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Paditz, Ludwig. "Using ClassPad-technology in the education of students of electricalengineering (Fourier- and Laplace-Transformation)." Proceedings of the tenth International Conference Models in Developing Mathematics Education. - Dresden : Hochschule für Technik und Wirtschaft, 2009. - S. 469 - 474, 2012. https://slub.qucosa.de/id/qucosa%3A1799.
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By the help of several examples the interactive work with the ClassPad330 is considered. The student can solve difficult exercises of practical applications step by step using the symbolic calculation and the graphic possibilities of the calculator. Sometimes several fields
of mathematics are combined to solve a problem. Let us consider the ClassPad330 (with the actual operating system OS 03.03) and discuss on some new exercises in analysis, e.g. solving a linear differential equation by the help of the Laplace transformation and using the inverse Laplace transformation or considering the Fourier transformation in discrete time (the Fast Fourier Transformation FFT and the inverse FFT). We use the FFT- and IFFT-function to study periodic signals, if we only have a sequence generated by sampling the time signal. We know several ways to get a solution. The techniques for studying practical applications fall into the following three categories: analytic, graphic and numeric. We can use the
Classpad software in the handheld or in the PC (ClassPad emulator version of the handheld).
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Paditz, Ludwig. "Using ClassPad-technology in the education of students of electrical engineering (Fourier- and Laplace-Transformation)." Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2012. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-80814.
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By the help of several examples the interactive work with the ClassPad330 is considered. The student can solve difficult exercises of practical applications step by step using the symbolic calculation and the graphic possibilities of the calculator. Sometimes several fields
of mathematics are combined to solve a problem. Let us consider the ClassPad330 (with the actual operating system OS 03.03) and discuss on some new exercises in analysis, e.g. solving a linear differential equation by the help of the Laplace transformation and using the inverse Laplace transformation or considering the Fourier transformation in discrete time (the Fast Fourier Transformation FFT and the inverse FFT). We use the FFT- and IFFT-function to study periodic signals, if we only have a sequence generated by sampling the time signal. We know several ways to get a solution. The techniques for studying practical applications fall into the following three categories: analytic, graphic and numeric. We can use the
Classpad software in the handheld or in the PC (ClassPad emulator version of the handheld).
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Li, Wei. "Thermal Barrier Effect, Non-Fourier Effect and Inertia Effect on a Cracked Plate under Thermal Shock Loading." Thesis, Sorbonne Paris Cité, 2016. http://www.theses.fr/2016USPCD089/document.
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Les chocs thermiques provoquent, en général, l’endommagement et la fissuration des matériaux. Ces phénomènes sont observés, par exemple, dans le revêtement de barrière thermique pour les moteurs des turbines, le traitement des surfaces ou la soudure par laser etc. Plusieurs travaux de recherche ont été réalisés au cours des dernières décennies dans l’objectif d’améliorer les performances thermiques et/ou mécaniques des matériaux sous chargement thermique. L’étude des dommages et de la fissuration des matériaux provoqués par les chocs thermiques, tels que le décollement des interfaces et de décohésion de revêtements, a reçu également une attention considérable par les chercheurs. La majorité de ces travaux utilisent les théories classiques, tels que la loi de Fourier de conduction thermique et l'hypothèse de quasi-statique. Malheureusement ces théories ne sont pas adaptées dans le cas de charges extrêmes provoqués par le choc thermique et dans le cas des matériaux micro-fissurés. En conséquence, les théories conventionnelles doivent être enrichies.L'objectif de la thèse est de montrer le rôle crucial des termes non Fourier et les termes inertiels dans le cas de choc thermique sous conditions sévères et dans le cas où les fissures sont petites. Pour cela nous avons mené des études sur deux structures particulières soumises à des chocs thermiques. Chaque structure contient une fissure parallèle au bord libre de la structure située au voisinage de ce dernier. L’influence de la présence de fissure sur la conductivité thermique est prise en compte. Nous avons utilisé la théorie Hyperbolique de transfert de chaleur par conduction pour les champs thermique et mécanique à la place de la théorie traditionnelle classique de Fourier. Pour mener cette étude, nous avons utilisé les Transformées de Laplace et de Fourier aux équations de mouvement et à l’équation de transfert de chaleur. En s’intéressant en particulier aux champs de contrainte au voisinage de la pointe de fissure et aux facteurs d'intensité de contrainte dynamiques. Le problème se ramène à la résolution d’un système d'équations intégrales singulières dans l'espace de Laplace-Fourier. On utilise une méthode d'intégration numérique pour obtenir les différents champs. Nous résolvons ensuite un système d'équations algébriques linéaires. En effectuant des inversions numériques des transformées, nous obtenons les champs de contrainte de température et les facteurs d'intensité de contrainte dynamiques dans le domaine temporel.Les résultats numériques montrent que la conductivité thermique du milieu est affectée par l’ouverture de la fissure ce qui perturberait fortement le champ de température ainsi que l'amplitude des facteurs d'intensité de contrainte dynamiques. Les amplitudes sont supérieures à celles obtenues à partir de la théorie classique de Fourier ainsi que dans le cadre de l'hypothèse quasi-statique. On constate également qu’elles oscillent au cours du temps. La prise en compte simultanément de l’influence de la fissure sur la conductivité thermique, de l'effet non-Fourier ainsi que les effetsIVd'inertie induit un couplage entre les trois phénomènes qui rendrait le problème de choc thermique très complexe. L'effet de barrière thermique induit par la fissure affecte d’une manière significative les champs de température et des contraintes. Les effets d’inertie, et des termes non-Fourier joueraient également un rôle non négligeable lorsque la longueur de la fissure est petite. Comme dans de nombreux problèmes d'ingénierie, l'initiation et la propagation des micro-fissures sont des mécanismes dont il faut tenir compte dans les prévisions de la rupture des structures. Ces effets non conventionnels ne sont plus négligeables et doivent être inclus dans l'analyse de la fracture des structures soumises à des chocs thermiquesThermal shock problems occur in many engineering materials and elements, which are used in high temperature applications such as thermal barrier coatings (TBCs), solid propellant of rocket-engine, pulsed-laser processing of materials, and so on. The thermal shock resistance performances and the thermal shock damages of materials, especially the interface debonding and spallation of coatings, have received considerable attention in both analysis and design. Some conventional theories, such as the Fourier’s law of thermal conduction and the quasi-static assumption of the thermoelastic body, may no longer be appropriate because of the extreme loads provoked by the thermal shock. Therefore, these conventional theories need to be enriched or revised.The objective of this thesis is to develop the solutions of the transient temperature field and thermal stresses around a partially insulated crack in a thermoelastic strip under thermal shock loading. The crack lies parallel to the heated traction free surface. The thermal conductivity of the crack gap is taken into account. Hyperbolic heat conduction theory is used in solving the temperature field instead of the traditional Fourier thermal conduction theory. Equations of motion are applied to obtain the stress fields and the dynamic stress intensity factors of the crack. The Laplace and Fourier transforms are applied to solve the thermal-elastic governing equations such that the mixed boundary value problems are reduced to solving a singular integral equations system in Laplace-Fourier space. The numerical integration method is applied to get the temperature field and stress fields, respectively. The problems are then solved numerically by converting the singular integral equations to a linear algebraic equations system. Finally, numerical inversions of the Laplace transform are performed to obtain the temperature field and dynamic stress intensity factors in the time domain.Numerical results show that the thermal conductivity of the crack gap strongly affects the uniformity of the temperature field and consequently, the magnitude of the dynamic stress intensity factors of the crack. The stress intensity factors would have higher amplitude and oscillating feature comparing to those obtained under the conventional Fourier thermal conduction and quasi-static hypotheses. It is also observed that the interactions of the thermal conductivity of the crack gap, the non-Fourier effect and the inertia effects would make the dynamic thermal shock problem more complex. The magnitude of the thermal barrier, non-Fourier and inertia effects is estimated for some practical cases
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Litman, Amélie. "Deux methodes d'inversion pour la caracterisation electromagnetique ou acoustique d'objets enfouis : transformee de fourier-laplace inverse et deformation d'ensembles de niveaux." Paris 11, 1997. http://www.theses.fr/1997PA112254.
