• Journal of the Korean Mathematical Society
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• v.54 no.1
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• pp.117-139
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• 2017

This paper presents a systematic study for theoretical aspects of a unified approach to the abstract relative Fourier transforms over canonical homogeneous spaces of semi-direct product groups with Abelian normal factor. Let H be a locally compact group, K be a locally compact Abelian (LCA) group, and ${\theta}:H{\rightarrow}Aut(K)$ be a continuous homomorphism. Let $G_{\theta}=H{\ltimes}_{\theta}K$ be the semi-direct product of H and K with respect to ${\theta}$ and $G_{\theta}/H$ be the canonical homogeneous space (left coset space) of $G_{\theta}$. We introduce the notions of relative dual homogeneous space and also abstract relative Fourier transform over $G_{\theta}/H$. Then we study theoretical properties of this approach.

• Interaction and multiscale mechanics
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• v.6 no.1
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• pp.1-14
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• 2013

The aim of this paper is to study the propagation of torsional surface waves in non-homogeneous isotropic layer of finite thickness placed over a homogeneous viscoelastic half-space, when both density and rigidity of the non-homogeneous medium are assumed to vary exponentially with depth. The frequency equations are obtained by using simple method of separation of variables. Further, it is seen that when viscoelastic parameter and non-homogeneity parameter is neglected, the dispersion equation gives the dispersion equations of Love waves in homogeneous, elastic and isotropic layer placed over homogeneous viscoelastic medium. The problem has been solved numerically and the effects of various inhomogeneities of the medium on torsional waves have been illustrated graphically.

• Structural Engineering and Mechanics
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• v.43 no.1
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• pp.89-103
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• 2012

In this study, the stability of laminated homogeneous and non-homogeneous orthotropic truncated conical shells with freely supported edges under a uniform hydrostatic pressure is investigated. It is assumed that the composite material is orthotropic and the material properties depend only on the thickness coordinate. The basic relations, the modified Donnell type stability and compatibility equations have been obtained for laminated non-homogeneous orthotropic truncated conical shells. Applying Galerkin method to the foregoing equations, the expression for the critical hydrostatic pressure is obtained. The appropriate formulas for the single-layer and laminated, cylindrical and complete conical shells made of homogeneous and non-homogeneous, orthotropic and isotropic materials are found as a special case. Finally, effects of non-homogeneity, number and ordering of layers and variations of shell characteristics on the critical hydrostatic pressure are investigated.

• Bulletin of the Korean Mathematical Society
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• v.56 no.3
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• pp.681-689
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• 2019

The $M{\ddot{o}}bius$ homogeneous submanifold in ${\mathbb{S}}^{n+1}$ is an orbit of a subgroup of the $M{\ddot{o}}bius$ transformation group of ${\mathbb{S}}^{n+1}$. In this note, We prove that a compact $M{\ddot{o}}bius$ homogeneous submanifold in ${\mathbb{S}}^{n+1}$ is the image of a $M{\ddot{o}}bius$ transformation of the isometric homogeneous submanifold in ${\mathbb{S}}^{n+1}$.

• Bulletin of the Korean Mathematical Society
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• v.42 no.1
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• pp.29-37
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• 2005

In this paper we present result on Pexider type of stability and superstability of homogeneous mappings. Some consequences for quadratic mappings and linear operators are also established.

• Bulletin of the Korean Mathematical Society
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• v.32 no.2
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• pp.281-285
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• 1995

The complete classification of the simply connected four dimensional naturally reductive homogeneous spaces is given in [3].

• East Asian mathematical journal
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• v.39 no.1
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• pp.37-42
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• 2023

The purpose of this paper is to establish the notion of semi-Riemannian manifolds M with the homogeneous geodesics, and investigate properties about certain homogeneity.

• Journal of the Korean Chemical Society
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• v.56 no.6
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• pp.720-724
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• 2012

Under pseudo-first order conditions, the monomeric species of Cr(VI) was found to be kinetically active in the absence of phenanthroline (phen) whereas in the phen-promoted path, the Cr(VI)-phen complex undergoes a nucleophilic attack by etane-1,2-diol to form a ternary complex which subsequently experience a redox decomposition leading to hydroxy ethanal and Cr(III)-phen complex. The effect of the cationic surfactant (CPC), anionic surfactant (SDS) and neutral surfactant (TX-100) on the unpromoted and phen-promoted path have been studied. Micellar effects have been explained by considering the preferential partitioning of reactants between the micellar and aqueous phase. Combination of TX-100 and phenanthroline will be the ideal for chromic acid oxidation of ethane-1,2-diol in aqueous media.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.31 no.8
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• pp.672-679
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• 2007

The combustion characteristics of a liquefied petroleum gas-di-methyl ether (LPG-DME) compression ignition engine was investigated under homogeneous charge and stratified charge conditions. LPG was used as the main fuel and injected into the combustion chamber directly. DME was used as an ignition promoter and injected into the intake port. Different LPG injection timings were tested to verify the combustion characteristics of the LPG-DME compression ignition engine. The combustion was divided into three region which are homogeneous charge, stratified charge, and diffusion flame region according to the injection timing of LPG. The hydrocarbon emission of stratified charge combustion was lower than that of homogeneous charge combustion. However, the carbon monoxide and nitrogen oxide emission of stratified charge combustion were slightly higher than those of the homogeneous charge region. The indicated mean effective pressure was reduced at stratified charge region, while it was almost same level as the homogeneous charge combustion region at diffusion combustion region. The start of combustion timing of the stratified charge combustion and diffusion combustion region were advanced compared to the homogeneous charge combustion. It attributed to the higher cetane number and mixture temperature distribution which locally stratified. However, the knock intensity was varied as the homogeneity of charge was increased.

• Journal of the Korean Applied Science and Technology
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• v.22 no.1
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• pp.56-61
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• 2005

Methanol was synthesized by homogeneous and catalytic reactions of partial oxidation of methane. The effect of pressure, temperature and oxygen concentration on methanol synthesis was investigated. The catalyst used was Bi-Cs-Mg-Cu-Mo mixed oxide. The partial oxidation reaction was carried out in a fixed bed reactor at 20${\sim}$46 bar and $450{\sim}480^{\circ}C$ and oxygen concentration of 5.3${\sim}$7.7mol%. The results were compared with results of homogeneous reaction performed at the same conditions. Methane conversions of the homogeneous and catalytic reactions increased with temperature. Methanol selectivity of the homogeneous reaction decreased with increasing temperature. However, the methanol selectivity of catalytic reaction increased with temperature. For both homogeneous and catalytic reactions, the methane conversions were around 5%. This may be due to the low oxygen concentration. Methanol selectivity of the catalytic reaction was higher than that of homogeneous one.