• Journal of Educational Research in Mathematics
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• v.13 no.3
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• pp.287-307
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• 2003

This study analyzed the concept of equal symbol(=) that is the most symbol used in learning of mathematics and investigated students' understanding of that. The equal symbol is endowed with the 'same', 'equal', and 'equivalent' meaning, represented by =, but students interpret the meaning of equal symbol according to the mathematical con text. Thus, we analyzed the equal symbol on the basis of the theory of conceptual fields. In the theory of conceptual fields, concept is a three-tuple of three sets of situation, operational invariants and symbolic representations, and the operational invariants are the concept-in-action and the theorems- in-action. With the analysis contents, we investigated how students read = by korean, what equals in the expression containing = or by what meaning students used =, and which they could correct the error for =. This study imply that we should consider the symbol notation agreed by mathematical society, the meaning, and the situational context that it used, when we teach the mathematics symbols.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.263-271
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• 2006

In this paper, a quasilinear second-order system with periodic boundary conditions is studied. By the least action principle and classical theorems of variational calculus, existence results of periodic solutions are obtained.

• Journal of the Korean Mathematical Society
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• v.31 no.3
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• pp.339-352
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• 1994

A sumbanifold M of a quaternionic Kaehlerian manifold $\tilde{M}^m$ of real dimension 4m is called a generic submanifold if the normal space N(M) of M is always mapped into the tangent space T(M) under the action of the quaternionic Kaehlerian structure tensors of the ambient manifold at the same time.The purpose of the present paper is to study generic submanifold of quaternionic Kaehlerian manifold of constant Q-sectional curvature with nonvanishing parallel mean curvature vector. In section 1, we state general formulas on generic submanifolds of a quaternionic Kaehlerian manifold of constant Q-sectional curvature. Section 2 is devoted to the study generic submanifolds with nonvanishing parallel mean curvature vector and compute the restricted Laplacian for the second fundamental form in the direction of the mean curvature vector. As applications of those results, in section 3, we prove our main theorems. In this paper, the dimension of a manifold will always indicate its real dimension.

• Bulletin of the Korean Mathematical Society
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• v.57 no.6
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• pp.1511-1528
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• 2020

A skew generalized power series ring R[[S, 𝜔]] consists of all functions from a strictly ordered monoid S to a ring R whose support contains neither infinite descending chains nor infinite antichains, with pointwise addition, and with multiplication given by convolution twisted by an action 𝜔 of the monoid S on the ring R. Special cases of the skew generalized power series ring construction are skew polynomial rings, skew Laurent polynomial rings, skew power series rings, skew Laurent series rings, skew monoid rings, skew group rings, skew Mal'cev-Neumann series rings, the "untwisted" versions of all of these, and generalized power series rings. In this paper we obtain some necessary conditions on R, S and 𝜔 such that the skew generalized power series ring R[[S, 𝜔]] is (uniquely) clean. As particular cases of our general results we obtain new theorems on skew Mal'cev-Neumann series rings, skew Laurent series rings, and generalized power series rings.