• Bulletin of the Korean Mathematical Society
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• v.57 no.6
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• pp.1475-1479
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• 2020

Let G be a finite group and ${\sigma}_1(G)={\frac{1}{{\mid}G{\mid}}}\;{\sum}_{H{\leq}G}\;{\mid}H{\mid}$. Under some restrictions on the number of conjugacy classes of (non-normal) maximal subgroups of G, we prove that if ${\sigma}_1(G)<{\frac{117}{20}}$, then G is solvable. This partially solves an open problem posed in [9].

• Journal of the Korean Society for Precision Engineering
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• v.18 no.9
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• pp.110-121
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• 2001

During hot pipe bending using induction heating, the wall of bending outside is thinned by tensile stress. In design requirement, the reduction of wall thickness is not allowed to exceed 12.5%. So in this study, two methods of bending, one is loading of reverse moment and the other is loading of temperature gradient, have been investigated to design pipe bending process that satisfy design requirements. For this purpose, finite element analysis with a bending radius 2Do(outer diameter of pipe) has been performed to calculate proper reverse moment and temperature gradient to be applied. Induction heating process has been analyzed to estimate influence of heating process parameters on heating characteristic by finite difference method. Then pipe bending experiments have been performed for verification of finite element and finite difference analysis results. Experimental results are in good agreement with the results of simulations.

• The korean journal of orthodontics
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• v.39 no.2
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• pp.83-94
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• 2009

Objective: The aim of this study was to investigate the 3-dimensional position of the center of resistance of the 4 maxillary anterior teeth, 6 maxillary anterior teeth, and the full maxillary dentition using 3-dimensional finite element analysis. Methods: Finite element models included the whole upper dentition, periodontal ligament, and alveolar bone. The crowns of the teeth in each group were fixed with buccal and lingual arch wires and lingual splint wires to minimize individual tooth movement and to evenly disperse the forces to the teeth. A force of 100 g or 200 g was applied to the wire beam extended from the incisal edge of the upper central incisor, and displacement of teeth was evaluated. The center of resistance was defined as the point where the applied force induced parallel movement. Results: The results of study showed that the center of resistance of the 4 maxillary anterior teeth group, the 6 maxillary anterior teeth group, and the full maxillary dentition group were at 13.5 mm apical and 12.0 mm posterior, 13.5 mm apical and 14.0 mm posterior, and 11.0 mm apical and 26.5 mm posterior to the incisal edge of the upper central incisor, respectively. Conclusions: It is thought that the results from this finite element models will improve the efficiency of orthodontic treatment.

• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.75-96
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• 2006

Let m, n be positive integers. We denote by R(m,n) (respectively P(m,n)) the class of all groups G such that, for every n subsets $X_1,X_2\ldots,X_n$, of size m of G there exits a non-identity permutation $\sigma$ such that $X_1X_2{\cdots}X_n{\cap}X_{\sigma(1)}X_{/sigma(2)}{\cdots}X_{/sigma(n)}\neq\phi$ (respectively $X_1X_2{\cdots}X_n=X_{/sigma(1)}X_{\sigma(2)}{\cdots}X_{\sigma(n)}$). Let G be a non-abelian group. In this paper we prove that (i) $G{\in}P$(2,3) if and only if G isomorphic to $S_3$, where $S_n$ is the symmetric group on n letters. (ii) $G{\in}R$(2, 2) if and only if ${\mid}G{\mid}\geq8$. (iii) If G is finite, then $G{\in}R$(3, 2) if and only if ${\mid}G{\mid}\geq14$ or G is isomorphic to one of the following: SmallGroup(16, i), $i\in$ {3, 4, 6, 11, 12, 13}, SmallGroup(32, 49), SmallGroup(32, 50), where SmallGroup(m, n) is the nth group of order m in the GAP [13] library.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2003.10a
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• pp.429-436
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• 2003

A new linkage framework between elastic shell element with finite rotation and computar-aided geometric design (CAGD) (or surface is developed in the present study. The framework of shell finite element is based on the generalized curved two-parametric coordinate system. To represent free-form surface, cubic B-spline tensor-product functions are used. Thus the present finite element can be directly linked into the geometric modeling produced by surface generation tool in CAD software. The efficiency and accuracy of the Previously developed linear elements hold for the nonlinear element with finite rotations. To handle the finite rotation behavior of shells, exponential mapping in the SO(3) group is employed to allow the large incremental step size. The integrated frameworks of shell geometric design and nonlinear computational analysis can serve as an efficient tool in shape and topological design of surfaces with large deformations.

