• 대한수학교육학회지:학교수학
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• 제9권1호
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• pp.141-160
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• 2007

본 연구의 목적은 대수 문장제를 해결하기 위하여 학생들이 이전지식이나 경험을 어떻게 적용하는가를 조사하고자 학생들의 풀이과정에 대한 유사성을 일련의 표시(chain of signification) 관점에서 분석하는 것이다. 이를 위하여 본 연구에서는 중학생 3명을 대상으로 사례 연구를 실시하였다. 연구 결과, 학생A나 학생C는 (반)열린 공식을 해법 원리로 생각하여 구체화하는 과정을 일련의 표시로 구성하였다. 학생A와 학생C는 문제를 읽으면서 숫자 정보와 텍스트를 기반으로 정신적 모델을 구성하였으며, 그 의미(기의)와 기록(기표) 과정을 점진적으로 구성함으로써 일련의 표시 과정을 구성하였다. 학생A의 표시과정은 숫자나 문자, 그리고 그리기가 혼합된 것이었다. 그러나 학생C와 학생B는 단지 숫자나 문자만으로 구성하였다. 특히, 학생B는 특정한 문제정보만을 근거로 그 상황을 생각하지 않고, 자신의 알고리즘을 적용하기 위하여 자신이 구성한 규칙을 적용하고자 하는 시행착오에 대한 유사성을 구성하였다.

• 대한전자공학회논문지
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• 제20권5호
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• pp.1-7
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• 1983

일반적으로 다치론리는 Modulo-M의 수 체계를 기초로 한다. 이 논문에서는 다치의 치의 요소를 서로 배타적인 상태를 나타내는 기호하여 집합의 방식으로 다치 논리를 설정하고, 기호 다치 논리극교와 그 변화를 정의하였으며, 그 성질을 정리, 증명하였다. 또, 경산외 변화에 의한 기회 다치 논리극교의 MacLaurin 전개와 Taylor 전개 방법을 제안하고 증명하였다.

• Journal of applied mathematics & informatics
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• 제33권5_6호
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• pp.545-557
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• 2015

A vague graph is a generalized structure of a fuzzy graph that gives more precision, flexibility and compatibility to a system when compared with systems that are designed using fuzzy graphs. In this paper, we define two new operation on vague graphs namely normal product and tensor product and study about the degree of a vertex in vague graphs which are obtained from two given vague graphs G₁ and G₂ using the operations cartesian product, composition, tensor product and normal product. These operations are highly utilized by computer science, geometry, algebra, number theory and operation research. In addition to the existing operations these properties will also be helpful to study large vague graph as a combination of small, vague graphs and to derive its properties from those of the smaller ones.

• 한국생활과학회지
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• 제17권1호
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• pp.35-43
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• 2008

The purpose of this study is to develop evaluation tools for young children's mathematical ability based on the content standards of NCTM and to verify the suitability of the tools. The tools consist of 5 sub-tests with 90 items, including number and operation, algebra, geometry, measurement, data analysis and probability. The tool analysis was examined with 300 three-to five-years-old children and 31 math education professionals. The results of this research are as follows : First, in order of age the passing rate increased. The gap between high and low score group reveals a statistically meaningful difference. Second, the internal consistency reliability coefficient, Cronbach ${\alpha}$, is .96. Test-retest reliability is around .90. The concurrent validity correlation between this tools and Choi Hye-Jin's test(2003) is .85. The analysis of the content validity was proved appropriately by math education professionals.

• 대한수학회논문집
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• 제35권2호
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• pp.533-546
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• 2020

Since Sheffer introduced the so-called Sheffer polynomials in 1939, the polynomials have been extensively investigated, applied and classified. In this paper, by using matrix algebra, specifically, some properties of Pascal and Wronskian matrices, we aim to present certain interesting identities involving the 2-variable truncated exponential based Sheffer polynomial sequences. Also, we use the main results to give some interesting identities involving so-called 2-variable truncated exponential based Miller-Lee type polynomials. Further, we remark that a number of different identities involving the above polynomial sequences can be derived by applying the method here to other combined generating functions.

