• Communications for Statistical Applications and Methods
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• v.3 no.3
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• pp.215-223
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• 1996

By using Tukey's generalized lambda distribution, appoximate posterior density is derived under the Bayes-empirical Bayes model. The sensitivity of posterior distribution to the hyperprior distribution is examined by using Tukey's generalized lambda distriburion which approximate many well-knmown distributions. Based upon Monte Varlo simulation studies it can be said that posterior distribution is sensitive to the cariance of the prior distribution and to the symmetry of the hyperprior distribution. Also posterior distribution is approximately obtained by using the following methods : Lindley method, Laplace method and Gibbs sampler method.

• Journal of the Chungcheong Mathematical Society
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• v.7 no.1
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• pp.141-152
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• 1994

We consider a numerical scheme for solving a nonlinear boundary integral equation (BIE) obtained by reformulation the nonlinear boundary value problem (BVP). We give a simple alternative to the standard collocation method for the nonlinear BIE. This method consists of one conventional linear system and another coupled linear system resulting from an auxiliary BIE which is obtained by differentiating both side of the nonlinear interior integral equations. We obtain an analogue BIE through the perturbation of the fundamental solution of Laplace's equation. We procure the super-convergence of approximate solutions.

• School Mathematics
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• v.10 no.2
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• pp.181-197
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• 2008

Bertrand's Paradox is known as a paradox because it produces different solutions when we apply different method. This essay analyzed diverse problem solving methods which result from no clear presenting of 'random chord'. The essay also tried to discover the difference between the mathematical calculation of three problem solvings and physical experiment in the real world. In the process for this, whether geometric statistic teaching related to measurement and integral calculus which is the basic concept of integral geometry is appropriate factor in current education curriculum based on Laplace's classical perspective was prudently discussed with its status.

• Kyungpook Mathematical Journal
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• v.52 no.4
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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.

• Structural Engineering and Mechanics
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• v.51 no.2
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• pp.199-214
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• 2014

The present investigation is concerned with the effect of two temperatures on functionally graded (FG) nanobeams subjected to sinusoidal pulse heating sources. Material properties of the nanobeam are assumed to be graded in the thickness direction according to a novel exponential distribution law in terms of the volume fractions of the metal and ceramic constituents. The upper surface of the FG nanobeam is fully ceramic whereas the lower surface is fully metal. The generalized two-temperature nonlocal theory of thermoelasticity in the context of Lord and Shulman's (LS) model is used to solve this problem. The governing equations are solved in the Laplace transformation domain. The inversion of the Laplace transformation is computed numerically using a method based on Fourier series expansion technique. Some comparisons have been shown to estimate the effects of the nonlocal parameter, the temperature discrepancy and the pulse width of the sinusoidal pulse. Additional results across the thickness of the nanobeam are presented graphically.

• The Pure and Applied Mathematics
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• v.1 no.1
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• pp.29-33
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• 1994

There are various aspects of the solution of boundary-value problems for second-order linear elliptic equations in two independent variables. One useful method of solving such boundary-value problems for Laplace's equation is by means of suitable integral representations of solutions and these representations are obtained most directly in terms of particular singular solutions, termed Green's functions.(omitted)

• Journal of Ocean Engineering and Technology
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• v.36 no.2
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• pp.101-107
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• 2022

