• Communications of the Korean Mathematical Society
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• v.12 no.4
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• pp.1039-1064
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• 1997

Existence and Uniqueness for Volterra equations (VE) with a weak regularity assumption on A, the relative closedness of A are investigaed by means of the Laplace transform theory. Also, (VE) are studied by means of the method of convoluted solution operator families.

• Communications of the Korean Mathematical Society
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• v.16 no.3
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• pp.371-383
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• 2001

In this survey article, we shall introduce the applications of the theory of reproducing kernels to inverse problems. At the same time, we shall present some operator versions of our fundamental general theory for linear transforms in the framework of Hilbert spaces.

• 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 the Chungcheong Mathematical Society
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• v.35 no.2
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• pp.177-196
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• 2022

The Elzaki Transform method is fuzzified to fuzzy Elzaki Transform by Rehab Ali Khudair. In this article, we propose a Double fuzzy Elzaki transform (DFET) method to solving fuzzy partial differential equations (FPDEs) and we prove some properties and theorems of DFET, fundamental results of DFET for fuzzy partial derivatives of the n^th order, construct the Procedure to find the solution of FPDEs by DFET, provide duality relation of Double Fuzzy Laplace Transform (DFLT) and Double Fuzzy Sumudu Transform(DFST) with proposed Transform. Also we solve the Fuzzy Poisson's equation and fuzzy Telegraph equation to show the DFET method is a powerful mathematical tool for solving FPDEs analytically.

• Kyungpook Mathematical Journal
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• v.45 no.2
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• pp.153-159
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• 2005

In the present paper, we obtain two Theorems connecting the unified fractional integral operators and the Laplace transform. Due to the presence of a general class of polynomials, the multivariable H-function and general functions ${\theta}$ and ${\phi}$ in the kernels of our operators, a large number of (new and known) interesting results involving simpler polynomials (which are special cases of a general class of polynomials) and special functions involving one or more variables (which are particular cases of the multivariable H-function) obtained by several authors and hitherto lying scattered in the literature follow as special cases of our findings. Thus the Theorems obtained by Srivastava et al. [9] follow as simple special cases of our findings.

• Journal of the Korean Society of Safety
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• v.22 no.4
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• pp.13-19
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• 2007

An numerical method to estimate thermal diffusivity has been developed for one-dimensional unsteady heat conduction problem, when the temperatures are know at two positions in a semi-infinite body. Using the closed form solution which has already derived an explicit solution for the inverse problem for one-dimensional transient heat conduction using Laplace transform technique, we first estimate the surface temperature. The thermal diffusivity can be estimated by using the estimated surface temperature and measured temperatures, which include some uncertainties. The estimated surface heat flux and thermal diffusivity are found to be in good agreement with those of the experimented conditions. This method will be extended to the simultaneous measurement of thermal diffusivity and thermal conductivity.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.4 no.1
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• pp.49-65
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• 2000

A method for inverting the Laplace transform is presented, using a finite series of the classical Legendre polynomials. The method recovers a real-valued function f(t) in a finite interval of the positive real axis when f(t) belongs to a certain class ${\mathcal{W}}_{\beta}$ and requires the knowledge of its Laplace transform F(s) only at a finite number of discrete points on the real axis s > 0. The choice of these points will be carefully considered so as to improve the approximation error as well as to minimize the number of steps needed in the evaluations. The method is tested on few examples, with particular emphasis on the estimation of the error bounds involved.

• Journal of the Korean Mathematical Society
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• v.50 no.1
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• pp.111-125
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• 2013

In this paper, we consider a continuous time risk model involving two types of dependent claims, namely main claims and by-claims. The by-claim is induced by the main claim and the occurrence of by-claim may be delayed depending on associated main claim amount. Using Rouch$\acute{e}$'s theorem, we first derive the closed-form solution for the Laplace transform of the survival probability in the dependent risk model from an integro-differential equations system. Then, using the Laplace transform, we derive a defective renewal equation satisfied by the survival probability. For the exponential claim sizes, we present the explicit formula for the survival probability. We also illustrate the influence of the model parameters in the dependent risk model on the survival probability by numerical examples.

• International Journal of Reliability and Applications
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• v.1 no.1
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• pp.49-64
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• 2000

We consider a system whose inherent life follows an Erlang distribution, which is subject to two heterogeneous random shocks. Minor shocks arrive according to a renewal process and each causes the system to fail independently with a certain probability. A major shock whose interarrival times follow an Erlang distribution causes the system to fail with probability one. The Laplace transform of the distribution of the time to system failure is derived in a functional form of the Laplace transform of the interarrival time distribution of minor shocks. An algorithm is given for the computation of the moments of the time to system failure.