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Deux problemes inverses bien precis de diffraction des ondes sont abordes : la caracterisation d'inclusions dans un bloc metallique par des courants electromagnetiques basses-frequences et celle d'un diffracteur homogene en espace libre ou stratifie. Ces deux problemes sont non-lineaires et mal-poses. Le premier probleme concerne le controle non-destructif en courants de foucault. C'est dans le cadre de la tomographie par diffraction que ce probleme, ici linearise, est aborde. L'equation obtenue est une transformee de fourier-laplace, ou le parametre de laplace est couple a celui de fourier. Deux algorithmes sont developpes. Le premier utilise le theoreme d'echantillonnage d'ostrowsky et la propriete d'invariance par dilatation des transformations de laplace. Une connaissance a priori du support du defaut est incorporee afin de raffiner le fenetrage de recherche et d'obtenir une meilleure resolution. Le deuxieme algorithme calcule la solution inverse generalisee du probleme. Une ponderation est introduite pour contrebalancer l'attenuation des ondes dans le metal. Le deuxieme probleme concerne la caracterisation d'objets binaires et se ramene a un probleme d'identification de domaine. Un algorithme iteratif est propose. Il consiste a deformer un domaine initial de maniere a minimiser l'erreur sur les champs diffractes simules et mesures. La vitesse de deformation permet de controler l'evolution du processus. Cette vitesse apparait dans la derivee de la fonctionnelle cout en compagnie d'un etat adjoint. Une fonction de niveaux est utilisee pour representer le domaine. Le contour de l'objet est alors la courbe de niveau 0 de cette fonction de niveaux. Cette representation permet de s'affranchir de contraintes topologiques fortes et d'effectuer de facon naturelle les changements topologiques tels que la fusion. Une equation de type hamilton-jacobi permet de suivre la deformation de cette fonction de niveaux.
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Feng, Le. "An in-depth examination of two-dimensional Laplace inversion and application to three-dimensional holography." University of Dayton / OhioLINK, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=dayton1406814392.
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Paolantoni, Thibault. "Application de Riemann-Hilbert-Birkhoff." Thesis, Université Paris-Saclay (ComUE), 2017. http://www.theses.fr/2017SACLS410/document.
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L'application exponentielle duale est une façon d'encoder les matrices de Stokes d'une connexion sur un fibré trivial sur la sphère de Riemann avec deux pôles : un pôle double en 0 et un pôle simple en l'infini.On donne ici une formule pour l'application exponentielle duale comme une série formelle non commutative. D'autres généralisations de cette formule sont donnéesThe exponential dual map is a way to encode Stokes data of a connection on a trivial vector bundle on the Riemann sphere with two poles: one double pole at 0 and one simple pole at infinity.We give here a formula for the exponential dual map expressed as a non commutative serie. Others generalizations of this formula are given
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Dušanka, Perišić. "On Integral Transforms and Convolution Equations on the Spaces of Tempered Ultradistributions." Phd thesis, Univerzitet u Novom Sadu, Prirodno-matematički fakultet u Novom Sadu, 1992. https://www.cris.uns.ac.rs/record.jsf?recordId=73337&source=NDLTD&language=en.
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In the thesis are introduced and investigated spaces of Burling and of Roumieu type tempered ultradistributions, which are natural generalization of the space of Schwartz’s tempered distributions in Denjoy-Carleman-Komatsu’s theory of ultradistributions. It has been proved that the introduced spaces preserve all of the good properties Schwartz space has, among others, a remarkable one, that the Fourier transform maps continuposly the spaces into themselves.In the first chapter the necessary notation and notions are given.In the second chapter, the spaces of ultrarapidly decreasing ultradifferentiable functions and their duals, the spaces of Beurling and of Roumieu tempered ultradistributions, are introduced; their topological properties and relations with the known distribution and ultradistribution spaces and structural properties are investigated; characterization of the Hermite expansions and boundary value representation of the elements of the spaces are given.The spaces of multipliers of the spaces of Beurling and of Roumieu type tempered ultradistributions are determined explicitly in the third chapter.The fourth chapter is devoted to the investigation of Fourier, Wigner, Bargmann and Hilbert transforms on the spaces of Beurling and of Roumieu type tempered ultradistributions and their test spaces.In the fifth chapter the equivalence of classical definitions of the convolution of Beurling type ultradistributions is proved, and the equivalence of, newly introduced definitions, of ultratempered convolutions of Beurling type ultradistributions is proved.In the last chapter is given a necessary and sufficient condition for a convolutor of a space of tempered ultradistributions to be hypoelliptic in a space of integrable ultradistribution, is given, and hypoelliptic convolution equations are studied in the spaces.Bibliograpy has 70 items.U ovoj tezi su proučavani prostori temperiranih ultradistribucija Beurlingovog i Roumieovog tipa, koji su prirodna uopštenja prostora Schwarzovih temperiranih distribucija u Denjoy-Carleman-Komatsuovoj teoriji ultradistribucija. Dokazano je ovi prostori imaju sva dobra svojstva, koja ima i Schwarzov prostor, izmedju ostalog, značajno svojstvo da Furijeova transformacija preslikava te prostore neprekidno na same sebe.U prvom poglavlju su uvedene neophodne oznake i pojmovi.U drugom poglavlju su uvedeni prostori ultrabrzo opadajucih ultradiferencijabilnih funkcija i njihovi duali, prostori Beurlingovih i Rumieuovih temperiranih ultradistribucija; proučavana su njihova topološka svojstva i veze sa poznatim prostorima distribucija i ultradistribucija, kao i strukturne osobine; date su i karakterizacije Ermitskih ekspanzija i graničnih reprezentacija elemenata tih prostora.Prostori multiplikatora Beurlingovih i Roumieuovih temperiranih ultradistribucija su okarakterisani u trećem poglavlju.Četvrto poglavlje je posvećeno proučavanju Fourierove, Wignerove, Bargmanove i Hilbertove transformacije na prostorima Beurlingovih i Rouimieovih temperiranih ultradistribucija i njihovim test prostorima.U petoj glavi je dokazana ekvivalentnost klasičnih definicija konvolucije na Beurlingovim prostorima ultradistribucija, kao i ekvivalentnost novouvedenih definicija ultratemperirane konvolucije ultradistribucija Beurlingovog tipa.U poslednjoj glavi je dat potreban i dovoljan uslov da konvolutor prostora temperiranih ultradistribucija bude hipoeliptičan u prostoru integrabilnih ultradistribucija i razmatrane su neke konvolucione jednačine u tom prostoru.Bibliografija ima 70 bibliografskih jedinica.
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Xu, Yangyi. "Frequentist-Bayesian Hybrid Tests in Semi-parametric and Non-parametric Models with Low/High-Dimensional Covariate." Diss., Virginia Tech, 2014. http://hdl.handle.net/10919/71285.
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We provide a Frequentist-Bayesian hybrid test statistic in this dissertation for two testing problems. The first one is to design a test for the significant differences between non-parametric functions and the second one is to design a test allowing any departure of predictors of high dimensional X from constant. The implementation is also given in construction of the proposal test statistics for both problems.
For the first testing problem, we consider the statistical difference among massive outcomes or signals to be of interest in many diverse fields including neurophysiology, imaging, engineering, and other related fields. However, such data often have nonlinear system, including to row/column patterns, having non-normal distribution, and other hard-to-identifying internal relationship, which lead to difficulties in testing the significance in difference between them for both unknown relationship and high-dimensionality. In this dissertation, we propose an Adaptive Bayes Sum Test capable of testing the significance between two nonlinear system basing on universal non-parametric mathematical decomposition/smoothing components. Our approach is developed from adapting the Bayes sum test statistic by Hart (2009). Any internal pattern is treated through Fourier transformation. Resampling techniques are applied to construct the empirical distribution of test statistic to reduce the effect of non-normal distribution. A simulation study suggests our approach performs better than the alternative method, the Adaptive Neyman Test by Fan and Lin (1998). The usefulness of our approach is demonstrated with an application in the identification of electronic chips as well as an application to test the change of pattern of precipitations.