• Bulletin of the Korean Mathematical Society
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• v.56 no.2
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• pp.365-371
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• 2019

If 𝖃 is a class of groups, denote by F𝖃 the class of groups G such that for every $x{\in}G$, there exists a normal subgroup of finite index H(x) such that ${\langle}x,h{\rangle}{\in}$ 𝖃 for every $h{\in}H(x)$. In this paper, we consider the class F𝖃, when 𝖃 is the class of nilpotent-by-finite, finite-by-nilpotent and periodic-by-nilpotent groups. We will prove that for the above classes 𝖃 we have that a finitely generated hyper-(Abelian-by-finite) group in F𝖃 belongs to 𝖃. As a consequence of these results, we prove that when the nilpotency class of the subgroups (or quotients) of the subgroups ${\langle}x,h{\rangle}$ are bounded by a given positive integer k, then the nilpotency class of the corresponding subgroup (or quotient) of G is bounded by a positive integer c depending only on k.

• Bulletin of the Korean Mathematical Society
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• v.61 no.3
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• pp.785-796
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• 2024

Let p be a prime. A group G is said to be residually p-finite if for each non-trivial element x of G, there exists a normal subgroup N of index a power of p in G such that x is not in N. In this note we shall prove that certain HNN extensions of free abelian groups of finite rank are residually p-finite. In addition some of these HNN extensions are subgroup separable. Characterisations for certain one-relator groups and similar groups including the Baumslag-Solitar groups to be residually p-finite are proved.

• Kyungpook Mathematical Journal
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• v.49 no.3
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• pp.419-424
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• 2009

Let J be the Jacobian variety of a hyperelliptic curve over $\mathbb{Q}$. Let M be the field generated by all square roots of rational integers over a finite number field K. Then we prove that the Mordell-Weil group J(M) is the direct sum of a finite torsion group and a free $\mathbb{Z}$-module of infinite rank. In particular, J(M) is not a divisible group. On the other hand, if $\widetilde{M}$ is an extension of M which contains all the torsion points of J over $\widetilde{\mathbb{Q}}$, then $J(\widetilde{M}^{sol})/J(\widetilde{M}^{sol})_{tors}$ is a divisible group of infinite rank, where $\widetilde{M}^{sol}$ is the maximal solvable extension of $\widetilde{M}$.

• Bulletin of the Korean Mathematical Society
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• v.44 no.2
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• pp.233-239
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• 2007

Let $\mathbb{A}=\mathbb{F}_q$[T] be the polynomial ring over a finite field $\mathbb{F}_q$[T] and K=$\mathbb{F}_q$(T) its field of fractions. Let ${\ell}$ be a fixed prime divisor of q-1. Let J be a finite set of monic irreducible polynomials $P{\in}{\mathbb{A}}$ with deg $P{\equiv}0$ (mod ${\ell})$. In this paper we define the group $C_K$ of circular units in K=k$(\{\sqrt[{\ell}]P\;:\;P{\in}J\})$ in the sense of Kucera [4] and compute the index of $C_K$ in the full unit group $O^*_K$.

• Structural Engineering and Mechanics
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• v.20 no.5
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• pp.575-587
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• 2005

Using the nonlinear load transfer function for pile side soil and the linear load transfer function for pile end soil, a combined approach of the incremental load transfer matrix method and the approximate differential equation solution method is presented for the nonlinear analysis of interaction between flexible pile group and soil. The proposed method provides an effective approach for the solution of the nonlinear interaction between flexible pile group under rigid platform and surrounding soil. To verify the accuracy of the proposed method, a static load test for a nine-pile group under a rigid platform is carried out. The finite element analysis is also conducted for comparison purposes. It is found that the results from the proposed method match very well with those from the experimental test and are better in comparison with the finite element method.