• East Asian mathematical journal
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• v.22 no.2
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• pp.215-221
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• 2006

On a groupoid satisfying the Austin's identity, every n-ary linear term is essentially n-ary. That is, if a term has no variables appearing more than once, then the term depends on every variable it involves.

• Journal of the Korean Mathematical Society
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• v.50 no.1
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• pp.127-136
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• 2013

The term rank of a matrix A is the least number of lines (rows or columns) needed to include all the nonzero entries in A. In this paper, we obtain a characterization of linear transformations that preserve term ranks of matrices over antinegative semirings. That is, we show that a linear transformation T from a matrix space into another matrix space over antinegative semirings preserves term rank if and only if T preserves any two term ranks $k$ and $l$.

• Bulletin of the Korean Mathematical Society
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• v.50 no.1
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• pp.233-240
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• 2013

In this paper, we use the elementary method and the theory of complex functions to study the computational problem of the fourth power mean of the generalized two-term exponential sums, and give two exact identities for them.

• Journal of the Korean Mathematical Society
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• v.42 no.2
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• pp.191-202
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• 2005

A condition on forcing term insuring the multiplicity of Dirichlet-periodic solutions of nonlinear dissipative hyperbolic equations is discussed. The nonlinear term is assumed to have coercive growth.

• Journal of the Korean Mathematical Society
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• v.36 no.6
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• pp.1181-1190
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• 1999

Zero-term rank of a matrix is the minimum number of lines (rows or columns) needed to cover all the zero entries of the given matrix. We characterized the linear operators that preserve zero-term rank of the m×n matrices over binary Boolean algebra.

• Journal of the Korean Mathematical Society
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• v.47 no.6
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• pp.1107-1122
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• 2010

In this paper, we shall use analytic methods to study the hybrid mean value involving the mixed two-term exponential sums C(m, n, r, $\chi$; q), and give several sharp asymptotic formulae.

• Proceedings of the Jangjeon Mathematical Society
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• v.20 no.2
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• pp.183-191
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• 2017

We get one theorem that there exist solutions for the fourth order semi- linear elliptic Dirichlet boundary value problem with fully nonlinear term. We prove this result by the critical point theory and the variation of linking method.

• Journal of the Korean Mathematical Society
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• v.45 no.3
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• pp.757-769
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• 2008

This paper deals with the existence of optimal controls and maximal principles for semilinear evolution equations with the nonlinear term satisfying Lipschitz continuity. We also present the necessary conditions of optimality which are described by the adjoint state corresponding to the linear equations without a condition of differentiability for nonlinear term.

• Journal of the Korean Mathematical Society
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• v.51 no.1
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• pp.113-123
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• 2014

The term rank of a matrix A over a semiring $\mathcal{S}$ is the least number of lines (rows or columns) needed to include all the nonzero entries in A. In this paper, we characterize linear operators that preserve the sets of matrix ordered pairs which satisfy extremal properties with respect to term rank inequalities of matrices over nonbinary Boolean semirings.

• Communications of Mathematical Education
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• v.18 no.2 s.19
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• pp.9-33
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• 2004

The purpose of this paper is to contribute to the dialogue about the notion of advanced mathematical thinking by offering an alternative characterization for this idea, namely advancing mathematical activity. We use the term advancing (versus advanced) because we emphasize the progression and evolution of students' reasoning in relation to their previous activity. We also use the term activity, rather than thinking. This shift in language reflects our characterization of progression in mathematical thinking as acts of participation in a variety of different socially or culturally situated mathematical practices. We emphasize for these practices the changing nature of student' mathematical activity and frame the process of progression in terms of multiple layers of horizontal and vertical mathematizing.