• 대한수학회논문집
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• 제37권1호
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• pp.303-326
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• 2022

Our aim is to construct Hermite-type exponentially fitted interpolation formulas that use not only the pointwise values of an 𝜔-dependent function f but also the values of its first derivative at three unequally spaced nodes. The function f is of the form, f(x) = g₁(x) cos(𝜔x) + g₂(x) sin(𝜔x), x ∈ [a, b], where g₁ and g₂ are smooth enough to be well approximated by polynomials. To achieve such an aim, we first present Hermite-type exponentially fitted interpolation formulas I_N built on the foundation using N unequally spaced nodes. Then the coefficients of I_N are determined by solving a linear system, and some of the properties of these coefficients are obtained. When N is 2 or 3, some results are obtained with respect to the determinant of the coefficient matrix of the linear system which is associated with I_N. For N = 3, the errors for I_N are approached theoretically and they are compared numerically with the errors for other interpolation formulas.

• 대한기계학회논문집A
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• 제20권11호
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• pp.3441-3453
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• 1996

A finite element anlaysis is performed for large deformations of a felxible beam. The total Lagrangian formulation for a general large deformation, which involves finite rotations, is chosen and the exponential map is used to treat finite rotations from the Eulerian point of view. The finite elements results are confirmed for several cases of deformations through comparison to a first order elasticity solution obtained by numerical integration, and the agreement between the two is found to be excellent. For lateral buckling, the point of vanishing determinant of the resulting unsymmetric tangent stiffness is traced to examine its relationship to bifurcation points. It is found that the points of vanishing determinant is not corresponding to bifurcation points for large deformation in general, which suggests that the present unsymmetric tangent stiffness is not an exact first derivative of internal forces with respect to displacement.

• 한국가구학회지
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• 제28권3호
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• pp.156-168
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• 2017

The digital information society that developed along with the 21st century is the 'Open-source Making Movement' which produces collective intelligence through open-source sharing and digital manufacturing tools, which is called 'Makers Movement'. The purpose of this paper is to analyze the case of Makers Movement in furniture design through 'IKEA Hacking' which arose simultaneously with the Makers Movement, and to study and present the prospect and direction of furniture design in the change of manufacturing industry. In this study, four design features were compared with IKEA hacking cases along with the establishment of 'community' which is a feature of Makers Movement. Four characteristics are first customized design, second derivative design through open source, third long -Tail effect design, and fourth, design using digital manufacturing tools. The prospect and direction of furniture design through this study are as follows: first, democratization of furniture design manufacturing, second job creation, third, coexistence of large and small enterprises, fourth promotion of various new technologies, and fifth, discovery of various furniture designers through 'Open System Organization'.

• Nonlinear Functional Analysis and Applications
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• 제28권2호
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• pp.449-471
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• 2023

In this paper, we study a linear system of homogeneous commensurate /incommensurate fractional-order differential equations by developing a new semi-analytical scheme. In particular, by decoupling the system into two fractional-order differential equations, so that the first equation of order (δ + γ), while the second equation depends on the solution for the first equation, we have solved the under consideration system, where 0 < δ, γ ≤ 1. With the help of using the Adomian decomposition method (ADM), we obtain the general solution. The efficiency of this method is verified by solving several numerical examples.

• 대한원격탐사학회:학술대회논문집
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• 대한원격탐사학회 2003년도 Proceedings of ACRS 2003 ISRS
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• pp.1055-1057
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• 2003

In this research, the concrete with paint film was classified using hyper-spectral remote sensing. First, spectral characteristics of concrete and concrete with some kinds of paint films were investigated with a spectrometer. Second, using reflectance and first order derivative, spectral characteristics of the normal concrete and the concrete with paint film were classified. By using hyper-spectral remote sensing, not only extraction of crack but also inspection of paint film distribution is possible.

