Bibliografías temáticas / Laplace transformation

Literatura académica sobre el tema "Laplace transformation"

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Publicado: 4 de junio de 2021

Última modificación: 7 de septiembre de 2023

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Artículos de revistas sobre el tema "Laplace transformation"

Devi, Rekha. "Applications of Laplace Transformation". Research Journal of Science and Technology 9, n.º 1 (2017): 167. http://dx.doi.org/10.5958/2349-2988.2017.00027.4.

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Khedkar, B. G. y S. B. Gaikwad. "Stieltjes transformation as the iterated Laplace transformation". International Journal of Mathematical Analysis 11 (2017): 833–38. http://dx.doi.org/10.12988/ijma.2017.7796.

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Ohshima, Hiroyuki. "Approximate Analytic Expression for the Time-Dependent Transient Electrophoretic Mobility of a Spherical Colloidal Particle". Molecules 27, n.º 16 (11 de agosto de 2022): 5108. http://dx.doi.org/10.3390/molecules27165108.

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The general expression is derived for the Laplace transform of the time-dependent transient electrophoretic mobility (with respect to time) of a spherical colloidal particle when a step electric field is applied. The transient electrophoretic mobility can be obtained by the numerical inverse Laplace transformation method. The obtained expression is applicable for arbitrary particle zeta potential and arbitrary thickness of the electrical double layer around the particle. For the low potential case, this expression gives the result obtained by Huang and Keh. On the basis of the obtained general expression for the Laplace transform of the transient electrophoretic mobility, we present an approximation method to avoid the numerical inverse Laplace transformation and derive a simple approximate analytic mobility expression for a weakly charged particle without involving numerical inverse Laplace transformations. The transient electrophoretic mobility can be obtained directly from this approximate mobility expression without recourse to the numerical inverse Laplace transformation. The results are found to be in excellent agreement with the exact numerical results obtained by Huang and Keh.

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Pérez-Esteva, Salvador. "Convolution operators for the one-sided Laplace transformation". Časopis pro pěstování matematiky 110, n.º 1 (1985): 69–76. http://dx.doi.org/10.21136/cpm.1985.118223.

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Rao, G. L. N. y L. Debnath. "A generalized Meijer transformation". International Journal of Mathematics and Mathematical Sciences 8, n.º 2 (1985): 359–65. http://dx.doi.org/10.1155/s0161171285000370.

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In a series of papers [1-6], Kratzel studies a generalized version of the classical Meijer transformation with the Kernel function(st)νη(q,ν+1; (st)q). This transformation is referred to as GM transformation which reduces to the classical Meijer transform whenq=1. He also discussed a second generalization of the Meijer transform involving the Kernel functionλν(n)(x)which reduces to the Meijer function whenn=2and the Laplace transform whenn=1. This is called the Meijer-Laplace (or ML) transformation. This paper is concerned with a study of both GM and ML transforms in the distributional sense. Several properties of these transformations including inversion, uniqueness, and analyticity are discussed in some detail.

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Horvath, Illes, Andras Meszaros y Miklos Telek. "Optimized numerical inverse Laplace transformation". ACM SIGMETRICS Performance Evaluation Review 50, n.º 2 (30 de agosto de 2022): 36–38. http://dx.doi.org/10.1145/3561074.3561087.

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Among the numerical inverse Laplace transformation (NILT) methods, those that belong to the Abate-Whitt framework (AWF) are considered to be the most efficient ones currently. It is a characteristic feature of the AWF NILT procedures that they are independent of the transform function and the time point of interest. In this work we propose an NILT procedure that goes beyond this limitation and optimize the accuracy of the NILT utilizing also the transform function and the time point of interest.

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Kamran, Niky y Keti Tenenblat. "Laplace transformation in higher dimensions". Duke Mathematical Journal 84, n.º 1 (julio de 1996): 237–66. http://dx.doi.org/10.1215/s0012-7094-96-08409-4.

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Jafarian, Ahmad, Alireza Khalili Golmankhaneh y Dumitru Baleanu. "On Fuzzy Fractional Laplace Transformation". Advances in Mathematical Physics 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/295432.

