• Bulletin of the Korean Mathematical Society
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• v.34 no.1
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• pp.1-8
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• 1997

Let G be a finiteg oroup. We denote BG a classifying space of G, which a contractible universal principal G bundle EG. The stable type of BG does not determine G up to isomorphism. A simple example [due to N. Minami]is given by $Q_{4p} \times Z/2$ and $D_{2p} \times Z/4$ where ps is an odd prime, $Q_{4p} is the generalized quarternion group of order 4p and $D_{2p}$ is the dihedral group of order 2p. However the paper [6] gives us a necessary and sufficient condition for $BG_1$ and $BG_2$ to be stably equivalent localized et pp. The local stable type of BG depends on the conjegacy classes of homomorphisms from the p-groups Q into G. This classification theorem simplifies if G has a normal sylow p-subgroup. Then the stable homotopy type depends on the Weyl group of the sylow p-subgroup.

• Journal of Power Electronics
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• v.19 no.6
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• pp.1515-1526
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• 2019

Ear-piercing high-frequency noise from electromagnetic vibrations in motors has become unacceptable in sensitive environments, due to the application of pulse width modulation (PWM) and in consideration of switching losses. This paper proposed a synchronous periodic frequency modulation (SPFM) method based on the interleaving technique for paralleled three-phase voltage source inverters (VSIs) to eliminate PWM vibration noise. The proposed SPFM technique is able to effectively remove unpleasant high-frequency vibration noise as well as acoustic noise more effectively than the conventional periodic carrier frequency modulation (PCFM) and interleaving technique. It completely eliminates the vibration noise near odd-order carrier frequencies and reduces the PWM vibration noise near even-order carrier frequencies depending on the switching frequency variation range. Furthermore, the SPFM method is simple to implement and does not employ additional circuits in the drive system. Finally, the effectiveness of the proposed method has been confirmed by detailed experimental results.

• Nuclear Engineering and Technology
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• v.53 no.12
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• pp.3861-3878
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• 2021

The steady-state simplified spherical harmonics equations (SP_N equations) are a higher order approximation to the neutron transport equations than the neutron diffusion equation that also have reasonable computational demands. This work extends these results for the analysis of transients by comparing of two formulations of time-dependent SP_N equations considering different treatments for the time derivatives of the field moments. The first is the full system of equations and the second is a diffusive approximation of these equations that neglects the time derivatives of the odd moments. The spatial discretization of these methodologies is made by using a high order finite element method. For the time discretization, a semi-implicit Euler method is used. Numerical results show that the diffusive formulation for the time-dependent simplified spherical harmonics equations does not present a relevant loss of accuracy while being more computationally efficient than the full system.

• Journal of the Optical Society of Korea
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• v.13 no.1
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• pp.15-21
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• 2009

High-order harmonic generation from a solid surface affected by the contrast of a laser pulse was studied using an oscillating mirror model. High-order harmonics generated from solid surfaces have unusual properties such as spectral redshift, and an intensity difference between even- and odd-order harmonics which is not reported for high-order harmonics generated by a gas medium. We confirmed that high-order harmonics from solid surfaces have selectivity of polarization as well as cut-off extension and the enhancement of conversion efficiency proportional to laser intensity. And the principle of operation and the characteristics of a plasma mirror system developed for achieving high contrast laser pulses to pursue the experimental realization of high-harmonic generation from solid surfaces are reported. Energy fluence on the plasma mirrors is tunable between $10\;J/cm^2$ and $1000\;J/cm^2$ and around 1000 shots are available before the plasma mirrors require replacement.

• Journal of Power Electronics
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• v.15 no.4
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• pp.1085-1092
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• 2015

In this paper, the expressions of the estimated information of a single-phase enhanced phase-locked loop (EPLL), when input signal contains harmonics and a DC offset while the fundamental component takes step changes, are derived. The theoretical analysis results indicate that in the estimated information, the n^th-order harmonics cause n+1^th-order periodic ripples, and the DC offset causes a periodic ripple at the fundamental frequency. Step changes of the amplitude, phase angle and frequency of the fundamental component cause a transient periodic ripple at twice the frequency. These periodic ripples deteriorate the performance of the EPLL. A hybrid filter based EPLL (HF-EPLL) is proposed to eliminate these periodic ripples. A delay signal cancellation filter is set at the input of the EPLL to cancel the DC offset and even-order harmonics. A sliding Goertzel transform-based filter is introduced into the amplitude estimation loop and frequency estimation loop to eliminate the periodic ripples caused by the residual input odd-order harmonics and step change of the input fundamental component. The parameter design rules of the two filters are discussed in detail. Experimental waveforms of both the conventional EPLL and the proposed HF-EPLL are given and compared with each other to verify the theoretical analysis and advantages of the proposed HF-EPLL.

