Relevant bibliographies by topics / Laplace and Fourier transforms

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Laplace and Fourier transforms'

Author: Grafiati
Published: 4 June 2021
Last updated: 30 January 2023

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Journal articles on the topic "Laplace and Fourier transforms"

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Corinthios, Michael J. "New Laplace, z and Fourier-related transforms." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 463, no. 2081 (February 6, 2007): 1179–98. http://dx.doi.org/10.1098/rspa.2007.1814.

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In this paper, the author uses his recently proposed complex variable generalized distribution theory to expand the domains of existence of bilateral Laplace and z transforms, as well as a whole new class of related transforms. A vast expansion of the domains of existence of bilateral Laplace and z transforms and continuous-time and discrete-time Hilbert, Hartley and Mellin transforms, as well as transforms of multidimensional functions and sequences are obtained. It is noted that the Fourier transform and its applications have advanced by leaps and bounds during the last century, thanks to the introduction of the theory of distributions and, in particular, the concept of the Dirac-delta impulse. Meanwhile, however, the truly two-sided ‘bilateral’ Laplace and z transforms, which are more general than Fourier, remained at a standstill incapable of transforming the most basic of functions. In fact, they were reduced by half to one-sided transforms and received no more than a passing reference in the literature. It is shown that the newly proposed generalized distributions expand the domains of existence and application of Laplace and z transforms similar to and even more extensively than the expansion of the domain of Fourier transform that resulted from the introduction, nearly a century ago, of the theory of distributions and the Dirac-delta impulse. It is also shown that the new generalized distributions put an end to an anomaly that still exists today, which meant that for a large class of basic functions, the Fourier transform exists while the more general Laplace and z transforms do not. The anomaly further manifests itself in the fact that even for the one-sided causal functions, such as the Heaviside unit step function u ( t ) and the sinusoid sin βtu ( t ), the Laplace transform does not exist on the j ω -axis, and the Fourier transform which does exist cannot be deduced thereof by the substitution s =j ω in the Laplace transform, which by definition it should. The extended generalized transforms are well defined for a large class of functions ranging from the most basic to highly complex fast-rising exponential ones that have so far had no transform. Among basic applications, the solution of partial differential equations using the extended generalized transforms is provided. This paper clearly presents and articulates the significant impact of extending the domains of Laplace and z transforms on a large family of related transforms, after nearly a century during which bilateral Laplace and z transforms of even the most basic of functions were undefined, and the domains of definition of related transforms such as Hilbert, Hartley and Mellin transforms were confined to a fraction of the space they can now occupy.
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Saberi-Nadjafi, Jafar. "A Computational Method for n-Dimensional Laplace Transforms Involved with Fourier Cosine Transform." ISRN Applied Mathematics 2013 (August 28, 2013): 1–4. http://dx.doi.org/10.1155/2013/748417.

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In 2007, the author published some results on n-dimensional Laplace transform involved with the Fourier sine transform. In this paper, we propose some new result in n-dimensional Laplace transforms involved with Fourier cosine transform; these results provide few algorithms for evaluating some n-dimensional Laplace transform pairs. In addition, some examples are also presented, which explain the useful applications of the obtained results. Therefore, one can produce some two- and three- as well as n-dimensional Laplace transforms pairs.
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Salamat, Kaushef, and Nousheen Ilyas. "DUALITIES BETWEEN FOURIER SINE AND SOME USEFUL INTEGRAL TRANSFORMATIONS." Journal of Mathematical Sciences & Computational Mathematics 2, no. 4 (July 5, 2021): 542–63. http://dx.doi.org/10.15864/jmscm.2408.

