• Bulletin of the Korean Mathematical Society
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• v.34 no.3
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• pp.351-358
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• 1997

A conjugacy theorem which holds for finite groups is proven to hold for Cernikov groups and locally finite CC-groups.

• Journal of the Korean Mathematical Society
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• v.32 no.2
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• pp.289-300
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• 1995

Every group G has a unique maximal normal locally nilpotent subgroup $\Phi(G)$, called the Hirsh-Plotkin radical of G [9]. If G is a group, we define the upper Hirsh-Plotkin series of G to be the ascending series $1 = R_0 \leq R_1 \leq \ldots$ in which $R_{\alpha+1}/R_\alpha = \{Phi(G/R_\alpha)$ for each ordinal $\alpha and R_\beta = \cup_{\alpha<\beta}R_\alpha$ for each limit ordinal $\beta$. If $R_r = G$ for some natural number r, then G is said to have locally nilpotent length r. $(LN)^r$ denotes the calss of groups of locally nilpotent length at most r.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.24 no.4
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• pp.405-412
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• 2011

This paper introduces the generalized finite element method with global-local enrichment functions using the preconditioned conjugate gradient method. The proposed methodology is able to generate enrichment functions for problems where limited a-priori knowledge on the solution is available and to utilize a preconditioner and initial guess of good quality with only small addition of computational cost. Thus, it is very effective to analyze problems where a complex behavior is locally exhibited. Several numerical experiments are performed to confirm its effectiveness and show that it is computationally more efficient than the analysis utilizing direct solvers such as Gauss elimination method.

• Bulletin of the Korean Mathematical Society
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• v.57 no.1
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• pp.207-218
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• 2020

Some modular representations of reflection groups related to Weyl groups are considered. The rational cohomology of the classifying space of a compact connected Lie group G with a maximal torus T is expressed as the ring of invariants, H*(BG; ℚ) ≅ H*(BT; ℚ)^W(G), which is a polynomial ring. If such Lie groups are locally isomorphic, the rational representations of their Weyl groups are equivalent. However, the integral representations need not be equivalent. Under the mod p reductions, we consider the structure of the rings, particularly for the Weyl group of symplectic groups Sp(n) and for the alternating groups A_n as the subgroup of W(SU(n)). We will ask if such rings of invariants are polynomial rings, and if each of them can be realized as the mod p cohomology of a space. For n = 3, 4, the rings under a conjugate of W(Sp(n)) are shown to be polynomial, and for n = 6, 8, they are non-polynomial. The structures of H*(BT^n-1; 𝔽_p)^A_n will be also discussed for n = 3, 4.

• The Journal of the Petrological Society of Korea
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• v.13 no.4
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• pp.179-190
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• 2004

Precambrian metamorphic rocks of Yeongyang-Uljin area, which is located in the eastern part of Sobaegsan Massif, Korea, are composed of Pyeonghae, Giseong, Wonnam Formations and Hada leuco granite gneisses. These show a zonal distribution of WNW-ESE trend, and are intruded by Mesozoic igneous rocks and are unconformably overlain by Mesozoic sedimentary rocks. This study clarifies the deformation history of Precambrian metamorphic rocks after the formation of gneissosity or schistosity on the basis of the geometric and kinematic features and the forming sequence of multi-deformed rock structures, and suggests that the geological structures of this area experienced at least four phases of deformation i.e. ductile shear deformation, one deformation before that, at least two deformations after that. (1) The first phase of deformation formed regional foliations and WNW-trending isoclinal folds with subhorizontal axes and steep axial planes dipping to the north. (2) The second phase of deformation occurred by dextral ductile shear deformation of top-to-the east movement, forming stretching lineations of E-W trend, S-C mylonitic structure foliations, and Z-shaped asymmetric folds. (3) The third phase deformation formed I-W trending open- or kink-type recumbent folds with subhorizontal axes and gently dipping axial planes. (4) The fourth phase deformation took place under compression of NNW-SSE direction, forming ENE-WSW trending symmetric open upright folds and asymmetric conjugate kink folds with subhorizontal axes, and conjugate faults thrusting to the both NNW and SSE with drag folds related to it. These four phases of deformation are closely connected with the orientation of regional foliation in the Yeongyang-Uljin area. 1st deformation produced regional foliation striking WNW and steeply dipping to the north, 2nd deformation locally change the strike of regional foliation into N-S direction, and 3rd and 4th deformations locally change dip-angle and dip-direction of regional foliation.