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Fuzzy and fractional differential equations are used to model problems with uncertainty and memory. Using the fractional fuzzy Laplace transformation we have solved the fuzzy fractional eigenvalue differential equation. By illustrative examples we have shown the results.

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XIAO, Y. "2-D Laplace-Z Transformation". IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E89-A, n.º 5 (1 de mayo de 2006): 1500–1504. http://dx.doi.org/10.1093/ietfec/e89-a.5.1500.

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Novikov, I. A. "Laplace transformation and dynamic measurements". Measurement Techniques 31, n.º 5 (mayo de 1988): 405–9. http://dx.doi.org/10.1007/bf00864455.

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Tesis sobre el tema "Laplace transformation"

BERNI, OLIVIER. "Cohomologie formelle. Transformation de laplace". Paris 6, 1999. http://www.theses.fr/1999PA066057.

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Pour resoudre le probleme de riemann-hilbert, m. Kashiwara introduit le foncteur de cohomologie temperee qui echange les faisceaux pervers et les d-modules holonomes. En 1995, m. Kashiwara et p. Schapira introduisent le foncteur de cohomologie formelle, dual en un certain sens du precedent. Dans la premiere partie de la these, nous montrons un theoreme d'annulation : sur une variete complexe de stein, les sections globales a support compact du foncteur de cohomologie formelle associe a un faisceau pervers sont concentrees en degre. La preuve utilise des resultats de siu et hormander, et la dualite dans les categories derivees des espaces vectoriels topologiques. Nous montrons d'abord la platitude du faisceau des fonctions holomorphes temperees sur un ouvert de stein sous-analytique relativement compact de x. Puis nous montrons une version temperee du theoreme b de cartan. Dans la deuxieme partie, nous montrons la stabilite sous la transformation de laplace du faisceau conique des fonctions holomorphes temperees (a l'origine et a l'infini) sur un espace vectoriel complexe. Nous utilisons le resultat connu : la transformation de laplace echange l'espace des distributions temperees de support contenu dans un cone convexe ferme d'un espace vectoriel reel et l'espace des fonctions holomorphes temperees sur le tube dual. Nous retrouvons alors le theoreme de brylinski-malgrange-verdier qui etablit la correspondance entre le transformee de fourier geometrique des solutions d'un d-module de type fini monodromique et les solutions de son transforme de fourier formel.

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Hunt, Colleen Helen. "Inference for general random effects models". Title page, table of contents and abstract only, 2003. http://web4.library.adelaide.edu.au/theses/09SM/09smh9394.pdf.

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"October 13, 2003" Bibliography: leaves 102-105. This work describes methods associated with general random effects models. Part one describes a technique for investigating mean-variance relationships in random effects models. Part two derives and approximation to the likelihood function using a Laplace expansion to the fourth order.

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Smith, James Raphael. "A vectorised Fourier-Laplace transformation and its application to Green's tensors". Thesis, Lancaster University, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.296967.

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Ngounda, Edgard. "Numerical Laplace transformation methods for integrating linear parabolic partial differential equations". Thesis, Stellenbosch : University of Stellenbosch, 2009. http://hdl.handle.net/10019.1/2735.