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The most useful technique of the mathematics which are used to finding the solutions of a lot of problems just like bending of beam, electrical network, heat related problems, which occurs in many disciplines of engineering and sciences are the techniques of integral transforms. In our research I discussed the duality between Fourier Sine transforms and some others effective integral transforms (namely Laplace transform, Mahgoub transform, Aboodh transform and Mohand transform). To justify the scope of dualities relation between Fourier Sine transform and other integral transforms (that are mentioned above, I presented the tabular representation of integral transform (namely Laplace transform, Aboodh transform, Mohand transform and Mahgoub transform) of various used functions by using Fourier Sine and other integral transforms dualities relation to signify fruitfulness of such connections. Results showed that these integral transform are strongly related with Fourier Sine transform.
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Fitzsimmons, Patrick, and Tucker McElroy. "On Joint Fourier–Laplace Transforms." Communications in Statistics - Theory and Methods 39, no. 10 (May 12, 2010): 1883–85. http://dx.doi.org/10.1080/03610920902923502.

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Kaneta, H. "Fourier-Laplace transforms decaying exponentially." Mathematical Proceedings of the Cambridge Philosophical Society 103, no. 2 (March 1988): 321–22. http://dx.doi.org/10.1017/s0305004100064896.

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Let ƒ(x) be a C-valued function which is integrable with respect to a positive measure m on the Borel σ-field of R = (– ∞, ∞). We shall give necessary and sufficient conditions under which the following Fourier-Laplace transform f(λ) of ƒ(x) decays exponentially as λ → ∞:where θ is a constant with –π/2 ≤ θ ≤ π/2.
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Bhandari, Piyush Kumar, and Sushil Kumar Bissu. "Inequalities for some classical integral transforms." Tamkang Journal of Mathematics 47, no. 3 (September 30, 2016): 351–56. http://dx.doi.org/10.5556/j.tkjm.47.2016.1981.

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By using a form of the Cauchy-Bunyakovsky-Schwarz inequality, we establish new inequalities for some classical integral transforms such as Laplace transform,Fourier transform, Fourier cosine transform, Fourier sine transform, Mellin transform and Hankel transform.
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Lima, Fátima D. P., Jorge M. A. Garcia, and Alfredo D. Egídio Dos Reis. "Fourier/Laplace Transforms and Ruin Probabilities." ASTIN Bulletin 32, no. 1 (May 2002): 91–105. http://dx.doi.org/10.2143/ast.32.1.1017.

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AbstractIn this paper we use Fourier/Laplace transforms to evaluate numerically relevant probabilities in ruin theory as an application to insurance. The transform of a function is split in two: the real and the imaginary parts. We use an inversion formula based on the real part only, to get the original function.By using an appropriate algorithm to compute integrals and making use of the properties of these transforms we are able to compute numerically important quantities either in classical or non-classical ruin theory. As far as the classical model is concerned the problems considered have been widely studied. In what concerns the non-classical model, in particular models based on more general renewal risk processes, there is still a long way to go. In either case the approach presented is an easy method giving good approximations for reasonable values of the initial surplus.To show this we compute numerically ruin probabilities in the classical model and in a renewal risk process in which claim inter-arrival times have an Erlang(2) distribution and compare to exact figures where available. We also consider the computation of the probability and severity of ruin in the classical model.
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Xuan Thao, Nguyen, Vu Kim Tuan, Le Xuan Huy, and Nguyen Thanh Hong. "On the Fourier–Laplace convolution transforms." Integral Transforms and Special Functions 26, no. 4 (January 28, 2015): 303–13. http://dx.doi.org/10.1080/10652469.2014.1002781.

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Lee, S. L. "Fourier–Laplace transforms and orthogonal polynomials." Journal of Approximation Theory 256 (August 2020): 105436. http://dx.doi.org/10.1016/j.jat.2020.105436.

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Dimitrov, Dimitar K., and Yuan Xu. "Wronskians of Fourier and Laplace transforms." Transactions of the American Mathematical Society 372, no. 6 (June 3, 2019): 4107–25. http://dx.doi.org/10.1090/tran/7809.

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Dissertations / Theses on the topic "Laplace and Fourier transforms"

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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 thermiques
Thermal 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 données
The 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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Books on the topic "Laplace and Fourier transforms"

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Dyke, Philip P. G. An Introduction to Laplace Transforms and Fourier Series. London: Springer London, 2001.

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An introduction to Laplace transforms and Fourier series. London: Springer, 1999.

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Dyke, Phil. An Introduction to Laplace Transforms and Fourier Series. London: Springer London, 2014. http://dx.doi.org/10.1007/978-1-4471-6395-4.

