• Journal of KIISE:Software and Applications
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• v.31 no.5
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• pp.577-585
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• 2004

Storing and estimating the high order probability distribution of classifiers and class labels is exponentially complex and unmanageable without an assumption or an approximation, so we rely on an approximation scheme using the dependency. In this paper, as an extended study of the second-order dependency-based approximation, the probability distribution is optimally approximated by the third-order dependency. The proposed third-order dependency-based approximation is applied to the combination of multiple classifiers recognizing handwritten numerals from Concordia University and the University of California, Irvine and its usefulness is demonstrated through the experiments.

• Journal of applied mathematics & informatics
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• v.26 no.5_6
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• pp.1057-1069
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• 2008

We consider singularly perturbed Boundary Value Problems (BVPs) for third and fourth order Ordinary Differential Equations(ODEs) of convection-diffusion type with discontinuous source term and a small positive parameter multiplying the highest derivative. Because of the type of Boundary Conditions(BCs) imposed on these equations these problems can be transformed into weakly coupled systems. In this system, the first equation does not have the small parameter but the second contains it. In this paper a computational method named as 'An asymptotic finite element method' for solving these systems is presented. In this method we first find an zero order asymptotic approximation to the solution and then the system is decoupled by replacing the first component of the solution by this approximation in the second equation. Then the second equation is independently solved by a fitted mesh Finite Element Method (FEM). Numerical experiments support our theoritical results.

• Journal of applied mathematics & informatics
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• v.35 no.3_4
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• pp.277-302
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• 2017

In this paper, we have proposed a numerical method for Singularly Perturbed Boundary Value Problems (SPBVPs) of reaction-diffusion type of third order Ordinary Differential Equations (ODEs). The SPBVP is reduced into a weakly coupled system of one first order and one second order ODEs, one without the parameter and the other with the parameter ${\varepsilon}$ multiplying the highest derivative subject to suitable initial and boundary conditions, respectively. The numerical method combines boundary value technique, asymptotic expansion approximation, shooting method and finite difference scheme. The weakly coupled system is decoupled by replacing one of the unknowns by its zero-order asymptotic expansion. Finally the present numerical method is applied to the decoupled system. In order to get a numerical solution for the derivative of the solution, the domain is divided into three regions namely two inner regions and one outer region. The Shooting method is applied to two inner regions whereas for the outer region, standard finite difference (FD) scheme is applied. Necessary error estimates are derived for the method. Computational efficiency and accuracy are verified through numerical examples. The method is easy to implement and suitable for parallel computing. The main advantage of this method is that due to decoupling the system, the computation time is very much reduced.

• Journal of the korean Society of Automotive Engineers
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• v.14 no.2
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• pp.54-64
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• 1992

During combustion process in a diesel engine radiation heat transfer is the same order of magnitude as the convection heat transfer. An approximation of heat and momentum source distributions is applied at a level consistent with those used in modelling the soot distribution and the turbulence instead of modelling the fuel spray and the chemical kinetics. This paper illustrates a use of the third order spherical harmonics approximation to the radiative transfer equation and delta-Eddington approximation to the scattering phase function for droplets in the flow. Results are obtained numerically by a time marching finite difference scheme. This study aims to compare heat transfer with convection heat transfer and to investigate the importance of scattering by fuel droplets and of accounting for spatial variations in the extinction coefficient on the radiative heat flux distributions at the walls of a disc shaped diesel engine.

• Steel and Composite Structures
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• v.8 no.5
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• pp.343-359
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• 2008

In the present study, an efficient method for the optimum design of three-dimensional (3D) steel framed structures is proposed. In this method, in addition to choosing the best position of columns based on architectural requirements, the optimum cross-sectional dimensions of elements are determined. The preliminary design variables are considered as the number of columns in structural plan, which are determined by a direct optimization method suitable for discrete variables, without requiring the evaluation of derivatives. After forming the geometry of structure, the main variables of the cross-sectional dimensions are evaluated, which satisfy the design constraints and also achieve the least-weight of the structure. To reduce the number of finite element analyses and the overall computational time, a new third order approximate function is introduced which employs only the diagonal elements of the higher order derivatives matrices. This function produces a high quality approximation and also, a robust optimization process. The main feature of the proposed techniques that the higher order derivatives are established by the first order exact derivatives. Several examples are solved and efficiency of the new approximation method and also, the proposed method for the best position of columns in 3D steel framed structures is discussed.