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Thesis (MSc (Applied Mathematics))--University of Stellenbosch, 2009.
ENGLISH ABSTRACT: In recent years the Laplace inversion method has emerged as a viable alternative method for the numerical solution of PDEs. Effective methods for the numerical inversion are based on the approximation of the Bromwich integral. In this thesis, a numerical study is undertaken to compare the efficiency of the Laplace inversion method with more conventional time integrator methods. Particularly, we consider the method-of-lines based on MATLAB’s ODE15s and the Crank-Nicolson method. Our studies include an introductory chapter on the Laplace inversion method. Then we proceed with spectral methods for the space discretization where we introduce the interpolation polynomial and the concept of a differentiation matrix to approximate derivatives of a function. Next, formulas of the numerical differentiation formulas (NDFs) implemented in ODE15s, as well as the well-known second order Crank-Nicolson method, are derived. In the Laplace method, to compute the Bromwich integral, we use the trapezoidal rule over a hyperbolic contour. Enhancement to the computational efficiency of these methods include the LU as well as the Hessenberg decompositions. In order to compare the three methods, we consider two criteria: The number of linear system solves per unit of accuracy and the CPU time per unit of accuracy. The numerical results demonstrate that the new method, i.e., the Laplace inversion method, is accurate to an exponential order of convergence compared to the linear convergence rate of the ODE15s and the Crank-Nicolson methods. This exponential convergence leads to high accuracy with only a few linear system solves. Similarly, in terms of computational cost, the Laplace inversion method is more efficient than ODE15s and the Crank-Nicolson method as the results show. Finally, we apply with satisfactory results the inversion method to the axial dispersion model and the heat equation in two dimensions.
AFRIKAANSE OPSOMMING: In die afgelope paar jaar het die Laplace omkeringsmetode na vore getree as ’n lewensvatbare alternatiewe metode vir die numeriese oplossing van PDVs. Effektiewe metodes vir die numeriese omkering word gebasseer op die benadering van die Bromwich integraal. In hierdie tesis word ’n numeriese studie onderneem om die effektiwiteit van die Laplace omkeringsmetode te vergelyk met meer konvensionele tydintegrasie metodes. Ons ondersoek spesifiek die metode-van-lyne, gebasseer op MATLAB se ODE15s en die Crank-Nicolson metode. Ons studies sluit in ’n inleidende hoofstuk oor die Laplace omkeringsmetode. Dan gaan ons voort met spektraalmetodes vir die ruimtelike diskretisasie, waar ons die interpolasie polinoom invoer sowel as die konsep van ’n differensiasie-matriks waarmee afgeleides van ’n funksie benader kan word. Daarna word formules vir die numeriese differensiasie formules (NDFs) ingebou in ODE15s herlei, sowel as die welbekende tweede orde Crank-Nicolson metode. Om die Bromwich integraal te benader in die Laplace metode, gebruik ons die trapesiumreël oor ’n hiperboliese kontoer. Die berekeningskoste van al hierdie metodes word verbeter met die LU sowel as die Hessenberg ontbindings. Ten einde die drie metodes te vergelyk beskou ons twee kriteria: Die aantal lineêre stelsels wat moet opgelos word per eenheid van akkuraatheid, en die sentrale prosesseringstyd per eenheid van akkuraatheid. Die numeriese resultate demonstreer dat die nuwe metode, d.i. die Laplace omkeringsmetode, akkuraat is tot ’n eksponensiële orde van konvergensie in vergelyking tot die lineêre konvergensie van ODE15s en die Crank-Nicolson metodes. Die eksponensiële konvergensie lei na hoë akkuraatheid met slegs ’n klein aantal oplossings van die lineêre stelsel. Netso, in terme van berekeningskoste is die Laplace omkeringsmetode meer effektief as ODE15s en die Crank-Nicolson metode. Laastens pas ons die omkeringsmetode toe op die aksiale dispersiemodel sowel as die hittevergelyking in twee dimensies, met bevredigende resultate.

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Wang, Tingting y 王婷婷. "Fast simulation of weakly nonlinear circuits based on multidimensionalinverse Laplace transform". Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2012. http://hub.hku.hk/bib/B49858610.

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This dissertation presents several solutions on the simulation of weakly nonlinear circuits. The work is motivated by the increasing demand on fast yet accurate simulation methods circuits (IC)s, and the current lack of such methods in the electronic design automation (EDA) / computer-aided design (CAD) community. Three types of frequency domain methods are studied to analyze weakly nonlinear circuits. The first method employs numerical multi-dimensional inverse Laplace transform based on Laguerre function expansion. An adaptive mesh refinement (AMR) technique is developed and its parallel implementation is introduced to speed up the computation. The second method applies a Fourier series based algorithm to invert Laplace transform. The algorithm is straightforward to implement, and gives increasing accuracy with increasing number of frequency sampling points. It employs a fast Fourier transform (FFT)-based method to directly invert the frequency domain solution. Its parallel routine is also studied. The third method is based on Gaver functional. It enjoys a high accuracy independent of the number of sampling points, and for multidimensional simulation, only the diagonal points in the matrix are required to be computer, which can be further speeded up by parallel implementation. Numerical results show that the aforementioned three methods enjoy good accuracy as well as high efficiency. A comparative study is carried out to investigate the strengths and drawbacks of each method.
published_or_final_version
Electrical and Electronic Engineering
Master
Master of Philosophy