For the second testing problem, currently numerous statistical methods have been developed for analyzing high-dimensional data. These methods mainly focus on variable selection approach, but are limited for purpose of testing with high-dimensional data, and often are required to have explicit derivative likelihood functions. In this dissertation, we propose ``Hybrid Omnibus Test'' for high-dimensional data testing purpose with much less requirements. Our Hybrid Omnibus Test is developed under semi-parametric framework where likelihood function is no longer necessary. Our Hybrid Omnibus Test is a version of Freqentist-Bayesian hybrid score-type test for a functional generalized partial linear single index model, which has link being functional of predictors through a generalized partially linear single index. We propose an efficient score based on estimating equation to the mathematical difficulty in likelihood derivation and construct our Hybrid Omnibus Test. We compare our approach with a empirical likelihood ratio test and Bayesian inference based on Bayes factor using simulation study in terms of false positive rate and true positive rate. Our simulation results suggest that our approach outperforms in terms of false positive rate, true positive rate, and computation cost in high-dimensional case and low-dimensional case. The advantage of our approach is also demonstrated by published biological results with application to a genetic pathway data of type II diabetes.Ph. D.
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Roy, Kirk Andrew. "Laplace transforms, probabilities and queues." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp01/MQ31000.pdf.
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Andreevska, Irena. "Mathematical modeling and analysis of options with jump-diffusion volatility." [Tampa, Fla.] : University of South Florida, 2008. http://purl.fcla.edu/usf/dc/et/SFE0002343.
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Lévy, Guillaume. "Fluides, graphes et transformée de Fourier : trois incarnations du laplacien." Thesis, Paris 6, 2017. http://www.theses.fr/2017PA066321/document.
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Cette thèse est consacrée à l'étude de propriétés du laplacien dans trois contextes bien distincts. Dans une première partie, celui-ci nous sera utile pour régulariser des solutions d'équations venues de la mécanique des fluides incompressibles. En application, on montrera un théorème dans la lignée des résultats de J. Serrin et de ses continuateurs. Dans une deuxième partie, le laplacien est vu comme le pendant stationnaire de l'opérateur des ondes sur un graphe, dont les modes et fréquences propres déterminent la propagation de perturbations sur le graphe. On y explore et démêle les liens entre la topologie du graphe, sa forme et sa première fréquence propre non nulle. Dans une dernière partie, le laplacien est pensé comme un opérateur linéaire à diagonaliser dans une base adaptée, objectif dont l'accomplissement est intimement lié à la transformée de Fourier. Deux difficultés majeures apparaissent ici : la non commutativité des groupes auxquels nous nous intéressons d'une part, l'apparition d'une limite singulière de la transformée de Fourier d'autre partThis thesis is devoted to the study of the laplacian properties in three fully distinct contexts.In a first part, it will be used to smooth solutions of equations coming from incompressible fluid mechanics.As an application, we will show a result in the spirit of J. Serrin and his continuators' theorem.In a second part, the laplacien is seen as the stationary counterpart of the wave operator on a graph, whose eigenmodes and eigenfrequencies determine the propagation of perturbations on the graph.We explore and disentangle the ties between the graph's topology, its shape and its first nonzero eigenfrequency.In the last part, the laplacian is thought of as a linear operator which we wish to diagonalize in an appropriate basis, a goal which is intimately tied to the Fourier transform.Two major difficulties appear in our context : the noncommutativity of the groups of interest on the one hand, the appearance of a singular limit in the Fourier transform on the other hand
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Debernardi, Pinos Alberto. "Convergence and integrability of fourier transforms." Doctoral thesis, Universitat Autònoma de Barcelona, 2018. http://hdl.handle.net/10803/463030.
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El propòsit d'aquesta tesi és el d'estudiar dos tipus de problema diferents per a certes transformades de Fourier.
Primer investiguem la convergència uniforme d'integrals sinusoidals en una i dos dimensions. Per a dur a terme aquesta investigació, utilitzem una condicio de monotonia general, recentment introduïda, tot desenvolupant aquesta teoria en concordança amb les nostres necessitats. Com a resultats principals, obtenim condicions necessàries i suficients que les funcions monòtones generals han de satisfer per tal de poder assegurar la convergència uniforme de les seves respectives transformades sinusoidals (en una i dues dimensions).
En segon lloc, estudiem la convergència puntual i uniforme de les transformades de Hankel amb pesos, a través de l'estudi de les condicions variacionals, d'integració i de magnitud de les funcions involucrades, amb especial èmfasi en les condicions variacionals. També utilitzem l'esmentada condició de monotonia general, que ens permet traduir condicions variacionals de les funcions en condicions d'integrabilitat o magnitud de les mateixes. Donem condicions suficients per a la convergència puntual, mentre que per a la convergència uniforme, també en donem de necessàries, quan és possible. En els casos en els quals només podem donar condicions suficients per a la convergència uniforme, també comentem l'optimalitat d'aquestes.
Finalment, considerem transformades de Fourier generalitzades, i estudiem condicions necessàries i suficients per tal de garantir desigualtats de normes amb pesos entre funcions i les seves transformades. Les desigualtats de normes amb pesos es poden considerar com a versions quantitatives del principi d'incertesa. Donem especial rellevància a les desigualtats amb pesos del tipus funció potencial i les transformades sinusoidals, cosinusoidals, de Hankel, i de Struve. També utilitzem la condició de monotonia general en aquest problema, que ens permet obtenir condicions necessàries i suficients menys restrictives per poder garantir desigualtats de normes amb pesos.The purpose of this dissertation is to study two different kind of problems for certain types of Fourier transforms. First, we investigate the uniform convergence of one and two-dimensional sine transforms. To this end, we make use of a general monotonicity condition that has been recently introduced, and develop the theory further according to our needs. We mainly obtain necessary and sufficient conditions on general monotone functions for the uniform convergence of their respective (single and double) sine integrals. Secondly, we study pointwise and uniform convergence of weighted Hankel transforms through an approach that consists on studying the variational, integrability, and magnitude conditions of the involved functions, with special emphasis on variational conditions. Here we also use the aforementioned general monotonicity, which allows us to translate from variational conditions to magnitude/integrability conditions of the functions. For the pointwise convergence only sufficient conditions are obtained, whilst for the uniform convergence, it is sometimes possible to obtain necessary and sufficient conditions. In the case when only sufficient conditions for the uniform convergence are given, the sharpness of those are discussed. Finally, we consider generalized Fourier transforms and study necessary and sufficient conditions for weighted norm inequalities between functions and their transforms to hold. Weighted norm inequalities can be considered as quantitative uncertainty principle relations. We particularly focus on inequalities with power weights and the sine, cosine, Hankel, and Struve transforms. We also make use of the general monotonicity condition in this problem, which allows us to obtain less restrictive necessary and sufficient for the weighted norm inequalities to hold.
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Khan, Aman Ullah. "Parallel computation of fast Fourier transforms." Thesis, Cardiff University, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.340239.
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Whittle, Gruffudd Hannah Rebecca. "Relaxation spectrum recovery using Fourier transforms." Thesis, Aberystwyth University, 2012. http://hdl.handle.net/2160/f2b30f89-dc62-4038-83c9-1857eca8a2b5.
