초등학교 6학년 학생들의 분수 조작 및 스킴 분석

한정이,이광호 대한수학교육학회 2017 학교수학 Vol.19 No.1

This study analyzed the 6th graders' constructions about fraction operations and schemes and figured out the relationships quantitatively between operations and schemes through the written test of 432 students. The results of this study showed that most of students could do partitioning operation well, however, there were many students who had difficulties on iterating operation. There were more students who constructed partitioning operation prior to iterating operation than the opposite. The rate of students who constructed high schemes was lower than that of students who constructed low schemes according to the hierarchy of fraction schemes. Especially, there were many students who construct partitive unit fraction scheme but not partitive fraction scheme, because they could compose unit fraction but not do iterating it. And there were the high correlations between fraction operations and schemes. Given these result, this paper suggests implications about the teaching and learning of fraction. 본 연구는 전국 초등학교 6학년 432명을 대상으로 분수 조작 능력과 분수 스킴 형성에 대해 조사하여 그 실태를 살펴보았고, 분수 조작과 스킴의 관계를 정량적으로 분석하였다. 학생들은 분할보다 반복 조작을 상대적으로 어려워하는 것으로 나타났으며, 반복보다 분할을 먼저 구성하는 학생들이 더 많았다. Steffe의 분수 위계에 따라 스킴이 높아질수록 형성률이 낮아지는 양상을 보였고, 특히, 분할 단위 분수 스킴(PUFS)은 형성되어 있지만, 단위분수를 반복하지 못해서 분할 분수 스킴(PFS)을 형성하지 못한 학생들이 많았다. 또한 분수 조작과 스킴은 서로 높은 연관성을 가지고 있는 것으로 나타났다. 본 논문은 이러한 연구 결과를 바탕으로 분수 교수·학습에 대한 시사점을 제공하고자 하였다.

부구조화 기법을 연동한 반복적인 동적 축소법 (Ⅱ)

최동수(Dongsoo Choi),김현기(Hyungi Kim),조맹효(Maenghyo Cho) 대한기계학회 2007 大韓機械學會論文集A Vol.31 No.2

An iterated improved reduced system (IIRS) procedure combined with sub-structuring scheme for nonclassically damped structural systems is presented. For dynamic analysis of such systems, complex eigenproperties are required to incorporate properly the nonclassical damping effect. In complex structural systems, the equations of motion are written in the state space form. Thus, the number of degrees of freedom of the new equations of motion and the size of the associated eigenvalue problem required to obtain the complex eigenvalues and eigenvectors are doubled. Iterated IRS method is an efficient reduction technique because the eigenproperties obtained in each iteration step improve the condensation matrix in the next iteration step. However, although this reduction technique reduces the size of problem drastically, it is not efficient to apply this technique to a single domain finite element model with degrees of freedom over several thousands. Therefore, for a practical application of the reduction method, accompanying sub-structuring scheme is necessary. In the present study, iterated IRS method combined with sub-structuring scheme for nonclssically damped structures is developed. Numerical examples demonstrate the convergence and the efficiency of a newly developed scheme.

AN ITERATIVE SCHEME FOR EQUILIBRIUM PROBLEMS AND FIXED POINT PROBLEMS OF ASYMPTOTICALLY k-STRICT PSEUDO-CONTRACTIVE MAPPINGS

Wang, Ziming,Su, Yongfu Korean Mathematical Society 2010 대한수학회논문집 Vol.25 No.1

In this paper, we propose an iterative scheme for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of an asymptotically k-strict pseudo-contractive mapping in the setting of real Hilbert spaces. We establish some weak and strong convergence theorems of the sequences generated by our proposed scheme. Our results are more general than the known results which are given by many authors. In particular, necessary and sufficient conditions for strong convergence of our iterative scheme are obtained.

Satellite Attitude Control with a Modified Iterative Learning Law for the Decrease in the Effectiveness of the Actuator

HoJin Lee,Youdan Kim,Hee Seob Kim 한국항공우주학회 2010 International Journal of Aeronautical and Space Sc Vol.11 No.2

A fault tolerant satellite attitude control scheme with a modified iterative learning law is proposed for dealing with actuator faults. The actuator fault is modeled to reflect the degradation of actuation effectiveness, and the solar arrayinduced disturbance is considered as an external disturbance. To estimate the magnitudes of the actuator fault and the external disturbance, a modified iterative learning law using only the information associated with the state error is applied. Stability analysis is performed to obtain the gain matrices of the modified iterative learning law using the Lyapunov theorem. The proposed fault tolerant control scheme is applied to the rest-to-rest maneuver of a large satellite system, and numerical simulations are performed to verify the performance of the proposed scheme.