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Merchant, Richard W. "Recursive estimation using the bilinear operator with applications to synchronous machine parameter identification /". Title page, contents and abstract only, 1992. http://web4.library.adelaide.edu.au/theses/09PH/09phm5543.pdf.

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Simonaitytė, Irena. "Priverstinės sinchronizacijos sistemos matematinio modelio sudarymas ir tyrimas". Master's thesis, Lithuanian Academic Libraries Network (LABT), 2005. http://vddb.library.lt/obj/LT-eLABa-0001:E.02~2005~D_20050608_132909-70485.

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The mathematical model of the forced synchronization system, composed of four oscillators is investigated. The mathematical model of the system is the matrix differential equation with delayed arguments. The matrix differential equation is solved using method of steps and applying Laplace transform. Using this method and exact solution of the matrix differential equation with delayed arguments was obtained and exact expressions of the elements of the step responses matrix, of the synchronization system are got. On the base of derived formulas the transition processes of the system are investigated.

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Kurban, Feyza Uyhan Ramazan. "Isıl yazıcı başlıkta matematiksel modelleme /". Isparta : SDÜ Fen Bilimleri Enstitüsü, 2007. http://tez.sdu.edu.tr/Tezler/TF01132.pdf.

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Ho, Lok-ping y 何樂平. "Laplace transform deep level transient spectroscopic study on PLD grown ZnO". Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2015. http://hdl.handle.net/10722/211117.

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The fundamental physics and techniques employed in Laplace transform deep level transient spectroscopy (L-DLTS) are reviewed. A Laplace-DLTS system has been constructed. The high resolving power of this system has been demonstrated experimentally. The L-DLTS system was applied to characterize the defects in undoped n-type ZnO thin film grown by the pulsed laser deposition (PLD) method. A 0.3 eV deep trap has been identified. The formations of Ec-0.39eV and Ec-0.20eVcan be enhanced when the sample surface is seriously damaged by high temperature annealing.AnEc-0.25eV trap is identified in the freshly grown samples, but would disappear after the storage of 3 months. Copper doped n-type ZnO thin film samples with low carrier concentration (n~〖10〗^16 〖cm〗^(-3)) were investigated by using both conventional and Laplace DLTS techniques. Positive DLTS signal peaks were detected that are suspected to be contributed by the minority carrier (hole carrier) emission. A physics model involving the inversion layer of a metal-insulator-semiconductor contact has been invoked to interpret the hole carrier concentration existing near the metal-semiconductor interface. Expression for the defect concentration is determined as a function of the temperature of DLTS peaks. AnEv+0.6eV defect with high concentration (N_T~〖10〗^17 〖cm〗^(-3)) was detected. The concentration of Ev+0.6eVcan be enhanced when the annealing temperature was increased from 750 to 900 degree C.
published_or_final_version
Physics
Master
Master of Philosophy

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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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Libros sobre el tema "Laplace transformation"

Weber, Hubert. Laplace-Transformation. Wiesbaden: Vieweg+Teubner Verlag, 1990. http://dx.doi.org/10.1007/978-3-322-96634-6.

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Weber, Hubert. Laplace-Transformation. Wiesbaden: Vieweg+Teubner Verlag, 2003. http://dx.doi.org/10.1007/978-3-322-96747-3.

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Bolton, W. Laplace and z-transforms. Harlow: Longman, 1994.

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Widder, D. V. The laplace transform. Mineola, N.Y: Dover Publications, 2010.