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In this thesis we consider the problem of recovering the relaxation spectrum from the storage and loss moduli. We invert an integral equation using Fourier transforms. Recovering the relaxation spectrum is an inverse, ill-posed problem and hence regularisation methods must be used to try and obtain the relaxation spectrum. We are particularily interested in establishing properties of the relaxation spectrum. We note from the literature that there are results of compact support for the relaxation spectrum; we review to what extent and in what sense, these results are valid. We consider the methods used in the literature and demonstrate their strengths and weaknesses, supplying some missing details. We demonstrate in chapter 3 the difficulty in obtaining an interval of compact support for the relaxation spectrum and in the remainder of chapter 3 and chapter 4 we prove results of non-compactness of support for non-trivial relaxation spectra. Our settings are square integrable functions in chapter 3, and Schwartz distributions in chapter 4; we make use of Paley-Wiener theorems. These are important results since they contradict results in the literature that we review in chapter 2. We are able to demonstrate, using examples and via direct calculations, that the relaxation spectrum becomes insignificant outside some closed interval. With regards to numerical computations, this could be considered as a weak form of compact support. We call this essential numerical support; this may be a useful concept for the practical rheologist.
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Horn, Wayne. "Laplace transforms of order statistics of Erlang random variables." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape10/PQDD_0014/MQ52571.pdf.
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Srivastava, Sachi. "Laplace transforms, non-analytic growth bounds and C₀-semigroups." Thesis, University of Oxford, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.249507.
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In this thesis, we study a non-analytic growth bound $\zeta(f)$ associated with an exponentially bounded measurable function $f: \mathbb{R}_{+} \to \mathbf{X},$ which measures the extent to which $f$ can be approximated by holomorphic functions. This growth bound is related to the location of the domain of holomorphy of the Laplace transform of $f$ far from the real axis. We study the properties of $\zeta(f)$ as well as two associated abscissas, namely the non-analytic abscissa of convergence, $\zeta_{1}(f)$ and the non-analytic abscissa of absolute convergence $\kappa(f)$. These new bounds may be considered as non-analytic analogues of the exponential growth bound $\omega_{0}(f)$ and the abscissas of convergence and absolute convergence of the Laplace transform of $f,$ $\operatorname{abs}(f)$ and $\operatorname{abs}(\|f\|)$. Analogues of several well known relations involving the growth bound and abscissas of convergence associated with $f$ and abscissas of holomorphy of the Laplace transform of $f$ are established. We examine the behaviour of $\zeta$ under regularisation of $f$ by convolution and obtain, in particular, estimates for the non-analytic growth bound of the classical fractional integrals of $f$. The definitions of $\zeta, \zeta_{1}$ and $\kappa$ extend to the operator-valued case also. For a $C_{0}$-semigroup $\mathbf{T}$ of operators, $\zeta(\mathbf{T})$ is closely related to the critical growth bound of $\mathbf{T}$. We obtain a characterisation of the non-analytic growth bound of $\mathbf{T}$ in terms of Fourier multiplier properties of the resolvent of the generator. Yet another characterisation of $\zeta(\mathbf{T}) $ is obtained in terms of the existence of unique mild solutions of inhomogeneous Cauchy problems for which a non-resonance condition holds. We apply our theory of non-analytic growth bounds to prove some results in which $\zeta(\mathbf{T})$ does not appear explicitly; for example, we show that all the growth bounds $\omega_{\alpha}(\mathbf{T}), \alpha >0,$ of a $C_{0}$-semigroup $\mathbf{T}$ coincide with the spectral bound $s(\mathbf{A})$, provided the pseudo-spectrum is of a particular shape. Lastly, we shift our focus from non-analytic bounds to sun-reflexivity of a Banach space with respect to $C_{0}$-semigroups. In particular, we study the relations between the existence of certain approximations of the identity on the Banach space $\xspace$ and that of $C_{0}$-semigroups on $\mathbf{X}$ which make $\mathbf{X}$ sun-reflexive.
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Sudler, Glenn F. "Asian Options: Inverse Laplace Transforms and Martingale Methods Revisited." Thesis, Virginia Tech, 1999. http://hdl.handle.net/10919/34300.
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Arithmetic Asian options are difficult to price and hedge, since, at the present, no closed-form analytical solution exists to price them. This difficulty, moreover, has led to the development of various methods and models used to price these instruments. The purpose of this thesis is two-fold. First, we present an overview of the literature. Secondly, we develop a pseudo-analytical method proposed by Geman and Yor and present an accurate and relatively quick algorithm which can be used to price European-style arithmetic Asian options and their hedge parameters.Master of Science
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Lucrecio, Armando. "ISAR imaging using Fourier and wavelet transforms." Thesis, Monterey, Calif. : Naval Postgraduate School, 2007. http://bosun.nps.edu/uhtbin/hyperion-image.exe/07Dec%5FLucrecio.pdf.
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Thesis (M.S. in Physics)--Naval Postgraduate School, December 2007.Thesis Advisor(s): Borden, Brett ; Cristi, Roberto. "December 2007." Description based on title screen as viewed on January 23, 2008 Includes bibliographical references (p. 61-62). Also available in print.
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Long, Na. "Basic theorems of distributions and Fourier transforms." Kansas State University, 2014. http://hdl.handle.net/2097/18731.
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Master of ScienceDepartment of Mathematics
Marianne Korten
Distribution theory is an important tool in studying partial differential equations. Distributions are linear functionals that act on a space of smooth test functions. Distributions make it possible to differentiate functions whose derivatives do not exist in the classical sense. In particular, any locally integrable function has a distributional derivative. There are different possible choices for the space of test functions, leading to different spaces of distributions. In this report, we take a look at some basic theory of distributions and their Fourier transforms. And we also solve some typical exercises at the end.
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Pester, M., and S. Rjasanow. "A parallel version of the preconditioned conjugate gradient method for boundary element equations." Universitätsbibliothek Chemnitz, 1998. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-199800455.
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The parallel version of precondition techniques is developed for
matrices arising from the Galerkin boundary element method for
two-dimensional domains with Dirichlet boundary conditions.
Results were obtained for implementations on a transputer network
as well as on an nCUBE-2 parallel computer showing that iterative
solution methods are very well suited for a MIMD computer. A
comparison of numerical results for iterative and direct solution
methods is presented and underlines the superiority of iterative
methods for large systems.
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Curnow, Paula. "Genealogy under fission-fusion models of population subdivision." Thesis, University of Oxford, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.275553.
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Conrad, Eric van Fossen. "Some Continued Fraction Expansions of Laplace Transforms of Elliptic Functions." The Ohio State University, 2002. http://rave.ohiolink.edu/etdc/view?acc_num=osu1029248229.
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Mukanov, Askhat. "Integrability of Fourier transforms, general monotonicity, and related problems." Doctoral thesis, Universitat Autònoma de Barcelona, 2018. http://hdl.handle.net/10803/463043.