Dean (1965) proposed the use of the root mean square error (RMSE) in the dynamic free surface boundary condition (DFSBC) and kinematic free-surface boundary condition (KFSBC) as an error evaluation criterion for wave theories. There are well known wave theories with RMSE more than 1%, such as Airy theory, Stokes theory, Dean's stream function theory, Fenton's theory, and trochodial theory for deep-water waves. However, none of them can be applied for deep-water breaking waves. The purpose of this study is to provide a closed-form solution for deep-water waves with RMSE less than 1% even for breaking waves. This study is based on a previous study (Shin, 2016), and all flow fields were simplified for deep-water waves. For a closed-form solution, all Fourier series coefficients and all related parameters are presented with Newton's polynomials, which were determined by curve fitting data (Shin, 2016). For verification, a wave in Miche's limit was calculated, and, the profiles, velocities, and the accelerations were compared with those of 5^th-order Stokes theory. The results give greater velocities and acceleration than 5^th-order Stokes theory, and the wavelength depends on the wave height. The results satisfy the Laplace equation, bottom boundary condition (BBC), and KFSBC, while Stokes theory satisfies only the Laplace equation and BBC. RMSE in DFSBC less than 7.25×10^-2% was obtained. The series order of the proposed method is three, but the series order of 5^th-order Stokes theory is five. Nevertheless, this study provides less RMSE than 5^th-order Stokes theory. As a result, the method is suitable for offshore structural design.

• Nuclear Engineering and Technology
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• v.52 no.4
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• pp.819-826
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• 2020

The method of the Laplace transform has been used to obtain an analytical solution of the three-dimensional steady state advection diffusion equation for the airborne radionuclide release from any nuclear installation such as the power reactor in an area source. The present treatment takes into account the removal of the pollutants through the nuclear reaction. We assume that the pollutants are emitted as a constant rate from the area source. This physical consideration is achieved by assuming that the vertical eddy diffusivity coefficient should be a constant. The prevailing wind speed is a constant in 𝑥- direction and a linear function of the vertical height z. The present model calculations are compared with the other models and the available data of the atmospheric dispersion experiments that were carried out in the nuclear power plant of Angra dos Reis (Brazil). The results show that the present treatment performs well as the analytical dispersion model and there is a good agreement between the values computed by our model and the observed data.

• Journal of the Society of Naval Architects of Korea
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• v.28 no.2
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• pp.187-194
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• 1991

Vibration analysis methods of a beam-column with elastically restrained ends and various intermediate constraints such as rectilinear springs, rotational springs and concentrated masses are presented. Firstly, an exact method of solutions based on Hamilton's principle and Laplace transform method is shown. This method of solutions is very complicate in cases of having Intermediate constraints more than two. Therefore, Rayleigh-Ritz method using the eigenfunctions of the base system, the system without intermediate constraints, are also investigated. Extensive numerical examples carried out for comparisons with known published works show that the latter method has easy adaptability for wide varieties of boundary conditions and intermediate constraints, and gloves good accuracy for various intermediate constraints with reasonable number of terms in construction of a trial function.

• International Journal of Computer Science & Network Security
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• v.21 no.2
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• pp.120-130
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• 2021

The spinal cord or CSF surgery is a very complex process. It requires continuous pre and post-surgery evaluation to have a better ability to diagnose the disease. To detect automatically the suspected areas of tumors and symptoms of CSF leakage during the development of the tumor inside of the brain. We propose a new method based on using computer software that generates statistical results through data gathered during surgeries and operations. We performed statistical computation and data collection through the Google Source for the UK National Cancer Database. The purpose of this study is to address the above problems related to the accuracy of missing hybrid KNN values and finding the distance of tumor in terms of brain cancer or CSF images. This research aims to create a framework that can classify the damaged area of cancer or tumors using high-dimensional image segmentation and Laplace transformation method. A high-dimensional image segmentation method is implemented by software modelling techniques with measures the width, percentage, and size of cells within the brain, as well as enhance the efficiency of the hybrid KNN algorithm and Laplace transformation make it deal the non-zero values in terms of missing values form with the using of Frobenius Matrix for deal the space into non-zero values. Our proposed algorithm takes the longest values of KNN (K = 1-100), which is successfully demonstrated in a 4-dimensional modulation method that monitors the lighting field that can be used in the field of light emission. Conclusion: This approach dramatically improves the efficiency of hybrid KNN method and the detection of tumor region using 4-D segmentation method. The simulation results verified the performance of the proposed method is improved by 92% sensitivity of 60% specificity and 70.50% accuracy respectively.