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Dewald, Lee Samuel. [Lambda]-Laplace processes. Monterey, Calif: Naval Postgraduate School, 1988.

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Mikami, Naoki. Fūrie henkan to rapurasu henkan: Kiso riron kara, denki kairo e no ōyō made. 8^a ed. Tōkyō-to Shinjuku-ku: Kōgakusha, 2013.

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Ulrich, Helmut y Stephan Ulrich. Laplace-Transformation, Diskrete Fourier-Transformation und z-Transformation. Wiesbaden: Springer Fachmedien Wiesbaden, 2022. http://dx.doi.org/10.1007/978-3-658-31877-2.

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Apelblat, Alexander. Laplace transforms and their applications. Hauppauge, N.Y: Nova Science Publishers, 2011.

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Buschman, R. G. Tables addenda for Laplace transforms. [Langlois, Or: R.G. Buschman], 1996.

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Ulrich, Helmut y Hubert Weber. Laplace-, Fourier- und z-Transformation. Wiesbaden: Springer Fachmedien Wiesbaden, 2017. http://dx.doi.org/10.1007/978-3-658-03450-4.

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Capítulos de libros sobre el tema "Laplace transformation"

Weber, Hubert. "Laplace — Transformation". En Laplace-Transformation, 39–201. Wiesbaden: Vieweg+Teubner Verlag, 1987. http://dx.doi.org/10.1007/978-3-322-96634-6_4.

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Weber, Hubert. "Laplace — Transformation". En Laplace-Transformation, 31–176. Wiesbaden: Vieweg+Teubner Verlag, 2003. http://dx.doi.org/10.1007/978-3-322-96747-3_4.

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Weber, Hubert. "Fourierreihen". En Laplace-Transformation, 9–25. Wiesbaden: Vieweg+Teubner Verlag, 1987. http://dx.doi.org/10.1007/978-3-322-96634-6_1.

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Weber, Hubert. "Fourierintegral". En Laplace-Transformation, 26–34. Wiesbaden: Vieweg+Teubner Verlag, 1987. http://dx.doi.org/10.1007/978-3-322-96634-6_2.

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Weber, Hubert. "Fouriertransformation". En Laplace-Transformation, 35–38. Wiesbaden: Vieweg+Teubner Verlag, 1987. http://dx.doi.org/10.1007/978-3-322-96634-6_3.

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Weber, Hubert. "Fourierreihen". En Laplace-Transformation, 1–16. Wiesbaden: Vieweg+Teubner Verlag, 2003. http://dx.doi.org/10.1007/978-3-322-96747-3_1.

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Weber, Hubert. "Fourierintegral". En Laplace-Transformation, 17–26. Wiesbaden: Vieweg+Teubner Verlag, 2003. http://dx.doi.org/10.1007/978-3-322-96747-3_2.

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Weber, Hubert. "Fouriertransformation". En Laplace-Transformation, 27–30. Wiesbaden: Vieweg+Teubner Verlag, 2003. http://dx.doi.org/10.1007/978-3-322-96747-3_3.

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Weber, Hubert. "Anhang". En Laplace-Transformation, 177–202. Wiesbaden: Vieweg+Teubner Verlag, 2003. http://dx.doi.org/10.1007/978-3-322-96747-3_5.

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Ohm, Jens-Rainer y Hans Dieter Lüke. "Laplace-Transformation". En Springer-Lehrbuch, 35–56. Berlin, Heidelberg: Springer Berlin Heidelberg, 2014. http://dx.doi.org/10.1007/978-3-642-53901-5_2.

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Actas de conferencias sobre el tema "Laplace transformation"

Łopuszański, O. "Polynomial ultradistributions: differentiation and Laplace transformation". En Linear and Non-Linear Theory of Generalized Functions and its Applications. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2010. http://dx.doi.org/10.4064/bc88-0-16.

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HRISTOV, Milen J. "VECTOR-VALUED LAPLACE TRANSFORMATION APPLIED TO RATIONAL BÉZIER CURVES". En 4th International Colloquium on Differential Geometry and its Related Fields. WORLD SCIENTIFIC, 2015. http://dx.doi.org/10.1142/9789814719780_0016.