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El propòsit d'aquesta tesi és el d'estudiar les propietats d'integrabilitat i convergència de sèries i transformades de Fourier. Els resultats principals són els següents: 1. Incestiguem les propietats d'integrabilitat de sèries trigonomètriques amb coeficients que satisfan una condició de monotonia general i demostrem resultats del tipus Hardy-Littlewood, és a dir, equivalències entre normes de les sumes de sèries trigonomètriques i normes amb pesos dels seus coeficients de Fourier. Demostrem aquestes equivalències en espais de Lorentz i espais de Lebesgue amb pesos. 2. Estudiem propietats de suavitat de funcions que poden ser representades per mitjà de sèries trigonomètriques amb coefficients que satisfan una condició de monotonia general. Es demostra una equivalència del Lp-mòdul de suavitat d'aquestes funcions i les sumes amb pesos dels seus coeficients de Fourier. 3. Obtenim versions multi-dimensionals de teoremes de tipus Boas en relació a les propietats d'integrabilitat de transformades de Fourier de funcions que són monòtones en totes les variable. 4. Finalment, estudiem criteris per a la convergència uniforme de sèries trigonomètriques amb coefficients que satisfan una condició de monotonia general. En particular, generalitzem el conegut criteri de Chaundy-Jolliffe per a la convergència uniforme de sèries sinusoidals i obtenim el resultat corresponent per sèries cosinusoidals. A més, provem condicions necessàries i suficients per tal que les sumes partials de Fourier d'aquestes sèries tinguin un cert ordre de convergència.This thesis is devoted to the study of integrability and convergence properties of Fourier series and transforms. The main results are the following. 1. We investigate the integrability properties of trigonometric series with general monotone coefficients and prove the Hardy-Littlewood-type results, i.e., equivalences of the norms of sums of trigonometric series and weighted norms of their Fourier coefficients. We prove such equivalences for the Lorentz and weighted Lebesgue spaces. Here we deal with the trigonometric series with general monotone coefficients. 2. We study the smoothness properties of functions that can be represented by trigonometric series with general monotone coefficients. The equivalence of the Lp-modulus of smoothness of such functions and weighted sums of their Fourier coefficients is proved. 3. We obtain the multidimensional versions of Boas-type theorem on integrability properties of the Fourier transforms of monotone in each variable functions. 4. Finally, we study criteria for the uniform convergence of trigonometric series with general monotone coefficients. In particular, we generalize the well-known Chaundy-Jolliffee criterion for the uniform convergence of sine series and obtain the corresponding result for cosine series. Moreover, we prove necessary and sufficient conditions for partial Fourier sums of such series to have certain convergence rate.
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Öhlin, Andreas. "Real-Time Multi-Dimensional Fast Fourier Transforms on FPGAs." Thesis, Linköpings universitet, Datorteknik, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-120250.
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This thesis presents a way of performing multi dimensional FFT in a continuousflow environment by calculating the FFT of each dimension separately ina pipeline. The result is a three dimensional pipelined FFT implemented on aStratix III FPGA. It can calculate the three dimensional FFT of a data set containing2563 samples with a word size of 32 bits. The biggest challenge and themain part of the work are the data permutations in between the one dimensionalFFT modules, this part of the design make use of an external DDR2 SDRAMas well as on-chip BRAM to store and permute data between the modules. Theevaluations show that the design is hardware efficient and the latency is relativelylow and determined to be 84.2 ms.Den här uppsatsen presenterar ett sätt att utföra multidimensionell fouriertransformi en omgivning med kontinuerligt flödande sample genom att beräkna transformenav varje dimension för sig i en pipeline. Resultatet är en tredimensionellpipelinad fouriertransform som är implementerad på en Stratix III FPGA. Dennaklarar av att beräkna fouriertransformen av en indatastorlek på 2563 samplersom är 32 bitar breda. Den största utmaningen och centrala delen av designen ärdatapermutation, denna del använder sig av DDR2 SDRAM och inbyggda BRAMför att spara och permutera data mellan de endimensionella transformmodulerna.Utvärderingen visar att designen är hårdvarueffektiv och att fördröjningen ärrelativt låg och ligger på 84.2 ms.
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Al-Harbi, Hamad F. "Crystal plasticity finite element simulations using discrete Fourier transforms." Diss., Georgia Institute of Technology, 2013. http://hdl.handle.net/1853/51788.
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Crystallographic texture and its evolution are known to be major sources of anisotropy in polycrystalline metals. Highly simplified phenomenological models cannot usually provide reliable predictions of the materials anisotropy under complex deformation paths, and lack the fidelity needed to optimize the microstructure and mechanical properties during the production process. On the other hand, physics-based models such as crystal plasticity theories have demonstrated remarkable success in predicting the anisotropic mechanical response in polycrystalline metals and the evolution of underlying texture in finite plastic deformation. However, the integration of crystal plasticity models with finite element (FE) simulations tools (called CPFEM) is extremely computationally expensive, and has not been adopted broadly by the advanced materials development community. The current dissertation has mainly focused on addressing the challenges associated with integrating the recently developed spectral database approach with a commercial FE tool to permit computationally efficient simulations of heterogeneous deformations using crystal plasticity theories. More specifically, the spectral database approach to crystal plasticity solutions was successfully integrated with the implicit version of the FE package ABAQUS through a user materials subroutine, UMAT, to conduct more efficient CPFEM simulations on both fcc and bcc polycrystalline materials. It is observed that implementing the crystal plasticity spectral database in a FE code produced excellent predictions similar to the classical CPFEM, but at a significantly faster computational speed. Furthermore, an important application of the CPFEM for the extraction of crystal level plasticity parameters in multiphase materials has been demonstrated in this dissertation. More specifically, CPFEM along with a recently developed data analysis approach for spherical nanoindentation and Orientation Imaging Microscopy (OIM) have been used to extract the critical resolved shear stress of the ferrite phase in dual phase steels. This new methodology offers a novel efficient tool for the extraction of crystal level hardening parameters in any single or multiphase materials.
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Pippig, Michael. "Massively Parallel, Fast Fourier Transforms and Particle-Mesh Methods." Doctoral thesis, Universitätsbibliothek Chemnitz, 2016. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-197359.
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The present thesis provides a modularized view on the structure of fast numerical methods for computing Coulomb interactions between charged particles in three-dimensional space. Thereby, the common structure is given in terms of three self-contained algorithmic frameworks that are built on top of each other, namely fast Fourier transform (FFT), nonequispaced fast Fourier transform (NFFT) and NFFT based particle-mesh methods (P²NFFT). For each of these frameworks algorithmic enhancement and parallel implementations are presented with special emphasis on scalability up to hundreds of thousands of parallel processes. In the context of FFT massively parallel algorithms are composed from hardware adaptive low level modules provided by the FFTW software library. The new algorithmic NFFT concepts include pruned NFFT, interlacing, analytic differentiation, and optimized deconvolution in Fourier space with respect to a mean square aliasing error. Enabled by these generalized concepts it is shown that NFFT provides a unified access to particle-mesh methods. Especially, mixed-periodic boundary conditions are handled in a consistent way and interlacing can be incorporated more efficiently. Heuristic approaches for parameter tuning are presented on the basis of thorough error estimatesDie vorliegende Dissertation beschreibt einen modularisierten Blick auf die Struktur schneller numerischer Methoden für die Berechnung der Coulomb-Wechselwirkungen zwischen Ladungen im dreidimensionalen Raum. Die gemeinsame Struktur ist geprägt durch drei selbstständige und auf einander aufbauenden Algorithmen, nämlich der schnellen Fourier-Transformation (FFT), der nicht äquidistanten schnellen Fourier-Transformation (NFFT) und der NFFT-basierten Teilchen-Gitter-Methode (P²NFFT). Für jeden dieser Algorithmen werden Verbesserungen und parallele Implementierungen vorgestellt mit besonderem Augenmerk auf massiv paralleler Skalierbarkeit. Im Kontext der FFT werden parallele Algorithmen aus den Hardware adaptiven Modulen der FFTW Softwarebibliothek zusammengesetzt. Die neuen NFFT-Konzepte beinhalten abgeschnittene NFFT, Versatz, analytische Differentiation und optimierte Entfaltung im Fourier-Raum bezüglich des mittleren quadratischen Aliasfehlers. Mit Hilfe dieser Verallgemeinerungen bietet die NFFT einen vereinheitlichten Zugang zu Teilchen-Gitter-Methoden. Insbesondere gemischt periodische Randbedingungen werden einheitlich behandelt und Versatz wird effizienter umgesetzt. Heuristiken für die Parameterwahl werden auf Basis sorgfältiger Fehlerabschätzungen angegeben
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Piyaratne, Hathurusinghege Dulip Bandara. "Fourier-Mukai transforms and stability conditions on abelian threefolds." Thesis, University of Edinburgh, 2014. http://hdl.handle.net/1842/9635.
