• 대한수학교육학회지:수학교육학연구
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• 제12권2호
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• pp.229-246
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• 2002

In this paper, we start with the question "what is algebraic thinking\ulcorner". The problem is that the algebraic thinking is not exactly defined. We consider algebraic thinking from the various perspectives. But in the discussion relating to the definition of algebraic thinking, we verify that there is the algebraic notations in the core of algebraic thinking. So we device algebraic notations into the six categories, and investigate these examples from the school mathematics. In order to investigate this relation of algebraic thinking and algebraic notations, we present 'the algebraic thinking process analysis model' from Frege' idea. In this model, there are three components of algebraic notations which interplays; sense, expression, denotapion. Thus many difficulties of algebraic thinking can be explained by this model. We suppose that the difficulty in the algebraic thinking may be caused by the discord of these three components. And through the transformation of conceptual frame, we can explain the dynamics of algebraic thinking. Also, we present examples which show these difficulties and dynamics of algebraic thinking. As a result of these analysis, we conclude that algebraic thinking can be explained through the semiotic aspects of algebraic notations.

• 정보보호학회논문지
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• 제16권1호
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• pp.65-70
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• 2006

Summation generator와 같이 메모리를 가지는 combiner 모델에 대해 대수적 공격이 적용 가능함은 잘 알려져 있다. [1.8] 메모리를 가지는 combiner 모델에 대하여 대수적 공격을 적용하기 위해서는 대수적 방정식 수립이 필요한데, 현재까지의 모든 결과는 2비트 이상의 연속적인 출력 키수열을 필요로 하였다 (1,4,8). 본 논문에서는 Summation generate에 대한 대수적 방정식을 1비트 키수열만으로 구성할 수 있음을 보인다. 또한 ISG 알고리즘 [9]에 대해서도 1비트 키수열만을 이용한 방정식 구성이 가능함을 보인다. 이를 이용하여, summation generator 및 ISG 여러 개를 하나의 부울함수로 결합한 형태의 키수열 발생기에 대해서도 대수적 공격이 가능함을 보인다.

• 대한수학회보
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• 제54권1호
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• pp.299-318
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• 2017

Sextic moment problems with an infinite algebraic variety are still widely open. We study the problem with a single cubic column relation associated to 3 parallel lines in which the variety is infinite. It turns out that this specific column relation has a strong connection with moment problems that have a symmetric algebraic variety. We present more concrete solutions to some sextic moment problems with a symmetric variety.

• 정보보호학회논문지
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• 제14권1호
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• pp.71-77
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• 2004

n개의 LFSR과 l 비트의 메모리를 이용하는 combiner에 대하여 [n(l+1)/2] 차 이하의 대수적 관계식이 존재하는 것이 이론적으로 밝혀졌다. 본 논문에서는 k 비트의 메모리를 사용하는 2$^{k}$ 개의 LFSR로 이루어진 summation Generator는 연속된 k+1개의 출력 값을 이용하여 초기 치에 관한 2$^{k}$ 차 이하의 대수적 관계식을 만들 수 있음을 보인다. 일반적으로 n개의 LFSR로 이루어진 summation Generator는 연속된 [lo $g_2$n]＋1개의 출력 값을 이용하여 초기 치에 관한 2$^{[lo[g_2]n}$ 차 이하의 대수적 관계식을 만들 수 있다.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제16권4호
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• pp.217-232
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• 2012

While many studies on early algebra have been conducted, there have been only a few studies on the operation sense as the fundamental element of algebraic thinking, especially the fraction operation sense. This study explored the dimensions of fraction operation sense and then investigated students' fraction operation sense. A total of 183 of sixth graders were surveyed and 5 students who showed high operation sense were clinically interviewed in order to analyze their algebraic thinking in detail. The results showed that students had a tendency to use direct calculation or employ inappropriate operation sense rather than to use the structure of operation or the relation between operations on the basis of algebraic thinking. This study implies that explicit instruction on early algebra is necessary from the elementary school years.

• East Asian mathematical journal
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• 제29권4호
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• pp.355-392
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• 2013

Generally school algebra is to start with introducing variables and algebraic expressions, which have major cognitive obstacles to students in the transfer from arithmetic to algebra. But the recent studies in the teaching school algebra argue the algebraic thinking from an early algebraic point of view. We compare the Korean elementary mathematics textbooks with Americans from this perspective. First, we discuss the history of school algebra in the school curriculum. And Second, we investigate the recent studies in relation to early algebra. We clarify the goals of this study(the importance of early algebra in the elementary school) through these discussions. Next we examine closely the number sense in the arithmetic and the symbol sense in the algebra. And we conclude that the operation sense can connect these senses within early algebra using the algebraic thinking. Finally, we compare the elementary mathematics books between Korean and American according to the components of the operation sense. In this comparative study, we identify a possibility of teaching algebraic thinking in the elementary mathematics and early algebra can be introduced to the elementary mathematics textbooks from aspects of the operation sense.

• 충청수학회지
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• 제25권3호
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• pp.455-462
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• 2012

The purpose of this paper is to show that the coset bound can be used to prove the floor bound. Our proof provides a natural relation between the floor bound and the order bound.

• 한국소성가공학회:학술대회논문집
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• 한국소성가공학회 1997년도 춘계학술대회논문집
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• pp.65-68
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• 1997

Vickers hardness is defined as indenting force per unit area indented by a pyramid-shaped diamond at the hardness test. It is well known that Vickers hardness has a direct relation with the flow stress of the strain-hardened material. This relation was theoretically investigated and the result was summerized in a form of algebraic equation in the last paper. In the present paper and experimental validation of this theoretical relation is given along with mathematical formulas for conversion of Vickers hardness into the flow stress in the strain-hardened material for practical use.

• 대한수학회보
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• 제50권2호
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• pp.507-524
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• 2013

The notion of $n$-ary algebraic hyperstructures is a generalization of ordinary algebraic hyperstructures. In this paper, we associate an n-ary hypergroupoid (H, $f$) with an ($n+1$)-ary relation ${\rho}_{n+1}$ defined on a non-empty set H. Then, we obtain some basic results in this respect. In particular, we investigate when it is an $n$-ary $H_v$-group, an $n$-ary hypergroup or a join $n$-ary space.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1993년도 한국자동제어학술회의논문집(국제학술편); Seoul National University, Seoul; 20-22 Oct. 1993
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• pp.562-565
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• 1993

It is well known that H$_{\infty}$ control problem involves solving an algebraic Riccati equation which includes a pair of parameters (.gamma., .epsilon.). Focusing on .epsilon. the maximum of .epsilon.. We discuss in this paper about the properties between the H$_{\infty}$ norm of a trnsfer function matrix and the parameters(.gamma., .epsilon.). We can change the algebraic relattion between .gamma. and .epsilon. by the similarity transformation of a considered system and we can find a proper transformation to get a simple quadratic algebraic equation between .gamma. and .epsilon.. This relation provide the H$_{\infty}$ norm of a transfer function.on.