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Ha, Wansoo, Changsoo Shin y Taeyoung Ha. "Efficient Laplace-domain modeling using an axis transformation technique". En SEG Technical Program Expanded Abstracts 2012. Society of Exploration Geophysicists, 2012. http://dx.doi.org/10.1190/segam2012-0565.1.

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Mustafa, Omar Saber. "A Study on Laplace and Fourier Transformation its Application". En 2020 6th International Conference on Advanced Computing and Communication Systems (ICACCS). IEEE, 2020. http://dx.doi.org/10.1109/icaccs48705.2020.9074384.

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Suzuki, Satoshi y Katsuhisa Furuta. "Real number Laplace transformation-based identification and its application". En 2009 International Conference on Mechatronics and Automation (ICMA). IEEE, 2009. http://dx.doi.org/10.1109/icma.2009.5246314.

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Onur, M. y A. C. Reynolds. "Well Testing Applications of Numerical Laplace Transformation of Sampled-Data". En SPE Annual Technical Conference and Exhibition. Society of Petroleum Engineers, 1996. http://dx.doi.org/10.2118/36554-ms.

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Yi, Sun, A. Galip Ulsoy y Patrick W. Nelson. "Solution of Systems of Linear Delay Differential Equations via Laplace Transformation". En Proceedings of the 45th IEEE Conference on Decision and Control. IEEE, 2006. http://dx.doi.org/10.1109/cdc.2006.377712.

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Zongying Li y Xiang Liu. "The image encryption algorithm based on the backward Laplace-like transformation". En 2010 International Conference on Computer Application and System Modeling (ICCASM 2010). IEEE, 2010. http://dx.doi.org/10.1109/iccasm.2010.5622411.

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Pavlov, Andrei Valerianovich. "The transform of Laplace, orthogonal transformations, moving fields". En II International Scientific and Practical Conference. TSNS Interaktiv Plus, 2022. http://dx.doi.org/10.21661/r-557130.

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It is proved in article, that from point of numbers and new scalar work of diagonal of arbitrary rhombus it is possible to consider identical as a result of the orthogonal transformation, when lengths of vectors are measured in the same units of measuring as on sides of the rhombus. In the second part of article some class of functions is resulted: the values of the functions restore on the known positive values of the transform of Laplace. In the third part of article the examples are resulted, when a function of points of complex plane become periodic with the arbitrary period (from point of some introduction of two systems of co-ordinates).

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Kitayama, Satoshi y Hiroshi Yamakawa. "A Study on Optimum Topology of Plate Structure Using Coordinate Transformation by Conformal Mapping". En ASME 2002 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2002. http://dx.doi.org/10.1115/detc2002/dac-34053.

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This paper presents a new method to determine an optimum topology of plate structure using coordinate transformation by conformal mapping. We have already proposed a method to determine an optimum topology of planar structure using coordinate transformation by conformal mapping. In that study first we defined simple design domain in which analysis and optimization were performed easily. We calculated optimum topology in this simple design domain. Then we applied coordinate transformation by conformal mapping to optimum topology calculated in simple design domain, and obtained some optimum topologies in complex design domain. We also showed that the invariants of stresses which were the sum and difference of principal stress satisfied Laplace equation and relationshi p between fluid mechanics and electromagnetic could be valid in the theory of elasticity. In this study we clarify two invariants of bending moments satisfy Laplace equation under a certain condition. We note the similarity between Airy stress function of 2-D elastic body and deflection of plate, and will show that the two invariants of bending moments which are the sum and difference of principal bending moments satisfy Laplace equation using this similarity. As a result we will show that corresponding relationship between fluid mechanics, electromagnetic and elasticity may be valid in the theory of plate. Then by using this relationship, we proposed a new method to determine optimum topology using coordinate transformation by conformal mapping. Our proposed method will be useful to determine optimum topology easily in complex design domain. Through numerical examples, we can examine the effectiveness of the proposed method.

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