Relevant bibliographies by topics / Integral transforms

Contents

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

Academic literature on the topic 'Integral transforms'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 August 2024

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Journal articles on the topic "Integral transforms"

1

Aghili, Arman. "Non-homogeneous impulsive time fractional heat conduction equation." Journal of Numerical Analysis and Approximation Theory 52, no. 1 (July 10, 2023): 22–33. http://dx.doi.org/10.33993/jnaat521-1316.

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This article provides a concise exposition of the integral transforms and its application to singular integral equation and fractional partial differential equations. The author implemented an analytical technique, the transform method, for solving the boundary value problems of impulsive time fractional heat conduction equation. Integral transforms method is a powerful tool for solving singular integral equations, evaluation of certain integrals involving special functions and solution of partial fractional differential equations. The proposed method is extremely concise, attractive as a mathematical tool. The obtained result reveals that the transform method is very convenient and effective.Certain new integrals involving the Airy functions are given.
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Mohammed, Nada Sabeeh, and Emad A. Kuffi. "The complex integral transform complex Sadik transform of error function." Journal of Interdisciplinary Mathematics 26, no. 6 (2023): 1145–57. http://dx.doi.org/10.47974/jim-1613.

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Recently, the focus of mathematics scientists on the use of integral transforms in solving problems in various fields such as engineering, science, and other scientific fields has led to the need to know the integral transforms of the error function in order to evaluate improper integrals. In this paper, we will use transform (complex Sadik transform) and prove its ability to evaluate improper integrals that have error functions.
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Sharma, M. D., and S. Nain. "Numerical evaluation of inverse integral transforms: Dynamic response of elastic materials." International Journal of Engineering, Science and Technology 12, no. 2 (June 1, 2020): 29–34. http://dx.doi.org/10.4314/ijest.v12i2.4.

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This study discusses the use of numerical integration in evaluating the improper integrals appearing as inverse integral transforms of non-analytic functions. These transforms appear while studying the response of various sources in an elastic medium through integral transform method. In these studies, the inverse Fourier transforms are solved numerically without bothering about the singularities and branch points in the corresponding integrands. References on numerical integration cited in relevant papers do not support such an evaluation but suggest contrary. Approximation of inverse Laplace transform integral into a series is used without following the essential restrictions and assumptions. Volume of the published papers using these dubious procedures has reached to an alarming level. The discussion presented aims to draw the attention of researchers as well as journals so as to stop this menace at the earliest possible.Keywords: Inverse Fourier transforms, inverse Laplace transforms, Romberg integration, improper integral, elastic waves
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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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Luchko, Yuri. "Some Schemata for Applications of the Integral Transforms of Mathematical Physics." Mathematics 7, no. 3 (March 12, 2019): 254. http://dx.doi.org/10.3390/math7030254.

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In this survey article, some schemata for applications of the integral transforms of mathematical physics are presented. First, integral transforms of mathematical physics are defined by using the notions of the inverse transforms and generating operators. The convolutions and generating operators of the integral transforms of mathematical physics are closely connected with the integral, differential, and integro-differential equations that can be solved by means of the corresponding integral transforms. Another important technique for applications of the integral transforms is the Mikusinski-type operational calculi that are also discussed in the article. The general schemata for applications of the integral transforms of mathematical physics are illustrated on an example of the Laplace integral transform. Finally, the Mellin integral transform and its basic properties and applications are briefly discussed.
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KABRA, SEEMA, and HARISH NAGAR. "INTEGRAL TRANSFORM OF K4-FUNCTION." Journal of Science and Arts 21, no. 2 (June 30, 2021): 429–36. http://dx.doi.org/10.46939/j.sci.arts-21.2-a10.

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In this present work we derived integral transforms such as Euler transform, Laplace transform, and Whittaker transform of K4-function. The results are given in generalized Wright function. Some special cases of the main result are also presented here with new and interesting results. We further extended integral transforms derived here in terms of Gauss Hypergeometric function.
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Kuffi, Emad A., and Eman A. Mansour. "Solving Partial Differential Equations Using the New Integral Transform “Double SEE Integral Transform”." Journal of Physics: Conference Series 2322, no. 1 (August 1, 2022): 012009. http://dx.doi.org/10.1088/1742-6596/2322/1/012009.

