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Resultados de controlabilidad para una ecuación de tipo Korteweg - de Vries con un pequeño término de dispersiónBautista Sánchez, George José January 2018 (has links)
Estudia las propiedades de controlabilidad para la ecuación Korteweg de Vries lineal e un intervalo limitado. Se establece un resultado, de controlabilidad nula para la ecuación lineal a través de la condijo de contorno tipo Durichlet. / Tesis
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Function spaces and rational inner functions on polydiscsBergqvist, Linus January 2021 (has links)
In this thesis we consider problems related to rational inner functionsand several different Hilbert spaces on the unit polydisc. In the general introduction the functions and the function spaces we will be interested in are introduced, and in particular we point outproblems and phenomena that occur in higher dimensions and are notpresent for one variable functions. For example, we provide a detailed construction of a non-trivial shift-invariant subspace of Dirichlet-type spaces on the bidisc which is not fnitely generated. Furthermore, Clark-Aleksandrov measures are generalized to higher dimensions, and certain results about such measures are proved. Paper I concerns containment of rational inner functions in Dirichlet-type spaces on polydiscs. In particular a theorem relating H^p integrability of the partial derivatives of a rational inner function to containment of the function in certain Dirichlet-type spaces is proved. As a corollary, we see that every rational inner function on D^n belongs to the isotropic Dirichlet-type space with weight 1/n. In Paper II, Zhu's sub-Bergman spaces of one variable functions on the unit disc are generalized to weighted Bergman spaces on D^n. Unlike in one variable,we show that sub-Bergman spaces associated to a rational inner function are generally not contained in a weighted Bergman space of higher regularity. We also show how Clark measures on the n-torus can be used to study model spaces on D^n associated to rational inner functions.
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De la géométrie à l’arithmétique en théorie inverse de Galois / From geometry to arithmetic in inverse Galois theoryMotte, François 31 May 2019 (has links)
Nous contribuons à la conjecture de Malle sur le nombre d'extensions galoisiennes finies E d'un corps de nombres K donné, de groupe de Galois G et dont la norme du discriminant est bornée par y. Nous établissons une minoration de ce nombre pour tout groupe fini G et sur tout corps de nombres K contenant un certain corps de nombres K'. Pour ce faire, on part d'une extension galoisienne régulière F/K(T) que l'on spécialise. On démontre une version forte du théorème d'Irréductibilté de Hilbert qui compte le nombre d'extensions spécialisées et pas seulement le nombre de points de spécialisation. Nous arrivons aussi à prescrire le comportement local en certains premiers des extensions spécialisées. En conséquence, on déduit de nouveaux résultats sur le problème local-global de Grunwald, en particulier pour certains groupes non résolubles. Afin d'arriver à nos fins, nous démontrons des résultats en géométrie diophantienne sur la recherche de points entiers sur des courbes algébriques. / We contribute to the Malle conjecture on the number of finite Galois extensions E of some number field K of Galois group G and of discriminant of norm bounded by y. We establish a lower bound for every group G and every number field K containing a certain number field K'. To achieve this goal, we start from a regular Galois extension F/K(T) that we specialize. We prove a strong version of the Hilbert Irreducibility Theorem which counts the number of specialized extensions and not only the specialization points. We can also prescribe the local behaviour of the specialized extensions at some primes. Consequently, we deduce new results on the local-global Grunwald problem, in particular for some non-solvable groups. To reach our goals, we prove some results in diophantine geometry about the number of integral points on an algebraic curve.
