• Honam Mathematical Journal
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• v.39 no.4
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• pp.677-688
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• 2017

Let P be a finitely generated projective module over a commutative ring R with identity. If P has finite rank, then it will be shown that the map ${\varphi}:Aut_R(P){\rightarrow}U(R)$ defined by ${\varphi}({\alpha})={\det}({\alpha})$ is locally surjective and $Ker({\varphi})=SL_R(P)$.

• Bulletin of the Korean Mathematical Society
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• v.48 no.1
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• pp.79-83
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• 2011

In the present paper we introduce the lower autocentral series of autocommutator subgroups of a given group. Following our previous work on the subject in 2009, it is shown that every finite abelian group is isomorphic with $n^{th}$-term of the lower autocentral series of some finite abelian group.

• Journal for History of Mathematics
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• v.13 no.2
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• pp.151-160
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• 2000

In this paper we prove that for all irreducible complex characters of a finite group, there exist F-representations and a finite degree field extension F ⊇ Q, where Q is the rational number field.

• The Journal of Advanced Prosthodontics
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• v.13 no.2
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• pp.79-88
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• 2021

Purpose. To assess peri-implant stress distribution using finite element analysis in implant supported fixed partial denture with occlusal schemes of cuspally loaded occlusion and implant protected occlusion. Materials and methods. A 3-D finite element model of mandible with D2 bone with partially edentulism with unilateral distal extension was made. Two Ti alloy identical implants with 4.2 mm diameter and 10 mm length were placed in the mandibular second premolar and the mandibular second molar region and prosthesis was given with the mandibular first molar pontic. Vertical load of 100 N and and oblique load of 70 N was applied on occlusal surface of prosthesis. Group 1 was cuspally loaded occlusion with total 8 contact points and Group 2 was implant protected occlusion with 3 contact points. Results. In Group 1 for vertical load, maximum stress was generated over implant having 14.3552 Mpa. While for oblique load, overall stress generated was 28.0732 Mpa. In Group 2 for vertical load, maximum stress was generated over crown and overall stress was 16.7682 Mpa. But for oblique load, crown stress and overall stress was maximum 22.7561 Mpa. When Group 1 is compared to Group 2, harmful oblique load caused maximum overall stress 28.0732 Mpa in Group 1. Conclusion. In Group 1, vertical load generated high implant stress, and oblique load generated high overall stresses, cortical stresses and crown stresses compared to vertical load. In Group 2, oblique load generated more overall stresses, cortical stresses, and crown stresses compared to vertical load. Implant protected occlusion generated lesser harmful oblique implant, crown, bone and overall stresses compared to cuspally loaded occlusion.

• Biomaterials and Biomechanics in Bioengineering
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• v.3 no.2
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• pp.71-84
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• 2016

The finite element method is wide used in simulation in the biomechanical structures, but a lack of studies concerning finite element mesh quality in biomechanics is a reality. The present study intends to analyze the importance of the mesh quality in the finite element model results from humeral structure. A sensitivity analysis of finite element models (FEM) is presented for the humeral bone and cartilage structures. The geometry of bone and cartilage was acquired from CT scan and geometry reconstructed. The study includes 54 models from same bone geometry, with different mesh densities, constructed with tetrahedral linear elements. A finite element simulation representing the glenohumeral-joint reaction force applied on the humerus during $90^{\circ}$ abduction, with external load as the critical condition. Results from the finite element models suggest a mesh with 1.5 mm, 0.8 mm and 0.6 mm as suitable mesh sizes for cortical bone, trabecular bone and humeral cartilage, respectively. Relatively to the higher minimum principal strains are located at the proximal humerus diaphysis, and its highest value is found at the trabecular bone neck. The present study indicates the minimum mesh size in the finite element analyses in humeral structure. The cortical and trabecular bone, as well as cartilage, may not be correctly represented by meshes of the same size. The strain results presented the critical regions during the $90^{\circ}$ abduction.

• Korean Journal of Mathematics
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• v.7 no.1
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• pp.71-77
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• 1999

We show that if the stable rank of $B^{\alpha}$ is one, then the stable rank of B is less than or equal to the order of G for any action of a finite group G. Also we give a short proof to the known fact that if the action of a finite group on a $C^*$-algebra B is saturated then the canonical conditional expectation from B to $B^{\alpha}$ is of index-finite type and the crossed product $C^*$-algebra is isomorphic to the algebra of compact operators on the Hilbert $B^{\alpha}$-module B.

• Bulletin of the Korean Mathematical Society
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• v.38 no.2
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• pp.317-324
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• 2001

A Cayley graph of a finite group G is called normal edge-transitive if its automorphism group has a subgroup which both normalized G and acts transitively on edges. In this paper, we consider Cayley graphs of finite cyclic groups, namely, finite circulant graphs. We characterize the normal edge-transitive circulant graphs and determine the normal edge-transitive circulant graphs of prime power order in terms of lexicographic products.

• Journal of the Korean Mathematical Society
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• v.42 no.4
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• pp.795-826
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• 2005

We study free actions of finite abelian groups on 3­dimensional nilmanifolds. By the works of Bieberbach and Waldhausen, this classification problem is reduced to classifying all normal nilpotent subgroups of almost Bieberbach groups of finite index, up to affine conjugacy. All such actions are completely classified.

• Honam Mathematical Journal
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• v.24 no.1
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• pp.93-101
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• 2002

The $S^1$-Eule characteristics of X is defined by $\bar{\chi}_{S^1}(X)\;{\in}\;HH_1(ZG)$, where G is the fundamental group of connected finite $S^1$-compact manifold or connected finite $S^1$-finite complex X and $HH_1$ is the first Hochsch ild homology group functor. The purpose of this paper is to find several cases which the $S^1$-Euler characteristic has a homotopic invariant.

• Bulletin of the Korean Mathematical Society
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• v.59 no.4
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• pp.951-960
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• 2022

In this paper, we determine the finite p-group such that the intersection of its any two distinct minimal nonabelian subgroups is a maximal subgroup of the two minimal nonabelian subgroups, and the finite p-group in which any two distinct 𝓐₁-subgroups generate an 𝓐₂-subgroup. As a byproduct, we answer a problem proposed by Berkovich and Janko.