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Abstract The immense importance of differential equations and integral transforms in scientific fields leads to inducting the integral transforms as a solving tool for partial differential equations. The “double SEE integral transform” is a novel integral transform suggested in this research. Its properties and applicability to some functions have been studied, and the ability of the proposed transform to solve partial differential equations has been proven through a practical application.
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ZORICH, Anton. "INVERSION OF HOROSPHERICAL INTEGRAL TRANSFORM ON REAL SEMISIMPLE LIE GROUPS." International Journal of Modern Physics A 07, supp01b (April 1992): 1047–71. http://dx.doi.org/10.1142/s0217751x92004178.

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There exists the wonderful integral transform on complex semisimple Lie groups, which assigns to a function on the group the set of its integrals over "generalized horospheres" — some specific submanifolds of the Lie group. The local inversion formula for this integral transform, discovered in 50's for [Formula: see text] by Gel'fand and Graev, made it possible to decompose the regular representation on [Formula: see text] into irreducible ones. In case of real semisimple Lie group the situation becomes more complicated, and usually there is no reasonable analogous integral transform at all. Nevertheless, in the present paper we succeed to define the integral transforms on the Lorentz group and some other real semisimple Lie groups, which are in a sense analogous to the integration over "horospheres". We obtain the inversion formulas for these integral transforms.
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Gwila, Nbila, and Ali Farhat. "GF1 Integral Transform and its Some Applications." مجلة الجامعة الأسمرية: العلوم التطبيقية 7, no. 2 (June 30, 2022): 84–93. http://dx.doi.org/10.59743/aujas.7.2.2.

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One of the significant methods for solving initial value problems and some integral equations is the use of integral transforms which serve for converting them to algebraic equations that can be solved by applying the inverse transforms. Resently, several integral transforms have been presented and applied for solving initial value problems and some integral equations such as Sumudu, Natural, Al-Tememe, Elzaki, Aboodh, T Kashuri and Fundo, Mahgoub, Kamal, Polynomial, Al-Zughair, Rangaig, Mohand and, Al-Zughair Transforms. In this paper, integral transform has been presented and studied which is in a clase of Laplace integral transform and related to Jafari general integral transform. Furthermore, theorems and some applications for solving initial value problems have been provided.
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Campos, Harren, Jezer Fernandez, and Jade Bong Natuil. "On Degenerate Laplace-type Integral Transform." European Journal of Pure and Applied Mathematics 16, no. 4 (October 30, 2023): 2213–33. http://dx.doi.org/10.29020/nybg.ejpam.v16i4.4868.

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This paper is motivated by the work of Taekyun Kim and Dae San Kim on the degenerate Laplace transform and degenerate gamma function, as published in the Russian Journal of Mathematical Physics. We introduce the degenerate Laplace-type integral transform and delve into its properties and interrelations. This paper focuses on the degenerate Laplace-type integral transforms of several fundamental functions, including the degenerate sine, degenerate cosine, degenerate hyperbolic sine, and degenerate hyperbolic cosine functions. Furthermore, we establish crucial connections between the degenerate Laplace-type integral transform and existing degenerate integral transforms. Specifically, we explore its relationships with the degenerate Laplace transform, the degenerate Elzaki transform, and the degenerate Sumudu transforms.
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Dissertations / Theses on the topic "Integral transforms"

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Li, Xiaochun. "Uniform bounds for the bilinear Hilbert transforms /." free to MU campus, to others for purchase, 2001. http://wwwlib.umi.com/cr/mo/fullcit?p3025634.

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Khan, Mumtaz Ahmad. "On fractional integral operators of three variables and integral transforms." Pontificia Universidad Católica del Perú, 2012. http://repositorio.pucp.edu.pe/index/handle/123456789/96049.

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The present paper is a continuation to authors paper [11]where three variable analogues of certain fractional integraloperators of M. Saigo were investigated. This paper dealswith the effect of operating three variable analogues of Mellinand Laplace transforms on these three variable analogues offractional integral operators of the earlier paper.
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Khan, Mumtaz Ahmad, and Abukhammash Ghazi Salama. "On certain fractional integral operators of two variables and integral transforms." Pontificia Universidad Católica del Perú, 2014. http://repositorio.pucp.edu.pe/index/handle/123456789/97226.