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Construction of Bridgeland stability conditions on a given Calabi-Yau threefold is an important problem and this thesis realizes the rst known examples of such stability conditions. More precisely, we construct a dense family of stability conditions on the derived category of coherent sheaves on a principally polarized abelian threefold X with Picard rank one. In particular, we show that the conjectural construction proposed by Bayer, Macr and Toda gives rise to Bridgeland stability conditions on X. First we reduce the requirement of the Bogomolov-Gieseker type inequalities to a smaller class of tilt stable objects which are essentially minimal objects of the conjectural stability condition hearts for a given smooth projective threefold. Then we use the Fourier-Mukai theory to prove the strong Bogomolov-Gieseker type inequalities for these minimal objects of X. This is done by showing any Fourier-Mukai transform of X gives an equivalence of abelian categories which are double tilts of coherent sheaves.
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Kopezhanova, Aigerim. "Summability of Fourier transforms of functions from Lorentz spaces." Doctoral thesis, Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:ltu:diva-63150.
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This PhD thesis is devoted to the study of relations between integrability properties of functions and summability properties of its Fourier coefficients and transforms. The relations are given in terms of generalized weighted Lorentz norms, where the weights have some additional growth properties. The thesis contains six papers (papers A-F) together with an introduction, which put these papers into a general frame. In paper A some relations between weighted Lorentz norms and some corresponding sums of Fourier coefficients are studied for the case with a general orthonormal bounded system. Under certain circumstances even two-sided estimates are obtained. In paper B we study relations between summability of Fourier coefficients and integrability of the corresponding functions for generalized weighted Lorentz spaces in the case of a regular system. Some new inequalities of Hardy-Littlewood-Paley type with respect to a regular system for these generalized Lorentz spaces are obtained. It is also proved that the obtained results are in a sense sharp. In paper C we investigate integrability properties of the orthogonal series with coefficients from generalized weighted Lorentz spaces in the case of a regular system. The upper and the lower estimates of some corresponding Lorentz type norms of the Fourier coefficients are obtained. In paper D some new Boas type theorems for generalized weighted Lorentz spaces with respect to regular systems for generalized monotone functions are proved. In paper E inequalities for the Fourier transform of functions from the generalized weighted Lorentz spaces are studied. The upper and the lower estimates of the norm of the Fourier transform in generalized weighted Lorentz spaces are derived. Finally, in paper F a new inequality concerning the Fourier transform is derived. Moreover, it is described conditions so that this result is sharp in the sense that both upper and lower bounds are obtained.
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Mavridou, Evanthia. "Robust image description with laplacian profile and radial Fourier transform." Thesis, Grenoble, 2014. http://www.theses.fr/2014GRENM065/document.
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L'objectif de cette thèse est l'étude d'un descripteur d'images adapté à une grande variété d'applications. Nous cherchons à obtenir un descripteur robuste et discriminant, facile à adapter et peu coûteux en calcul et en mémoire.Nous définissons un nouveau descripteur, composé de valeurs du Laplacien à différentes échelles et de valeurs d'une transformée de Fourier radiale, calculées à partir d'une pyramide Gaussienne. Ce descripteur capture une information de forme multi-échelle autour d'un point de l'image. L'expérimentation a montré que malgré une taille mémoire réduite les performances en robustesse et en pouvoir discriminant de ce descripteur sont à la heuteur de l'état de l'art.Nous avons expérimenté ce descripteur avec trois types de tâches différentes.Le premier type de tâche est la mise en correspondance de points-clés avec des images transformées par rotation, changement d'échelle, floutage, codage JPEG, changement de point de vue, ou changement d'éclairage. Nous montrons que la performance de notre descripteur est au niveau des meilleurs descripteurs connus dans l'état de l'art. Le deuxième type de tâche est la détection de formes. Nous avons utilisé le descripteur pour la création de deux détecteurs de personnes, construits avec Adaboost. Comparé à un détecteur semblable construit avec des histogrammes de gradients (HOG) nos détecteurs sont très compétitifs tout en utilisant des descripteurs sensiblement plus compacts. Le dernier type de tâche est la détection de symétries de réflexion dans des images "du monde réel". Nous proposons une technique de détection d'axes potentiels de symétries en miroir. Avec cette tâche nous montrons que notre descripteur peut être genéralisé à des situations complexes. L'expérimentation montre que cette méthode est robuste et discriminante, tout en conservant un faible coût en calcul et en mémoireIn this thesis we explore a new image description method composed of a multi-scale vector of Laplacians of Gaussians, the Laplacian Profile, and a Radial Fourier Transform. This method captures shape information with different proportions around a point in the image. A Gaussian pyramid of scaled images is used for the extraction of the descriptor vectors. The aim of this new method is to provide image description that can be suitable for diverse applications. Adjustability as well as low computational and memory needs are as important as robustness and discrimination power. We created a method with the ability to capture the image signal efficiently with descriptor vectors of particularly small length compared to the state of the art. Experiments show that despite its small vector length, the new descriptor shows reasonable robustness and discrimination power that are competitive to the state of the art performance.We test our proposed image description method on three different visual tasks. The first task is keypoint matching for images that have undergone image transformations like rotation, scaling, blurring, JPEG compression, changes in viewpoint and changes in light. We show that against other methods from the state of the art, the proposed descriptor performs equivalently with a very small vector length. The second task is on pattern detection. We use the proposed descriptor to create two different Adaboost based detectors for people detection in images. Compared to a similar detector using Histograms of Oriented Gradients (HOG), the detectors with the proposed method show competitive performance using significantly smaller descriptor vectors. The last task is on reflection symmetry detection in real world images. We introduce a technique that exploits the proposed descriptor for detecting possible symmetry axes for the two reflecting parts of a mirror symmetric pattern. This technique introduces constraints and ideas of how to collect more efficiently the information that is important to identify reflection symmetry in images. With this task we show that the proposed descriptor can be generalized for rather complicated applications. The set of the experiments confirms the qualities of the proposed method of being easily adjustable and requires relatively low computational and storage requirements while remaining robust and discriminative
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Brand, Tristan. "A Fast Fourier Transform for the Symmetric Group." Scholarship @ Claremont, 2006. https://scholarship.claremont.edu/hmc_theses/179.
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A discrete Fourier transform, or DFT, is an isomorphism from a group algebra to a direct sum of matrix algebras. An algorithm that efficiently applies a DFT is called a fast Fourier transform, or FFT. The concept of a DFT will be introduced and examined from both a general and algebraic perspective. We will then present and analyze a specific FFT for the symmetric group.
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Garcia, Jorge. "As Transformadas de Fourier e Laplace na Teoria do Risco." Doctoral thesis, Instituto Superior de Economia e Gestão, 2004. http://hdl.handle.net/10400.5/1910.
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Doutoramento em Matemática Aplicada à Economia e GestãoSão por demais conhecidas as aplicações de transformadas em diversos ramos da ciência e da engenharia. Em particular, na teoria colectiva do risco, as transformadas de Fourier e Laplace têm uma importância acrescida, não só devido à natureza estocástica do processo de risco e das suas componentes, como também pelo facto de variadas soluções, para grande parte dos problemas que se colocam em torno deste tipo de processos, se apresentarem sob a forma de equações diferenciais ou integro-diferenciais, com especial relevo para as equações de renovamento, para resolução das quais aquelas transformadas são fundamentais. A obtenção unívoca de uma determinada função, ou de um seu valor particular, por inversão algébrica ou numérica da respectiva transformada, uma vez encontrada esta, constituiu um dos principais objectivos do trabalho de investigação desenvolvido. Desde a determinação de distribuições agregadas de sinistros, tanto no modelo clássico como em modelos de renovamento, até à determinação de probabilidades de ruína em horizonte finito ou infinito, o presente trabalho procura acentuar as potencialidades da investigação nesta área, bem como a necessidade de aprofundar o papel directo ou indirecto das duplas transformadas, por vezes implícitas, e das fórmulas de inversão complexas disponíveis, tanto sob o ponto de vista analítico, como do ponto de vista prático e numérico. Sobre este último domínio, importa por um lado sublinhar a importância das tranformadas do Coseno e do Seno na inversão da transformada de Fourier, para funções não negativas, as quais, embora conhecidas, têm sido pouco referidas na literatura actuarial, tanto quanto nos é dado conhecer, bem como a necessidade de construir algoritmos de integração numérica potentes, rápidos e precisos, especialmente adaptados à integração de funções circulares, ou funções de rápida oscilação, em intervalos de dimensão por vezes elevada, quando não infinita. Foi este, aliás, um dos objectivos iniciais da investigação prosseguida, que se viria a revelar bastante compensador, pela qualidade dos resultados alcançados, através da construção de um algoritmo arborescente que apelidamos de Integral Dicotómico, o qual se encontra descrito em anexo.
