Статті в журналах: "Laplace transformation"

1

Devi, Rekha. "Applications of Laplace Transformation." Research Journal of Science and Technology 9, no. 1 (2017): 167. http://dx.doi.org/10.5958/2349-2988.2017.00027.4.

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2

Ohshima, Hiroyuki. "Approximate Analytic Expression for the Time-Dependent Transient Electrophoretic Mobility of a Spherical Colloidal Particle." Molecules 27, no. 16 (August 11, 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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3

Khedkar, B. G., and 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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4

Rao, G. L. N., and L. Debnath. "A generalized Meijer transformation." International Journal of Mathematics and Mathematical Sciences 8, no. 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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5

Pérez-Esteva, Salvador. "Convolution operators for the one-sided Laplace transformation." Časopis pro pěstování matematiky 110, no. 1 (1985): 69–76. http://dx.doi.org/10.21136/cpm.1985.118223.

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6

Horvath, Illes, Andras Meszaros, and Miklos Telek. "Optimized numerical inverse Laplace transformation." ACM SIGMETRICS Performance Evaluation Review 50, no. 2 (August 30, 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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7

Kamran, Niky, and Keti Tenenblat. "Laplace transformation in higher dimensions." Duke Mathematical Journal 84, no. 1 (July 1996): 237–66. http://dx.doi.org/10.1215/s0012-7094-96-08409-4.

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8

Jafarian, Ahmad, Alireza Khalili Golmankhaneh, and 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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9

XIAO, Y. "2-D Laplace-Z Transformation." IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E89-A, no. 5 (May 1, 2006): 1500–1504. http://dx.doi.org/10.1093/ietfec/e89-a.5.1500.

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10

Novikov, I. A. "Laplace transformation and dynamic measurements." Measurement Techniques 31, no. 5 (May 1988): 405–9. http://dx.doi.org/10.1007/bf00864455.

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11

Gaba, Gagan. "A Study on the Applications of Laplace Transformation." Journal of University of Shanghai for Science and Technology 23, no. 08 (August 3, 2021): 84–91. http://dx.doi.org/10.51201/jusst/21/08354.

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Mathematics plays an important role in our everyday life. Laplace transform is one of the important tools which is used by researchers to find the solutions of various real life problems modeled into differential equations or simultaneous differential equations or Integral equations. In this paper, we are going to study the details on lapace transform, its properties and “Applications of Laplace Transform in Various Fields”. Various uses of Laplace Transforms in the research problems have been highlighted. Detailed applications of Laplace Transform have been discussed.

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12

Saltas, Vassilios, Vassilios Tsiantos, and Dimitrios Varveris. "Mathematic Attributions of Laplace Transform." European Journal of Mathematics and Statistics 3, no. 6 (December 23, 2022): 8–19. http://dx.doi.org/10.24018/ejmath.2022.3.6.173.

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The purpose of this work is to define the Laplace transform and the Laplace inverse transformation, to describe their basic properties and to calculate the corresponding transforms of selected functions. To achieve these, the concept of the real function image is first defined, and in particular the conversion of the complex variable function. The examples used are initially pure mathematics, followed by reference to the practical application of these two transformations since they relate to the conversion of a continuous time signal into a complex variable function.

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13

Onur, M., and A. C. Reynolds. "Well Testing Applications of Numerical Laplace Transformation of Sampled-Data." SPE Reservoir Evaluation & Engineering 1, no. 03 (June 1, 1998): 268–77. http://dx.doi.org/10.2118/36554-pa.

