• 대한수학교육학회지:학교수학
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• 제11권3호
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• pp.415-429
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• 2009

본 연구에서는 교과서 연립방정식 단원에 제시된 수학사의 내용을 살펴보고 이를 활용하기 위한 교수학적인 시사점을 분석하였다. 교과서에서 수학사는 읽을거리나 방정식을 푸는 과정에서 문제로 제공되는 경우가 대부분이다. 따라서 교사가 수업내용을 발전시키거나 자유 탐구를 위한 측면에서 수학사를 활용하기 위해, 그 시대의 사람들은 어떻게 문제를 해결하였는지 탐구할 수 있는 발문을 제시하고 향후 소개되는 연립방정식의 풀이에 대한 기대와 필요성에 대해 생각할 수 있는 기회를 제공하여 현재 사용하고 있는 풀이 방법의 편리성과 우수성을 인식하게 할 수 있다. 또한, 수학사에 나타난 연립방정식의 다양한 풀이에 대해 토론하여 자동화된 풀이를 반복하는 단순함에서 벗어나 수학을 비판적으로 바라보고 새롭게 변화 발전시킬 수 있는 반성적인 사고를 유발할 수 있다.

• Journal of applied mathematics & informatics
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• 제31권1_2호
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• pp.285-297
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• 2013

This paper deals with parabolic equations coupled via nonstandard growth sources, subject to homogeneous Dirichlet boundary conditions. Three kinds of necessary and sufficient conditions are obtained, which determine the complete classifications for non-simultaneous and simultaneous blowup phenomena. Moreover, blowup rates are given.

• Wind and Structures
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• 제22권3호
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• pp.349-368
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• 2016

A preconditioning technique is presented for a simultaneous solution to wind-membrane interaction. In the simultaneous equations, a linear elastic model was employed to deal with the fluid-structure data transfer at the interface. A Lagrange multiplier was introduced to impose the specified boundary conditions at the interface and strongly coupled simultaneous equations are derived after space and time discretization. An initial linear elastic model preconditioner and modified one were derived by treating the linearized elastic model equation as a saddle point problem, respectively. Accordingly, initial and modified fluid-structure interaction (FSI) preconditioner for the simultaneous equations were derived based on the initial and modified linear elastic model preconditioners, respectively. Wind-membrane interaction analysis by the proposed preconditioners, for two and three dimensional membranous structures respectively, was performed. Comparison was made between the performance of initial and modified preconditioners by comparing parameters such as iteration numbers, relative residuals and convergence in FSI computation. The results show that the proposed preconditioning technique greatly improves calculation accuracy and efficiency. The priority of the modified FSI preconditioner is verified. The proposed preconditioning technique provides an efficient solution procedure and paves the way for practical application of simultaneous solution for wind-structure interaction computation.

• Journal of electromagnetic engineering and science
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• 제2권2호
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• pp.87-92
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• 2002

A short-ended electromagnetically coupled coaxial dipole array antenna is investigated theoretically. The antenna has an advantage of structural simplicity. The integral equations are derived for the proposed structure by use of the Fourier transform and mode expansion, and the simultaneous linear equations are obtained. The slot electric field and strip current are obtained by solving the simultaneous linear equations. The effects of slot and strip numbers on the radiation efficiency, beamwidth and directivity gain of the antenna are presented.

• East Asian mathematical journal
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• 제37권2호
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• pp.265-288
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• 2021

In the 2015 revised mathematics curriculum, the system of equations is first introduced in 'Variables and Expressions' of [Middle School Grades 1-3]. Then, It is constructed that after learning the linear function in 'Functions', the relationship between the graphs of two linear functions and the systems of linear equations are learned so that students could improve the geometric representation of the systems of equations. However, in of Elective-Centered Curriculum Common Courses, Instruction is limited to algebraic manipulation when teaching and learning systems of quadratic equations. This paper presented the teaching and learning method that can improve students' mathematical connection through various representations by providing geometric representations in parallel using GeoGebra, a mathematics learning software, with algebraic solutions in the teaching and learning situation of simultaneous quadratic equations.