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The present paper is in continuation to authors earlier paper {9} where two variable analogues of certain fractional integral operators of M. Saigo were investigated. This paper deals with the effect of operating two variable analogues of Mellin and Laplace transforms on these two variable analogues of fractional integral operators of the earlier paper.
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Alkauskas, Giedrius. "Integral transforms of the Minkowski question mark function." Thesis, University of Nottingham, 2008. http://eprints.nottingham.ac.uk/10641/.

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The Minkowski question mark function F(x) arises as a real distribution function of rationals in the Farey (alias, Stern-Brocot or Calkin-Wilf) tree. In this thesis we introduce its three natural integral transforms: the dyadic period function G(z), defined in the cut plane; the dyadic zeta function zeta_M(s), which is an entire function; the characteristic function m(t), which is an entire function as well. Each of them is a unique object, and is characterized by regularity properties and a functional equation, which reformulates in its own terms the functional equation for F(x). We study the interrelations among these three objects and F(x). It appears that the theory is completely parallel to the one for Maass wave forms for PSL_2(Z). One of the main purposes of this thesis is to clarify the nature of moments of the Minkowski question mark function.
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Kerr, Fiona Helen. "Fractional powers of integral transforms for classical and generalized functions." Thesis, University of Strathclyde, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.303285.

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Ramaseshan, Karthik. "Microlocal analysis of the doppler transform on R³ /." Thesis, Connect to this title online; UW restricted, 2003. http://hdl.handle.net/1773/5739.

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Sanja, Kostadinova. "Some classes of integral transforms on distribution spaces and generalized asymptotics." Phd thesis, Univerzitet u Novom Sadu, Prirodno-matematički fakultet u Novom Sadu, 2014. https://www.cris.uns.ac.rs/record.jsf?recordId=87772&source=NDLTD&language=en.

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In this doctoral dissertation several integral transforms are discussed.The first one is the Short time Fourier transform (STFT). We present continuity theorems for the STFT and its adjoint on the test function space K1(ℝn) and the topological tensor product K1(ℝn) ⊗ U(ℂn), where U(ℂn) is the space of entirerapidly decreasing functions in any horizontal band of ℂn. We then use such continuity results to develop a framework for the STFT on K'1(ℝn). Also, we devote one section to the characterization of K’1(ℝn) and related spaces via modulation spaces. We also obtain various Tauberian theorems for the short-time Fourier transform.Part of the thesis is dedicated to the ridgelet and the Radon transform. We define and study the ridgelet transform of (Lizorkin) distributions and we show that the ridgelet transform and the ridgelet synthesis operator can be extended as continuous mappings Rψ : S’0(ℝn) → S’(Yn+1) and Rtψ: S’(Yn+1) → S’0(ℝn). We then use our results to develop a distributional framework for the ridgelet transform that is, we treat the ridgelet transform on S’0(ℝn) via a duality approach. Then, the continuity theorems for the ridgelet transform are applied to discuss the continuity of the Radon transform on these spaces and their duals. Finally, we deal with some Abelian and Tauberian theorems relating the quasiasymptotic behavior of distributions with the quasiasymptotics of the its Radon and ridgelet transform.The last chapter is dedicated to the MRA of M-exponential distributions. We study the convergence of multiresolution expansions in various test function and distribution spaces and we discuss the pointwise convergence of multiresolution expansions to the distributional point values of a distribution. We also provide a characterization of the quasiasymptotic behavior in terms of multiresolution expansions and give an MRA sufficient condition for the existence of α-density points of positive measures.
U ovoj doktorskoj disertaciji razmotreno je nekoliko integralnih transformacija. Prva je short time Fourier transform (STFT). Date su i dokazane teoreme o neprekidnosti STFT i njena sinteza na prostoru test funkcije K1(ℝn) i na prostoru K1(ℝn) ⊗ U(ℂn), gde je U(ℂn) prostor od celih brzo opadajućih funkcija u proizvoljnom horizontalnom opsegu na ℂn. Onda, ovi rezultati neprekidnosti su iskorišteni za razvijanje teorije STFT na prostoru K’1(ℝn). Jedno poglavlje je posvećeno karakterizaciji K’1(ℝn) sa srodnih modulaciskih prostora. Dokazani su i različiti Tauberovi rezultata za STFT. Deo teze je posvećen na ridglet i Radon transformacije. Ridgelet transformacija je definisana na (Lizorkin) distribucije i pokazano je da ridgelet transformacija i njen operator sinteze mogu da se prošire kako neprekidna preslikava Rψ : S’0(ℝn) → S’(Yn+1) and RtΨ: S’(Yn+1) → S’0(ℝn). Ridgelet transformacija na S’0(ℝn) je data preko dualnog pristupa. Naše teoreme neprekidnosti ridgelet transformacije su primenjene u dokazivanju neprekidnosti Radonove transformacije na Lizorkin test prostorima i njihovim dualima. Na kraju, dajemo Abelovih i Tauberovih teorema koji daju veze izmedju kvaziasimptotike distribucija i kvaziasimptotike rigdelet i Radonovog transfomaciju.Zadnje poglavje je posveceno multirezolucijskog analizu M - eksponencijalnih distrubucije. Proucavamo konvergenciju multirezolucijkog razvoja u razlicitih prostori test funkcije i distribucije i razmotrena je tackasta konvergencija multirezolucijkog razvoju u tacku u distributivnog smislu. Obezbedjena je i karakterizacija kvaziasimptotike u pogled multirezolucijskog razvoju i dat dovoljni uslov za postojanje α-tacka gustine za pozitivne mere.
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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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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 - PhD
In 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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Pirbudak, Ozan. "Reconstruction of Radar Images by Using Spherical Mean and Regular Radon Transforms." Scholar Commons, 2019. https://scholarcommons.usf.edu/etd/7889.