Satellite Attitude Control with a Modified Iterative Learning Law for the Decrease in the Effectiveness of the Actuator

Lee, Ho-Jin,Kim, You-Dan,Kim, Hee-Seob The Korean Society for Aeronautical and Space Scie 2010 International Journal of Aeronautical and Space Sc Vol.11 No.2

A fault tolerant satellite attitude control scheme with a modified iterative learning law is proposed for dealing with actuator faults. The actuator fault is modeled to reflect the degradation of actuation effectiveness, and the solar array-induced disturbance is considered as an external disturbance. To estimate the magnitudes of the actuator fault and the external disturbance, a modified iterative learning law using only the information associated with the state error is applied. Stability analysis is performed to obtain the gain matrices of the modified iterative learning law using the Lyapunov theorem. The proposed fault tolerant control scheme is applied to the rest-to-rest maneuver of a large satellite system, and numerical simulations are performed to verify the performance of the proposed scheme.

비비례 감쇠 구조시스템에 대한 효율적인 동적 축소법

최동수(Dongsoo Choi),조맹효(Maenghyo Cho) 대한기계학회 2006 대한기계학회 춘추학술대회 Vol.2006 No.11

An iterated improved reduced system (IIRS) procedure combined with sub-structuring scheme for nonclassically damped structural systems is presented. For a dynamic analysis of such systems, complex eigenproperties are required to incorporate properly the nonclassical damping effect. Iterated IRS method is an efficient reduction technique because the eigenproperties obtained in an iteration step are used to improve the condensation matrix in the following steps. However, although this reduction technique reduce the size of problem drastically, it is not efficient to apply to the finite element model with the degrees of freedom over several thousands. Therefore, for the practical application of the reduction method, accompaning substructuring scheme is necessary. Some numerical examples verify the convergence and the efficiency of the newly developed scheme.

반복적인 동적 축소법과 대형 구조물 해석을 위한 부구조화 기법의 적용

최동수(Dongsoo Choi),조맹효(Meanghyo Cho) 대한기계학회 2006 대한기계학회 춘추학술대회 Vol.2006 No.6

This work presents an iterative dynamic condensation procedure combined with sub-structuring scheme for large structures. Iterative dynamic condensation techniques are usually more efficient than others because the dynamic condensation matrix is updated repeatedly until the desired convergent values are obtained. However, using these methods simply for large structures causes very expensive computational cost and even makes analyses impossible because of the limited computer storage. Therefore, the application of subtructuring scheme is necessary to calculate eigenproperties for large structures. Because the large structures are subdivided into several (or more) sub-domains, the construction of dynamic condensation matrix does not need much computation cost in every iteration. This makes the present method much more efficient to compute the eigenpairs both in lower and higher modes. Numerical examples are applied to demonstrate the features of this method.

Iterative Learning Control for a Class of Mixed Hyperbolic-parabolic Distributed Parameter Systems

Qin Fu,Wei-Guo Gu,Pan-Pan Gu,Jian-Rong Wu 제어·로봇·시스템학회 2016 International Journal of Control, Automation, and Vol.14 No.6

This paper deals with the problem of iterative learning control algorithm for a class of mixed distributedparameter systems. Here, the considered distributed parameter systems are composed of mixed hyperbolicparabolicpartial differential equations. The domain of the system is divided into two parts in which the system ishyperbolic and parabolic, respectively, with transmission conditions at the interface. According to the characteristicsof the systems, iterative learning control laws are proposed for such mixed hyperbolic-parabolic distributedparameter systems based on P-type learning scheme. Using the contraction mapping method, it is shown that thescheme can guarantee the output tracking errors on L2 space converge along the iteration axis. A simulation exampleillustrates the effectiveness of the proposed method.

Decentralized Iterative Learning Control for Large-Scale Interconnected Linear Systems with Fixed Initial Shifts

Qin Fu,Pan-Pan Gu,Jian-Rong Wu 제어·로봇·시스템학회 2017 International Journal of Control, Automation, and Vol.15 No.5

This paper deals with the problem of iterative learning control for large-scale interconnected linear systemsin the presence of fixed initial shifts. According to the characteristics of the systems, iterative learning controllaws are proposed for such large-scale interconnected linear systems based on the PD-type learning schemes. Theproposed controller of each subsystem only relies on local output variables without any information exchanges withother subsystems. Using the contraction mapping method, we show that the schemes can guarantee the output ofthe system converges uniformly to the corresponding output limiting trajectory over the whole time interval alongthe iteration axis. Simulation examples illustrate the effectiveness of the proposed method.

새로운 반복이완법에 의한 선소의 정합

강창순,배종갑 동의공업대학 2000 論文集 Vol.26 No.1

The line segment matching problem in stereo vision is solved by a new iteration scheme. A match function which directly reflects the requirements of the epipolar and disparity constraints is proposed for line segment matching. The information contained in the match function can be used to determine line segment correspondences indirectly. After a match network is established according to the match function values, a new iteration algorithm is employed to tune the strengths of the match links in the match network so that the match network can converge to a stable state. No explicit compatibility coefficient need be defined for computing the support function values in the iterations, so that computation time can be saved, compared with conventional relation matching techniques. The inherent anti-symmetric characteristic of relaxation matching for the correspondence problem is also avoided naturally. The experimental results show that the proposed iteration scheme is effective and suitable for various stereo images.