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Abstract In recent years, the numerical Laplace transformation of sampled-data has proven to be useful for well test analysis applications. However, the success of this approach is highly dependent on the algorithms used to transform sampled-data into Laplace space and to perform the numerical inversion. In this work, we investigate several functional approximations (piecewise linear, quadratic, and log-linear) for sampled-data to achieve the "forward" Laplace transformation and present new methods to deal with the "tail" effects associated with transforming sampled-data. New algorithms that provide accurate transformation of sampled-data into Laplace space are provided. The algorithms presented can be applied to generate accurate pressure-derivatives in the time domain. Three different algorithms investigated for the numerical inversion of sampled-data. Applications of the algorithms to convolution, deconvolution, and parameter estimation in Laplace space are also presented. By using the algorithms presented here, it is shown that performing curve-fitting in the Laplace domain without numerical inversion is computationally more efficient than performing it in the time domain. Both synthetic and field examples are considered to illustrate the applicability of the proposed algorithms. Introduction Due to its efficiency, the Stehfest algorithm for the numerical inversion of the Laplace transform is now a well established tool in pressure transient analysis research and applications. Roumboutsos and Stewart showed that convolution and deconvolution in Laplace domain with the aid of the numerical Laplace transformation of measured pressure and/or rate data is more efficient and stable than techniques based on the discretized form of convolution integral in the time domain. Use of the numerical Laplace transformation of tabulated (pressure and/or rate) data has become increasingly popular in recent years for other well testing analysis purposes in a variety of applications; see for example, Refs. 3-10. Guillot and Horne were the first to use piecewise constant and cubic spline interpolations to represent measured flow rate data in Laplace space for the purpose of analyzing pressure tests under variable (downhole or surface) flow rate history by nonlinear regression. Roumboutsos and Stewart were the first to introduce the idea of using the numerical Laplace transformation of measured data for convolution and deconvolution purposes. They presented an algorithm based on piecewise linear interpolation of sampled-data, which can be used to transform measured pressure or rate data into Laplace space. Mendes et al. presented a Laplace domain deconvolution algorithm based on cubic spline interpolation of sampled-data. By considering deconvolution of DST data, they showed that Laplace domain deconvolution is fast and more stable than deconvolution methods based on the discretized forms of the convolution integral in the time domain. However, they noted that noise in pressure and flow rate measurements can also cause instability in Laplace space deconvolution methods, but they did not present any specific results on this issue. Both Corre and Thompson et al. showed that the convolution methods based on a representation of the linear interpolation of the tabulated unit-rate response solution and numerical inversion to the time domain are far more computationally efficient for generating variable rate solutions for complex well/reservoir systems (e.g., partially penetrating wells and horizontal wells) than convolution methods based on the direct use of analytical solutions in Laplace space. Using the numerical Laplace transformation of measured pressure data, Bourgeois and Horne introduced the so-called Laplace pressure and its derivative, and presented Laplace type curves based on these functions for model recognition and parameter estimation purposes. They also deconvolved data using these Laplace pressure functions in the Laplace domain without inversion to the time domain. Wilkinson investigated the applicability of performing nonlinear regression based on the Laplace pressure as suggested in Ref. 7 for parameter estimation purposes.

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14

Nápoles Valdés, Juan E. "On the generalized laplace transform and applications." Physics & Astronomy International Journal 6, no. 4 (December 6, 2022): 196–200. http://dx.doi.org/10.15406/paij.2022.06.00274.

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In this work we present the main properties of the Generalized Laplace Transform, recently defined, and we show some applications. Laplace’s transformation has been very useful in the studies of engineering, mathematics, physics, among other scientific areas. One of the main mathematical areas where it has many applications is in the topic of differential equations and their solution methods. In this paper, we study the stability and analysis of linear systems with the Generalized Laplace Transform.

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15

Wünsche, Alfred. "Sumudu Transformation or What Else Can Laplace Transformation Do." Advances in Pure Mathematics 09, no. 02 (2019): 111–42. http://dx.doi.org/10.4236/apm.2019.92007.

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16

Agashe, S. D. "A ‘derivation’ of the Laplace transformation." International Journal of Mathematical Education in Science and Technology 24, no. 1 (January 1993): 73–76. http://dx.doi.org/10.1080/0020739930240109.

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17

Pilipović, S. "Quasiasymptotic expansion and the laplace transformation." Applicable Analysis 35, no. 1-4 (January 1990): 247–61. http://dx.doi.org/10.1080/00036819008839913.

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18

Naimi, Mohammad Nasim, Mohammad Jawid Mohammadi, and Gulaqa Anwari. "Application of Laplace Transform in Solving Linear Differential Equations with Constant Coefficients." Technium: Romanian Journal of Applied Sciences and Technology 8 (March 8, 2023): 12–24. http://dx.doi.org/10.47577/technium.v8i.8565.