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The goal of this study is the recovery of functions and finite parametric distributions from their spherical means over spheres and designing a general formula or algorithm for the reconstruction of a function f via its spherical mean transform. The theoretical study is and supported with a numerical implementation based on radar data. In this study, we approach the reconstruction problem in two different way. The first one is to show how the reconstruction problem could be converted to a Prony-type system of equations. After solving this Prony-type system of equations, one can extract the parameters that describe the corresponding functions or distributions efficiently. The second way is to solve this problem via a backprojection procedure.
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Books on the topic "Integral transforms"

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Banerjea, Sudeshna, and Birendra Nath Mandal. Integral Equations and Integral Transforms. Singapore: Springer Nature Singapore, 2023. http://dx.doi.org/10.1007/978-981-99-6360-7.

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Banerji, P. K. Distributional integral transforms. Jodhpur: Scientific Publishers Journals Dept (India), 2005.

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Hitzer, Eckhard, ed. Quaternionic Integral Transforms. Cham: Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-28375-8.

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1954-, Kolyshkin A. A., and Vaillancourt Rémi 1934-, eds. Applied integral transforms. Providence, R.I., USA: American Mathematical Society, 1993.

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Davies, B. Integral transforms and theirapplications. 2nd ed. New York: Springer-Verlag, 1985.

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Zhdanov, Michael S. Integral Transforms in Geophysics. Berlin, Heidelberg: Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/978-3-642-72628-6.

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K, Shivamoggi Bhimsen, and Society of Photo-optical Instrumentation Engineers., eds. Integral transforms for engineers. Bellingham, Wash: SPIE Optical Engineering Press, 1999.

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Zhdanov, Mikhail Semenovich. Integral transforms in geophysics. Berlin: Springer-Verlag, 1988.

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Zhdanov, M. S. Integral transforms in geophysics. Berlin: Springer-Verlag, 1987.

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Brychkov, Yu A. Multidimensional integral transformations. Philadelphia: Gordon and Breach Science Publishers, 1991.

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Book chapters on the topic "Integral transforms"

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Müller, Claus. "Integral Transforms." In Analysis of Spherical Symmetries in Euclidean Spaces, 151–71. New York, NY: Springer New York, 1998. http://dx.doi.org/10.1007/978-1-4612-0581-4_7.

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Evans, Gwynne A., Jonathan M. Blackledge, and Peter D. Yardley. "Integral Transforms." In Springer Undergraduate Mathematics Series, 123–62. London: Springer London, 1999. http://dx.doi.org/10.1007/978-1-4471-0379-0_4.

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Capelas de Oliveira, Edmundo. "Integral Transforms." In Studies in Systems, Decision and Control, 115–67. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-20524-9_4.

