• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.03a
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• pp.3-6
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• 1998

We introduce the notion of TL-p-subgroups that is an extension of the notion of fuzzy p-subgroups and show that a torsion TL-subgroup of an Abelian group with T=∧ can be written as the intersection of its minimal TL-p-subgroups.

• Journal of the Chungcheong Mathematical Society
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• v.32 no.1
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• pp.87-95
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• 2019

The homothety classes of lattices in a two dimensional vector space over a nonarchimedean local field form a regular tree ${\mathcal{T}}$ of degree q + 1 on which the projective linear group acts naturally where q is the order of the residue field. We show that for any finite regular combinatorial graph of even degree q + 1, there exists a torsion free discrete subgroup ${\Gamma}$ of the projective linear group such that ${\mathcal{T}}/{\Gamma}$ is isomorphic to the graph.

• Clinical and Experimental Pediatrics
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• v.48 no.1
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• pp.75-80
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• 2005

Purpose : Internal tibial torsion is prevalent in East Asian countries such as Korea and Japan, where sitting on the floor is common behavior. Internal tibial torsion or excessive lateral tibial torsion may cause esthetical, functional, or psychological problems and also may induce degenerative arthritis in older age. The purpose of this study is to measure the tibial torsion in children of the Jeju area. Methods : Tibial torsion was measured in 1,042 lower extremities of 521 children from one to 12 years of age. The values of transmalleolar angles were analyzed for each age group divided by 6 months. Quadratic and linear regression models were used to fit patterns of changes in mean values of transmalleolar angles. The age at seven, which provides the highest coefficient of determination for quadratic regression analysis, was used as a cut-off point to fit different statistical models. Results : The mean transmalleolar angle was $0.10{\pm}5.79^{\circ}$ in all children,$ 0.90{\pm}5.49^{\circ}$ in males, and $-0.80{\pm}5.97^{\circ}$ in females. The value was $4.25{\pm}4.04$ in 1 year of age, gradually decreased to the lowest level of $-1.98^{\circ}$ in four years and seven months of age, increased again with age until it reached $0.67{\pm}1.10^{\circ}$ at seven years of age, and stayed at that level thereafter. Conclusion : Internal tibial torsion in infancy is known to correct spontaneously in the normal developing process. But in this study, the mean transmalleolar angle in children of Jeju area annually decreased after one year of age; to the lowest angle at four years and seven months of age; increased again gradually to the age of seven; and persisted in that level, about $10^{\circ}$ less than western children, not correcting further thereafter. These findings suggest tibial torsion might be caused by lifestyle, especially sitting on feet. To prevent abnormalities of joints and gaits, early diagnosis of tibial torsion in childhood and posture correction or early treatment when needed, seems to be necessary.

• East Asian mathematical journal
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• v.39 no.3
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• pp.349-354
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• 2023

The motivation in this paper comes from the recent results about Bell inequalities and topological insulators from group theory. Symmetries which are interested in group theory could be mainly used to find material structures. In this point of views, we study group extending by adding one relator which is easily called an equation. So a relative group extension by a adding relator is aspherical if the natural injection is one-to-one and the group ring has no zero divisor. One of concepts of asphericity means that a new group by a adding relator is well extended. Also, we consider that several equations and relative presentations over torsion-free groups are related to zero divisors.

• Bulletin of the Korean Mathematical Society
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• v.42 no.4
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• pp.807-815
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• 2005

Let R be a ring with identity, X the set of all nonzero, nonunits of Rand G the group of all units of R. We will consider two group actions on X by G, the regular action and the conjugate action. In this paper, by investigating two group actions we can have some results as follows: First, if G is a finitely generated abelian group, then the orbit O(x) under the regular action on X by G is finite for all nilpotents x $\in$ X. Secondly, if F is a field in which 2 is a unit and F $\backslash\;\{0\}$ is a finitley generated abelian group, then F is finite. Finally, if G in a unit-regular ring R is a torsion group and 2 is a unit in R, then the conjugate action on X by G is trivial if and only if G is abelian if and only if R is commutative.

• Journal of the Korean Mathematical Society
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• v.40 no.2
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• pp.225-239
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• 2003

(G, <) is an ordered group if'<'is a total order relation on G in which f < g implies that xfy < xgy for all f, g, x, y $\in$ G. We say that (G, <) is centrally ordered if (G, <) is ordered and ［G,D］ $\subseteq$ C for every convex jump C $\prec$ D in G. Equivalently, if $f^{-1}g f{\leq} g^2$ for all f, g $\in$ G with g > 1. Every order on a torsion-free locally nilpotent group is central. We prove that if every order on every two-generator subgroup of a locally soluble orderable group G is central, then G is locally nilpotent. We also provide an example of a non-nilpotent two-generator metabelian orderable group in which all orders are central.

• Honam Mathematical Journal
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• v.39 no.4
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• pp.637-647
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• 2017

Elastica is known as classical curve that is a solution of variational problem, which minimize a thin inextensible wire's bending energy. Studies on elastica has been conducted in Euclidean space firstly, then it has been extended to Riemannian manifold by giving different characterizations. In this paper, we focus on energy of the elastic curve in a Lie group. We attepmt to compute its energy by using geometric description of the curvature and the torsion of the trajectory of the elastic curve of the trajectory of the moving particle in the Lie group. Finally, we also investigate the relation between energy of the elastic curve and energy of the same curve in Frenet vector fields in the Lie group.

• Earthquakes and Structures
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• v.8 no.2
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• pp.305-377
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• 2015

The problem of earthquake induced torsion in buildings is quite old and although it has received a lot of attention in the past several decades, it is still open. This is evident not only from the variability of the pertinent provisions in various modern codes but also from conflicting results debated in the literature. Most of the conducted research on this problem has been based on very simplified, highly idealized models of eccentric one-story systems, with single or double eccentricity and with load bearing elements of the shear beam type, sized only for earthquake action. Initially, elastic models were used but were gradually replaced by inelastic models, since building response under design level earthquakes is expected to be inelastic. Code provisions till today have been based mostly on results from one-story inelastic models or on results from elastic multistory idealizations. In the past decade, however, more accurate multi story inelastic building response has been studied using the well-known and far more accurate plastic hinge model for flexural members. On the basis of such research some interesting conclusions have been drawn, revising older views about the inelastic response of buildings based on one-story simplified model results. The present paper traces these developments and presents new findings that can explain long lasting controversies in this area and at the same time may raise questions about the adequacy of code provisions based on results from questionable models. To organize this review better it was necessary to group the various publications into a number of subtopics and within each subtopic to separate them into smaller groups according to the basic assumptions and/or limitations used. Capacity assessment of irregular buildings and new technologies to control torsional motion have also been included.

• Communications of the Korean Mathematical Society
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• v.18 no.2
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• pp.367-374
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• 2003

Let N be a Closed n-manifold with residually finite, torsion free $\pi$$_1$(N) and finite H$_1$,(N). Suppose that $\pi$$\_$k/(N)=0 for 1 < k < n-1. We show that N is a codimension-n PL fibrator if and only if N does not cover itself regularly and cyclically up to homotopy type, provided $\pi$$_1$(N) satisfies a certain condition.

• Honam Mathematical Journal
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• v.40 no.2
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• pp.265-280
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• 2018

In this study, we firstly define equations of motion based on the traditional model Newtonian mechanics in terms of the Frenet frame adapted to the trajectory of the moving particle in Lie groups. Then, we compute energy on the moving particle in resultant force field by using geometrical description of the curvature and torsion of the trajectory belonging to the particle. We also investigate the relation between energy on the moving particle in different force fields and energy on the particle in Frenet vector fields.