• 대한수학회논문집
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• 제27권4호
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• pp.721-732
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• 2012

The principal aim of the paper is to investigate new integral expression $${\int}_0^{\infty}x^{s+1}e^{-{\sigma}x^2}L_m^{(\gamma,\delta)}\;({\zeta};{\sigma}x^2)\;L_n^{(\alpha,\beta)}\;({\xi};{\sigma}x^2)\;J_s\;(xy)\;dx$$, where $y$ is a positive real number; $\sigma$, $\zeta$ and $\xi$ are complex numbers with positive real parts; $s$, $\alpha$, $\beta$, $\gamma$ and $\delta$ are complex numbers whose real parts are greater than -1; $J_n(x)$ is Bessel function and $L_n^{(\alpha,\beta)}$ (${\gamma};x$) is generalized Laguerre polynomials. Some integral formulas have been obtained. The Maple implementation has also been examined.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1997년도 한국자동제어학술회의논문집; 한국전력공사 서울연수원; 17-18 Oct. 1997
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• pp.175-178
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• 1997

This study was carried out to obtain an analytical expression for the specifications of the Stewart Platform that minimize the maximum force acting on the hydraulic cylinder. The position and orientation of the platform were calculated by means of the inverse kinematic analysis. The maximum force to be exerted on a cylinder was calculated using the Newton's second law for the case when the platform is moved along a horizontal axis with 0.6 g, the maximum translational acceleration possible. This paper suggests a mathematical model to minimize the maximum actuating force using radius and angle ratios as design variables. Finally, a fuzzy set for the minimum actuating force is proposed for this dynamic optimal design problem.

• 한국경영과학회:학술대회논문집
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• 대한산업공학회/한국경영과학회 2004년도 춘계공동학술대회 논문집
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• pp.742-745
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• 2004

Most of options pricing theory including Black and Scholes continuous model and Cox, Ross, and Rubinstein(CRR)'s binomial lattice model were developed based on the notion that continually revised risk-free hedges involving options and stock should earn the risk-free interest rate. This notion is valid with the assumption that the investor's attitude toward risk is neutral. In reality, this assumption may be frequently violated. Therefore, Hodder, Mello, and Sick proposed the way to value real options using the risk-adjusted interest rate. However, they did not show how to derive the mathematical expression for it. In this paper, we will clearly present how to obtain the mathematical expression for the risk-adjusted interest rate for real options and demonstrate two numerical examples to show its applicability.

• 대한수학회지
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• 제40권3호
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• pp.461-486
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• 2003

It is known that the CR geometries of Levi non-degen-erate hypersurfaces in $\C^n$ and of the elliptic or hyperbolic CR submanifolds of codimension two in $\C^4$ share many common features. In this paper, a special class of normalized coordinates is introduced for any CR manifold M which is one of the above three kinds and it is shown that the explicit expression in these coordinates of an isotropy automorphism $f{\in}Aut(M)_o {\subset}Aut(M),\;o{\in}M$, is equal to the expression of a corresponding element of the automorphism group of the homogeneous model. As an application of this property, an extension theorem for CR maps is obtained.

• 한국수학교육학회지시리즈A:수학교육
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• 제46권2호
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• pp.141-153
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• 2007

The purpose of the study is to analyze children's proportional reasoning and problem solving in proportional problems with/without iconic representations. Proportional problems include 3 tasks such as (a) without any picture, (b) with simple picture, and (c) with/without iconic representation. As a result, children didn't show any significant differences in two tasks such as (a) and (b). However, children showed better proportional reasoning with iconic representation. In addition, 'build-up expression' strategy was used mostly in solving problems and 'additive strategy' was shown as an error which students didn't make an appropriate proportional relation expression and they made a wrong additive strategy.

• East Asian mathematical journal
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• 제35권4호
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• pp.451-465
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• 2019

Textbooks are official materials so that these are the most frequently used teaching materials in school. The teacher constructs the lesson based on the contents of the textbook to achieve the learning goal. Thus, textbooks play an important role because the quality of the contents in textbooks affects the cognitive level of students. This study investigates the cognitive domain based on Bloom's Taxonomy of Educational Objectives(knowledge, understanding, application, analysis, synthesis and evaluation) of 'Values and Expression' in the mathematics textbook of the first grade of middle school reflecting the 2015 revised mathematics curriculum. We also looked at cognitive levels based on Bloom's Taxonomy of Educational Objectives. As a result, it was found that understanding was dominant in 'Values and Expression'. Also, although the problem of requiring a higher level of cognition is increasing as the unit finishes, there are still a high percentage of low level of problems.