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Pap, Endre. "Integral transforms." In Complex Analysis through Examples and Exercises, 255–311. Dordrecht: Springer Netherlands, 1999. http://dx.doi.org/10.1007/978-94-017-1106-7_10.

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Peterson, James K. "Integral Transforms." In BioInformation Processing, 39–44. Singapore: Springer Singapore, 2016. http://dx.doi.org/10.1007/978-981-287-871-7_3.

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Beigi, Homayoon. "Integral Transforms." In Fundamentals of Speaker Recognition, 647–771. Boston, MA: Springer US, 2011. http://dx.doi.org/10.1007/978-0-387-77592-0_24.

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Beals, Richard, and Roderick S. C. Wong. "Integral transforms." In Explorations in Complex Functions, 255–68. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-54533-8_18.

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Gilbert, Robert P., George C. Hsiao, and Robert J. Ronkese. "Integral Transforms." In Differential Equations, 167–90. 2nd ed. Boca Raton: Chapman and Hall/CRC, 2021. http://dx.doi.org/10.1201/9781003175643-10.

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Georgiev, Svetlin G. "Integral Transforms." In Theory of Distributions, 205–18. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-81265-2_8.

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Ames, William F. "Integral Transforms." In Mathematics for Mechanical Engineers, 8–1. Boca Raton: CRC Press, 2022. http://dx.doi.org/10.1201/9781003067672-8.

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Conference papers on the topic "Integral transforms"

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KILBAS, ANATOLY A. "BESSEL-TYPE INTEGRAL TRANSFORMS AND H-TRANSFORMS." In Proceedings of the 3rd ISAAC Congress. World Scientific Publishing Company, 2003. http://dx.doi.org/10.1142/9789812794253_0013.

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Roy Frieden, B. "Integral logarithmic transform: theory and applications." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1991. http://dx.doi.org/10.1364/oam.1991.wv6.

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Mathematical properties and potential uses of a new class of integral transforms are described. Its input functions f(x) or f(x,w) must have limited support, as is true of any image. For a 1-D input f(x), the 1-D integral logarithmic transform is defined as F(y) = ∫f(xy)d(logx). For a 2-D input function f(x,w) the alternative 2-D transforms F(y,z) = ∫∫f(xy,wz)d(logx)d(logw) or G(y,z) = ∫∫fρ(yr, zθ)d(logr)dθ are defined. In the latter, function fρ (r,0) is the 1:1 polar remapping of input function f(x,w). Mathematically, it is found that transforms F(y) and F(y,z) are invariant to linear change of scale (magnification) of input coordinates x or (x,w). This is without incurring an objectionable magnification-dependent translation in the output, as is incurred by simple 1:1 log-polar mapping. Of further interest, transform G(y,z) is invariant to both magnification and rotation of the input function f(x,w). Also, the transform F(y) due to a nonlinear power-law change of scale f(x) is itself a power-law change of scale on the original F(y). Finally, the log-transforms are conveniently inverted: for example, in the 1-D case of a given F(y), the input f(x) can be computed as f(x) = (x/xo)F'(x/xo), where xO is the upper support coordinate for f(x). An optical implementation of transform F(y,z) is described.
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Obradović, Milutin. "Starlikeness of certain integral transforms." In Third CMFT Conference. WORLD SCIENTIFIC, 1999. http://dx.doi.org/10.1142/9789812833044_0033.

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Kumar, Prvindra, and Harendra Singh. "Integral transforms of double integrals involving a product of special functions." In INTERNATIONAL SCIENTIFIC AND PRACTICAL CONFERENCE “TECHNOLOGY IN AGRICULTURE, ENERGY AND ECOLOGY” (TAEE2022). AIP Publishing, 2022. http://dx.doi.org/10.1063/5.0103848.

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Lorenzo, Carl F., and Tom T. Hartley. "Initialization of Fractional Differential Equations: Theory and Application." In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-34814.

