• The Pure and Applied Mathematics
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• v.5 no.2
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• pp.123-132
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• 1998

Let F and G denote the distribution functions of the failure times and the censoring variables in a random censorship model. Susarla and Van Ryzin(1978) verified consistency of $F_{\alpha}$, he NPBE of F with respect to the Dirichlet process prior D($\alpha$), in which they assumed F and G are continuous. Assuming that A, the cumulative hazard function, is distributed according to a beta process with parameters c, $\alpha$, Hjort(1990) obtained the Bayes estimator $A_{c,\alpha}$ of A under a squared error loss function. By the theory of product-integral developed by Gill and Johansen(1990), the Bayes estimator $F_{c,\alpha}$ is recovered from $A_{c,\alpha}$. Continuity assumption on F and G is removed in our proof of the consistency of $A_{c,\alpha}$ and $F_{c,\alpha}$. Our result extends Susarla and Van Ryzin(1978) since a particular transform of a beta process is a Dirichlet process and the class of beta processes forms a much larger class than the class of Dirichlet processes.

• The Journal of the Society of Korean Medicine Diagnostics
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• v.10 no.1
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• pp.46-53
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• 2006

Magnetocardiography provides non-invasive three-dimensional electroanatomical imaging of cardiac electrophysiology. The aim of this study is to find the index for using the indicator of magnetocardiography. An object of this study is 214 papers registered on www.pubmed.com. The index used in magnetocardiography is the interval, morphology, amplitude and integrals of QRS complex, P wave, T wave. The current density and electric field map are used, too. A new try of the index is LAS, W-HEAD, Relative Smoothness index(RS index) etc.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.12 no.1
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• pp.43-50
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• 1992

The purpose of this study is to ascertain the robustness of p-version model with hierarchic intergrals of Legendre shape functions in various applications including plane stress/strain, axisymmetric and shell problems. The most important symptoms of accuracy failure in modern finite elements are spurious mechanisms and a phenomenon known as locking which are exhibited for incompressible materials and irregular shapes which contain aspect ratios(R/t, a/b), tapered ratio(d/b), and skewness. The condition numbers and energy norms are used to estimate numerical errors, convergence characteristics and algorithmic efficiencies for verifying the aforementioned symptoms of accuracy failure. Numerical results from p-version models are compared with those from NASTRAN, SAP90, and Cheung's hybrid elements.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.7
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• pp.2148-2158
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• 1996

Uncoupled, quasi-static and linear thermoviscoelastic problems are analyzed in time domain by the finite element approximation which is developed using the principle of virtual work and viscoelasticity matrices instead of shear and bulk relaxation functions as in usual formulations. The material is assumed to be isotropic, homegeneous and thermorheologically simple, which means that the temperature-time equivalence postulate is effective. The stress-strain laws are expressed by relaxation-type hereditary integrals. In spatial and time discritizations, isoparametric quadratic quadrilateral finite elements and linear time variations are adopted. For explicit derivations, the viscoelastic material is assumed to behave standard linear solid in shear and elastically in dilatation. Two-dimensional examples are solved under general temperature distributions T = T(x, t), and compared with other opproximate solutions to show the versatility of the presented analysis.

• Proceedings of the Korean Vacuum Society Conference
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• 2013.02a
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• pp.153-153
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• 2013

Turbomolecular pump (TMP) is widely used to obtain and maintain high vacuum by spinning turbine rotors to migrate gas molecules to the exhaust of the pump. However, performance of the TMP has not been well observed when it is influenced by strong magnetic field. Such study may give useful information about magnetic field tolerance of TMP, development of magnetic shielding technique for key components of TMP, etc. For this purpose, magnetic field induced by a circular current source was firstly designed and investigated. Using spherical coordinates and vector potential, magnetic field throughout the space including axis of rotation was calculated. Due to the rotational symmetry of the circular current source, induced magnetic field is azimuthally symmetric and, thus, is analyzed by radial and polar components of the magnetic fields. In order to enhance the numerical accuracy for the calculation, magnetic field was expressed by complete elliptic integrals of first and second kinds. According to the calculation, when 1 A of DC-current passes through a 1 turned circular wire with 50 cm of diameter, overall magnitude of the inducedmagnetic field was about 0.02 Gauss, which was used to the determination of the current and the number of turns of wires to fabricate the coil for the study on the magnetic field tolerance of TMP.

