduction, conservation laws in one spatial dimension were presented&nbsp;and the Cauchy and Riemann problems were defined. In the second chapter, the basic properties of&nbsp;nonlinear hyperbolic conservation laws were intorduced, as well as the terms such as strictly hyperbolic&nbsp;system and weak solution of conservation law. Also, Rankine -Hugoniot and entropy conditions were<br />introduced and the general solution to the Riemann problem (for sufficiently small initial conditions) were&nbsp;defined. Glimm&rsquo;s difference scheme was explained in the third chapter. The wave front tracking method&nbsp;was introduced in the fourth chapter. It was shown that, using this method, for sufficiently small initial&nbsp;conditions, it could be obtained a unique solution with bounded total variation for t &ge;0. In the fifth&nbsp;chapter, the Euler equations for isentropic fluid inLagrangian coordinates were observed. Under the&nbsp;assumption that the initial condition was bounded and had bounded total variation, it was shown that the&nbsp;Cauchy problem had a weak unique solution, provided that the total variation of initial condition&nbsp;multiplied by 0&lt;&epsilon;&lt;&lt;1 was sufficiently &nbsp;small. Weak solution was obtained by applying the wave front&nbsp;tracking method. In the sixth chapter, the interaction of two delta shock waves were examined. Delta&nbsp;shock waves were regarded as special kind of shadowwaves. In the chapter seven, it was shown that for&nbsp;arbitrarily large initial conditions, solution to the Riemann problem of one-dimensional Euler&nbsp;conservation laws of gas dynamics existed, it was unique and admissible. New bounds on the strength of&nbsp;elementary waves in the wave front tracking algorithm were given. The numerical verification of two&nbsp;delta shock waves interaction via wave front tracking method was given at the end of the thesis.</p>
403

Asymptotic Analysis of Structured Determinants via the Riemann-Hilbert Approach

Gharakhloo, Roozbeh 08 1900 (has links)
Indiana University-Purdue University Indianapolis (IUPUI) / In this work we use and develop Riemann-Hilbert techniques to study the asymptotic behavior of structured determinants. In chapter one we will review the main underlying definitions and ideas which will be extensively used throughout the thesis. Chapter two is devoted to the asymptotic analysis of Hankel determinants with Laguerre-type and Jacobi-type potentials with Fisher-Hartwig singularities. In chapter three we will propose a Riemann-Hilbert problem for Toeplitz+Hankel determinants. We will then analyze this Riemann-Hilbert problem for a certain family of Toeplitz and Hankel symbols. In Chapter four we will study the asymptotics of a certain bordered-Toeplitz determinant which is related to the next-to-diagonal correlations of the anisotropic Ising model. The analysis is based upon relating the bordered-Toeplitz determinant to the solution of the Riemann-Hilbert problem associated to pure Toeplitz determinants. Finally in chapter ve we will study the emptiness formation probability in the XXZ-spin 1/2 Heisenberg chain, or equivalently, the asymptotic analysis of the associated Fredholm determinant.
404

A novel Chebyshev wavelet method for solving fractional-order optimal control problems

Ghanbari, Ghodsieh 13 May 2022 (has links) (PDF)
This thesis presents a numerical approach based on generalized fractional-order Chebyshev wavelets for solving fractional-order optimal control problems. The exact value of the Riemann– Liouville fractional integral operator of the generalized fractional-order Chebyshev wavelets is computed by applying the regularized beta function. We apply the given wavelets, the exact formula, and the collocation method to transform the studied problem into a new optimization problem. The convergence analysis of the proposed method is provided. The present method is extended for solving fractional-order, distributed-order, and variable-order optimal control problems. Illustrative examples are considered to show the advantage of this method in comparison with the existing methods in the literature.
405

And Yet, She Persists: An Investigation of the Effects of Stereotype Threat on Women's Construction of their Mathematical and Gender Identities

Benjamin, Judy I. 12 August 2022 (has links)
No description available.
406

Reger, Riemann und die neo-riemannian theory

Sprick, Jan Philipp 17 October 2023 (has links)
No description available.
407

Equivariant Moduli Theory on K3 Surfaces

Chen, Yuhang 08 September 2022 (has links)
No description available.
408

Theoretical and numerical aspects of advection-pressure splitting for 1D blood flow models

