• Journal of the Optical Society of Korea
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• v.18 no.2
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• pp.134-145
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• 2014

The number of lens groups in modern zoom camera systems is increased above that of conventional systems in order to improve the speed of the auto focus with the high quality image. As a result, it is difficult to calculate zoom loci using the conventional analytic method, and even the recent one-step advanced numerical calculation method is not optimal because of the time-consuming problem generated by the iteration method. In this paper, in order to solve this problem, we suggest a new unified analytic method for zoom lens loci with finite object distance including infinite object distance. This method is induced by systematically analyzing various distances between the object and other groups including the first lens group, for various situations corresponding to zooming equations of the finite lens systems after using a spline interpolation for each lens group. And we confirm the justification of the new method by using various zoom lens examples. By using this method, we can easily and quickly obtain the zoom lens loci not only without any calculation process of iteration but also without any limit on the group number and the object distance in every zoom lens system.

• 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.

• Journal of the Chungcheong Mathematical Society
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• v.36 no.2
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• pp.77-86
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• 2023

The purpose of this paper is to show that a certain finite dimensional representation of the rational Cherednik algebra of type A has a basis consisting of simultaneous eigenvectors for the actions of a certain family of commuting elements, which are introduced in the author's previous paper. To this end, we introduce a combinatorial object, which is called a restricted arrangement of colored beads, and consider an action of the affine symmetric group on the set of the arrangements.

• Transactions of Materials Processing
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• v.22 no.4
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• pp.183-188
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• 2013

Scroll compressors are widely used in air conditioning systems and in automobiles due to their low pressure loss, minimal vibrations, and light-weight. Open-die forging with back pressure is used to forge the rotating scroll, and it requires special care since the forging die can be severely damaged at the fixed end of the spiral cavity similar to a fracture of a cantilever beam. To overcome the inevitable weakness of the forging die due to such damage, an innovative design is necessary. In this study, structural analysis using the finite element method was conducted to determine the reason for the fracture of the forging die. A novel design to avoid stress concentrations and vertical deflection, causing serious damage to the die, is suggested.

• Geomechanics and Engineering
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• v.10 no.5
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• pp.577-598
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• 2016

This paper presents a numerical study of pile force distribution in a pile group foundation subjected to vertical load and large moment. The physical modeling of a pile foundation for a wind turbine is analyzed using 3D finite element software, PLAXIS 3D. The soil profile consists of several clay layers, which are modeled as Mohr-Coulomb material in an undrained condition. The piles in the pile group foundation are modeled as special elements called embedded pile elements. To model the problem of a pile group foundation, a small gap is created between the pile cap and underlying soil. The pile cap is modeled as a rigid plate element connected to each pile by a hinge. As a result, applied vertical load and large moment are transferred only to piles without any load sharing to underlying soil. Results of the study focus on pile load distribution for the square shape of a pile group foundation. Mathematical expression is proposed to describe pile force distribution for the cases of vertical load and large moment and purely vertical load.

• Bulletin of the Korean Mathematical Society
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• v.58 no.1
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• pp.225-234
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• 2021

Let D be a division ring and n > 1 be an integer. In this paper, it is shown that if D ≠ ��3, then every subpermutable subgroup of the general skew linear group GLn(D) is normal. By applying this result, we show that every subpermutable subgroup of the unit group (ℝG)∗ of the real group algebras RG of finite groups G is normal in (ℝG)∗.

• Journal of the Society of Naval Architects of Korea
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• v.60 no.1
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• pp.20-30
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• 2023

In this paper, the Energy Flow Finite Element Analysis (EFFEA) was performed to predict the acoustic and vibrational responses of complicated plate structures considering improved Fluid-Structure Interaction (FSI). For this, a new power transfer relationship was derived at the area junction where two different fluids are in contact on both sides of the plate. In order to increase the reliability of EFFEA of complicated plate structures immersed in a high-density fluid, the corrected flexural wavenumber and group velocity considering fluid-loading effect were derived. As the specific acoustic impedance of the fluid in contact with the plate increases, the flexural wavenumber of the plate increases. As a result, the flexural group velocity is reduced, and the spatial damping effect of the flexural energy density is increased. Additionally, for the EFFEA of arbitary-shaped built-up structures, the energy flow finite element formulation for the acoustic tetrahedral element was newly performed. Finally, for validation of the derived theory and developed software, numerical applications of complicated plate structures submerged in seawater or air were successfully performed.

• 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].

• Bulletin of the Korean Mathematical Society
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• v.30 no.2
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• pp.213-221
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• 1993

In this paper, we will show that the multiplicative group G in a finite ring R with identity 1 has a (B, N)-pair satisfying the following conditions; (1) G=BNB where B and N are subgroups of G. (2) B.cap.N is a normal subgroup of N and W = N/(B.cap.N), is generated by a set S = { $s_{1}$, $s_{2}$, .., $s_{k}$} where $s_{i}$.mem.N/(B.cap.N), $s_{i}$$^{2}$.iden.1 and $s_{i}$.neq.1. (3) For any s.mem.S and w.mem.W, we have sBw.contnd.BwB.cup.BswB. (4) We have sBs not .subeq. B for any s.mem.S. When G, B, N and S satisfy the above conditions, we say that the quadruple (G, B, N, S) is a Tits system. The group W is called the Weyl gorup of the Tits system.ystem.m.

• Honam Mathematical Journal
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• v.32 no.1
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• pp.45-51
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• 2010

Let A be an abelian variety defined over a number field K and let L be a cyclic extension of K with Galois group G = <${\sigma}$> of order n. Let III(A/K) and III(A/L) denote, respectively, the Tate-Shafarevich groups of A over K and of A over L. Assume III(A/L) is finite. Let M(x) be a companion matrix of 1+x+${\cdots}$+$x^{n-1}$ and let $A^x$ be the twist of $A^{n-1}$ defined by $f^{-1}{\circ}f^{\sigma}$ = M(x) where $f:A^{n-1}{\rightarrow}A^x$ is an isomorphism defined over L. In this paper we compute [III(A/K)][III($A^x$/K)]/[III(A/L)] in terms of cohomology, where [X] is the order of an finite abelian group X.