• Communications of the Korean Mathematical Society
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• v.29 no.1
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• pp.65-74
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• 2014

The well known quadratic transformation formula due to Gauss: $$(1-x)^{-2a}{_2F_1}\[{{a,b;}\\\hfill{21}{2b;}}\;-\frac{4x}{(1-x)^2}\]={_2F_1}\[{{a,a-b+\frac{1}{2};}\\\hfill{65}{b+\frac{1}{2};}}\;x^2\]$$ plays an important role in the theory of (generalized) hypergeometric series. In 2001, Rathie and Kim have obtained two results closely related to the above quadratic transformation for $_2F_1$. Our main objective of this paper is to deduce some interesting known or new results for the series $_2F_1(x)$ by using the above Gauss's quadratic transformation and its contiguous relations and then apply our results to provide a list of a large number of integrals involving confluent hypergeometric functions, some of which are (presumably) new. The results established here are (potentially) useful in mathematics, physics, statistics, engineering, and so on.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.18 no.8
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• pp.1059-1068
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• 1993

We will put the emphasis on the analysis of arbitrarily shaped microstrip antennas. The most general and rigorous treatment of microstrip antennas is given by the electric field integral equation(EFIE), usally formulated in the spectral domain. In this paper, we use a modification of EFIE, called the mixed potential integral equation(MPIE) , and we solve it in the space domain. This technique uses Green's functions associated with the scalar and vector potential which are calculated by using stratified media theory and are expressed as Sommerfeld integrals. The integral equation is solved by a moment's method using rooftop subsectional basis function. Thus, microstrip patches of any shape can be analysed at any frequency and for any substrate. Numerical results for a rectangular patch and for a L-shaped patch are given and compared with measured values.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1999.04a
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• pp.121-128
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• 1999

This paper presents a time domain method for soil-structure interaction analysis for seismic loadings. It is based on the finite element formulation incorporating analytical frequency-dependent infinite elements for the far field soil. The dynamic stiffness matrices of the far field region formulated using the present method in frequency domain can be easily transformed into the corresponding matrices in time domain. At first, the equivalent earthquake forces are evaluated along the interface between the near and the far fields from the free-field response analysis carried out in frequency domain, and the results are transformed into the time domain. An efficient procedure is developed for the convolution integrals to evaluate the interaction force along the interface, which depends on the response on the interface at the past time instances as well as the concurrent instance. Then, the dynamic responses are obtained for the equivalent earthquake force and the interaction force using Newmark direct integration technique. Since the response analysis is carried out in time domain, it can be easily extended to the nonlinear analysis. Example analysis has been carried out to verify the present method in a multi-layered half-space.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.23 no.2
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• pp.243-253
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• 1999

The dual reciprocity boundary element method (DRBEM) is used to solve the Graetz problem of laminar flow inside circular duct. In this method the domain integral tenn of boundary integral equation resulting from source term of governing equation is transformed into equivalent boundary-only integrals by using the radial basis interpolation function, and therefore complicate domain discretization procedure Is completely removed. Velocity profile is obtained by solving the momentum equation first and then, using this velocities as Input data, energy equation Is solved to get the temperature profile by advancing from duct entrance through the axial direction marching scheme. DRBEM solution is tested for the uniform temperature and heat flux boundary condition cases. Local Nusselt number, mixed mean temperature and temperature profile inside duct at each dimensionless axial location are obtained and compared with exact solutions for the accuracy test Solutions arc in good agreement at the entry region as well as fully developed region of circular duct, and their accuracy are verified from error analysis.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.17 no.8 s.111
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• pp.788-794
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• 2006

In this paper, a Sommerfeld integral for an impedance half-plane is considered, which is one of classical problems in electromagnetic theory. First, the integral is evaluated into two series representations which are expressed in terms of exponential integral and Lommel function, respectively. Then based on the Lommel function expansion, an exact, closed-form expression of the integral is formulated, written in terms of incomplete Weber integrals. Additionally, based on the exponential integral expansion, an approximate expression of the integral is obtained. Validity of all formulations derived in this paper is demonstrated through comparisons with a numerical integration of the integral for various situations.