• Carbon letters
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• 제14권1호
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• pp.14-21
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• 2013

Physically and chemically activated carbons (ACs) exhibited high adsorption capacities for organic and inorganic pollutants compared with other adsorbents due to their expanded surface areas and wide pore volume distribution. In this work, seven steam-ACs with different burn-off have been prepared from cotton stalks. The textural properties of these sorbents were determined using nitrogen adsorption at $-196^{\circ}C$. The chemistry of the surface of the present sorbents was characterized by determining the surface functional C-O groups using Fourier transform infrared spectroscopy, surface pH, $pH_{pzc}$, and Boehm's acid-base neutralization method. The textural properties and the morphology of the sorbent surface depend on the percentage of burn-off. The surface acidity and surface basicity are related to the burn-off percentage. A theoretical model was developed to find a mathematical expression that relates the % burn-off to ash content, surface area, and mean pore radius. Also, the chemistry of the carbon surface is related to the % burn-off. A mathematical expression was proposed where % burn-off was taken as an independent factor and the other variable as a dependent factor. This expression allows the choice of the value of % burn-off with required steam-AC properties.

• 디지털산업정보학회논문지
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• 제10권4호
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• pp.29-35
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• 2014

The formula contains up between the text and the structural information, as well as their mathematical symbols. Research on-line or off-line recognition formula is underway actively used in various fields, and various forms of the equation are implemented recognition system. Although many documents are included in the various formulas, it is not easy to enter a formula into the computer. Recognition of the expression is divided into two processes of symbol recognition and structural analysis. After analyzing the location information of each character is specified to recognize the effective area after each symbol, and to the structure analysis based on the proximity between the characters is recognized as an independent single formula. Furthermore, analyzing the relationship between the front and back each time a combination of the position relationship between each symbol, and then to add the symbol which was able to easily update the structure of the entire formula. In this paper, by using a scanner to scan the book formula was used to interpret the meaning of the recognized symbol has a relative size and location information of the expression symbol. An algorithm to remove the formulas for calculation of the number of formula is present at the same time is proposed. Using the proposed algorithms to scan the books in the formula in order to evaluate the performance verification as 100% separation and showed the recognition rate equation.

• 한국학교수학회논문집
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• 제24권3호
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• pp.283-308
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• 2021

본 연구는 한국과 싱가포르의 중학교 1학년 교과서의 통계영역에 제시된 과제를 수학적 모델링 관점에서 비교·분석함으로써 두 나라의 학생들이 각각 접할 학습 내용과 학습 경험의 기회를 확인하고자 하였다. 또한 이를 바탕으로 통계영역의 교과서 개발 및 보완 측면에서 시사점을 찾아보고자 하였다. 교과서 과제는 수학적 모델링 과정 반영, 데이터 제공 유형, 표현 형식, 문제 상황 맥락, 수학적 활동의 5가지 측면으로 분석하였다. 분석 결과, 한국과 싱가포르 교과서 모두 수학적 결론을 구하는 과제와 과제 해결에 필요한 데이터만 제공되는 과제, 표나 그림으로 표현되는 과제의 비중이 가장 높았다. 한국과 싱가포르 교과서에 반영된 실세계 맥락과 수학적 활동의 경우는 서로 비중에 차이가 있었다. 이를 바탕으로 향후 수학적 모델링 활동을 지원하기 위한 교과서 과제 개발에 대한 다음과 같은 시사점을 도출하였다. 수학적 모델링 과정의 균형 있는 경험 제공과 다양한 표현 형식의 과제를 제시함으로써 학생들의 인지적 수준을 높이며, 의미 있는 수학화 과정을 경험할 수 있는 기회의 확대가 필요하다. 또한, 수학적 모델링 활동에 대한 학생들의 흥미 또는 학습동기를 위해 맥락적 현실성이 높은 과제를 제시할 필요가 있다.

• 한국멀티미디어학회논문지
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• 제17권8호
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• pp.1025-1032
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• 2014

Until now, there were few supports on reading the mathematical expressions except text based expressions, so it is important to provide the reading of the mathematical expressions. Also, there are various of obstacles for people who are not visually impaired when reading the mathematical expressions such as the situation of presbyopia, reading the mathematical expressions in the vehicles, and so on. Therefore, supports for people to read mathematical expressions in various situations are needed. In the previous research, the main goal was to transform the mathematical expressions into Korean text based on Content MathML. In this paper, we expanded the range of the research from a reading disabilities to people who are not reading disabilities. We tested appropriacy of the rules we made to convert the MathML based expressions into speech and defined 3 math-to-speech rules in korean based on levels. We implemented the mathematical expressions by using 3 math-to-speech rules. We took comprehension test to find out whether our math to speech rules are well-defined or not.