• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.151.1-151
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• 2001

This paper establishes some integral equalities formulated by zeros located in the convergence region of Laplace transformable function. Using the definition of Laplace transform, it is shown that time-domain integral equalities have to be satisfied by the function, and those can be applied to understanding of the fundamental limitations of the control system represented by the transfer function, which has been Laplace transform. In the unity-feedback control scheme, another integral equality is also derived on the output response of the system with open-loop poles and zeros located in the convergence region.

• Journal of applied mathematics & informatics
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• v.36 no.5_6
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• pp.505-519
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• 2018

In this paper we define a (p, q)-Laplace transform. By using this definition, we obtain many properties including the linearity, scaling, translation, transform of derivatives, derivative of transforms, transform of integrals and so on. Finally, we solve the differential equation using the (p, q)-Laplace transform.

• 한국데이터정보과학회:학술대회논문집
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• 2005.10a
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• pp.171-176
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• 2005

An infinite dam with compound Poisson inputs and a state-dependent release rate is considered. We build the Kolmogorov's backward differential equation and solve it to obtain the Laplace transforms of the first exit times for this dam.

• Honam Mathematical Journal
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• v.43 no.2
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• pp.359-371
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• 2021

In this paper, we define a fractional conformable fuzzy Laplace transform and prove some related theorems. Also by using this transform we solve some fuzzy fractional differential equations.

• International Journal of Control, Automation, and Systems
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• v.1 no.1
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• pp.76-82
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• 2003

This paper establishes some integral equalities formulated by zeros located in the convergence region of a Laplace transformable function. Using the definition of the Laplace transform, it shows that Laplace transformable functions have to satisfy the integral equalities in the time-domain, which can be applied to the understanding of the fundamental limitations on the control system represented by the transfer function. In the unity-feedback control scheme, another integral equality is derived on the output response of the system with open-loop poles located in the convergence region of the output function. From these integral equalities, two sufficient conditions related to undershoot and overshoot phenomena in the step response, respectively, are investigated.

• Steel and Composite Structures
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• v.18 no.4
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• pp.889-907
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• 2015

This paper aims to present an alternative analytical method for transient vibration analysis of doubly-curved laminated shells subjected to dynamic loads. In the method proposed, the governing differential equations of laminated shell are derived using the dynamic version of the principle of virtual displacements. The governing equations of first order shear deformation laminated shell are obtained by Navier solution procedure. Time-dependent equations are transformed to the Laplace domain and then Laplace parameter dependent equations are solved numerically. The results obtained in the Laplace domain are transformed to the time domain with the help of modified Durbin's numerical inverse Laplace transform method. Verification of the presented method is carried out by comparing the results with those obtained by Newmark method and ANSYS finite element software. Also effects of number of laminates, different material properties and shell geometries are discussed. The numerical results have proved that the presented procedure is a highly accurate and efficient solution method.

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.933-941
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• 2009

In this paper, we consider p-Laplace equation which models the turbulent flow in a porous medium. Using a continuation principle (cf. [R. $Man{\acute{a}}sevich$ and J. Mawhin, Periodic solutions for nonlinear systems with p-Lplacian-like operators, J. Diff. Equa. 145(1998), 367-393]), we prove the existence of solutions for p-Laplace equation subject to periodic boundary conditions, under some sign and growth conditions for f. With the help of Leray-Schauder degree theory, the multiplicity of periodic solutions for p-Laplace equation is obtained under the similar conditions above and some known results are improved.

• The Korean Journal of Applied Statistics
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• v.15 no.1
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• pp.139-151
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• 2002

This study is concerned with model selection and diagnostics for nonlinear regression model through Bayes factor. In this paper, we use informative prior and simulate observations from the posterior distribution via Markov chain Monte Carlo. We propose the Laplace approximation method and apply the Laplace-Metropolis estimator to solve the computational difficulty of Bayes factor.

• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.11
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• pp.2773-2781
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• 1993

Laplace's equation is, perhaps, the most important equation, which governs various kinds of physical phenomena. Due to its importance, there have been several numerical techniques such as the finite element method, the finite difference method, and the boundary element method. However, these techniques do not appear very effective as they require a substantial amount of numerical calculation. In this paper, we develop a new most efficient technique based on analytic solutions for Laplace's equation in some convex polygons. Although a similar approach was used for the same problem, the present technique is unique as it solves directly Laplace's equation with the utilization of analytical solutions.

• Nonlinear Functional Analysis and Applications
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• v.26 no.2
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• pp.381-392
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• 2021

During the last several decades, a great variety of fractional kinetic equations involving diverse special functions have been broadly and usefully employed in describing and solving several important problems of physics and astrophysics. In this paper, we aim to find solutions of a type of fractional kinetic equations associated with the (p, q)-extended 𝜏 -hypergeometric function and the (p, q)-extended 𝜏 -confluent hypergeometric function, by mainly using the Laplace transform. It is noted that the main employed techniques for this chosen type of fractional kinetic equations are Laplace transform, Sumudu transform, Laplace and Sumudu transforms, Laplace and Fourier transforms, P_𝛘-transform, and an alternative method.