Mathematical transforms and their applications are well known tools and widely used by scientists, engineers and actuaries. In the Collective Risk Theory, Fourier and Laplace transforms have an extra importance due to the stochastic nature of the usual models, either classical or non classical, also to the fact that a great variety of problems emerging from those models have solutions that appear as differential or integral-differential equations, from which renewal equations are the most interesting example. The main goal of this research is the search of an analytic expression for a function, or a particular value by complex or numerical inversion of its transform. The work starts with the study of characteristic functions of the aggregate claims process, either classical or the more general renewal model, goes through the evaluation of survival and ruin probabilities, and wants to enhance a deeper research on these topics using tools as the double Laplace and Fourier transforms. A special attention has been devoted to cosine and sine transforms of non-negative functions. Although well known, they are not frequently referenced in the actuarial literature, however their properties for numerical inversion of Fourier transforms are fundamental. For that purpose, the development of a good algorithm of integration was necessary, a goal which we have achieved successfully by developing the dichotomic approach described in the Appendix.
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Vadrevu, Aditya M. "Random sampling estimates of fourier transforms antithetical stratified Monte Carlo /." Diss., Connect to a 24 p. preview or request complete full text in PDF format. Access restricted to UC campuses, 2008. http://wwwlib.umi.com/cr/ucsd/fullcit?p1450161.
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Thesis (M.S.)--University of California, San Diego, 2008.Title from first page of PDF file (viewed Mar. 27, 2008). Available via ProQuest Digital Dissertations. Includes bibliographical references (p. 33-34).
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Letellier, Emmanuel. "Fourier transforms of invariant functions on finite reductive Lie algebras /." Berlin [u.a.] : Springer, 2005. http://www.loc.gov/catdir/toc/fy0715/2004115717.html.
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Berg, Sivert. "Evolution of Cellular Automata using Lindenmayer Systems and Fourier Transforms." Thesis, Norges teknisk-naturvitenskapelige universitet, Institutt for datateknikk og informasjonsvitenskap, 2013. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-23601.
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Cellular automata (CAs) are a class of highly parallel computing systems consisting of many simple computing elements called cells. The cells can only communicate with neighboring cells, meaning there is no global communication in the system. Programming such a system to solve complex problems can be a daunting task, and indirect methods are often applied to make it easier. In this thesis we use evolutionary algorithms (EAs) to evolve CAs. We also look at the possibility of employing L-systems to develop complex CAs while maintaining a relatively small genome. Input and output are handled by streaming them through the edge cells, and we look at the use of a discrete Fourier transform (DFT) as a way to interpret the output. Experiments show that it is possible to evolve uniform and semi-uniform CAs that solve various problems. On harder problems semi-uniform CAs outperform uniform CAs, and using an L-system further improves the performance. However, on simpler problems the extra complexity of semi-uniform CAs seem to only hinder evolution. The experiments also show that interpreting the output with a DFT works well, and outperforms a more direct approach.
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Arof, H. "Texture classification and segmentation using one dimensional discrete Fourier transforms." Thesis, Swansea University, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.635797.
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This thesis introduces a texture descriptor that is invariant to rotation. The new texture descriptor utilizes the property of the magnitudes of Fourier transform coefficients that do not change with spatial shift of input elements. Since rotating an image by an arbitrary angle does not change pixel intensities in an image but shifts them in circular motion, the notion of producing texture features invariant to rotation using 1-D Fourier transform coefficients can be realized if the relationship between circular motion and spatial shift can be established. By analyzing individual circular neighbourhoods centered at every pixel in an image, local and global texture attributes of the image can be described. Rotating the image has a similar effect as spatially shifting the pixels in the circular neighbourhood around without altering their intensities. A number of sequences can be formed by the intensities of pixels at various fixed distances from the center of the neighbourhood. Fourier transforming the sequences would generate coefficients that contain the texture information of the neighbourhood. From the magnitudes of these coefficients, several rotation invariant features are obtained. The capabilities of the new features are investigated in a number of classification and segmentation experiments. The experimental results compare favourably with those of prominent descriptors like the circular autoregressive model, the wavelet transform, the Gaussian Markov radom field and the co-occurrence matrix. In the majority of the instances, the new method shows superior performance.
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Sarybekova, Lyazzat. "Some new Lizorkin multiplier theorems for Fourier series and transforms." Licentiate thesis, Luleå : Luleå University of Technology, 2009. http://pure.ltu.se/ws/fbspretrieve/2732730.
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Malm, Eric. "Decimation-in-Frequency Fast Fourier Transforms for the Symmetric Group." Scholarship @ Claremont, 2005. https://scholarship.claremont.edu/hmc_theses/173.
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In this thesis, we present a new class of algorithms that determine fast Fourier transforms for a given finite group G. These algorithms use eigenspace projections determined by a chain of subgroups of G, and rely on a path algebraic approach to the representation theory of finite groups developed by Ram (26). Applying this framework to the symmetric group, Sn, yields a class of fast Fourier transforms that we conjecture to run in O(n2n!) time. We also discuss several future directions for this research.
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Yonemoto, Akihiro. "Study on Numerical Laplace Transforms and Their Applications to Analysis of Transmission Lines." 京都大学 (Kyoto University), 2004. http://hdl.handle.net/2433/147622.
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Thornton, A. L. "Colour object recognition using a complex colour representation and the frequency domain." Thesis, University of Reading, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.301911.
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Ngounda, Edgard. "Efficient numerical methods based on integral transforms to solve option pricing problems." Thesis, University of the Western Cape, 2012. http://hdl.handle.net/11394/4223.
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Philosophiae Doctor - PhDIn this thesis, we design and implement a class of numerical methods (based on integral transforms) to solve PDEs for pricing a variety of financial derivatives. Our approach is based on spectral discretization of the spatial (asset) derivatives and the use of inverse Laplace transforms to solve the resulting problem in time. The conventional spectral methods are further modified by using piecewise high order rational interpolants on the Chebyshev mesh within each sub-domain with the boundary domain placed at the strike price where the discontinuity is located. The resulting system is then solved by applying Laplace transform method through deformation of a contour integral. Firstly, we use this approach to price plain vanilla options and then extend it to price options described by a jump-diffusion model, barrier options and the Heston’s volatility model. To approximate the integral part in the jump-diffusion model, we use the Gauss-Legendre quadrature method. Finally, we carry out extensive numerical simulations to value these options and associated Greeks (the measures of sensitivity). The results presented in this thesis demonstrate the spectral accuracy and efficiency of our approach, which can therefore be considered as an alternative approach to price these class of options.
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Wade, Jeremy. "Summability of Fourier orthogonal expansions and a discretized Fourier orthogonal expansion involving Radon projections for functions on the cylinder /." Connect to title online (Scholars' Bank) Connect to title online (ProQuest), 2009. http://hdl.handle.net/1794/10245.
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Smith, James Raphael. "A vectorised Fourier-Laplace transformation and its application to Green's tensors." Thesis, Lancaster University, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.296967.
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Cain, Jonathan Aaron. "Parallelization of the Dempster-Shafer Application to Talbot's Method for Numerical Inverse Laplace Transforms." Thesis, The University of Arizona, 2011. http://hdl.handle.net/10150/144252.