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Bounds on Hilbert FunctionsGreco, Ornella January 2013 (has links)
This thesis is constituted of two articles, both related to Hilbert functions and h-vectors. In the first paper, we deal with h-vectorsof reduced zero-dimensional schemes in the projective plane, and, in particular, with the problem of finding the possible h-vectors for the union of two sets of points of given h-vectors. In the second paper, we generalize the Green’s Hyperplane Restriction Theorem to the case of modules over the polynomial ring. / <p>QC 20131114</p>
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Advanced techniques for analyzing time-frequency dynamics of BOLD activity in schizophreniaBuck, Samuel Peter 09 March 2022 (has links)
Magnetic resonance imaging of neuronal activity is one of the most promising techniques in modern psychiatric research. While clear functional links with phenotypic variables have been established and detailed networks of activity robustly identified, fMRI scans have not yet yielded the robust biomarkers of psychiatric diseases, such as schizophrenia, which would allow for their use as a clinical diagnostic tool. One possible explanation for the lack of such results is that neural activity is highly non- stationary, whereas most analysis techniques assume that signal properties remain relatively static over time. Time-frequency analysis is a family of analytic techniques which do not assume that data is stationary, and thus is well suited to the analysis of neural time series. Resting state fMRI scans from a publicly available dataset were decomposed using the Wavelet transform and Hilbert Huang Transform, techniques from time-frequency analysis. The results of these processes were then used as the basis for calculating several properties of the fMRI signal within each voxel. The wavelet transform, a simpler technique, generated measures which showed broad differences between patients with schizophrenia and healthy controls but failed to reach statistical significance in the vast majority of situations. The Hilbert Huang transform, in contrast, showed significant increases in certain measures throughout areas associated with sensory processing, dysfunction in which is a symptom of schizophrenia. These results support the use of analysis techniques able to capture the nonstationarities in neural data and encourages the use of such techniques to explore the nature of the neural differences in psychiatric disorders.
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Experimental Investigation of Laser-Induced Optoacoustic Wave Propagation for Damage DetectionJanuary 2019 (has links)
abstract: This thesis intends to cover the experimental investigation of the propagation of laser-generated optoacoustic waves in structural materials and how they can be utilized for damage detection. Firstly, a system for scanning a rectangular patch on the sample is designed. This is achieved with the help of xy stages which are connected to the laser head and allow it to move on a plane. Next, a parametric study was designed to determine the optimum testing parameters of the laser. The parameters so selected were then used in a series of tests which helped in discerning how the Ultrasound Waves behave when damage is induced in the sample (in the form of addition of masses). The first test was of increasing the mases in the sample. The second test was a scan of a rectangular area of the sample with and without damage to find the effect of the added masses. Finally, the data collected in such a manner is processed with the help of the Hilbert-Huang transform to determine the time of arrival. The major benefits from this study are the fact that this is a Non-Destructive imaging technique and thus can be used as a new method for detection of defects and is fairly cheap as well. / Dissertation/Thesis / Masters Thesis Mechanical Engineering 2019
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ADMM-Type Methods for Optimization and Generalized Nash Equilibrium Problems in Hilbert Spaces / ADMM-Methoden für Optimierungs- und Verallgemeinerte Nash-Gleichgewichtsprobleme in HilberträumenBörgens, Eike Alexander Lars Guido January 2020 (has links) (PDF)
This thesis is concerned with a certain class of algorithms for the solution of constrained optimization problems and generalized Nash equilibrium problems in Hilbert spaces. This class of algorithms is inspired by the alternating direction method of multipliers (ADMM) and eliminates the constraints using an augmented Lagrangian approach. The alternating direction method consists of splitting the augmented Lagrangian subproblem into smaller and more easily manageable parts.
Before the algorithms are discussed, a substantial amount of background material, including the theory of Banach and Hilbert spaces, fixed-point iterations as well as convex and monotone set-valued analysis, is presented. Thereafter, certain optimization problems and generalized Nash equilibrium problems are reformulated and analyzed using variational inequalities and set-valued mappings. The analysis of the algorithms developed in the course of this thesis is rooted in these reformulations as variational inequalities and set-valued mappings.
The first algorithms discussed and analyzed are one weakly and one strongly convergent ADMM-type algorithm for convex, linearly constrained optimization. By equipping the associated Hilbert space with the correct weighted scalar product, the analysis of these two methods is accomplished using the proximal point method and the Halpern method.
The rest of the thesis is concerned with the development and analysis of ADMM-type algorithms for generalized Nash equilibrium problems that jointly share a linear equality constraint. The first class of these algorithms is completely parallelizable and uses a forward-backward idea for the analysis, whereas the second class of algorithms can be interpreted as a direct extension of the classical ADMM-method to generalized Nash equilibrium problems.