• Journal of the Korean School Mathematics Society
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• v.18 no.1
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• pp.1-14
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• 2015

In this paper, in order to improve the teaching contents on even and odd number, composition and decomposition of numbers, and (1 digit)+(1 digit) with carrying, (10 and 1 digit)-(1 digit) with borrowing, the corresponding teaching contents in ${\ll}$Math 1-1${\gg}$, ${\ll}$Math 1-2${\gg}$ are critically reviewed. Implications obtained through this review can be summarized as follows. First, the current incomplete definition of even and odd numbers would need to be reconsidered, and the appropriateness of dealing with even and odd numbers in first grade would need to be reconsidered. Second, it is necessary to deal with composition and decomposition of numbers less than 20. That is, it need to be considered to compose (10 and 1 digit) with 10 and (1 digit) and to decompose (10 and 1 digit) into 10 and (1 digit) on the basis of the 10. And the sequence dealing with composition and decomposition of 10 before dealing with composition and decomposition of (10 and 1 digit) need to be considered. And it need to be considered that composing (10 and 1 digit) with (1 digit) and (1 digit) and decomposing (10 and 1 digit) into (1 digit) and (1 digit) are substantially useless. Third, it is necessary to eliminate the logical leap in the calculation process. That is, it need to be considered to use the composing (10 and 1 digit) with 10 and (1 digit) and decomposing (10 and 1 digit) into 10 and (1 digit) on the basis of the 10 to eliminate the leap which can be seen in the explanation of calculating (1 digit)+(1 digit) with carrying, (10 and 1 digit)-(1 digit) with borrowing. And it need to be considered to deal with the vertical format for calculation of (1 digit)+(1 digit) with carrying and (10 and 1 digit)-(1 digit) with borrowing in ${\ll}$Math 1-2${\gg}$, or it need to be considered not to deal with the vertical format for calculation of (1 digit)+(1 digit) with carrying and (10 and 1 digit)-(1 digit) with borrowing in ${\ll}$Math 1-2 workbook${\gg}$ for the consistency.

• Applied Chemistry for Engineering
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• v.21 no.2
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• pp.230-237
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• 2010

A homologous series of linear liquid crystal dimers, ${\alpha},{\omega}$-bis(4-nitroazobenzene-4'-carbonyloxy)alkanes (NATWESn, n = 2~8, 10, the number of methylene units in the spacer) have been synthesized, and the thermal behavior of the series has been investigated. All the dimers formed enantiotropic nematic phases. The nematic-isotropic transition temperatures of the dimers and their entropy variation at the phase transition showed a large odd-even effect as a function of n. This behavior was rationalized in terms of the change in the average shape of the spacer on varing the parity of the spacer. The thermal stability and degree of order in the nematic phase and the magnitude of the odd-even effect of NATWESn were very similar to those of the corresponding ether compounds, while they were significantly different from those of the monomesogenic compounds, 4-{4'-(nitrophenylazo)phenoxy}alkanoyl chlorides and the side-chain liquid-crystalline polymers, the poly[1-{4-(4'-nitrophenylazo) phenoxycarbonylalkanoyloxy}ethylene]s. The results were discussed in terms of the 'irtual trimer model'by Imrie.

• Applied Chemistry for Engineering
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• v.19 no.5
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• pp.504-511
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• 2008

Two kinds of nitroazobenzene derivatives: 4-{4'-(nitrophenylazo)phenoxy}alkanoic acids (NAAn, n = 2~8, 10, number of methylene units in the alkyl chain) and 4-{4'-(nitrophenylazo)phenoxy}alkanoyl chlorides (NACn, n = 2~8, 10) were synthesized, and their thermotropic liquid crystalline behaviors were investigated. NAA6 formed an enantiotropic nematic phase, while the remainders, except NAA2, showed monotropic nematic phases. Isotropic-nematic transition temperature ($T_{iN}$) and change of entropy (${\Delta}S$) at $T_{iN}$ for both of NAAn and NACn varied by the change of n, and pronounced odd-even effects of n were also observed. However, the $T_{iN}$ and ${\Delta}S$ values of NAAn were much higher than those of NACn. This fact may be attributed to the hydrogen bonding between carboxyl groups. Thermal properties and degree of order in the mesophase and the magnitude of the odd-even effects of both NAAn and NACn were significantly different from those reported for 4-(alkoxy)-4'-nitroazobenzenes. It was discussed in terms of the differences in the molecular anisotropy and the temperature-dependent flexibility of the substituted groups.

• Applied Chemistry for Engineering
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• v.22 no.4
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• pp.358-366
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• 2011

A homologous series of linear liquid crystal dimers, the ${\alpha},{\omega}$-bis(4-cyano-azobenzene-4'-oxy)alkanes (CATWETn, where n, the number of methylene units in the spacer, is 2~10) were synthesized, and their thermotropic liquid crystalline phase behavior were investigated. The CATWETn with n of 3 and 6 exhibited monotropic nematic phases, whereas other derivatives showed enantiotropic nematic phases. The nematic-isotropic transition temperatures of the dimers and their entropy variation at the phase transition showed a large odd-even effect as a function of n. This phase transition behavior was rationalized in terms of the change in the average shape of the spacer on varying the parity of the spacer. The thermal stability and degree of order in the nematic phase and the magnitude of the odd-even effect of CATWETn were similar to those for the methoxy-, nitro-, and pentyl-substituted dimers, while they were significantly different from those for the monomesogenic compounds, 1-{4-(4'-cyanophenylazo)phenoxy}alkylbromides and the side-chain liquid-crystalline polymers, the poly[1-{4-(4'-cyanophenylazo)phenoxyalkyloxy}ethylene]s. The results were discussed in terms of 'virtual trimer model' by Imrie.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.38 no.3
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• pp.35-43
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• 2001

A method is newly presented to synthesize the modal impedances satisfying the desired coupling factor of a reflective (or hack ward) coupled-line. The synthesis is achieved by optimal perturbations of repeating null points of lobes inherent to the solution of the first order nonlinear differential equation for coupling. It is based on the synthesis method of nonlinear source distribution functions for the prescribed space factor pattern in the one-dimensional array antenna. Here, the conventional synthesis method for the even distribution function is extended to the odd case. Resulting modal impedances will have continuously varying profiles. The design procedure of asymmetrical and symmetrical couplers corresponding to the even and odd distribution functions, is examplified to show the generalization and the simplicity of the proposed method.