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Ruderer, Martin [Verfasser], and Ulrich [Akademischer Betreuer] Bunke. "Fourier-Mukai Transforms from T-Duality / Martin Ruderer. Betreuer: Ulrich Bunke." Regensburg : Universitätsbibliothek Regensburg, 2015. http://d-nb.info/1068669624/34.
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Bridgeland, Tom. "Fourier-Mukai transforms for surfaces and moduli spaces of stable sheaves." Thesis, University of Edinburgh, 2002. http://hdl.handle.net/1842/12070.
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In this thesis we study Fourier-Mukai transforms for complex projective surfaces. Extending work of A.I. Bondal and D.O. Orlov, we prove a theorem giving necessary and sufficient conditions for a functor between the derived categories of sheaves on two smooth projective varieties to be an equivalence of categories, and use it to construct examples of Fourier-Mukai transforms for surfaces. In particular we construct new transforms for elliptic surfaces and quotient surfaces. This enables us to identify all pairs of complex projective surfaces having equivalent derived categories of sheaves. We also derive some general properties of Fourier-Mukai transforms, and gives examples of their use. The main applications are to the study of moduli spaces of stable sheaves. In particular we identify many such moduli spaces on elliptic surfaces, generalising results of R. Friedman.
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Barrera, David. "Quenched Asymptotics for the Discrete Fourier Transforms of a Stationary Process." University of Cincinnati / OhioLINK, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1460652609.
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Demiroren, Ayse Nazli. "Inferring interwell connectivity from injection and production data using frequency domain analysis." Texas A&M University, 2003. http://hdl.handle.net/1969.1/5998.
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This project estimates interwell connectivity, a characteristic that is crucial to determine reservoir
continuity while developing a waterflooding project. It tests the combination of Fourier transforms (FTâÂÂs)
of the flow rate data and analytical solutions from analog electrical circuits to infer the inverse diffusivity
coefficient (IDC). I solved the transmission line equation analytically for 0D, 1D, and 2D
resistance/capacitance (RC) network models and used those solutions to compare with the flow rate FTâÂÂs
to determine the diffusivity parameters. I used the analogy between the electrical response of RC
networks and the fluid response of permeable reservoirs on the basis of the similarities in the governing
equations.
I conclude that the analogy works accurately in simple reservoirs, where the assumptions of an analytical
solution are met, i.e. single-phase fluid and a homogeneous system. For two-phase liquid cases, I
determined that the analogy remains applicable because we still could produce accurate interwell
connectivity information. When I investigated cases with dissolved-gas production around the wellbore,
however, the analogy broke down and the results were not as good as the liquid systems.
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Pinto, Ana Cristina Rodrigues. "Soluções fundamentais dos operadores discretos de Laplace e Dirac." Master's thesis, Universidade de Aveiro, 2008. http://hdl.handle.net/10773/9500.
Full textAbstract:
Mestrado em Matemática e AplicaçõesA presente dissertação tem por objectivo a construção de soluções fundamentais discretas para os operadores discretos de Laplace e de Dirac. No primeiro capítulo discutiremos alguns aspectos básicos da discretização de funções, respectivos domínios e representação discretas das suas derivadas parciais. Esta representação dependerá do ponto do domínio em que nos encontrarmos e do tipo de aproximação efectuada, como veremos. No segundo capítulo relembraremos a transformada de Fourier contínua e suas propriedades, para em seguida, introduzirmos a transformada de Fourier discreta e suas propriedades e teoremas mais relevantes. Finalmente, no último capítulo serão definidos os operadores de Laplace e Dirac, nos casos contínuo e discreto, bem como algumas das suas propriedades que ajudarão na construção das soluções fundamentais para os equivalentes discretos destes operadores.
The purpose of the present dissertation is the construction of discrete fundamental solutions for the Laplace and Dirac discrete operators. In the first chapter, we will discuss some basic aspects of discretization of functions, their domains and the discrete representation of their partial derivatives. These representations will depend on the localization of the point of the domain and the approximation type, as we will see. In second chapter we will remember the continuous Fourier transform and its properties so that afterwards we can introduce the discrete Fourier transform, its properties and relevant theorems. Finally, in the last chapter we will define the Laplace and Dirac operators in continuous and discrete case, as well as we will give some of their properties that will help in the construction of the fundamental solutions to the equivalent discrete of these operators.
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Koyama, Masanori. "A Decimation-in-Frequency Fast-Fourier Transform for the Symmetric Group." Scholarship @ Claremont, 2007. https://scholarship.claremont.edu/hmc_theses/199.
Full textAbstract:
A Discrete Fourier Transform (DFT) changes the basis of a group algebra from the standard basis to a Fourier basis. An efficient application of a DFT is called a Fast Fourier Transform (FFT). This research pertains to a particular type of FFT called Decimation in Frequency (DIF). An efficient DIF has been established for commutative algebra; however, a successful analogue for non-commutative algebra has not been derived. However, we currently have a promising DIF algorithm for CSn called Orrison-DIF (ODIF). In this paper, I will formally introduce the ODIF and establish a bound on the operation count of the algorithm.
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Pippig, Michael. "Massively Parallel, Fast Fourier Transforms and Particle-Mesh Methods: Massiv parallele schnelle Fourier-Transformationen und Teilchen-Gitter-Methoden." Doctoral thesis, Universitätsverlag der Technischen Universität Chemnitz, 2015. https://monarch.qucosa.de/id/qucosa%3A20398.
Full textAbstract:
The present thesis provides a modularized view on the structure of fast numerical methods for computing Coulomb interactions between charged particles in three-dimensional space. Thereby, the common structure is given in terms of three self-contained algorithmic frameworks that are built on top of each other, namely fast Fourier transform (FFT), nonequispaced fast Fourier transform (NFFT) and NFFT based particle-mesh methods (P²NFFT). For each of these frameworks algorithmic enhancement and parallel implementations are presented with special emphasis on scalability up to hundreds of thousands of parallel processes.
In the context of FFT massively parallel algorithms are composed from hardware adaptive low level modules provided by the FFTW software library. The new algorithmic NFFT concepts include pruned NFFT, interlacing, analytic differentiation, and optimized deconvolution in Fourier space with respect to a mean square aliasing error. Enabled by these generalized concepts it is shown that NFFT provides a unified access to particle-mesh methods. Especially, mixed-periodic boundary conditions are handled in a consistent way and interlacing can be incorporated more efficiently. Heuristic approaches for parameter tuning are presented on the basis of thorough error estimates.Die vorliegende Dissertation beschreibt einen modularisierten Blick auf die Struktur schneller numerischer Methoden für die Berechnung der Coulomb-Wechselwirkungen zwischen Ladungen im dreidimensionalen Raum. Die gemeinsame Struktur ist geprägt durch drei selbstständige und auf einander aufbauenden Algorithmen, nämlich der schnellen Fourier-Transformation (FFT), der nicht äquidistanten schnellen Fourier-Transformation (NFFT) und der NFFT-basierten Teilchen-Gitter-Methode (P²NFFT). Für jeden dieser Algorithmen werden Verbesserungen und parallele Implementierungen vorgestellt mit besonderem Augenmerk auf massiv paralleler Skalierbarkeit. Im Kontext der FFT werden parallele Algorithmen aus den Hardware adaptiven Modulen der FFTW Softwarebibliothek zusammengesetzt. Die neuen NFFT-Konzepte beinhalten abgeschnittene NFFT, Versatz, analytische Differentiation und optimierte Entfaltung im Fourier-Raum bezüglich des mittleren quadratischen Aliasfehlers. Mit Hilfe dieser Verallgemeinerungen bietet die NFFT einen vereinheitlichten Zugang zu Teilchen-Gitter-Methoden. Insbesondere gemischt periodische Randbedingungen werden einheitlich behandelt und Versatz wird effizienter umgesetzt. Heuristiken für die Parameterwahl werden auf Basis sorgfältiger Fehlerabschätzungen angegeben.