• School Mathematics
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• v.9 no.1
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• pp.141-160
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• 2007

The purpose of this paper was to evaluate how students apply prior knowledge or experience in solving algebra word problems from the chain of signification-based perspective. Three middle school students were evaluated in this case study. The results showed that the subjects formed similarities in the process of applying knowledge needed for solving a problem. The student A and C used semi-open-end formulas and closed formulas as solutions. They then formed concrete shape for each solution using the chain of signification that was applied for solution by forming procedural similarity. At this time, the chain of signification could be the combination of numbers, words, and pictures (such as diagrams or graphs) or just numbers or words. On the other hand, the student C who recognized closed formulas and her own rule as a solution method could not formulate completely procedural similarity due to many errors arising from number information. Nonetheless, all of the subjects showed something in common in the process of coming up with a algorithm that was semi-open-end formula or closed formula.

• Journal of the Korean Institute of Telematics and Electronics
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• v.20 no.5
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• pp.1-7
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• 1983

Generally, multiple-valued logic algebra is based on the number system of modulo-M. In this paper, characters a, b, c‥… each of them represents the independent state, are regarded as the elements of the symbolic multiple-valued logic. By using the set theory, the symbolic multiple - valued logic and their functions are defined. And Varation for the symbolic logic function due to the variation of a variable and their properties are suggested and analized. With these variations, the MacLaurin's and Taylor's Series expansions of the symbolic logic functions are proposed and proved.

• Journal of applied mathematics & informatics
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• v.33 no.5_6
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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.

• Korean Journal of Human Ecology
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• v.17 no.1
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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.

• Communications of the Korean Mathematical Society
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• v.35 no.2
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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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• v.61 no.2
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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.

• Bulletin of the Korean Mathematical Society
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• v.32 no.2
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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.

• Journal of KSNVE
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• v.9 no.2
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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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• v.32 no.3
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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.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.06a
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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.