• Journal of Educational Research in Mathematics
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• v.17 no.2
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• pp.163-177
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• 2007

Studies on mathematically gifted students have been conducted following Krutetskii. There still exists a necessity for a more detailed research on how these students' mathematical competence is actually displayed during the problem solving process. In this study, it was attempted to analyse the algebraic thinking process in the problem solving a peg puzzle in which 4 mathematically gifted students, who belong to the upper 0.01% group in their grade of elementary school in Korea. They solved and generalized the straight line peg puzzle. Mathematically gifted elementary school students had the tendency to find a general structure using generic examples rather than find inductive rules. They did not have difficulty in expressing their thoughts in letter expressions and in expressing their answers in written language; and though they could estimate general patterns while performing generalization of two factors, it was revealed that not all of them can solve the general formula of two factors. In addition, in the process of discovering a general pattern, it was confirmed that they prefer using diagrams to manipulating concrete objects or using tables. But as to whether or not they verify their generalization results using generalized concrete cases, individual difference was found. From this fact it was confirmed that repeated experiments, on the relationship between a child's generalization ability and his/her behavioral pattern that verifies his/her generalization result through application to a concrete case, are necessary.

• School Mathematics
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• v.16 no.2
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• pp.355-386
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• 2014

Algebraic generalization of patterns is based on the capability of grasping a structure inherent in several objects with awareness that this structure applies to general cases and ability to use it to provide an algebraic expression. The purpose of this study is to investigate how students generalize patterns using an algebraic object such as parameters and what are difficulties in geometric-arithmetic pattern tasks related to algebraic generalization and to determine whether the students can use parameters meaningfully through pattern generalization tasks that this researcher designed. During performing tasks of pattern generalization we designed, students differentiated parameters from letter 'n' that is used to denote a variable. Also, the students understood the relations between numbers used in several linear equations and algebraically expressed the generalized relation using a letter that was functions as a parameter. Some difficulties have been identified such that the students could not distinguish parameters from variables and could not transfer from arithmetical procedure to algebra in this process. While trying to resolve these difficulties, generic examples helped the students to meaningfully use parameters in pattern generalization.

• The Journal of Society for e-Business Studies
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• v.7 no.3
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• pp.49-60
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• 2002

Many researchers have studied component technologies with concept, methodology and implementation for partial business domain, however there are rarely researches for component classification to manage these systematically. In this paper, we suggest a component classification model, which can make component reusability higher and can derive higher productivity of software development. We take four focuses generalization, abstraction, technology and size. The generalization means which category a component belongs to. The abstraction means how specific a component encapsulates its inside. The technology means which platform for hardware environment a component can be plugged in. The size means the physical component volume.

• Communications of the Korean Mathematical Society
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• v.31 no.1
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• pp.53-64
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• 2016

In this paper, we give generalization of the $Fej\acute{e}r$-Hadamard inequality by using definition of convex functions on n-coordinates. Results given in [8, 12] are particular cases of results given here.

• Communications of the Korean Mathematical Society
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• v.23 no.4
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• pp.607-610
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• 2008

We aim mainly at presenting a generalization of a transformation formula found by Baillon and Bruck. The result is derived with the help of the well-known quadratic transformation formula due to Gauss.

• Communications of the Korean Mathematical Society
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• v.12 no.1
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• pp.113-126
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• 1997

In this paper we introduce a new definition of a lattice fuzzy topology which is a generalization of Lowen's fuzzy topology and show that the category of Lowen's fuzzy topological spaces is a bireflective full subcategory of the category of lattice fuzzy topological spaces.

• Bulletin of the Korean Mathematical Society
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• v.41 no.4
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• pp.599-608
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• 2004

Let R be an associative ring with identity and J(R) be the Jacobson radical of R. In this paper we investigate the generalization of the Jacobson radical of R, J＊ (R) say. Also we study the rings that J＊(R) = J(R).

• Bulletin of the Korean Mathematical Society
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• v.42 no.1
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• pp.149-155
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• 2005

The notion of U-exact sequence (or quasi-exact sequence) of modules was introduced by Davvaz and Parnian-Garamaleky as a generalization of exact sequences. In this paper, we prove further results about quasi-exact sequences. In particular, we give a generalization of Schanuel's Lemma. Also we obtain some relation-ship between quasi-exact sequences and superfluous (or essential) submodules.

• Bulletin of the Korean Mathematical Society
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• v.44 no.1
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• pp.87-94
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• 2007

We in this note introduce the concept of g-IFP rings which is a generalization of IFP rings. We show that from any IFP ring there can be constructed a right g-IFP ring but not IFP. We also study the basic properties of right g-IFP rings, constructing suitable examples to the situations raised naturally in the process.

• Journal of the Korean Statistical Society
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• v.34 no.3
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• pp.185-195
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• 2005

This article is concerned with the intraclass correlation in survey sampling. From a design-based viewpoint the intraclass correlation is generalized to a finite population with unequal sized clusters. Under simple random cluster sampling the intraclass correlation is given in an explicit form, which is a generalization of the usual one. The range of it is found and the design effect is expressed by means of it. An example is given to compare the intraclass correlation with the homogeneity measure numerically, which shows that two measures are not the same except some limited cases.