• 대한수학회논문집
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• 제16권3호
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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.

• Kyungpook Mathematical Journal
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• 제46권1호
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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.

• 한국의학물리학회지:의학물리
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• 제4권2호
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• pp.37-47
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• 1993

Jones 모델 및 HKB모델을 이용하여 Laplace transform방법으로 6MV X-ray의 대략적인 에너지 스펙트럼을 분석하였다. Jones모델은 투과계수 0.1이하에서는 Laplace transform방법이 적용될 수 없는 심한 제약을 받는다는 것을 알 수 있었다. HKB모델에 의한 에너지 스펙트럼은 대체로 실제의 에너지 스펙트럼과 일치하는 형태를 나타내지만 6MeV에너지 이상의 영역에서 길게 꼬리를 이루는 단점이 있었다.

• Journal of the Korean Data and Information Science Society
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• 제10권1호
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• pp.243-250
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• 1999

We consider $Y=X{\lambda}Z,\;{\lambda}>0$, where X and Z are independent random variables, and Y is the length biased distribution or the equilibrium distribution of X. The purpose of this paper is to consider the distribution of X or Y when the distribution of Z is given and the distribution of Z when the distribution of X or Y is given, In particular, we obtain that the necessary and sufficient conditions for X to be $X^{2}({\upsilon})\;is\;Z{\sim}X^{2}(2)\;and\;for\;Z\;to\;be\;X^{2}(1)\;is\;X{\sim}IG({\mu},\;{\mu}^{2}/{\lambda})$, where $IG({\mu},\;{\mu}^{2}/{\lambda})$ is two-parameter inverse Gaussian distribution. Also we show that X is smaller than Y in the reverse Laplace transform ratio order if and only if $X_{e}$ is smaller than $Y_{e}$ in the Laplace transform ratio order. Finally, we can get the results that if X is smaller than Y in the Laplace transform ratio order, then $Y_{L}$ is smaller than $X_{L}$ in the Laplace transform order, and that if X is smaller than Y in the reverse Laplace transform ratio order, then $_{\mu}X_{L}$ is smaller than $_{\nu}Y_{L}$ in the Laplace transform order.

• 한국안전학회지
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• 제22권4호
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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.

• Steel and Composite Structures
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• 제18권4호
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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.

• 대한기계학회논문집
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• 제18권11호
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• pp.3075-3083
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• 1994

The applications of the electrical transmission line theory to the pressure propagation characteristics in the volume loaded fluid transmission line with step and impulse input wave is demonstrated in this paper. The method is based on the premise that the time response is the inverse Fourier transform of frequency spectrum of the wave which spectrum is a product of frequency spectrum of input pressure wave and system transfer function. The frequency response and transient response of step and impulse input wave in the volume loaded fluid transmission line is analysed by the Laplace transform and inverse Laplace transform with FFT numerical algorithm. The numerical solution of the distributed friction model is compared with the average friction model and the infinite product model. And the result is showed that FFT method may have major advantages for the simulation of fluid circuitary.

• Structural Engineering and Mechanics
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• 제15권6호
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• pp.735-752
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• 2003

The quasi-static and dynamic responses of a linear viscoelastic circular beam on Winkler foundation are studied numerically by using the mixed finite element method in transformed Laplace-Carson space. This element VCR12 has 12 independent variables. The solution is obtained in transformed space and Schapery, Dubner, Durbin and Maximum Degree of Precision (MDOP) transform techniques are employed for numerical inversion. The performance of the method is presented by several quasi-static and dynamic example problems.

• Journal of applied mathematics & informatics
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• 제37권5_6호
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• pp.507-519
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• 2019

The ground for this paper is to examine the generalized Stokes' first and second issues for an incompressible couple pressure liquid under isothermal conditions. Exact solutions for each problem are acquired by using the Laplace transform (LT) with respect to the time variable t and the sine Fourier transform (FT) with respect to the y-variable. Further, a comparison is given of the obtained results and the results of Devakar and Lyengar [1] and by using the four inverse Laplace transform algorithms (Stehfest's, Tzou's, Talbot, Fourier series) in the space time domain utilizing a numerical methodology. Moreover, velocity profiles are plotted and considered for various occasions and distinctive estimations of couple stress parameters. At the end, the outcomes are exhibited by graphs and in tabular forms.

• Kyungpook Mathematical Journal
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• 제52권4호
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• pp.383-395
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• 2012

In this paper, we use a computational algorithm for the inversion of the one and two-dimensional $\mathcal{L}_2$-transform based on the Bromwich's integral and the Fourier series. The new inversion formula can evaluate the inverse of the $\mathcal{L}_2$-transform with considerable accuracy over a wide range of values of the independent variable and can be devised for the functions which are not Laplace transformable and have damping motion in small interval near origin.