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Dyke, Philip P. G. An Introduction to Laplace Transforms and Fourier Series. London: Springer London, 2001. http://dx.doi.org/10.1007/978-1-4471-0505-3.

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Distribution theory: Convolution, fourier transform, and laplace transform. Berlin: De Gruyter, 2013.

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1950-, Arendt Wolfgang, ed. Vector-valued Laplace transforms and Cauchy problems. Basel: Birkhäuser Verlag, 2001.

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Seslavin, Andrey. Theory of automatic control. Linear, continuous systems. ru: INFRA-M Academic Publishing LLC., 2021. http://dx.doi.org/10.12737/1014654.

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The textbook presents the basics of the classical theory of automatic control, based on mathematical models of real systems, given in the form of systems of linear differential equations with constant coefficients. Methods based on Laplace and Fourier transforms, stability, controllability, and observability theory, as well as directed graph theory and linear algebra are used. Meets the requirements of the federal state educational standards of higher education of the latest generation. For students of higher educational institutions studying in the areas of training and specialties 15.00.00 "Mechanical Engineering", 27.00.00 "Management in technical systems".
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Sneddon, Ian Naismith. Fourier transforms. New York: Dover Publications, 1995.

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Gray, Robert M., and Joseph W. Goodman. Fourier Transforms. Boston, MA: Springer US, 1995. http://dx.doi.org/10.1007/978-1-4615-2359-8.

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Clausen, Michael. Fast Fourier transforms. Mannheim: B.I. Wissenschaftsverlag, 1993.

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Book chapters on the topic "Laplace and Fourier transforms"

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De Concini, Corrado, and Claudio Procesi. "Fourier and Laplace Transforms." In Topics in Hyperplane Arrangements, Polytopes and Box-Splines, 69–75. New York, NY: Springer New York, 2010. http://dx.doi.org/10.1007/978-0-387-78963-7_3.

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Pipkin, A. C. "Fourier and Laplace Transforms." In Lectures on Viscoelasticity Theory, 22–32. New York, NY: Springer New York, 1986. http://dx.doi.org/10.1007/978-1-4612-1078-8_3.

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Cicogna, Giampaolo. "Fourier and Laplace Transforms. Distributions." In Undergraduate Lecture Notes in Physics, 73–125. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-76165-7_3.

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Sirovich, Lawrence. "The Fourier and Laplace Transforms." In Introduction to Applied Mathematics, 261–93. New York, NY: Springer New York, 1988. http://dx.doi.org/10.1007/978-1-4612-4580-3_8.

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Cicogna, Giampaolo. "Fourier and Laplace Transforms. Distributions." In Undergraduate Lecture Notes in Physics, 73–127. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-59472-5_3.

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Wunsch, A. David. "Transforms: Laplace, Fourier, Z, and Hilbert." In A MATLAB® Companion to Complex Variables, 235–307. Boca Raton : Taylor & Francis, 2016. | Series: Textbooks in mathematics ; 41 | “A CRC title.”: CRC Press, 2018. http://dx.doi.org/10.1201/9781315380339-6.

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Karpfinger, Christian. "Solving PDEs with Fourier and Laplace Transforms." In Calculus and Linear Algebra in Recipes, 1015–23. Berlin, Heidelberg: Springer Berlin Heidelberg, 2022. http://dx.doi.org/10.1007/978-3-662-65458-3_91.

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Andrews, George E., and Bruce C. Berndt. "A Partial Manuscript on Fourier and Laplace Transforms." In Ramanujan's Lost Notebook, 285–305. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-4081-9_13.

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Saitoh, Saburou. "The Hilbert Spaces of Szegö Type and Fourier-Laplace Transforms on ℝ n." In Generalized Functions and Their Applications, 197–212. Boston, MA: Springer US, 1993. http://dx.doi.org/10.1007/978-1-4899-1591-7_19.

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Jones, W. D., H. J. Doucet, and J. M. Buzzi. "The Cookbook Everything You Always Wanted to Know About Fourier, Laplace, and Hilbert Transforms, but Were Afraid to Ask ..." In An Introduction to the Linear Theories and Methods of Electrostatic Waves in Plasmas, 1–47. Boston, MA: Springer US, 1985. http://dx.doi.org/10.1007/978-1-4757-0211-8_1.