• Kyungpook Mathematical Journal
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• 제61권2호
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• pp.223-237
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• 2021

Let n be a fixed natural number. Menger algebras of rank n can be regarded as a canonical generalization of arbitrary semigroups. This paper is concerned with studying algebraic properties of Menger algebras of rank n by first defining a special class of full n-place functions, the so-called a left translation, which possess necessary and sufficient conditions for an (n + 1)-groupoid to be a Menger algebra of rank n. The isomorphism parts begin with introducing the concept of homomorphisms, and congruences in Menger algebras of rank n. These lead us to establish a quotient structure consisting a nonempty set factored by such congruences together with an operation defined on its equivalence classes. Finally, the fundamental homomorphism theorem and isomorphism theorems for Menger algebras of rank n are given. As a consequence, our results are significant in the study of algebraic theoretical Menger algebras of rank n. Furthermore, we extend the usual notions of ordinary semigroups in a natural way.

• 대한수학회보
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• 제32권2호
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• pp.337-342
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• 1995

A semiring is a binary system $(S, +, \times)$ such that (S, +) is an Abelian monoid (identity 0), (S,x) is a monoid (identity 1), $\times$ distributes over +, 0 $\times s s \times 0 = 0$ for all s in S, and $1 \neq 0$. Usually S denotes the system and $\times$ is denoted by juxtaposition. If $(S,\times)$ is Abelian, then S is commutative. Thus all rings are semirings. Some examples of semirings which occur in combinatorics are Boolean algebra of subsets of a finite set (with addition being union and multiplication being intersection) and the nonnegative integers (with usual arithmetic). The concepts of matrix theory are defined over a semiring as over a field. Recently a number of authors have studied various problems of semiring matrix theory. In particular, Minc [4] has written an encyclopedic work on nonnegative matrices.

• 소음진동
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• 제9권2호
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• pp.340-347
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• 1999

The acoustic performance of reactive type single expansion chamber can be calculated theoretically by plane wave theory. But higher order model should be considered to widen the frequency range. Mode matching method has been developed to consider higher order modes, but very complicated algebra should be used. Munjal suggested a numerical collocation method, which can overcome the shortcomings of mode matching method, using the compatibility conditions for acoustic pressure and particle velocity at the junctions of area discontinuities. But the restriction of Munjal's method is that the ratio between the area of inlet(or outlet) pipe and that of chamber must be natural number. In this paper, the new method was suggested to overcome the shortcomings of Munjal's method. The predictions by this method was also compared with those by the finite element method and Munjal's method in order to demonstrate the accuracy of the modified method presented here.

• Korean Journal of Mathematics
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• 제32권3호
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• pp.533-544
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• 2024

Given a groupoid (X, *) and a real-valued function d : X → R, a new (derived) function Φ(X, *)(d) is defined as [Φ(X, *)(d)](x, y) := d(x * y) + d(y * x) and thus Φ(X, *) : R^X → R^X2 as well, where R is the set of real numbers. The mapping Φ(X, *) is an R-linear transformation also. Properties of groupoids (X, *), functions d : X → R, and linear transformations Φ(X, *) interact in interesting ways as explored in this paper. Because of the great number of such possible interactions the results obtained are of necessity limited. Nevertheless, interesting results are obtained. E.g., if (X, *, 0) is a groupoid such that x * y = 0 = y * x if and only if x = y, which includes the class of all d/BCK-algebras, then (X, *) is *-metrizable, i.e., Φ(X, *)(d) : X² → X is a metric on X for some d : X → R.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 1998년도 The Third Asian Fuzzy Systems Symposium
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• pp.537-542
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• 1998

Logic functions such as fuzzy switching functions and multiple-valued Kleenean functions, that are models of Kleene algebra have been studied as foundation of fuzzy logic. This paper deals with a new kinds of functions-fuzzy switching functions with constants-which have features of both the above two kinds of functions . In this paper, we propose new canonical forms for enumerating them. They are much useful to estimate simply the number of fuzzy switching functions with constants.