• Journal of applied mathematics & informatics
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• 제28권3_4호
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• pp.763-772
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• 2010

This paper deals with the existence of triple positive solutions for the nonlinear second-order three-point boundary value problem z"(t)+a(t)f(t, z(t), z'(t))=0, t $\in$ (0, 1), $z(0)={\nu}z(1)\;{\geq}\;0$, $z'(\eta)=0$, where 0 < $\nu$ < 1, 0 < $\eta$ < 1 are constants. f : [0, 1] $\times$ [0, $+{\infty}$) $\times$ R $\rightarrow$ [0, $+{\infty}$) and a : (0, 1) $\rightarrow$ [0, $+{\infty}$) are continuous. First, Green's function for the associated linear boundary value problem is constructed, and then, by means of a fixed point theorem due to Avery and Peterson, sufficient conditions are obtained that guarantee the existence of triple positive solutions to the boundary value problem. The interesting point is that the nonlinear term f is involved with the first-order derivative explicitly.

• 한국공작기계학회논문집
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• 제15권3호
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• pp.8-16
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• 2006

This paper discusses design sensitivity analysis and its application to a structural dynamics modification. Eigenvalue derivatives are determined with respect to the element parameters, which include intrinsic property parameters such as Young's modulus, density of the material, diameter of a beam element, thickness of a plate element, and shape parameters. Derivatives of stiffness and mass matrices are directly calculated by derivatives of element matrices. The first and the second order derivatives of the eigenvalues are then mathematically derived from a dynamic equation of motion of FEM model. The calculation of the second order eigenvalue derivative requires the sensitivity of its corresponding eigenvector, which are developed by Nelson's direct approach. The modified eigenvalue of the structure is then evaluated by the Taylor series expansion with the first and the second derivatives of eigenvalue. Numerical examples for simple beam and plate are presented. First, eigenvalues of the structural system are numerically calculated. Second, the sensitivities of eigenvalues are then evaluated with respect to the element intrinsic parameters. The most effective parameter is determined by comparing sensitivities. Finally, we predict the modified eigenvalue by Taylor series expansion with the derivatives of eigenvalue for single parameter or multi parameters. The examples illustrate the effectiveness of the eigenvalue sensitivity analysis for the optimization of the structures.

• Journal of applied mathematics & informatics
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• 제26권5_6호
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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.

• 한국항행학회논문지
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• 제19권6호
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• pp.636-642
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• 2015

본 논문에서는 계단응답으로부터 시 지연을 갖는 선형 연속시스템을 식별하기 위해 HS 최적화 알고리즘을 적용에 관하여 연구하였다. 인식 모델은 1차 시 지연 모델 (FOPDT)로써, FOPDT은 많은 화학 공정과 HAVC 공정에 실효성이 있으며 PID 튜닝에도 적합하다. 최근에 개발된 HS 알고리즘은 완벽한 하모니를 찾아가는 음악적 과정을 개념화 한 것이다. 수학을 기반으로 하는 전통적 기법과 달리 HS는 확률적인 방법을 사용하므로 미분과 같은 수학적 접근을 필요로 하지 않는다. 제시된 인식 방법의 효과를 입증하기 위해 많은 수치 예를 수행하여 결과를 제시하였다.

• 디지털콘텐츠학회 논문지
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• 제9권1호
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• pp.17-26
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• 2008

본 논문은 기준 화소의 인접 가해 성분값과 선형 축소 성분값의 평균으로 축소 성분값을 정하는 적응형 선형 축소기를 제안하고 주관적 화질과 하드웨어 복잡도 측면에서 그 성능을 분석함에 목적이 있다. 제안된 적응형 선형 축소기는 우선, 일차 미분 연산자를 이용하여 기준 화소의 우측 및 하측 인접화소의 기울기의 크기를 각각 계산한다. 이후, 두 기울기의 크기를 합산한 결과로 각 기울기의 크기를 나누어 우측 및 하측 인접 화소 각각의 국부 가해 가중치를 구한다. 다음으로, 각각의 국부 가해 가중치를 우측 및 하측 인접 화소값에 곱한 후에 그 결과를 합산함으로써 인접 가해 성분값을 정의한다. 제안된 방법은 인접 화소들의 유효 가해 정보를 각각의 국부 가해 가중치에 따라 축소 성분값에 적응적으로 반영함으로써 선형 축소기의 단점인 몽롱화 현상을 효과적으로 억제시킬 수 있다. 또한 적은 연산량을 요하면서도 평균적으로 양호한 결과를 제공하는 선형 축소 방식의 장점을 취할 수 있는 이점이 있다.