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In recent years, the interest in using Laplace transforms as a useful method to solve certain types of differential equations and integral equations has grown significantly. In addition, the applications of Laplace transform are closely related to some important parts of pure mathematics. Laplace transform is one of the methods for solving differential equations. This method is especially useful for solving inhomogeneous differential equations with constant coefficients and it has advantages compared to other methods of solving differential equations. Linear differential equations with constant coefficients are among the equations that can be solved using the Laplace transform. Because the transformation Laplace is one of the transformations that easily converts exponential functions, trigonometric functions, and logarithmic functions into algebraic functions. Therefore, it is considered a better method for solving linear differential equations with constant coefficients.

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19

YAMADA, H. "MODIFIED LAPLACE TRANSFORMATION METHOD AT FINITE TEMPERATURE: APPLICATION TO INFRARED PROBLEMS OF N COMPONENT ϕ4 THEORY". International Journal of Modern Physics A 13, № 24 (30 вересня 1998): 4133–45. http://dx.doi.org/10.1142/s0217751x98001943.

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The modified Laplace transformation method is applied to N component ϕ4 theory and the finite temperature problem in the massless limit is re-examined in the large N limit. We perform perturbation expansion of the dressed thermal mass in the massive case to several orders and try the massless approximation with the help of modified Laplace transformation. The contribution with fractional power of the coupling constant is recovered from the truncated massive series. The use of inverse Laplace transformation with respect to the mass square is crucial in evaluating the coefficients of fractional power terms.

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20

Kim, YunJae, Byung Kim, Lee-Chae Jang, and Jongkyum Kwon. "A Note on Modified Degenerate Gamma and Laplace Transformation." Symmetry 10, no. 10 (October 10, 2018): 471. http://dx.doi.org/10.3390/sym10100471.

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Kim-Kim studied some properties of the degenerate gamma and degenerate Laplace transformation and obtained their properties. In this paper, we define modified degenerate gamma and modified degenerate Laplace transformation and investigate some properties and formulas related to them.

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21

LI, JUAN, BO TIAN, GUANG-MEI WEI, and HAI-QIANG ZHANG. "INTEGRABLE PROPERTIES AND SIMILARITY REDUCTIONS OF THE SINE-LAPLACE EQUATION FROM AN INVISCID INCOMPRESSIBLE FLUID WITH SYMBOLIC COMPUTATION." International Journal of Modern Physics B 24, no. 09 (April 10, 2010): 1173–85. http://dx.doi.org/10.1142/s0217979210053628.

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Several integrable properties of the Sine-Laplace equation arising from an inviscid incompressible fluid are symbolically presented, including the Lax pair, auto-Bäcklund transformation, nonlinear superposition formula, bilinear form, and static N-soliton solution. Furthermore, with symbolic computation, two similarity reductions for the Sine-Laplace equation are derived by virtue of the classical Lie group method of infinitesimal transformations. One reduces to the third Painlevé equation and the other to a known ordinary differential equation. Sample static solutions are discussed and pictured.

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22

Fang, Pan, Kexin Wang, Liming Dai, and Chixiang Zhang. "Numerical calculation for coupling vibration system by Piecewise-Laplace method." Science Progress 103, no. 3 (July 2020): 003685042093855. http://dx.doi.org/10.1177/0036850420938555.

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To improve the reliability and accuracy of dynamic machine in design process, high precision and efficiency of numerical computation is essential means to identify dynamic characteristics of mechanical system. In this paper, a new computation approach is introduced to improve accuracy and efficiency of computation for coupling vibrating system. The proposed method is a combination of piecewise constant method and Laplace transformation, which is simply called as Piecewise-Laplace method. In the solving process of the proposed method, the dynamic system is first sliced by a series of continuous segments to reserve physical attribute of the original system; Laplace transformation is employed to separate coupling variables in segment system, and solutions of system in complex domain can be determined; then, considering reverse Laplace transformation and residues theorem, solution in time domain can be obtained; finally, semi-analytical solution of system is given based on continuity condition. Through comparison of numerical computation, it can be found that precision and efficiency of numerical results with the Piecewise-Laplace method is better than Runge-Kutta method within same time step. If a high-accuracy solution is required, the Piecewise-Laplace method is more suitable than Runge-Kutta method.

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23

Minggani, Fitriana. "Analisis Solusi Model Rangkaian Listrik Menggunakan Metode Transformasi Laplace Modifikasi." Jurnal Ilmiah Soulmath : Jurnal Edukasi Pendidikan Matematika 8, no. 1 (April 20, 2020): 21. http://dx.doi.org/10.25139/smj.v8i1.2380.

