• Kyungpook Mathematical Journal
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• v.19 no.2
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• pp.223-230
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• 1979

• Kyungpook Mathematical Journal
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• v.26 no.1
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• pp.31-36
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• 1986

• Bulletin of the Korean Chemical Society
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• v.23 no.12
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• pp.1733-1736
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• 2002

• The Mathematical Education
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• v.21 no.3
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• pp.15-17
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• 1983

• Bulletin of the Korean Mathematical Society
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• v.30 no.2
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• pp.285-293
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• 1993

In [4], Baumslag and Tretkoff proved a residual finiteness criterion for HNN extensions (Theorem 1.2, below). This result has been used extensively in the study of the residual finiteness of HNN extensions. Note that every one-relator group can be embedded in a one-relator group whose relator has zero exponent sum on a generator, and the latter group can be considered as an HNN extension. Hence the properties of an HNN extension play an important role in the study of one-relator groups [3], [2]. In this paper we prove a criterion for HNN extensions to be .pi.$_{c}$(Theorem 2.2). Moreover, we can prove that certain one-relator groups, known to be residually finite, are actually .pi.$_{c}$. It was known by Mostowski [10] that the word problem is solvable for finitely presented, residually finite groups. In the same way, the power problem is solvable for finitely presented .pi.$_{c}$ groups. Another application of subgroup separability with respect to special subgroups was mentioned by Thurston [12, Problem 15].m 15].

• 제어로봇시스템학회:학술대회논문집
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• 1996.10a
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• pp.60-63
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• 1996

This study deals with the nonlinear H$_{\infty}$ control problem of linear system using nonlinear weight. Generally the solvable condition of nonlinear H$_{\infty}$ control problem is given by the Hamilton Jacobi equality or inequality, but it is very difficult to solve. In this study, some constraints of nonlinear weight reduce the solvable condition to linear Riccati equation. Some examples of the control system design using nonlinear weight are shown.n.

• Journal of Korean Institute of Industrial Engineers
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• v.29 no.3
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• pp.222-229
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• 2003

In this paper, we address a layout design problem, PTN[2], for determining an appropriate 2-class-based dedicated storage layout in a class of unit load storage systems. Our strong conjecture is that PTNI2] is NP-hard. Restricting PTN[2], we provide three solvable cases of PTN[2] in which an optimal solution to the solvable cases is one of the partitions based on the PAI(product activity index)-nonincreasing ordering. However, we show with a counterexample that a solution based on the PAI-non increasing ordering does not always give an optimal solution to PTN[2]. Utilizing the derived properties, we construct an effective heuristic algorithm for solving PTN[2] based on a PAI-non increasing ordering with performance ratio bound. Our algorithm with O($n^2$) is effective in the sense that it guarantees a better class-based storage layout than a randomized storage layout in terms of the expected single command travel time.

• Communications of the Korean Mathematical Society
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• v.37 no.4
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• pp.1181-1197
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• 2022

We give a complete classification of simply connected and solvable real Lie groups whose nontrivial coadjoint orbits are of codimension 1. This classification of the Lie groups is one to one corresponding to the classification of their Lie algebras. Such a Lie group belongs to a class, called the class of MD-groups. The Lie algebra of an MD-group is called an MD-algebra. Some interest properties of MD-algebras will be investigated as well.

• Journal for History of Mathematics
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• v.15 no.1
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• pp.57-68
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• 2002

Mathematical problems are classified into two families, i.e. the solvable ones and the others. There are some such problems in the documentary records of tile Chosun Dynasty ages. In those days, a ‘normal right triangle’ whose ratio of the three sides in the triangle is 3 : 4 : 5 was defined and had been used tacitly. This paper intends to introduce the problems having errors.

• Honam Mathematical Journal
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• v.21 no.1
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• pp.171-177
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• 1999

We find the properties of the defects and textures in an ordered medium. Especially, the space X, e.g., the residually solvable space or space satisfying the conditions ($T^{**}$) with respect to the defect and texture.