• Communications of the Korean Mathematical Society
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• v.18 no.4
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• pp.587-602
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• 2003

본 논문에서는 벡터값을 가지는 함수로 이루어진 벡터 변분 부등식들의 해집합사이의 관계, 미분 불가능한 볼록함수로 이루어진 벡터 볼록 최적화 문제의 해집합들과 볼록함수의 아래미분으로 표현된 벡터 변분부등식의 해집합들과의 관계, 제약집합이 볼록 함수로 구체적으로 주어질 때의 벡터 변분부등식의 해가 될 필요 충분조건, 섭동된 강 단조 벡터 변분부등식의 안정성 결과와 섭동된 벡터 강 볼록 최적화문제에의 적용에 대한 최근 연구 결과를 정리한다.

• Proceedings of the Korean Information Science Society Conference
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• 1998.10b
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• pp.588-590
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• 1998

현대 웹 기반의 시스템에 대한 개발이 활발하게 이루어지고 있으나 아직까지 등식 추론을 위한 시스템은 개발되어 있지 않다. 본 논문에서는 웹에서 동작하는 조건 등식 추론 시스템 구현에 대해서 기술하였다. 개발된 시스템은 조건 등식 추론이 가능하며, 완료 프로시저, 다양한 개서 전략, 다양한 순서와 방법등을 지원한다.

• Journal of Elementary Mathematics Education in Korea
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• v.20 no.4
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• pp.583-599
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• 2016

In this paper, aspects of equalities with monomial left-hand side presented in Korean elementary school mathematics textbooks are analyzed focusing on the component of expressions. According to this analysis, the textbooks deal with equalities with monomial left-hand side as though the students already know them, rather than to introduce and deal with them systematically. In this paper, the following four suggestions based on this analysis are proposed as conclusions. First, A-type equalities (with one kinds of calculation symbols and two or more numbers, variables, denominative numbers in the right-hans side) and B-type equalities (with two or more kinds of calculation symbols and two or more numbers, variables, denominative numbers in the right-hans side) may need to be introduced by the explicit description. Second, it is necessary to establish clearly the order of dealing with numeric expressions, expressions with ${\Box}$(blank) expression, expressions with words, expressions with ${\Box}$(variable), expressions with variables. Third, it needs to be noted that equalities with monomial left-hand side cab be used with a variety of meanings. Fourth, it is necessary to widen the range of the number constituting equalities with monomial left-hand side to the natural number 0 and as well as fractions, decimals.

• Communications of the Korean Mathematical Society
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• v.15 no.2
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• pp.197-231
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• 2000

평형문제들에서의 기본적인 정리들이 일반화 볼록공간에서 어떻게 확장되는가를 보인다. KKM 이론의 중요한 정리들 대부분이 위상벡터공간에서의 선형성을 가정하지 않아도 위상적인 성질만으로 성립한다. 이같은 정리들의 예로는 KKM정리, von Neumann의 최소최대정리와 교차정리, Nash의 평형정리, 여러 가지 부동점정리, 극대원정리, Ky Fan의 최소최대부등식, 변분부등식들, 최량근사정리, 일반화 의사평형문제들의 해의 존재정리들이 있다.

• Journal of the Korean Vacuum Society
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• v.16 no.6
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• pp.424-432
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• 2007

Luminance properties of external electrode fluorescent lamps and optical components in backlight unit (BLU) and optical transmission rates of optical sheets, are investigated for LCD-TV of 32" in diagonal with WXGA level resolution (1366$\times$768). The luminance is measured in 12-lamps and 18-lamps of BLU. The luminance uniformity preserves about 85 % in the 12-lamps backlight, while the luminance of optical components and the efficiency of backlight in the 12-lamps are lower than those in the 18-lamps backlight. When the lamp luminance in BLU having 12-lamps and 18-lamps is normalized as 100 %, the relative luminance of a diffusion plate, a diffusion sheet, a prism sheet (BEF), a polarization sheet (DBEF), has a constant value without dependence on a lamp luminance. The relative luminance of optical components in 12-lamps BLU is lower than that in 18-lamps backlight. The light transmission rate, the relative luminance of liquid crystal display panel with the luminance 100 % of backlight, is 7.14 % in the use of DBEF and BEF, 6.12 % in the use of only DBEF, and 3.21 % in the use of only BEF. Those Data obtained in this experiment for the lamps and optical components, are the design parameters for the LCD backlight.