• 한국철도학회:학술대회논문집
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• 한국철도학회 2005년도 추계학술대회 논문집
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• pp.1165-1170
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• 2005

In order to perform the spatial buckling analysis of the curved beam element with nonsymmetric thin-walled cross section, exact static stiffness matrices are evaluated using equilibrium equations and force-deformation relations. Contrary to evaluation procedures of dynamic stiffness matrices, 14 displacement parameters are introduced when transforming the four order simultaneous differential equations to the first order differential equations and 2 displacement parameters among these displacements are integrated in advance. Thus non-homogeneous simultaneous differential equations are obtained with respect to the remaining 8 displacement parameters. For general solution of these equations, the method of undetermined parameters is applied and a generalized linear eigenvalue problem and a system of linear algebraic equations with complex matrices are solved with respect to 12 displacement parameters. Resultantly displacement functions are exactly derived and exact static stiffness matrices are determined using member force-displacement relations. The buckling loads are evaluated and compared with analytic solutions or results by ABAQUS's shell element.

• STI Policy Review
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• 제6권1호
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• pp.1-23
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• 2015

Based on the work of Anand et al. (2013) we measure inclusive income growth, which combines growth in gross domestic product (GDP) per capita and growth in the equity of the income distribution. Extending the work of Causa et al. (2014), we estimate a dynamic simultaneous structural equations model of GDP per capita and inclusive income on panel data for 63 countries over the 1990-2013 period. We estimate both equations in error correction form by difference GMM (generalized method of moments). Among the explanatory variables of the level and the distribution of GDP per capita we include R&D (research and development) expenditure per capita. In OECD countries we obtain a large positive effect of R&D on GDP. R&D is found to have a positive effect on the social mobility index but its impact on the income equity index at first decreases, then switches around to become slightly positive in the long run. In non- OECD countries, R&D is found to decrease inclusive income, mostly through a negative growth effect but also because of a slightly increasing income inequity effect.

• 대한산업공학회지
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• 제4권2호
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• pp.107-118
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• 1978

The paper illustrates a possible application of control theory to an economic growth system. Simultaneous nonlinear system of differential equations has been modeled which is different from the traditional formulation, based on the theory of economic growth for a two-sector (dual) economy. Necessary and sufficient conditions for the existence of the optimal control are derived directly from the Hamiltonian, and the optimal controls are also obtained by solving simultaneous equations. Obtaining the trajectories of the optimal control and state variables, however, should rely on the numerical procedures. Empirical application has been conducted for the case of the Korean economy as an illustration.

• 한국전자파학회:학술대회논문집
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• 한국전자파학회 2000년도 종합학술발표회 논문집 Vol.10 No.1
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• pp.399-403
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• 2000

A new type of collinear antenna called short-ended coaxial slot-coupled strip array antenna is investigated theoretically. The antenna has an advantage of structural simplicity. The integral equations are derived for the proposed structure by use of the Fourier transform and mode expansion, and the simultaneous linear equations are obtained. The slot electric field and strip current are then obtained by solving the simultaneous linear equation. The effects of slot and strip number on the radiation efficienty, beamwidth and directivity gain are also presented.

• Structural Engineering and Mechanics
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• 제19권1호
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• pp.73-96
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• 2005

For the spatially coupled free vibration analysis of shear deformable thin-walled non-symmetric curved beam subjected to initial axial force, an exact dynamic element stiffness matrix of curved beam is evaluated. Firstly equations of motion and force-deformation relations are rigorously derived from the total potential energy for a curved beam element. Next a system of linear algebraic equations are constructed by introducing 14 displacement parameters and transforming the second order simultaneous differential equations into the first order simultaneous differential equations. And then explicit expressions for displacement parameters are numerically evaluated via eigensolutions and the exact $14{\times}14$ dynamic element stiffness matrix is determined using force-deformation relations. To demonstrate the accuracy and the reliability of this study, the spatially coupled natural frequencies of shear deformable thin-walled non-symmetric curved beams subjected to initial axial forces are evaluated and compared with analytical and FE solutions using isoparametric and Hermitian curved beam elements and results by ABAQUS's shell elements.