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It has been known that the initialization of fractional operators requires time-varying functions, a complicating factor. This paper simplifies the process of initialization of fractional differential equations by deriving Laplace transforms for the initialized fractional integral and derivative that generalize those for the integer-order operators. A companion paper in this conference determines the Laplace transforms for initialized fractional integrals of any order and fractional derivatives of order less than one. This paper extends the theory for the Laplace transform of the derivative to higher order and provides applications.
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Karmazin, Alexander, Evgenia Kirillova, Wolfgang Seemann, and Pavel Syromyatnikov. "Analysis of Spatial Steady-State Vibrations of a Layered Anisotropic Plate Using the Green’s Functions." In ASME 2010 10th Biennial Conference on Engineering Systems Design and Analysis. ASMEDC, 2010. http://dx.doi.org/10.1115/esda2010-25430.

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Spatial steady-state harmonic vibrations of a layered anisotropic plate excited by the distributed sources are considered. The work is based on the classical methods of the integral Fourier transforms and integral representations of the Green’s functions. In Fourier transform domain, the displacement vector is represented in terms of the Green’s matrix transform and the transform of the surface load vector. The two-dimensional inverse Fourier transform of the displacement vector is computed by reducing double integral to the iterated one with integrating along a contour, which deviates from the real axis while bypassing the real poles, and with subsequent integrating along the wave propagation angle. Three numerical algorithms of computing related iterated integrals are presented. The features of the application of these algorithms for the near- and far-field zones of the source are discussed. All of presented methods are compared for the numerical examples of vibrations on the surface of 24-layer symmetrical composite.
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Kejie Li and Yanzhao Xie. "A brief introduction of Sumudu transform and comparison with other integral transforms." In 2012 6th Asia-Pacific Conference on Environmental Electromagnetics (CEEM 2012). IEEE, 2012. http://dx.doi.org/10.1109/ceem.2012.6410623.

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Lindsey, Alan R., and Bruce W. Suter. "Convolution theorems: partitioning the space of integral transforms." In AeroSense '99, edited by Harold H. Szu. SPIE, 1999. http://dx.doi.org/10.1117/12.342937.

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Rappoport, Juri M. "Some aspects of modified Kontorovitch-Lebedev integral transforms." In Proceedings of the 7th International ISAAC Congress. WORLD SCIENTIFIC, 2010. http://dx.doi.org/10.1142/9789814313179_0039.

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"Modern aspects of the theory of integral transforms." In Proceedings of the 7th International ISAAC Congress. WORLD SCIENTIFIC, 2010. http://dx.doi.org/10.1142/9789814313179_others07.

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Reports on the topic "Integral transforms"

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Brizard, Jean-Claude. Breaking With the Past: Embracing Digital Transformation in Education. Digital Promise, April 2023. http://dx.doi.org/10.51388/20.500.12265/176.

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Today's businesses know that driving innovation is integral to succeeding not just in the present, but more importantly in the decades to come. Through the years, the innovation of digital technologies has transformed entire industries. Now it’s time to put those technologies to use and apply that same mentality to transform our schools. We need digital transformation of teaching and learning at scale across the United States. This report examines how the traditional one-size-fits-all approach to teaching and learning compares to more learner-centered, personalized frameworks; why we need to transition to them at scale; and how digital technologies can enable that scaling.
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Saldaña Medina, Caleb, Nadia García Sicard, and Stefany Hernández Arrieta. ¿Cómo las habilidades para la vida transforman la experiencia universitaria? Universidad del Rosario, June 2024. http://dx.doi.org/10.12804/dvcn_10336.42747_num7.

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‘Habilidades para sentir, vivir y disfrutar’ es la nueva propuesta de la Decanatura del Medio Universitario de la Universidad del Rosario para que las electivas formativas, conocidas como Humanidades y del Medio (HM), se conviertan en el espacio donde los estudiantes desarrollen cualidades sociales que puedan integrar en su vida profesional.
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Hart, Carl, Gregory Lyons, and Michael White. Spherical shock waveform reconstruction by heterodyne interferometry. Engineer Research and Development Center (U.S.), May 2024. http://dx.doi.org/10.21079/11681/48471.