• Journal of the Korean School Mathematics Society
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• v.12 no.2
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• pp.281-308
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• 2009

In the process of solving a linear equation, some questions had equal sign('=') relation properly, while other questions did not have equal sign('=') relation properly. Since whether students could express equal sign('=') relation properly or not is determined by questions, the direction for teaching should be instituted, and instruction and teaching should be conducted by comparing and analyzing after conducing tests on may items. Most of students who got the answer for items without the method of solving a linear equation solved the items using binomial. For questions asking to solve using the characteristic of equality, most of students solved the questions using binomial instead of using the characteristic of equality. Therefore, instruction and learning to solve equations using both the characteristic of equality and binomial have to be achieved.

• Journal of Elementary Mathematics Education in Korea
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• v.21 no.4
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• pp.643-662
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• 2017

The first appearance of the equations in elementary school mathematics is in the expression of the equal sign in the addition sentences without its definition. Most elementary school students have operational understanding of the equal sign in equations. Moreover, students' opportunities to have a clear concept of the properties of operations are limited because they are used implicitly in the textbooks. Based on this fact, it has been argued that it is necessary to introduce the properties of operations explicitly in terms of specific numbers and to deal with various types of equations for understanding a relational meaning of the equal sign. In this study, we use equations to represent the implicit properties of operations and the relational meaning of the equal sign in elementary school mathematics with respect to students' level of understanding. In addition, we give some explicit examples which show how to apply them to make efficient computations.

• The Mathematical Education
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• v.62 no.3
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• pp.341-362
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• 2023

This study analyzed student noticing in a lesson that emphasized relational understanding of equal signs for first graders from four aspects: centers of focus, focusing interactions, mathematical tasks, and nature of the mathematical activity. Specifically, the instructional factors that emphasize the relational understanding of equal signs derived from previous research were applied to a first-grade addition and subtraction unit, and then lessons emphasizing the relational understanding of equal signs were conducted. Students' noticing in this lesson was comprehensively analyzed using the focusing framework proposed in the previous study. The results showed that in real classroom contexts centers of focus is affected by the structure of the equation and the form of the task, teacher-student interactions, and normed practices. In particular, we found specific teacher-student interactions, such as emphasizing the meaning of the equals sign or using examples, that helped students recognize the equals sign relationally. We also found that students' noticing of the equation affects reasoning about equation, such as being able to reason about the equation relationally if they focuse on two quantities of the same size or the relationship between both sides. These findings have implications for teaching methods of equal sign.

• Communications of Mathematical Education
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• v.20 no.3 s.27
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• pp.373-389
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• 2006

The purpose of this study is to compare the way of proving using combinational proof with the way of proving presented in the existing math textbook in the proof of combinational equation and to classify the problem-solving into some categories using combinational proof in combinational equation. Corresponding with these, this study suggests the application of combinational equation using combinational proof and the fundamental material to develop material for advanced study.

• Journal of the Korean School Mathematics Society
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• v.10 no.4
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• pp.519-533
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• 2007

In this paper we study a equality $\frac{1}{h_a}+\frac{1}{h_b}+\frac{1}{h_c}=\frac{1}{r}$ which contains altitudes and radius of inscribed circle of triangle. We search some paths for proving the equality, and find out 9 proof method of the equality which is related with descriptive geometry, coordinate geometry, and vector geometry.