• Journal of the Chungcheong Mathematical Society
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• v.29 no.4
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• pp.573-584
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• 2016

Invertible transformations over n-bit words are essential ingredients in many cryptographic constructions. Such invertible transformations are usually represented as a composition of simpler operations such as linear functions, S-P networks, Feistel structures and T-functions. Among them T-functions are probably invertible transformations and are very useful in stream ciphers. In this paper we will characterize a secure trinomial on ${\mathbb{Z}}_{2^n}$ which generates an n-bit word sequence without consecutive elements of period $2^n$.

• Journal of the Korean Mathematical Society
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• v.35 no.2
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• pp.399-422
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• 1998

A useful method of proving the finite decidability of an equationally definable class V of algebras (i.e., variety) is to prove the decidability of the class of finite directly indecomposable members of V. The validity of this method relies on the well-known result of Feferman-Vaught: if a class K of first-order structures is decidable, then so is the class {$\prod$$_{i}$＜n/ $A_{i}$│ $A_{i}$ $\in$ X (i < n), n $\in$ $\omega$}. In this paper we show that the converse of this does not necessarily hold.d.d.

• Journal of applied mathematics & informatics
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• v.29 no.5_6
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• pp.1409-1420
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• 2011

In this paper we present an operational method for solving linear Volterra-Fredholm integral equations (VFIE). The method is con- structed based on three matrices with simple structures which lead to a simple and high accurate algorithm. We also present an error estimation and demonstrate accuracy of the method by numerical examples.

• Research in Mathematical Education
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• v.6 no.1
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• pp.29-38
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• 2002

The purpose of this paper was to examine early numerical representations between American and Korean children. Fifty-five first graders (35 Korean and 20 American) participated in the study. According to the findings of the current study, the author concluded that the Korean children had a stronger conception of base ten representations of numbers than that of the American children. The Korean children used various strategic reasoning such as decomposition and recomposition on the basis of base 10 structure to solve addition and subtraction problems effectively. However, the author cannot conclude that language differences would be the largest factor that would make Korean children sapient in the representations of base ten structures.

• Communications of the Korean Mathematical Society
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• v.12 no.3
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• pp.543-551
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• 1997

In this paper, we call a loop F kinematic if for $a, b \in F\{0}$, the following two conditions are valid : (i) the centralizer Z(a) of a is a commutative group under the induced operation from the loop F, and (ii) Z(a) = Z(b) or $Z(a) \cap Z(b) = {0}$, where 0 is the identity of F. Some example of kinematic loops are given.

• Journal of the Korean Mathematical Society
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• v.33 no.3
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• pp.669-677
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• 1996

Let $M_n$ be the $C^*$-algebra of all $n \times n$ matrices over the complex field, and $P[M_m, M_n]$ the convex cone of all positive linear maps from $M_m$ into $M_n$ that is, the maps which send the set of positive semidefinite matrices in $M_m$ into the set of positive semi-definite matrices in $M_n$. The convex structures of $P[M_m, M_n]$ are highly complicated even in low dimensions, and several authors [CL, KK, LW, O, R, S, W]have considered the possibility of decomposition of $P[M_m, M_n] into subcones.

• Bulletin of the Korean Mathematical Society
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• v.53 no.6
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• pp.1685-1695
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• 2016

In this article we consider Lie super-bialgebra structures on the generalized loop super-Virasoro algebra ${\mathcal{G}}$. By proving that the first cohomology group $H^1({\mathcal{G}},{\mathcal{G}}{\otimes}{\mathcal{G}})$ is trivial, we obtain that all such Lie bialgebras are triangular coboundary.

• Journal of the Korean Mathematical Society
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• v.33 no.4
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• pp.1139-1171
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• 1996

The purpose of our research is to understand geometric and topological aspects of real projective structures on surfaces. A real projective surface is a differentiable surface with an atlas of charts to $RP^2$ such that transition functions are restrictions of projective automorphisms of $RP^2$. Since such an atlas lifts projective geometry on $RP^2$ to the surface locally and consistently, one can study the global projective geometry of surfaces.

• Korean Management Science Review
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• v.12 no.1
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• pp.139-156
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• 1995

This study addresses basic requirements for mathematical programming software, discusses considerations in designing these software, implementation issues facing in these types of applications development, and shows some examples of codes being developed in the course. This type of projects requires long and ever-changing evolutionary phases. The experience is therefore, valuaable in suggesting some useful hints which may be salvaged for similar projects as well as providing reusable codes. In particular, scanning and parsing the free-format inputs, symbol table management, mixed-language programming, and data structures dealing with large sparse matrices are indispensable to many management science software development. Extensions to be made are also discussed.

• Journal of the Korean Mathematical Society
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• v.49 no.3
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• pp.623-639
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• 2012

The convex cone $\mathbb{V}_1$ generated by separable states is contained in the cone $\mathbb{T}$ of all positive semi-definite block matrices whose block transposes are also positive semi-definite. We characterize faces of the cone $\mathbb{V}_1$ induced by faces of the cone $\mathbb{T}$ which are determined by pairs of subspaces of matrices.