• Communications of the Korean Mathematical Society
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• v.18 no.4
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• pp.755-765
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• 2003

Krylov-Bogoliubov-Mitropolskii method has been extended to obtain asymptotic solution of n-th order nonlinear differential system characterized by certain non-oscillatory processes. The damping force is considered in such a manner that one of the characteristic roots of the linear system becomes small and others are in integral multiple. The method is illustrated by an example. The solutions for different initial conditions show a good agreement with those obtained by numerical method.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.27 no.4
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• pp.245-271
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• 2023

In this paper we discuss some recovery of H(div)-conforming flux approximations from the equilibrated fluxes of Ainsworth and Oden for quadratic finite element methods of second-order elliptic problems. Combined with the hypercircle method of Prager and Synge, these flux approximations lead to a posteriori error estimators which provide guaranteed upper bounds on the numerical error. Furthermore, we prove some superconvergence results for the flux approximations and asymptotic exactness for the error estimator under proper conditions on the triangulation and the exact solution. The results extend those of the previous paper for linear finite element methods.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.1 no.1
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• pp.81-86
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• 1989

Herein the surge-heave-pitch motion of a ship has been analyzed within the framework of linear potential theory. The ship is assumed slender weakly moored along the centerline of a rectangular harbor with constant depth and straight coastline. The method of matched asymptotic expansion is us-ed to obtain the leading-order solution. The ship and harbor responses to incident long waves can be re-presented in terms of Green's function, which is the solution of the Helmholtz equation satisfying necessary boundary conditions. Numerical results clearly indicate the importance of the surge motion.

• East Asian mathematical journal
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• v.37 no.5
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• pp.553-566
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• 2021

In the over-the-counter market, option's buyers could have a problem for default risk caused by option's writers. In addition, many participants try to maximize their benefits obviously in investing the financial derivatives. Taking all these circumstances into consideration, we deal with the vulnerable power options under a constant elasticity variance (CEV) model. We derive an analytic pricing formula for the vulnerable power option by using the asymptotic analysis, and then we verify that the analytic formula can be obtained accurately by comparing our solution with Monte-Carlo price. Finally, we examine the effect of CEV on the option price based on the derived solution.

• Journal of Mechanical Science and Technology
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• v.16 no.8
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• pp.1117-1126
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• 2002

A conducting crack in an electrostrictive ceramic under combined electric and mechanical loading is investigated. Analysis based on linear dielectric model predicts that the surfaces of the crack are not open completely but they are contact near the crack tip. The complete solution for the crack with a contact zone in a linear electrostrictive ceramic under combined electric and mechanical loading is obtained by using the complex variable formula. The asymptotic problems for a semi-infinite crack with a partial opening zone as well as for a fully open semi-infinite crack in a nonlinear electrostrictive ceramic are analyzed in order to investigate the effect of the electrical nonlinearity on the stress intensity factor under small scale nonlinear conditions. Particular attention is devoted to a finite crack in the nonlinear electrostrictive ceramic subjected to combined electric and mechanical loading. The stress intensity factor for the finite crack under small scale nonlinear conditions is obtained from the asymptotic analysis.

• Journal of applied mathematics & informatics
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• v.33 no.5_6
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• pp.485-502
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• 2015

A computational method for solving singularly perturbed boundary value problem of differential equation with shift arguments of mixed type is presented. When shift arguments are sufficiently small (o(ε)), most of the existing method in the literature used Taylor's expansion to approximate the shift term. This procedure may lead to a bad approximation when the delay argument is of O(ε). The main idea for this work is to deal with constant shift arguments, which are independent of ε. In the present method, we construct the formally asymptotic solution of the problem using the method of composite expansion. The reduced problem is solved numerically by using operator compact implicit method, and the second problem is solved analytically. Error estimate is derived by using the maximum norm. Numerical examples are provided to support the theoretical results and to show the efficiency of the proposed method.

• Journal of the Korean Mathematical Society
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• v.57 no.1
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• pp.215-247
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• 2020

In this paper, we deal with a two-species chemotaxis-Stokes system with Lotka-Volterra competitive kinetics under homogeneous Neumann boundary conditions in a general three-dimensional bounded domain with smooth boundary. Under appropriate regularity assumptions on the initial data, by some L^p-estimate techniques, we show that the system possesses at least one global and bounded weak solution, in addition to discussing the asymptotic behavior of the solutions. Our results generalizes and improves partial previously known ones.

• Journal of Biomedical Engineering Research
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• v.5 no.1
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• pp.9-14
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• 1984

The asymptotic solution using the Tailor series has been given explicit form for the solute concentration and overall solute removal in hemodiafilter using one dimensional model. The numerical solutions have been calculated within 0.001% error by the Romberg integration method. Compared with the numerical solutions, the oneterm asymptotic solutions were found to be within 3% error for the condition > 3.0 and three-terms asymtotic solutions were required for the condition >0.7 where denotes measure of convection over diffusional transport and a the ratio of blood flow rate over dialysate flow rate.

• Journal of the Korean Statistical Society
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• v.36 no.1
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• pp.57-76
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• 2007

Kriging is a nonparametric regression method used in geostatistics for estimating curves and surfaces for spatial data. It may come as a surprise that the Kriging estimator, normally derived as the best linear unbiased estimator, is also the solution of a particular variational problem. Thus, Kriging estimators can also be interpreted as generalized smoothing splines where the roughness penalty is determined by the covariance function of a spatial process. We build off the early work by Silverman (1982, 1984) and the analysis by Cox (1983, 1984), Messer (1991), Messer and Goldstein (1993) and others and develop an equivalent kernel interpretation of geostatistical estimators. Given this connection we show how a given covariance function influences the bias and variance of the Kriging estimate as well as the mean squared prediction error. Some specific asymptotic results are given in one dimension for Matern covariances that have as their limit cubic smoothing splines.

• Structural Engineering and Mechanics
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• v.10 no.2
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• pp.111-123
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• 2000

An asymptotic solution for snap-through buckling of single-layer squarely-reticulated shallow spherical shells continuously supported on springs is developed in this paper. Based on the fundamental governing equations and boundary conditions, a nondimensional analytical expression associated with the external load, stiffness of spring and central transverse displacement (deflection) is derived with the aid of asymptotic iteration method. The effects of stiffness of spring and characteristic geometrical parameter on buckling of the structures are given by the analyses of numerical examples. In a special case, for reticulated circular plates, the influence of stiffness of spring on the characteristic relation between load and deflection is also demonstrated.