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The indirect measurement of shock waveforms by acousto-optic sensing requires a method to reconstruct the field from the projected data. Under the assumption of spherical symmetry, one approach is to reconstruct the field by the Abel inversion integral transform. When the acousto-optic sensing modality measures the change in optical phase difference time derivative, as for a heterodyne Mach–Zehnder interferometer, e.g., a laser Doppler vibrometer, the reconstructed field is the fluctuating refractive index time derivative. A technique is derived that reconstructs the fluctuating index directly by assuming plane wave propagation local to a probe beam. With synthetic data, this approach is compared to the Abel inversion integral transform and then applied to experimental data of laser-induced shockwaves. Time waveforms are reconstructed with greater accuracy except for the tail of the waveform that maps spatially to positions near a virtual origin. Furthermore, direct reconstruction of the fluctuating index field eliminates the required time integration and results in more accurate shock waveform peak values, rise times, and positive phase duration.
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Christie, Benjamin, Osama Ennasr, and Garry Glaspell. ROS integrated object detection for SLAM in unknown, low-visibility environments. Engineer Research and Development Center (U.S.), November 2021. http://dx.doi.org/10.21079/11681/42385.

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Integrating thermal (or infrared) imagery on a robotics platform allows Unmanned Ground Vehicles (UGV) to function in low-visibility environments, such as pure darkness or low-density smoke. To maximize the effectiveness of this approach we discuss the modifications required to integrate our low-visibility object detection model on a Robot Operating System (ROS). Furthermore, we introduce a method for reporting detected objects while performing Simultaneous Localization and Mapping (SLAM) by generating bounding boxes and their respective transforms in visually challenging environments.
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Enria, Luisa. Citizen Ethnography in Outbreak Response: Guidance for Establishing Networks of Researchers. SSHAP, May 2022. http://dx.doi.org/10.19088/sshap.2022.001.

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This guidance outlines the steps for designing and implementing ethnographic research which is led by citizens. It explains what citizen ethnography is and then sets out what should be considered throughout the process of working with networks of citizen researchers, from recruitment, training and supporting them to collect and analyse ethnographic data, and how to transform the insights they gain to support preparedness and responses for disease outbreaks. It also provides suggestions for further resources to support the process. The guidance is for social scientists who would like to integrate citizen-led ethnographic approaches into their research, and for practitioners working on community engagement or other outbreak responses, who seek to use social science insights in their operations. It was written for SSHAP by Luisa Enria (London School of Hygiene & Tropical Medicine). It is the responsibility of SSHAP.
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Enria, Luisa. Etnografía ciudadana en la respuesta a brotes de enfermedades: recomendaciones para la creación de redes de investigadores. SSHAP, May 2022. http://dx.doi.org/10.19088/sshap.2022.029.

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Este documento de orientación describe los pasos que deben seguirse para diseñar y una investigación etnográfica dirigida por los ciudadanos. Se explica qué es la etnografía ciudadana y se indica qué debe tenerse en cuenta a lo largo del proceso de trabajo con redes de investigadores ciudadanos, desde su reclutamiento, capacitación y apoyo para la recogida y el análisis de datos etnográficos, hasta como transformar los conocimientos que se obtienen para apoyar la preparación y las respuestas a los brotes de enfermedades. El documento también ofrece sugerencias sobre otros recursos para apoyar el proceso. Las recomendaciones están dirigidas a los científicos sociales que deseen integrar a sus investigaciones un enfoque etnográfico dirigido por los ciudadanos, y a aquellos profesionales abocados a tareas de participación comunitaria u otras respuestas a brotes de enfermedades que busquen sumar la perspectiva de las ciencias sociales a sus operaciones. Su autora, Luisa Enria (London School of Hygiene & Tropical Medicine), las escribió para SSHAP. Son responsabilidad de SSHAP.
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Ostashev, Vladimir, Michael Muhlestein, and D. Wilson. Extra-wide-angle parabolic equations in motionless and moving media. Engineer Research and Development Center (U.S.), September 2021. http://dx.doi.org/10.21079/11681/42043.

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Wide-angle parabolic equations (WAPEs) play an important role in physics. They are derived by an expansion of a square-root pseudo-differential operator in one-way wave equations, and then solved by finite-difference techniques. In the present paper, a different approach is suggested. The starting point is an extra-wide-angle parabolic equation (EWAPE) valid for small variations of the refractive index of a medium. This equation is written in an integral form, solved by a perturbation technique, and transformed to the spectral domain. The resulting split-step spectral algorithm for the EWAPE accounts for the propagation angles up to 90° with respect to the nominal direction. This EWAPE is also generalized to large variations in the refractive index. It is shown that WAPEs known in the literature are particular cases of the two EWAPEs. This provides an alternative derivation of the WAPEs, enables a better understanding of the underlying physics and ranges of their applicability, and opens an opportunity for innovative algorithms. Sound propagation in both motionless and moving media is considered. The split-step spectral algorithm is particularly useful in the latter case since complicated partial derivatives of the sound pressure and medium velocity reduce to wave vectors (essentially, propagation angles) in the spectral domain.
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Arana, María Teresa. Mujeres y cambio climático en tiempos de la COVID 19: retos para la pospandemia. Fundación Carolina, April 2022. http://dx.doi.org/10.33960/ac_10.2022.

