• Korean Journal of Mathematics
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• 제16권2호
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• pp.165-172
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• 2008

We investigate the multiplicity of solutions of the nonlinear biharmonic equation with Dirichlet boundary condition,${\Delta}^2u+c{\Delta}u=bu^{+}+s$, in ­${\Omega}$, where $c{\in}R$ and ${\Delta}^2$ denotes the biharmonic operator. We show by degree theory that there exist at least three solutions of the problem.

• 한국경영과학회지
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• 제9권2호
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• pp.28-33
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• 1984

In this paper some procedures are given whereby an analytic solution may be found for the Riccati differential equation and algebraic Riccati equation in optimal control theory. Some iterative techniques for solving these equations are presented. Rate of convergence and initialization of the iterative processes are discussed.

• 호남수학학술지
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• 제26권4호
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• pp.589-608
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• 2004

We investigate the multiplicity of the periodic solutions of the nonlinear wave equation with jumping nonlinearity. By category theory we prove that the jumping problem has at least 2k+1 solutions for the positive source term.

• 한국수학교육학회지시리즈A:수학교육
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• 제57권3호
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• pp.231-246
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• 2018

In this paper, we applied Sfard's reification theory to analyze the secondary students' level of conceptualization with regard to the formula of quadratic equation. Through the generation and development of mathematical concepts from a historical perspective, Sfard classified the formulation process into three stages of interiorization, condensation, and reification, and proposed levels of formulation. Based on this theory, we constructed a test tool reflecting the reversibility of the nature of manipulation of Piaget's theory as a criterion of content judgement in order to grasp students' conceptualization level of the formula of quadratic equation. By applying this tool, we analyzed the conceptualization level of the formula of quadratic equation of the $9^{th}$ and $10^{th}$ graders. The main results are as follows. First, approximately 45% of $9^{th}$ graders can not memorize the formula of quadratic equation, or even if they memorize, they do not have the ability of accurate calculation to apply for it. Second, high school curriculum requires for students to use the formula of the quadratic equation, but about 60% of $10^{th}$ graders have not reached at the level of reification that they can use the formula of quadratic equation. Third, as a result of imaginarily correcting the error of the previous concept, there was a change in the levels of $9^{th}$ graders, and there was no change in $10^{th}$ graders.

• 대한화학회지
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• 제44권6호
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• pp.587-591
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• 2000

고분자액체의 상태방정식을 구하기 위하여 많은 이론들이 제안되어 왔다. 이론들의 대부분은 cell, hole, free volume 또는 lattice 등의 개념에 근거를 두고 있다. 가장 성공적인 이론중의 하나로 평가받고 있는 것이 free volume의 개념을 근거로 한 Flory의 상태방정식 이론이다. 본 연구에서는 Flory 이론에서 사용한 van der Waals 포텐셜을 수정하여 새로운 상태방정식을 만들었다. 계산결과 새로운 상태방정식은 Flory 이론보다 PVT 실험값과 더 잘 일치함을 알 수 있었다.

• 대한토목학회논문집
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• 제3권3호
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• pp.53-61
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• 1983

침투능을 계산하기 위한 공식으로서 Green-Ampt 공식은 식의 간편성과 정확성으로 인하여 많은 연구의 대상이 되어왔다. 그러나 이 공식의 변수인 습윤전선(Wetting Front)에서의 모세관 압력수두항은 연구자에 따라 해석이 많이 다르다. 침투능해석을 위하여 2개 유체의 흐름방정식의 해는 Green-Ampt 공식과 같은 형태를 가지므로서 Green-Ampt 공식의 모세관 압력 수두항을 결정할 수 있게 되었다. 이러한 2개 유체 해석에 의한 침투능 산정공식의 유도는 1개층으로만 구성되어 있는 경우에 이루어 졌으나 특성이 각각 다른 여러 층의 흙으로 구성 되어 있는 경우에는 아직 이루어진 바 없다. 본 논문에서는 이러한 2개 유체의 흐름 해석에 의하여 여러층의 흙인 경우 침투능 산정공식을 유도하였다.

• Journal of Advanced Marine Engineering and Technology
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• 제40권5호
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• pp.389-396
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• 2016

The theory of Fourier heat conduction predicts accurately the temperature profiles of a system in a non-equilibrium steady state. However, in the case of transient states at the nanoscale, its applicability is significantly limited. The limitation of the classical Fourier's theory was overcome by C. Cattaneo and P. Vernotte who developed the theory of non-Fourier heat conduction in 1958. Although this new theory has been used in various thermal science areas, it requires considerable mathematical skills for calculating analytical solutions. The aim of this study was the identification of a newer and a simpler type of solution for the hyperbolic partial differential equations of the non-Fourier heat conduction. This constitutes the first trial in a series of planned studies. By inspecting each term included in the proposed solution, the theoretical feasibility of the solution was achieved. The new analytical solution for the non-Fourier heat conduction is a simple exponential function that is compared to the existing data for justification. Although the proposed solution partially satisfies the Cattaneo-Vernotte equation, it cannot simulate a thermal wave behavior. However, the results of this study indicate that it is possible to obtain the theoretical solution of the Cattaneo-Vernotte equation by improving the form of the proposed solution.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2007년도 정기 학술대회 논문집
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• pp.663-668
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• 2007

An enhanced first shear deformation theory for composite plate is developed. The detailed process is as follows. Firstly, the theory is formulated by modifying higher order zigzag theory. That is, the higher order theory is separated into the warping function representing the higher order terms and lower order terms. Secondly, the relationships between higher order zig-zag field and averaged first shear deformation field based on the Reissner-Mindlin's plate theory are derived. Lastly, the effective shear modulus is calculated by minimizing error between higher order energy and first order energy. Then the governing equation of FSDT is solved by substituting shear modulus into effective shear modulus. The recovery processing with the nodal unknown obtained from governing equation is performed. The accuracy of the present proposed theory is demonstrated through numerical examples. The proposed method will serve as a powerful tool in the prediction of laminated composite plate.

• 한국수학사학회지
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• 제26권5_6호
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• pp.355-370
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• 2013

Thomas Harriot has been introduced in middle school textbooks as a great mathematician who created the sign of inequality. This study is about Harriot's symbolism and the theory of equation. Harriot made symbols of mathematical concepts and operations and used the algebraic visual representation which were combinations of symbols. He also stated solving equations in numbers, canonical, and by reduction. His epoch-making inventions of algebraic equation using notation of operation and letters are similar to recent mathematical representation. This study which reveals Harriot's contribution to general and structural approach of mathematical solution shows many developments of algebra in 16th and 17th centuries from Viete to Harriot and from Harriot to Descartes.

• Structural Engineering and Mechanics
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• 제37권4호
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• pp.401-413
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• 2011

The aerodynamic stability of orthotropic tensioned membrane structures with rectangular plane is theoretically studied under the uniform ideal potential flow. The aerodynamic force acting on the membrane surface is determined by the potential flow theory in fluid mechanics and the thin airfoil theory in aerodynamics. Then, based on the large amplitude theory and the D'Alembert's principle, the interaction governing equation of wind-structure is established. Under the circumstances of single mode response, the Bubnov-Galerkin approximate method is applied to transform the complicated interaction equation into a system of second order nonlinear differential equation with constant coefficients. Through judging the stability of the system characteristic equation, the critical divergence instability wind velocity is determined. Finally, from different parametric analysis, we can conclude that it has positive significance to consider the characteristics of orthotropic and large amplitude for preventing the instability destruction of structures.