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AbstractLaplace transform is one typr of integral transformation that allows to be used to solve homogeneous and non- homogeneous second order linear differential equations. Laplace transform modification is obtained by adding coefficients through the corresponding variables in the Laplace transform equation expressed in term of = with that a transformation kernel function and is a transformation variable for . There are several applications of differential equations, one of which is the electrical circuit model. The prblem that often becomes an obstacle is when encountering a limit value problem. This paper aims to obtain the solution of linear differential equations in a simple electric circuits (RLC) model connected in series, using a modified Laplace transform. The results of this study provide solutions in the form of second order linear differential equations: Keywords: electrical circuits, Laplace transform modifications, second order linear differential equations AbstrakTransformasi Laplace merupakan salah satu jenis transformasi integral yang memungkinkan digunakan untuk menyelesaikan persamaan diferensial linear orde dua homogen maupun non homogen. Transformasi Laplace Modifikasi diperoleh dengan melakukan penambahan koefisien melalui variabel yang sesuai pada persamaan Transformasi Laplace yang dinyatakan dalam bentuk = dengan dan merupakan fungsi kernel transformasi, serta merupakan variabel transformasi untuk . Terdapat beberapa penerapan persamaan diferensial, salah satunya yaitu pada model rangkaian listrik. Permasalahan yang seringkali menjadi kendala yaitu ketika menjumpai masalah nilai batas. Paper ini bertujuan untuk mendapatkan penyelesaian persamaan diferensial linear pada model rangkaian listrik sederhana (RLC) yang dihubungkan secara seri, dengan menggunakan transformasi Laplace modifikasi. Hasil penelitian ini memberikan solusi persamaan diferensial linear orde dua yang berbentuk: Kata kunci: persamaan diferensial linear orde dua, rangkaian listrik, transformasi Laplace modifikasi

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24

Gorty, V. R. Lakshmi. "The Finite Generalized Laplace Hankel-Clifford Transformation." Journal of Advanced Mathematics and Applications 4, no. 2 (December 1, 2015): 103–9. http://dx.doi.org/10.1166/jama.2015.1078.

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25

Dyer. "Inverse laplace transformation of rational functions. 1." IEEE Instrumentation and Measurement Magazine 9, no. 6 (October 2006): 13–15. http://dx.doi.org/10.1109/mim.2006.1708344.

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26

Hoogenboom, J. E. "The Laplace transformation of adjoint transport equations." Annals of Nuclear Energy 12, no. 3 (January 1985): 151–52. http://dx.doi.org/10.1016/0306-4549(85)90091-x.

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27

Pirdawood, Mardan A., Shadman R. Kareem, and Dashne Ch Zahir. "Audio Encryption Framework Using the Laplace Transformation." ARO-THE SCIENTIFIC JOURNAL OF KOYA UNIVERSITY 11, no. 2 (August 25, 2023): 31–37. http://dx.doi.org/10.14500/aro.11165.

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Digital information, especially multimedia and its applications, has grown exponentially in recent years. It is important to strengthen sophisticated encryption algorithms due to the security needs of these innovative systems. The security of real-time audio applications is ensured in the present study through a framework for encryption. The design framework protects the confidentiality and integrity of voice communications by encrypting audio applications. A modern method of securing communication and protecting data is cryptography. Using cryptography is one of the most important techniques for protecting data and ensuring the security of messaging. The main purpose of this paper is to present a novel encryption scheme that can be used in real-time audio applications. We encrypt the sound using a combination of an infinite series of hyperbolic functions and the Laplace transform, and then decrypt it using the inverse Laplace transform. The modular arithmetic rules are used to generate the key for the coefficients acquired from the transformation. There is no loss of data or noise in the decryption sound. We also put several sound examples to the test

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28

Kitsos, Christos P., and Ioannis S. Stamatiou. "LAPLACE TRANSFORMATION FOR THE -ORDER GENERALIZED NORMAL,." Far East Journal of Theoretical Statistics 68, no. 1 (December 6, 2023): 1–21. http://dx.doi.org/10.17654/0972086324001.

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29

Mezentsev, Anton, Anton Pomelnikov, and Matthias Ehrhardt. "Efficient Numerical Valuation of Continuous Installment Options." Advances in Applied Mathematics and Mechanics 3, no. 2 (April 2011): 141–64. http://dx.doi.org/10.4208/aamm.10-m1025.