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Este análisis muestra los factores de vulnerabilidad de las mujeres ante el cambio climático, agudizada por la pandemia de la COVID-19. También propone algunos lineamientos para el seguimiento de los compromisos asumidos por los países iberoamericanos, motivando el debate y seguimiento a sus políticas públicas sobre cambio climático desde una perspectiva de género. La evidencia empírica muestra que las mujeres desarrollan acciones y estrategias para sobreponerse a situaciones adversas, y asumen el reto del cuidado de la salud a pesar de las inequidades, violencias e injusticias del sistema patriarcal. Es necesario mejorar los estándares y la evaluación de los resultados de las intervenciones, pero no basta con que integren un enfoque de género; además es indispensable que las medidas transformen las condiciones de vulnerabilidad. Para lograrlo, se requiere de la voluntad política de los Estados y del financiamiento de las intervenciones. No actuar sobre las condiciones sociopolíticas y culturales que generan mayor vulnerabilidad en las mujeres, y desarrollar planes neutros al género, constituiría una negligencia de los Estados y reforzaría las condiciones estructurales de exclusión patriarcal.
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Arana, María Teresa. Mujeres y cambio climático en tiempos de la COVID 19: retos para la pospandemia. Fundación Carolina, April 2022. http://dx.doi.org/10.33960/ac_10.2022.

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Este análisis muestra los factores de vulnerabilidad de las mujeres ante el cambio climático, agudizada por la pandemia de la COVID-19. También propone algunos lineamientos para el seguimiento de los compromisos asumidos por los países iberoamericanos, motivando el debate y seguimiento a sus políticas públicas sobre cambio climático desde una perspectiva de género. La evidencia empírica muestra que las mujeres desarrollan acciones y estrategias para sobreponerse a situaciones adversas, y asumen el reto del cuidado de la salud a pesar de las inequidades, violencias e injusticias del sistema patriarcal. Es necesario mejorar los estándares y la evaluación de los resultados de las intervenciones, pero no basta con que integren un enfoque de género; además es indispensable que las medidas transformen las condiciones de vulnerabilidad. Para lograrlo, se requiere de la voluntad política de los Estados y del financiamiento de las intervenciones. No actuar sobre las condiciones sociopolíticas y culturales que generan mayor vulnerabilidad en las mujeres, y desarrollar planes neutros al género, constituiría una negligencia de los Estados y reforzaría las condiciones estructurales de exclusión patriarcal.
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Arana, María Teresa. Mujeres y cambio climático en tiempos de la COVID 19: retos para la pospandemia. Fundación Carolina, April 2022. http://dx.doi.org/10.33960/ac_10.2022.

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Este análisis muestra los factores de vulnerabilidad de las mujeres ante el cambio climático, agudizada por la pandemia de la COVID-19. También propone algunos lineamientos para el seguimiento de los compromisos asumidos por los países iberoamericanos, motivando el debate y seguimiento a sus políticas públicas sobre cambio climático desde una perspectiva de género. La evidencia empírica muestra que las mujeres desarrollan acciones y estrategias para sobreponerse a situaciones adversas, y asumen el reto del cuidado de la salud a pesar de las inequidades, violencias e injusticias del sistema patriarcal. Es necesario mejorar los estándares y la evaluación de los resultados de las intervenciones, pero no basta con que integren un enfoque de género; además es indispensable que las medidas transformen las condiciones de vulnerabilidad. Para lograrlo, se requiere de la voluntad política de los Estados y del financiamiento de las intervenciones. No actuar sobre las condiciones sociopolíticas y culturales que generan mayor vulnerabilidad en las mujeres, y desarrollar planes neutros al género, constituiría una negligencia de los Estados y reforzaría las condiciones estructurales de exclusión patriarcal.
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