• Journal of applied mathematics & informatics
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• v.7 no.2
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• pp.391-408
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• 2000

In the curved geometries, from the solution of the classical Riemann problem in the plane, the asymptotic solutions of the compressible Euler equation are presented. The explicit formulae are derived for the third order approximation of the generalized Riemann problem form the conventional setting of a planar shock-interface interaction.

• Journal of the Korean Society for Precision Engineering
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• v.29 no.12
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• pp.1290-1295
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• 2012

Oblique astigmatism according to the rotation of the eye has to be removed for obtaining peripheral clear vision in ophthalmic lenses. For this reason, we calculated tangential and sagittal power using third-order approximation theory and then controlled conic constant for the difference of the two powers to converge to 0 regardless of the rotation angle of the eye. As a result, an aspherical ophthalmic lens without oblique astigmatism was designed. Also, we found optimal machining condition to the lens material using factorial design and finally fabricated the designed lens through ultra-precision machining with that condition.

• Journal of Convergence for Information Technology
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• v.11 no.12
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• pp.14-21
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• 2021

In this paper, it is shown how the performance of the monopulse algorithm in the presence of an additive noise can be obtained analytically. In the previous study, analytic performance analysis based on the first-order Taylor series and the second-order Taylor series has been conducted. By adopting the third-order Taylor series, it is shown that the analytic performance based on the third-order Taylor series can be made closer to the performance of the original monopulse algorithm than the analytic performance based on the first-order Taylor series and the second-order Taylor series. The analytic MSE based on the third-order Taylor approximation reduces the analytic MSE error based on the second-order Taylor approximation by 89.5%. It also shows faster results in all cases than the Monte Carlo-based MSE. Through this study, it is possible to explicitly analyze the angle estimation ability of monopulse radar in an environment where noise jamming is applied.

• Journal of the Optical Society of Korea
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• v.2 no.2
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• pp.58-63
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• 1998

Cross-talk effects in high-density volume holographic interconnections are investigated using perturbative iteration method of the integral form of Maxwell's wave equation. In this method, the paraxial approximation and negligence of backward scattering introduced in conventional coupled mode theory is not assumed. Interaction geometries consisting of non-coplanar light waves and multiple index gratings are studied. Arbitrary light polarization is considered. Systematic analysis of cross-talk effects due to multiple index gratings is performed in increasing level of diffraction orders corresponding to successive iterations. Some numerical examples are given for first and third order diffraction.

• Composites Research
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• v.25 no.4
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• pp.117-125
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• 2012

Warpage of the film insert molded (FIM) part is caused by an asymmetric residual stress distribution. Asymmetric residual stress and temperature distribution is generated by the retarded heat transfer in the perpendicular direction to the attached film surface. Since warpage was not prevented by controlling injection molding conditions, glass fiber (GF) filled composites were employed as substrates for film insert molding to minimize the warpage. Distribution of short GFs was evaluated by using micro-CT equipment. Proper models for micro mechanics, anisotropic thermal expansion coefficients, and closure approximation should be selected in order to calculate fiber orientation tensor and warpage of the FIM part with the composite substrate. After six kinds of micro mechanics models, three models of the thermal expansion coefficient and five models of the closure approximation had been considered, the Mori-Tanaka model, the Rosen and Hashin model, and the third orthotropic closure approximation were selected in this study. The numerically predicted results on fiber orientation tensor and warpage were in good agreement with experimental results and effects of GF reinforcement on warpage of the FIM composite specimen were identified by the numerical results.