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AbstractIn this work we investigate the novel Kryzhnyi method for the numerical inverse Laplace transformation and apply it to the pricing problem of continuous installment options. We compare the results with the one obtained using other classical methods for the inverse Laplace transformation, like the Euler summation method or the Gaver-Stehfest method.

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30

Haider, Syed Sabyel, Mujeeb Ur Rehman, and Thabet Abdeljawad. "A Transformation Method for Delta Partial Difference Equations on Discrete Time Scale." Mathematical Problems in Engineering 2020 (July 10, 2020): 1–14. http://dx.doi.org/10.1155/2020/3902931.

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The aim of this study is to develop a transform method for discrete calculus. We define the double Laplace transforms in a discrete setting and discuss its existence and uniqueness with some of its important properties. The delta double Laplace transforms have been presented for integer and noninteger order partial differences. For illustration, the delta double Laplace transforms are applied to solve partial difference equation.

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31

Prangoski, Bojan. "Laplace transform in spaces of ultradistributions." Filomat 27, no. 5 (2013): 747–60. http://dx.doi.org/10.2298/fil1305747p.

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32

Ha, Wansoo, and Changsoo Shin. "Efficient Laplace-domain modeling and inversion using an axis transformation technique." GEOPHYSICS 77, no. 4 (July 1, 2012): R141—R148. http://dx.doi.org/10.1190/geo2011-0424.1.

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We tested an axis-transformation technique for modeling wave propagation in the Laplace domain using a finite-difference method. This technique enables us to use small grids near the surface and large grids at depth. Accordingly, we can reduce the number of grids and attain computational efficiency in modeling and inversion in the Laplace domain. We used a dispersion analysis and comparisons between modeled wavefields obtained on the regular and transformed axes. We demonstrated in a synthetic Laplace-domain inversion technique shows that this method is efficient and yields a result comparable to that of a Laplace-domain inversion using a regular grid. In a synthetic inversion example, the memory usage reduced to less than 33%, and the computation time reduced to 39% of those required for the regular grid case using a logarithmic transformation function.

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33

Berdnyk, M. G. "New finite integral transform for the Laplace equation in an arbitrary domain." Mathematical machines and systems 3 (2020): 115–24. http://dx.doi.org/10.34121/1028-9763-2020-3-115-124.

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Reliability, survivability, as well as the optimal operating mode of operation of the supercomputer will depend on the architecture and efficiency of the cooling system of the hot components of the supercomputer. That is why the number of problems, of great theoretical and practical interest, is the problem of studying the temperature fields arising in elements of arbitrary configuration, cooling a supercomputer. To solve this class of heat conduction problems, the method of finite integral transformations turned out to be the most convenient. This article is the first to construct a new finite integral transformation for the Laplace equation in an arbitrary domain bounded by several closed piecewise-smooth contours. An inverse transformation formula is given. Finding the core of the constructed new finite integral transformation by the finite element method in the Galerkin form for simplex first-order elements reduces to solving a system of algebraic equations. To test the operability of the new integral transformation, calculations were carried out of solutions of the boundary value problem for the Laplace equation obtained using the developed new integral transformation and the well-known analytical solution. The results of comparison the calculations of the solution of the Laplace equation are presented. In the case of a square with a side length equal to one and on one side of the square, the temperature is unity, and on the other, the temperature is zero, with a well-known analytical solution and a solution obtained using the new integral transformation. These results were obtained for 228 simplex first-order elements and 135 nodes. The maximum deviation modulo of these solutions is 0,096, the mathematical expectation of deviations is 0,009, and the variance of the type is 0,001. The developed integral transformation makes it possible to obtain a solution to complex boundary value problems of mathematical physics.

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34

Moazzam, Ali, Zainab Ijaz, Muhammad Hussain, Nimra Maqbool, and Emad A. Kuffi. "Applications of Fractional-Laplace Transformation in the Field of Electrical Engineering." Journal of Kufa for Mathematics and Computer 10, no. 2 (August 31, 2023): 70–75. http://dx.doi.org/10.31642/jokmc/2018/100211.

