• Kyungpook Mathematical Journal
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• v.46 no.3
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• pp.329-336
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• 2006

In the category of the group theoretic methods using invertible discrete group transformation, we give a useful relation between Emden-Fowler equations and nonlinear heat equation. In this paper, by means of appropriate transformations of discrete group analysis, the nonlinear hate equation transformed into the class of the Emden-Fowler equations. This approach shows that, under the group action, the solution of reference equation can be transformed into the solution of the transformed equation.

• Journal of the Korean Mathematical Society
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• v.45 no.2
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• pp.575-585
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• 2008

Suppose that D is a $C^*$-discrete quantum group and $D_0$ a discrete quantum group associated with D. If there exists a continuous action of D on an operator algebra L(H) so that L(H) becomes a D-module algebra, and if the inner product on the Hilbert space H is D-invariant, there is a unique $C^*$-representation $\theta$ of D associated with the action. The fixed-point subspace under the action of D is a Von Neumann algebra, and furthermore, it is the commutant of $\theta$(D) in L(H).

• Bulletin of the Korean Mathematical Society
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• v.38 no.1
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• pp.143-148
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• 2001

First, we show the finiteness property of the homotopy fixed point set of p-discrete toral group. Let $G_\infty$ be a p-discrete toral group and X be a finite complex with an action of $G_\infty such that X^K$ is nilpotent for each finit p-subgroup K of $G_\infty$. Assume X is $F_\rho-complete$. Then X(sup)hG$\infty$ is F(sub)p-finite. Using this result, we give the condition so that X$^{hG}$ is $F_\rho-finite for \rho-compact$ toral group G.

• Journal of the Korean Mathematical Society
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• v.44 no.3
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• pp.615-626
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• 2007

A pair of pants $\sum(0,\;3)$ is a building block of oriented surfaces. The purpose of this paper is to determine the discrete conditions for the holonomy group $\pi$ of hyperbolic structure of a pair of pants. For this goal, we classify the relations between the locations of principal lines and entries of hyperbolic matrices in $\mathbf{PSL}(2,\;\mathbb{R})$. In the level of the matrix group $\mathbf{SL}(2,\;\mathbb{R})$, we will show that the signs of traces of hyperbolic elements playa very important role to determine the discreteness of holonomy group of a pair of pants.

• 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.

• Journal of the Korean Mathematical Society
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• v.34 no.1
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• pp.77-86
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• 1997

Let $\Gamma$ be a discrete subgroup of hyperbolic isometries acting on the Poincare disc $B^m, m \geq 2$. The discrete group $\Gamma$ acts properly discontinously in $B^m$, and acts on $\partial B^m$ as a group of conformal homemorphisms, but need not act properly discontinously on $\partial B^m$.

• Journal of the Korean Mathematical Society
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• v.43 no.1
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• pp.29-43
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• 2006

The article deals with the problem of extending representations of a closed normal subgroup H to a topological group G. We show that the standard technique using group cohomology to solve the problem in the case of finite groups can be generalized in the category of topological groups if G/H is discrete.

• Journal of the Korean Mathematical Society
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• v.36 no.1
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• pp.1-13
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• 1999

Let G be the 3-dimensional Heisenberg group. A discrete subgroup of Isom(G), acting freely on G with non-compact quotient, must be isomorphic to either 1, Z, Z2 or the fundamental group of the Klein bottle. We classify all discrete representations of such groups into Isom(G) up to affine conjugacy. This yields an affine calssification of 3-dimensional non-compact infra-nilmanifolds.

• Proceedings of the KIPE Conference
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• 2002.07a
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• pp.589-592
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• 2002

The CCM (Continuous Conduction Mode) boost topology is generally used in the PFC (Power Factor Correction) regulator of household air-conditioning systems. There are three kinds of power devices-bridge rectifier diodes, FRDs (Fast Recovery Diodes), and IGBTs (or MOSFETs) - used In a boost PFC regulator. Selecting the appropriate device is very cumbersome work, specially, in the case of FRDs and IGBTs, because there are several considerations as described below: 1) High frequency leakage current regulation (conducted and radiated EMI regulation) 2) Power losses and thermal design 3) Device cost. It should be noted that there are trade-offs between the power loss characteristic of 2) and the other characteristics of 1) and 3). This paper presents a detailed evaluation by using several types of power devices, which can be unintentionally used, to show that optimal selection can be achieved. Based on the given thermal resistances, thermal analysis and design procedures are also described from a practical viewpoint.

• Structural Engineering and Mechanics
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• v.44 no.4
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• pp.501-519
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• 2012

Truss weight is one of the most important factors in the cost of construction that should be reduced. Different methods have been proposed to optimize the weight of trusses. The artificial bee colony algorithm has been proposed recently. This algorithm selects the lightest section from a list of available profiles that satisfy the existing provisions in the design codes and specifications. An important issue in optimization algorithms is how to impose constraints. In this paper, the artificial bee colony algorithm is used for the discrete optimization of trusses. The fly-back mechanism is chosen to impose constraints. Finally, with some basic examples that have been introduced in similar articles, the performance of this algorithm is tested using the fly-back mechanism. The results indicate that the rate of convergence and the accuracy are optimized in comparison with other methods.