• 대한수학교육학회지:수학교육학연구
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• 제19권1호
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• pp.123-142
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• 2009

운동학 맥락은 미적분 학습에서 미적분의 형식적인 내용의 직관적인 이해의 원천으로 간주된다. 속도 그래프 아래의 넓이와 이동 거리 관계는 적분 영역에서 다루는 운동학적 맥락의 토대이며, 미적분의 기본정리가 역사적으로 발달한 맥락이다. 본 연구는 속도 그래프 아래의 넓이와 거리 계산 사이의 관계를 통해서 미적분의 기본정리를 조명하고, 이를 통해서 교과서 및 학생들의 이해에서 나타나는 문제점을 분석하였다. 그리고 이상의 논의 결과를 종합하여 미적분의 기본정리에 대한 교육적 시사점을 제안하였다.

• 턱관절균형의학회지
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• 제2권1호
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• pp.13-16
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• 2012

Objectives: The quadrant theorem is a theorem proposed by C. M. Guzay in the field of functional, holistic dentistry. There are not much of scientific literature on the quadrant theorem. This study briefly reviewed basic concepts of quadrant theorem. Methods: A publication by Guzay and research articles were searched and reviewed. The quadrant theorem is depicted as a series of illustrations and accompanied explanations. Results: The primary concept of the quadrant theorem was presented in 1952. Based on geometric biophysics of the occlusion and related anatomical functions, physiological pivotal axis of the mandible is analyzed to occurs at the dens (the sub-atlas area). Composite muscular activity links the mandibular posture with C1-C2, which is then linked with the spinal posture. Twenty illustrations are progressively presented on the physiognomy, occlusion, and analysis of anatomical functions. The balanced distribution of the forces gives the durability of the functions in life. Conclusions: The quadrant theorem provides a functional linkage between the mandibular posture and the upper cervical vertebrae.

• 대한수학회논문집
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• 제34권3호
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• pp.841-854
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• 2019

In this article, a subclass of univalent harmonic mapping is introduced by restricting its analytic part to lie in the class $S^{\delta}[{\alpha}]$, $0{\leq}{\alpha}<1$, $-{\infty}<{\delta}<{\infty}$ which has been introduced and studied by Kumar [17] (see also [20], [21], [22], [23]). Coefficient estimations, growth and distortion properties, area theorem and covering estimates of functions in the newly defined class have been established. Furthermore, we also found bound for the Bloch's constant for all functions in that family.

• 대한수학교육학회지:학교수학
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• 제4권3호
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• pp.347-360
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• 2002

This study analyzed the mathematical and didactical contexts of the Euclid's proof about Pythagorean theorem and compared with the teaching methods about Pythagorean theorem in school mathematics. Euclid's proof about Pythagorean theorem which does not use the algebraic methods provide students with the spatial intuition and the geometric thinking in school mathematics. Furthermore, it relates to various mathematical concepts including the cosine rule, the rotation, and the transfor-mation which preserve the area, and so forth. Visual demonstrations can help students analyze and explain mathematical relationship. Compared with Euclid's proof, Algebraic proof about Pythagorean theorem is very simple and it supplies the typical example which can give the relationship between algebraic and geometric representation. However since it does not include various spatial contexts, it forbid many students to understand Pythagorean theorem intuitively. Since both approaches have positive and negative aspects, reciprocal complementary role is required in pedagogical aspects.

• 한국의류학회지
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• 제27권6호
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• pp.665-674
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• 2003

The purpose of this study was to develop a grading increment at armhole area by apparel CAD(Computer Aided Design) system. In developing a grading increment at armhole area, we analyzed ease values of armhole area in bodice and sleeve by manual drafting patterns of five sizes. We suggested grading increments applied Pythagorean theorem to development the grading increment of the armhole of sleeve. The results and discussions of this study were as follows: 1. In drafting each size, the ease values were not identical. It was difficult to draft perfectly the same armhole line shape between sizes. 2. According to our developed grading increments applied Pythagorean theorem, the ease values were identical between sizes and difference of the armhole length between sizes was also identical. 3. The grading formulas were made out for apparel CAD system. Once grading increment or formula is set in the computer, it can be easily altered to various clothing items at any time. The efficiency of grading work will be also improved and grading time will be reduced.