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Conference papers on the topic "Laplace and Fourier transforms"

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Maljar, David, and Viera Stopjakova. "Understanding the Fourier and Laplace transforms through visual interpretation." In 2021 19th International Conference on Emerging eLearning Technologies and Applications (ICETA). IEEE, 2021. http://dx.doi.org/10.1109/iceta54173.2021.9726659.

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Khalaf, Rihab F., and Fethi Bin Muhammad Belgacem. "Extraction of the Laplace, Fourier, and Mellin transforms from the Sumudu transform." In 10TH INTERNATIONAL CONFERENCE ON MATHEMATICAL PROBLEMS IN ENGINEERING, AEROSPACE AND SCIENCES: ICNPAA 2014. AIP Publishing LLC, 2014. http://dx.doi.org/10.1063/1.4907309.

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El-Shahed, Moustafa, and Ahmed Salem. "On the Generalized Navier-Stokes Equations." In ASME 2003 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/detc2003/vib-48399.

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In this paper, we present a general Inodel of the classical Navier-Stokes equations. With the help of Laplace, Fourier Sine transforms, finite Fourier Sine transforms, and finite Hankel transforms, an exact solutions for three different special cases have been obtained.
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Smith, G. A. "The prosaic Laplace and Fourier transform." In The 6th workshop on beam instrumentation. AIP, 1995. http://dx.doi.org/10.1063/1.48047.

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Ortigueira, Manuel D., and Juan J. Trujillo. "Generalized GL Fractional Derivative and Its Laplace and Fourier Transform." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-87238.

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It is well known the difficulties that the Riesz fractional derivative present, as the spatial fractional derivative involved in many models of the dynamics of anomalous processes. The generalized Gru¨nwal-Letnikov fractional derivative is analysed in this paper. Its Laplace and Fourier Transforms are computed and some current results criticized. It is shown that only the forward derivative of a sinusoid exists. This result is used to define the frequency response of a fractional linear system.
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Mitrofanov, Georgy, and Viatcheslav Priimenko. "Role of discrete Laplace and Fourier‐Bessel transforms in direct problems in frequency domain." In SEG Technical Program Expanded Abstracts 2009. Society of Exploration Geophysicists, 2009. http://dx.doi.org/10.1190/1.3255621.

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Sharma, Kal Renganathan. "Mesoscopic Heat Conduction and Onset of Periodicity." In ASME 2003 Heat Transfer Summer Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/ht2003-47391.

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Mesoscopic approach deals with study that considers temporal fluctuations which is often averaged out in a macroscopic approach without going into the molecular or microscopic approach. Transient heat conduction cannot be fully described by Fourier representation. The non-Fourier effects or finite speed of heat propagation effect is accounted for by some investigators using the Cattaneo and Vernotte non-Fourier heat conduction equation: q=−k∂T/∂x−τr∂q/∂t(1) A generalized expression to account for the non-Fourier or thermal inertia effects suggested by Sharma (5) as: q=−k∂T/∂x−τr∂q/∂t−τr2/2!∂2q/∂t2−τr3/3!∂3q/∂t3−…(2) This was obtained by a Taylor series expansion in time domain. Manifestation of higher order terms in the modified Fourier’w law as periodicity in the time domain is considered in this study. When a CWT is maintained at one end of a medium of length L where L is the distance from the isothermal wall beyond which there is no appreciable temperature change from the initial condition during the duration of the study the transient temperature profile is obtained by the method of Laplace transforms. The space averaged heat flux is obtained and upon inversion from Laplace domain found to be a constant for the the case obeying Fourier’s law; 1 − exp(−τ) using the Cattaneo and Vernotte non-Fourier heat conduction equation, and upon introduction of the second derivative in time of the heat flux the expression becomes, 1 − exp(−τ)(Sin(τ) + Cos(τ)). Thus the periodicity in time domain is lost when the higher order terms in the generalized Fourier expression is neglected.
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Lu, Wen-Qiang, and Qing-Mei Fan. "Non-Fourier Heat Conduction Phenomena Applied Different Temperature and Heat Flux Pulses on Boundary." In ASME 2008 First International Conference on Micro/Nanoscale Heat Transfer. ASMEDC, 2008. http://dx.doi.org/10.1115/mnht2008-52287.