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This study examines the various ways that fractional Laplace transform can be used to solve three different kinds of mathematical equations: the equation of analysis of electric circuits, simultaneous differential equations, and the heat conduction equation. This article how to use the fractional Laplace transform to calculate heat flow in semi-infinite solids in the context of heat conduction. The answers that are developed offer important information about how temperatures vary across time and space. The essay also examines how to analyse electrical circuits using the Fractional Laplace transform. This method allows researchers to measure significant electrical parameters including charge and current, which improves their comprehension of circuit dynamics. Practical examples are included throughout the essay to show how useful the Fractional Laplace transform is in various fields. As a result of the answers found using this methodology, researchers and engineers working in the fields of heat conduction, system dynamics, and circuit analysis can gain important new knowledge. In conclusion, this study explains the applicability and effectiveness of the fractional Laplace transform in resolving a variety of mathematical equations. It is a vital tool for researchers because it may be used in a wide range of scientific and engineering areas.

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35

Zhang, Yang, Yu Feng Nie, and Ya Tao Wu. "The Statistical Two-Scale Method for Predicting Viscoelastic Properties of Composites with Consistent Random Distribution of Particles." Applied Mechanics and Materials 697 (November 2014): 3–6. http://dx.doi.org/10.4028/www.scientific.net/amm.697.3.

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This study presents a statistical two-scale method to predict the viscoelastic properties of composite materials with consistent random distribution of particles. The explicit formulation for predicting the effective viscoelastic relaxation modulus is given. At first, the Laplace transformation is used to the linear viscoelastic problem, the effective generalized relaxation modulus in Laplace domain for composites is derived. Then, the effective relaxation modulus in time domain is obtained by the least-square and inverse Laplace transformation. At the end of this paper, some numerical examples are given to validate that the presented method is feasible and effective.

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36

Wang, Ming Lu, and Gao Feng Wei. "Bending of Thermoviscoelastic Functionally Graded Materials Beams." Advanced Materials Research 503-504 (April 2012): 305–8. http://dx.doi.org/10.4028/www.scientific.net/amr.503-504.305.

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According to the constitutive relation of linear thermovisoelasticity, with the help of Laplace transformation method and the introduction of structure functions and thermal functions, the mathematical model and its corresponding variational principle for thermoviscoelastic FGM beams are set up on the basis of the assumption that plane section remains plane and normal to the beam axis. Using Laplace transformation method, the deflection and the stress distribution are discussed.

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37

D. K. Sharma, Himani Mittal, Sita Ram Sharma, and Inder Parkash. "Effect of Deformation on Semi–infinite Viscothermoelastic Cylinder Based on Five Theories of Generalized Thermoelasticity." Mathematical Journal of Interdisciplinary Sciences 6, no. 1 (September 1, 2017): 17–35. http://dx.doi.org/10.15415/mjis.2017.61003.

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We considera dynamical problem for semi-infinite viscothermoelastic semi infinite cylinder loaded mechanically and thermally and investigated the behaviour of variations of displacements, temperatures and stresses. The problem has been investigated with the help of five theories of the generalized viscothermoelasticity by using the Kelvin – Voigt model. Laplace transformations and Hankel transformations are applied to equations of constituent relations, equations of motion and heat conduction to obtain exact equations in transformed domain. Hankel transformed equations are inverted analytically and for the inversion of Laplace transformation we apply numerical technique to obtain field functions. In order to obtain field functions i.e. displacements, temperature and stresses numerically we apply MATLAB software tools. Numerically analyzed results for the temperature, displacements and stresses are shown graphically.

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38

Kamran, N., and K. Tenenblat. "Periodic systems for the higher-dimensional Laplace transformation." Discrete & Continuous Dynamical Systems - A 4, no. 2 (1998): 359–78. http://dx.doi.org/10.3934/dcds.1998.4.359.

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39

Choi, H., I. Vinograd, C. Chaffey, and N. J. Curro. "Inverse Laplace transformation analysis of stretched exponential relaxation." Journal of Magnetic Resonance 331 (October 2021): 107050. http://dx.doi.org/10.1016/j.jmr.2021.107050.

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40

Dyer, Stephen. "Inverse Laplace Transformation of Rational Functions: Part 2." IEEE Instrumentation & Measurement Magazine 10, no. 3 (June 2007): 40–42. http://dx.doi.org/10.1109/mim.2007.4284256.

