• 대한수학교육학회지:수학교육학연구
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• 제12권3호
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• pp.389-408
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• 2002

This paper is based on a teaching experiment research conducted in a differential equations course at Ewha Womans University. The purpose of this paper lies in seeking a new direction in the teaching and learning of college mathematics by applying RME's theoretical essence to the teaching of differential equations. For this purpose, the emergent procedure had to be carefully considered before to analyzing the existing problems in teaching differential equations and alternative access to reformed differential equations. Methods of developmental research, ideas concerning teaching procedure and instructional design are offered. This research demonstrates that a deeper understanding of differential equations by students can be achieved with the instructional design which reflects the RME theory.

• 한국수학사학회지
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• 제29권6호
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• pp.317-324
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• 2016

Since Jiuzhang Suanshu, mathematical structures in the traditional East Asian mathematics have been revealed by practical problems. Since then, polynomial equations are mostly the type of $p(x)=a_0$ where p(x) has no constant term and $a_0$ is a positive number. This restriction for the polynomial equations hinders the systematic development of theory of equations. Since tianyuanshu (天元術) was introduced in the 11th century, the polynomial equations took the form of p(x) = 0, but it was not universally adopted. In the mean time, East Asian mathematicians were occupied by kaifangfa so that the concept of zeros of polynomials was not materialized. We also show that Suanxue Qimeng inflicted distinct developments of the theory of equations in three countries of East Asia.

• Journal of Biosystems Engineering
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• 제23권4호
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• pp.335-342
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• 1998

The objectives of this study were to evaluate respiration characteristics and develop empirical respiratory rate equations for short gain rough rice. The carbon dioxide concentrations generated from mush rice at four level temperatures(10, 20, 30, 4$0^{\circ}C$) and 4 level moisture contents(17.2, 21.5, 25.9, 31.6％, d.b.) were measured by gas chromatography. The respiratory rates' increased exponentially with gain temperature and also with moisture content The relationship between respiratory rate and gain temperature fitted the Arrehenius' and Core's equations very well. Two empirical respiratory rate equations were presented as a function of gain temperature and moisture content. The values of determination coefficient for the developed respiratory rate equations were 0.999, and the result of t-test showed that there were no significant differences between predicted and measured respiratory rates on significance level of 1%. Therefore, it appeared that respiratory rates predicted by the respiratory rate equations agreed well with measured values. An equation for predicting dry matter losses of rough rice during storage was presented by modifying the respiratory rate equations based on chemical reaction of decomposition of carbohydrate.

• Journal of Mechanical Science and Technology
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• 제14권2호
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• pp.159-167
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• 2000

A computational method for the dynamic analysis of a constrained mechanical system is presented in this paper. The partial velocity matrix, which is the null space of the Jacobian of the constraint equations, is used as the key ingredient for the derivation of reduced equations of motion. The acceleration constraint equations are solved simultaneously with the equations of motion. Thus, the total number of equations to be integrated is equivalent to that of the pseudo generalized coordinates, which denote all the variables employed to describe the configuration of the system of concern. Two well-known conventional methods are briefly introduced and compared with the present method. Three numerical examples are solved to demonstrate the solution accuracy, the computational efficiency, and the numerical stability of the present method.

• Journal of applied mathematics & informatics
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• 제29권1_2호
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• pp.145-159
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• 2011

The numerical solution to the linear and nonlinear and linear system of Fredholm and Volterra integral equations of the second kind are investigated. We have used crooked lines which includ the nodes specified by modified rationalized Haar functions. This method differs from using nominal Haar or Walsh wavelets. The accuracy of the solution is improved and the simplicity of the method of using nominal Haar functions is preserved. In this paper, the crooked lines with unknown coefficients under the specified conditions change the system of integral equations to a system of equations. By solving this system the unknowns are obtained and the crooked lines are determined. Finally, error analysis of the procedure are considered and this procedure is applied to the numerical examples, which illustrate the accuracy and simplicity of this method in comparison with the methods proposed by these authors.

• 한국콘크리트학회:학술대회논문집
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• 한국콘크리트학회 2005년도 봄학술 발표회 논문집(I)
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• pp.443-446
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• 2005

The shear strength equations of the joint with RC column and steel beam are used the proposed equations of ASCE, Kanno and AIJ but there are not applied variable joint details. Until now the variable experimental studies are practiced but the studies of predicted shear strength equation are not integrated and only the applicable equations to each case are proposed. The purpose of this study is statistical analysis for the proposed equations applied existing experiments. The proposed equations are ASCE, Kanno, M-Kanno, AIJ and M-AIJ. The 47 of shear failure experiments are used in this study The consequence is that the Kanno's equation is very analogized with the experimental result but ASCE equation underestimates about 42$\%$. AIJ and M-AIJ are not proper equations for estimating the shear strength of RCS joint.

• 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.

• 한국해안해양공학회지
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• 제8권1호
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• pp.52-60
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• 1996

소류사 이동량 산정에 사용되는 여러 종류의 산정식들을 살펴보았다. 기존 산정식의 수식에 내포된 의미와 수식 전개과정 등을 종합적으로 검토하고 관측자료와의 비교로부터 각 산정식의 문제점을 파악하고자 하였다. 기존 산정식들의 종합적인 검토에 기초하여 개선방법을 제안하였으며, 보다 광범위하게 합리적으로 적용할 수 있는 여러 종류의 소류사량 산정식을 개발하였다. 각 형태의 산정식들을 Brownlie (1985)가 수집한 관측자료와 대비하여 산정식들에 도입된 경험 계수들을 조정하여 결정하였으며, 최종적으로 개선된 소류사량 산정식들을 관측자료와 대비하여 불일치률의 범위에 대하여 검토하였다.

• Structural Engineering and Mechanics
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• 제27권3호
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• pp.333-345
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• 2007

In this study, the nonlinear vibrations of stepped beams having different boundary conditions were investigated. The equations of motions were obtained using Hamilton's principle and made non dimensional. The stretching effect induced non-linear terms to the equations. Forcing and damping terms were also included in the equations. The dimensionless equations were solved for six different set of boundary conditions. A perturbation method was applied to the equations of motions. The first terms of the perturbation series lead to the linear problem. Natural frequencies for the linear problem were calculated exactly for different boundary conditions. Second order non-linear terms of the perturbation series behave as corrections to the linear problem. Amplitude and phase modulation equations were obtained. Non-linear free and forced vibrations were investigated in detail. The effects of the position and magnitude of the step, as well as effects of different boundary conditions on the vibrations, were determined.

• Nonlinear Functional Analysis and Applications
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• 제28권1호
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• pp.57-79
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• 2023

We investigate the existence and uniform attractivity of solutions of a class of functional integral equations which contain a number of classical nonlinear integral equations as special cases. Using the technique of measures of noncompactness and a fixed point theorem of Darbo type we prove the existence of solutions of these equations in the Banach space of continuous and bounded functions on the nonnegative real half axis. Our results extend and improve some known results in the recent literature. An example illustrating the main result is presented in the last section.