Spilimbergo, Alessandra 19 April 2024 (has links)
In this Thesis we explore, both theoretically and numerically, splitting strategies for a hyperbolic system of one-dimensional (1D) blood flow equations with a passive scalar transport equation. Our analysis involves a two-step framework that includes splitting at the level of partial differential equations (PDEs) and numerical methods for discretizing the ensuing problems. This study is inspired by the original flux splitting approach of Toro and Vázquez-Cendón (2012) originally developed for the conservative Euler equations of compressible gas dynamics. In this approach the flux vector in the conservative case, and the system matrix in the non-conservative one, are split into advection and pressure terms: in this way, two systems of partial differential equations are obtained, the advection system and the pressure system. From the mathematical as well as numerical point of view, a basic problem to be solved is the special Cauchy problem called the Riemann problem. This latter provides an analytical solution to evaluate the performance of the numerical methods and, in our approach, it is of primary importance to build the presented numerical schemes. In the first part of the Thesis a detailed theoretical analysis is presented, involving the exact solution of the Riemann problem for the 1D blood flow equations, depicted for a general constant momentum correction coefficient and a tube law that allows to describe both arteries and veins with continuous or discontinuous mechanical and geometrical properties and an advection equation for a passive scalar transport. In literature, this topic has been already studied only for a momentum correction coefficient equal to one, that is related to the prescribed velocity profile and in this case corresponds to a flat one, i.e. an inviscid fluid. In the case of discontinuous properties, only the subsonic regime is considered. In addition we propose a procedure to compute the obtained exact solution and finally we validate it numerically, by comparing exact solutions to those obtained with well-known, numerical schemes on a carefully designed set of test problems. Furthermore, an analogous theoretical analysis and resolution algorithm are presented for the advection system and the pressure system arising from the splitting at the level of PDEs of the complete system of 1D blood flow equations. It is worth noting that the pressure system, in case of veins, presents a loss of genuine non-linearity resulting in the formation of rarefactions, shocks and compound waves, these latter being a composition of rarefactions and shocks. In the second part of the Thesis we present novel finite volume-type, flux splitting-based, numerical schemes for the conservative 1D blood flow equations and splitting-based numerical schemes for the non-conservative 1D blood flow equations that incorporate an advection equation for a passive scalar transport, considering tube laws that allow to model blood flow in arteries and veins and take into account a general constant momentum correction coefficient. A detailed efficiency analysis is performed in order to showcase the advantages of the proposed methodologies in comparison to standard approaches.
409

Harmonicity in Slice Analysis: Almansi decomposition and Fueter theorem for several hypercomplex variables

Binosi, Giulio 10 June 2024 (has links)
The work is situated within the theory of slice analysis, a generalization of complex analysis for hypercomplex numbers, considering function of both quaternionic and Clifford variables, in both one and several variables. %We first characterize some partial slice sets of The primary focus of the thesis is on the harmonic and polyharmonic properties of slice regular functions. We derive explicit formulas for the iteration of the Laplacian on slice regular functions, proving that their degree of harmonicity increases with the dimension of the algebra. Consequently, we present Almansi-type decompositions for slice functions in several variables. Additionally, using the harmonic properties of the partial spherical derivatives and their connection with the Dirac operator in Clifford analysis, we achieve a generalization of the Fueter and Fueter-Sce theorems in the several variables context. Finally, we establish that regular polynomials of sufficiently low degree are the unique slice regular functions in the kernel of the iteration of the Laplacian, whose power is less than Sce index.
410

Contribution à la manipulation dextre dynamique pour les aspects conceptuels et de commande en ligne optimale / Contribution to dynamic dexterous manipulation : design elements and optimal control

Rojas Quintero, Juan Antonio 31 October 2013 (has links)
Nous nous intéressons à la conception des mains mécaniques anthropomorphes destinées à manipuler des objets dans un environnement humain. Via l'analyse du mouvement de sujets humains lors d'une tâche de manipulation de référence, nous proposons une méthode pour évaluer la capacité des mains robotiques à manipuler les objets. Nous montrons comment les rapports de couplage angulaires entre les articulations et les limites articulaires, influent sur l'aptitude à manipuler dynamiquement des objets. Nous montrons également l'impact du poignet sur les tâches de manipulation rapides. Nous proposons une stratégie pour calculer les forces de manipulation en bout de doigts et dimensionner les moteurs d'un tel préhenseur. La méthode proposée est dépendante de la tâche visée et s'adapte à tout type de mouvement dès lors qu'il peut être capturé et analysé. Dans une deuxième partie, consacrée aux robots manipulateurs, nous élaborons des algorithmes de commande optimale. En considérant l'énergie cinétique du robot comme une métrique, le modèle dynamique est formulé sous forme tensorielle dans le cadre de la géométrie Riemannienne. La discrétisation temporelle est basée sur les Éléments Finis d'Hermite. Nous intégrons les équations de Lagrange du mouvement par une méthode de perturbation. Des exemples de simulation illustrent la superconvergence de la technique d'Hermite. Le critère de contrôle est choisi indépendant des paramètres de configuration. Les équations de la commande associées aux équations du mouvement se révèlent covariantes. La méthode de commande optimale proposée consiste à minimiser la fonction objective correspondant au critère invariant sélectionné. / We focus on the design of anthropomorphous mechanical hands destined to manipulate objects in a human environment. Via the motion analysis of a reference manipulation task performed by human subjects, we propose a method to evaluate a robotic hand manipulation capacities. We demonstrate how the angular coupling between the fingers joints and the angular limits affect the hands potential to manipulate objects. We also show the influence of the wrist motions on the manipulation task. We propose a strategy to calculate the fingertip manipulation forces and dimension the fingers motors. In a second part devoted to articulated robots, we elaborate optimal control algorithms. Regarding the kinetic energy of the robot as a metric, the dynamic model is formulated tensorially in the framework of Riemannian geometry. The time discretization is based on the Hermite Finite Elements.A time integration algorithm is designed by implementing a perturbation method of the Lagrange's motion equations. Simulation examples illustrate the superconvergence of the Hermite's technique. The control criterion is selected to be coordinate free. The control equations associated with the motion equations reveal to be covariant. The suggested control method consists in minimizing the objective function corresponding to the selected invariant criterion.

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