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A new numerical method [1], which combines the dual reciprocity boundary element method with Laplace transforms, has been used to solve ultrafast heat conduction problems. By this method, the time micro scale heat transfer problems applied different extreme high frequency temperature and heat flux pulses (the width of a single pulse is less than 10−12 s) on the boundary are simulated in this paper. Numerical results open out some phenomena of non-Fourier heat conduction. “Thermal accumulation (TA)” as a typical phenomenon of non-Fourier heat conduction takes on different characteristics under different pulsed conditions. The pulse time-width has important effect on the non-Fourier characteristics for single pulse, while different pulse periods for seriate pulse make obvious different non-Fourier characteristics.
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Jialei Hu, Changhong Liu, and Xuguang Li. "Fourier and laplace transform used in pretreatment for neural network battery modeling." In 2012 7th International Power Electronics and Motion Control Conference (IPEMC 2012). IEEE, 2012. http://dx.doi.org/10.1109/ipemc.2012.6258892.

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Markel, V. A., and J. C. Schotland. "Inversion formulas for optical diffusion tomography based on the Fourier-Laplace transform." In Conference on Lasers and Electro-Optics (CLEO 2000). Technical Digest. Postconference Edition. TOPS Vol.39. IEEE, 2000. http://dx.doi.org/10.1109/cleo.2000.907391.

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Reports on the topic "Laplace and Fourier transforms"

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Teugels, Jozef L. Real Inversion Formulas for Laplace and Stieltjes Transforms. Fort Belvoir, VA: Defense Technical Information Center, July 1985. http://dx.doi.org/10.21236/ada161270.

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Yegulalp, A. F. Asymptotic Error for Windowed Discrete Fourier Transforms. Fort Belvoir, VA: Defense Technical Information Center, August 2006. http://dx.doi.org/10.21236/ada452964.

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Sorets, Eugene. Fast Fourier Transforms of Piecewise Constant Functions. Fort Belvoir, VA: Defense Technical Information Center, September 1993. http://dx.doi.org/10.21236/ada272648.

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Scheinker, Alexander. Introduction to Control Theory. Part 2. Laplace Transforms and Linear Systems. Office of Scientific and Technical Information (OSTI), September 2015. http://dx.doi.org/10.2172/1214624.

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Zaevski, Tsvetelin S. Laplace Transforms for the First Hitting Time of a Brownian Motion. "Prof. Marin Drinov" Publishing House of Bulgarian Academy of Sciences, July 2020. http://dx.doi.org/10.7546/crabs.2020.07.05.

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Zaevski, Tsvetelin N. Laplace Transforms of the Brownian Motion’s First Exit from a Strip. "Prof. Marin Drinov" Publishing House of Bulgarian Academy of Sciences, May 2021. http://dx.doi.org/10.7546/crabs.2021.05.04.

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Tang, Xiaoou, and W. K. Stewart. Texture Classification Using Wavelet Packet and Fourier Transforms. Fort Belvoir, VA: Defense Technical Information Center, January 1995. http://dx.doi.org/10.21236/ada324161.

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Ueng, Neng-Tsann, and Louis L. Scharf. Frames and Orthonormal Bases for Variable Windowed Fourier Transforms. Fort Belvoir, VA: Defense Technical Information Center, July 1996. http://dx.doi.org/10.21236/ada311766.

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Bennett, Paul. Parallelization of Two- and Three-Dimensional Fast Fourier Transforms. Fort Belvoir, VA: Defense Technical Information Center, February 2001. http://dx.doi.org/10.21236/ada387428.

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Warshaw, S. I. Fourier Transforms of Pulses Containing Exponential Leading and Trailing Profiles. Office of Scientific and Technical Information (OSTI), July 2001. http://dx.doi.org/10.2172/15002784.

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