• Structural Engineering and Mechanics
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• 제80권5호
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• pp.585-594
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• 2021

Ductility is very important parameter in seismic design of RC members such as beams where it allows RC beams to dissipate the seismic energy. In this field, the curvature ductility has taken a large part of interest compared to the deflection ductility. For this reason, the present paper aims to propose a general formula for predicting the deflection ductility factor of RC beams under mid-span load. Firstly, the moment area theorem is used to develop a model in order to calculate the yield and the ultimate deflections; then this model is validated by using some results extracted from previous researches. Secondly, a general formula of deflection ductility factor is written based on the developed deflection expressions. The new formula is depended on curvature ductility factor, beam length, and plastic hinge length. To facilitate the use of this formula, a parametric study on the curvature ductility factor is conducted in order to write it in simple manner without the need for curvature calculations. Therefore, the deflection ductility factor can be directly calculated based on beam length, plastic hinge length, concrete strength, reinforcement ratios, and yield strength of steel reinforcement. Finally, the new formula of deflection ductility factor is compared with the model previously developed based on the moment area theorem. The results show the good performance of the new formula.

• ETRI Journal
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• 제35권4호
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• pp.644-654
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• 2013

In this paper, a signal detection scheme for cognitive radio (CR) based on the Bussgang theorem is proposed. The proposed scheme calculates the statistical difference between Gaussian noise and the primary user signal by applying the Bussgang theorem to the received signal. Therefore, the proposed scheme overcomes the noise uncertainty and gives scalable complexity according to the zero-memory nonlinear function for a mobile device. We also present the theoretical analysis on the detection threshold and the detection performance in the additive white Gaussian noise channel. The proposed detection scheme is evaluated by computer simulations based on the IEEE 802.22 standard for the wireless regional area network. Our results show that the proposed scheme is robust to the noise uncertainty and works well in a very low signal-to-noise ratio.

• Bulletin of the Korean Chemical Society
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• 제33권9호
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• pp.3039-3042
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• 2012

Pressure tensors at the planar surface of liquid-vapor argon are evaluated from the virial theorem, Irving-Kirkwood, and Harasima versions using a test-area molecular dynamics simulation method through a Lennard-Jones intermolecular potential at two temperatures. We found that the normal and transverse components of the pressure tensor, $p_N(z)$ and $p_T(z)$, obtained from the virial theorem and Harasima version are essentially the same. The normal component of the pressure tensor from Irving-Kirkwood version, $p_N^{IK}(z)$, is shown to be a nearly constant at the lower temperature, independent of z, as agreed in a previous study, but not for $p_N^H$(z), while the transverse components, $p_T^{IK}(z)$ and $p_T^H(z)$, are almost the same. The values of surface tension for both versions computed from $p_N(z)-p_T(z)$ are also the same and are fully consistent with the experimental data.

• 한국수학사학회지
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• 제31권6호
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• pp.315-337
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• 2018

Pythagorean thoerem exists in several equivalent forms in the Euclidean plane, that is, the Hilbert plane which in addition satisfies the parallel axiom. In this article, we investigate the truthness and mutual relationships of those propositions in various non-Hilbert planes which satisfy the parallel axiom and all the Hilbert axioms except the SAS axiom.

• Nonlinear Functional Analysis and Applications
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• 제27권3호
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• pp.641-648
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• 2022

Fixed point theory has been a flourishing area of mathematical research for decades, because of its many diverse applications. In this paper, we present a fixed point theorem for s - 𝜌-contractive type multi-valued mappings in modular spaces which will generalize some old results.