• Communications of the Korean Mathematical Society
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• v.38 no.4
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• pp.1163-1173
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• 2023

In this paper, we prove the Hyers-Ulam stability and Mittag-Leffler-Hyers-Ulam stability of a differential equation of Logistic growth in a population by applying Laplace transforms method.

• Honam Mathematical Journal
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• v.37 no.2
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• pp.245-252
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• 2015

This paper is in continuation of the paper very recently published [New Laplace transforms of Kummer's confluent hypergeometric functions, Math. Comp. Modelling, 55 (2012), 1068-1071]. In this paper, our main objective is to show one can obtain so far unknown Laplace transforms of three rather general cases of generalized hypergeometric function $_2F_2(x)$ by employing generalized Watson's, Dixon's and Whipple's summation theorems for the series $_3F_2$ obtained earlier in a series of three research papers by Lavoie et al. [5, 6, 7]. The results established in this paper may be useful in theoretical physics, engineering and mathematics.

• Transactions of the Korean Society of Mechanical Engineers
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• v.15 no.2
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• pp.396-403
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• 1991

A solution is presented for the computation of the elastic-creep stresses in a hollow cylinder subjected to nonaxisymmetric temperature distribution. The creep problem is treated by the Maxwell creep model. Laplace transformation is used for reformation of the governing equation of elastic problem and Hooke's law in a function of .gamma. , .theta. , and creep constant. The governing equation is set up using the Airy stress function which leads to the biharmonic equation. The solution is obtained by using Fourer series method and Laplace inverse method used to obtain the stress components which include the variation of time. This solution shows excellent agreement with Lamkin's and Boley & Weiner's solution. The viscoelastic stresses are also obtained for the fuel rob tube subjecting nonaxisymmetric thermal load.

• Communications for Statistical Applications and Methods
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• v.24 no.5
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• pp.457-480
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• 2017

We develop a random partition procedure based on a Dirichlet process prior with Laplace distribution. Gibbs sampling of a Laplace mixture of linear mixed regressions with a Dirichlet process is implemented as a random partition model when the number of clusters is unknown. Our approach provides simultaneous partitioning and parameter estimation with the computation of classification probabilities, unlike its counterparts. A full Gibbs-sampling algorithm is developed for an efficient Markov chain Monte Carlo posterior computation. The proposed method is illustrated with simulated data and one real data of the energy efficiency of Tsanas and Xifara (Energy and Buildings, 49, 560-567, 2012).

• Journal for History of Mathematics
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• v.32 no.6
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• pp.271-279
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• 2019

Pierre-Simon de Laplace(1749-1827) is considered one of the most influential scientists in history. He was known to his contemporaries as the Newton of France, and a scientific sage valued for his magisterial syntheses of scientific works through the 18th century. Laplace was a determined mathematician, astronomer, writer, philosopher, and educator. In this paper, we take a survey of his achievements in the areas of astronomy and mathematical statistics, along with his scientific philosophy, the universal determinism.

• Journal of Korea Multimedia Society
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• v.17 no.3
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• pp.294-299
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• 2014

In this paper, we propose a novel algorithm to improve the performance of a voice activity detection(VAD) which is based on the generalized normal-Laplace(GNL) distribution. In our algorithm, the probability density function(PDF) of the noisy speech signal is represented by the GNL distribution and the variance of the speech and noise of GNL distribution are estimated using higher order moments. Experimental results show that the proposed algorithm yields better results compared to the conventional VAD algorithms.

• Proceedings of the KIEE Conference
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• 1997.07a
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• pp.309-311
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• 1997

In this paper, it is proposed that a algorithm which is applicable to the transient analysis by combined use of the Laplace transform and the finite element method. The proposed method removes the time terms using the Laplace transform and then solves the associated equation with the finite element method. The solution which is solved at frequency domain is transformed into time domain by use of the Laplace inversion. To verify proposed algorithm, heat conduction problem is analysed and found a good agreement with analytic solution.

• ETRI Journal
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• v.33 no.6
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• pp.949-952
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• 2011

In this letter, a simplified suboptimum receiver based on soft-limiting for the detection of binary antipodal signals in non-Gaussian noise modeled as a generalized normal-Laplace (GNL) distribution combined with Gaussian noise is presented. The suboptimum receiver has low computational complexity. Furthermore, when the number of diversity branches is small, its performance is very close to that of the Neyman-Pearson optimum receiver based on the probability density function obtained by the Fourier inversion of the characteristic function of the GNL-plus-Gaussian distribution.

• Kyungpook Mathematical Journal
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• v.46 no.1
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• pp.49-56
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• 2006

The aim of the present work is to obtain the inverse Laplace transform of the product of the factors of the type $s^{-\rho}\prod\limit_{i=1}^{\tau}(s^{li}+{\alpha}_i)^{-{\sigma}i}$, a general class of polynomials an the multivariable H-function. The polynomials and the functions involved in our main formula as well as their arguments are quite general in nature. On account of the general nature of our main findings, the inverse Laplace transform of the product of a large variety of polynomials and numerous simple special functions involving one or more variables can be obtained as simple special cases of our main result. We give here exact references to the results of seven research papers that follow as simple special cases of our main result.

• Economic and Environmental Geology
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• v.57 no.5
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• pp.499-512
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• 2024

Random noise in seismic data can significantly impair hydrocarbon exploration by degrading the quality of subsurface imaging. We propose a deep learning approach to attenuate random noise in Laplace-domain seismic wavefields. Our method employs a modified U-Net architecture, trained on diverse synthetic P-wave velocity models simulating the Gulf of Mexico subsurface. We rigorously evaluated the network's denoising performance using both the synthetic Pluto velocity model and real Gulf of Mexico field data. We assessed the effectiveness of our approach through Laplace-domain full waveform inversion. The results consistently show that our U-Net approach outperforms traditional singular value decomposition methods in noise attenuation across various scenarios. Numerical examples demonstrate that our method effectively attenuates random noise and significantly enhances the accuracy of subsequent seismic imaging processes.