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41

Wells, Charles E., and John L. Bryant. "An Adaptive Estimation Procedure Using the LaPlace Transformation." IIE Transactions 17, no. 3 (September 1985): 242–51. http://dx.doi.org/10.1080/07408178508975299.

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42

Kryzhniy, V. V. "Regularizing operators of real-valued inverse Laplace Transformation." Inverse Problems in Engineering 11, no. 6 (December 2003): 561–74. http://dx.doi.org/10.1080/1068276032000101724.

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43

Schalla, Michael, and Michael Weiss. "Pharmacokinetic curve fitting using numerical inverse Laplace transformation." European Journal of Pharmaceutical Sciences 7, no. 4 (March 1999): 305–9. http://dx.doi.org/10.1016/s0928-0987(98)00042-6.

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44

Rokhlin, V. "A fast algorithm for the discrete laplace transformation." Journal of Complexity 4, no. 1 (March 1988): 12–32. http://dx.doi.org/10.1016/0885-064x(88)90007-6.

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45

Dhingra, Swati, Archana A., and Swati Jain. "Laplace Transformation based Cryptographic Technique in Network Security." International Journal of Computer Applications 136, no. 7 (February 17, 2016): 6–10. http://dx.doi.org/10.5120/ijca2016908482.

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46

Glaeske, Hans-Jürgen, and Dietmar Müller. "Abelsche Sätze für die Laplace-Transformation von Distributionen." Zeitschrift für Analysis und ihre Anwendungen 10, no. 2 (1991): 231–38. http://dx.doi.org/10.4171/zaa/446.

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47

Apelblat, A. "Application of Laplace Transformation to Evaluation of Integrals." Journal of Mathematical Analysis and Applications 186, no. 1 (August 1994): 237–53. http://dx.doi.org/10.1006/jmaa.1994.1296.

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48

Fitria, Trisonia, Wipsar Sunu Brams Dwandaru, Warsono, R. Yosi Aprian Sari, Dian Puspita Eka Putri, and Adiella Zakky Juneid. "Application Of Inverted Pendulum in Laplace Transformation of Mathematics Physics." Jurnal Penelitian Pendidikan IPA 9, no. 7 (July 25, 2023): 5446–52. http://dx.doi.org/10.29303/jppipa.v9i7.2953.

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The Laplace transform is a technique used to convert differential equations into algebra, it is often used for the analysis of dynamic systems and inverted pendulum systems. An inverted pendulum is a mechanism that moves objects from one place to another and shows the function of its activity while walking. This system is widely used in various fields, for example in the fields of robotics, industry, technology and organics. In an inverted pendulum there is an inverted pendulum dynamic system with a reading and driving force. The results of the study show that using the Laplace transform can make it easier to find solutions regarding the inverted pendulum system for a variety of conditions, both in the initial conditions and when given an additional force or load. The application of the Laplace transform is useful for understanding how an inverted pendulum system will react to various forces, loads and initial conditions, which can be used to predict how the system will operate in the real world

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49

Köklü, Kevser. "Resolvent, Natural, and Sumudu Transformations: Solution of Logarithmic Kernel Integral Equations with Natural Transform." Mathematical Problems in Engineering 2020 (May 30, 2020): 1–7. http://dx.doi.org/10.1155/2020/9746318.

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In this paper, the resolvent of an integral equation was found with natural transform which is a new transformation which converged to Laplace and Sumudu transformations, and the result was confirmed by the Sumudu transform. At the same time, a solution to the first type of logarithmic kernel Volterra integral equations has been produced by the natural transform.

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50

Moazzam, Ali, Emad Kuffi, Zain Abideen, and Ayza Anjum. "Two parametric SEE transformation and its applications in solving differential equations." Al-Qadisiyah Journal for Engineering Sciences 16, no. 2 (June 30, 2023): 116–20. http://dx.doi.org/10.30772/qjes.v16i2.891.

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Transformation plays a much more important role in every science. In this research article, two parametric forms of SEE transformation have been explored and the fundamental properties of two parametric SEE transformations have been shown. Furthermore, the transformed function of some fundamental functions and their time derivative rule has been shown. The application of two parametric SEE transformations in solving differential equations has been shown. The radioactive decay problem in first-order linear differential equations has been solved in this article which has large applications in nuclear energy engineering. Further, the solution to the beam deflection problem has been shown to have many applications in the engineering field. These results can be compared with other Laplace-type transformations.

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