At the end of this thesis, the numerical behavior of the discussed algorithms is demonstrated on a collection of examples. / Die vorliegende Arbeit behandelt eine Klasse von Algorithmen zur Lösung restringierter Optimierungsprobleme und verallgemeinerter Nash-Gleichgewichtsprobleme in Hilberträumen. Diese Klasse von Algorithmen ist angelehnt an die Alternating Direction Method of Multipliers (ADMM) und eliminiert die Nebenbedingungen durch einen Augmented-Lagrangian-Ansatz. Im Rahmen dessen wird in der Alternating Direction Method of Multipliers das jeweilige Augmented-Lagrangian-Teilproblem in kleinere Teilprobleme aufgespaltet.
Zur Vorbereitung wird eine Vielzahl grundlegender Resultate präsentiert. Dies beinhaltet entsprechende Ergebnisse aus der Literatur zu der Theorie von Banach- und Hilberträumen, Fixpunktmethoden sowie konvexer und monotoner mengenwertiger Analysis. Im Anschluss werden gewisse Optimierungsprobleme sowie verallgemeinerte Nash-Gleichgewichtsprobleme als Variationsungleichungen und Inklusionen mit mengenwertigen Operatoren formuliert und analysiert. Die Analysis der im Rahmen dieser Arbeit entwickelten Algorithmen bezieht sich auf diese Reformulierungen als Variationsungleichungen und Inklusionsprobleme.
Zuerst werden ein schwach und ein stark konvergenter paralleler ADMM-Algorithmus zur Lösung von separablen Optimierungsaufgaben mit linearen Gleichheitsnebenbedingungen präsentiert und analysiert. Durch die Ausstattung des zugehörigen Hilbertraums mit dem richtigen gewichteten Skalarprodukt gelingt die Analyse dieser beiden Methoden mit Hilfe der Proximalpunktmethode und der Halpern-Methode.
Der Rest der Arbeit beschäftigt sich mit Algorithmen für verallgemeinerte Nash-Gleichgewichtsprobleme, die gemeinsame lineare Gleichheitsnebenbedingungen besitzen. Die erste Klasse von Algorithmen ist vollständig parallelisierbar und es wird ein Forward-Backward-Ansatz für die Analyse genutzt. Die zweite Klasse von Algorithmen kann hingegen als direkte Erweiterung des klassischen ADMM-Verfahrens auf verallgemeinerte Nash-Gleichgewichtsprobleme aufgefasst werden.
Abschließend wird das Konvergenzverhalten der entwickelten Algorithmen an einer Sammlung von Beispielen demonstriert.
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Introduction to Algebraic Geometry with a View Toward Hilbert SchemesLindström, Oliver January 2022 (has links)
In this bachelor’s thesis an introduction to the fundamentals of algebraic geometry is given. Some concepts in algebraic geometry are introduced such as Spec of a ring and Proj of a graded ring and several results related to these are either proven or stated. Special focus is directed towards defining the so called ”Hilbert scheme” which is the main topic in a lot of modern algebraic geometry research.
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Comparison of Hilbert Transform and Derivative Methods for Converting ECG Data Into Cardioid Plots to Detect Heart AbnormalitiesGoldie, Robert George 01 June 2021 (has links) (PDF)
Electrocardiogram (ECG) time-domain signals contain important information about the heart. Several techniques have been proposed for creating a two-dimensional visualization of an ECG, called a Cardioid, that can be used to detect heart abnormalities with computer algorithms. The derivative method is the prevailing technique, which is popular for its low complexity, but it can introduce distortion into the Cardioid plot without additional signal processing. The Hilbert transform is an alternative method which has unity gain and phase shifts the ECG signal by 90 degrees to create the Cardioid plot. However, the Hilbert transform is seldom used and has historically been implemented with a computationally expensive process. In this thesis we show a low-complexity method for implementing the Hilbert transform as a finite impulse response (FIR) filter. We compare the fundamental differences between Cardioid plots generated with the derivative and Hilbert transform methods and demonstrate the feature-preserving nature of the Hilbert transform method. Finally, we analyze the RMS values of the transformed signals to show how the Hilbert transform method can create near 1:1 aspect ratio Cardioid plots with very little distortion for any patient data.
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The Hilbert TransformMcGovern, James Denis 04 1900 (has links)
Abstract Not Provided. / Thesis / Master of Science (MSc)
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