• 대한수학회논문집
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• 제27권4호
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• pp.721-732
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• 2012

The principal aim of the paper is to investigate new integral expression $${\int}_0^{\infty}x^{s+1}e^{-{\sigma}x^2}L_m^{(\gamma,\delta)}\;({\zeta};{\sigma}x^2)\;L_n^{(\alpha,\beta)}\;({\xi};{\sigma}x^2)\;J_s\;(xy)\;dx$$, where $y$ is a positive real number; $\sigma$, $\zeta$ and $\xi$ are complex numbers with positive real parts; $s$, $\alpha$, $\beta$, $\gamma$ and $\delta$ are complex numbers whose real parts are greater than -1; $J_n(x)$ is Bessel function and $L_n^{(\alpha,\beta)}$ (${\gamma};x$) is generalized Laguerre polynomials. Some integral formulas have been obtained. The Maple implementation has also been examined.

• 충청수학회지
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• 제21권4호
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• pp.501-510
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• 2008

The distribution of the sum of n independent random variables having exponential distributions with different parameters ${\beta}_i$ ($i=1,2,{\ldots},n$) is given in [2], [3], [4] and [6]. In [1], by using Laplace transform, Jasiulewicz and Kordecki generalized the results obtained by Sen and Balakrishnan in [6] and established a formula for the distribution of this sum without conditions on the parameters ${\beta}_i$. The aim of this note is to present a method to find the distribution of the sum of n independent exponentially distributed random variables with different parameters. Our method can also be used to handle the case when all ${\beta}_i$ are the same.

• 한국지구과학회지
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• 제41권4호
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• pp.344-355
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• 2020

Tropical cyclone scale vortices and associated Rossby waves were investigated numerically using high-resolution barotropic models on the global domain. The equations of the barotropic model were discretized using the spectral transform method with the spherical harmonics function as orthogonal basis. The initial condition of the vortex was specified as an axisymmetric flow in the gradient wind balance, and four types of basic zonal states were employed. Vortex tracks showed similar patterns as those on the beta-plane but exhibited more eastward displacement as they moved northward. The zonal-mean flow appeared to control not only the west-east translation but also the meridional translation of the vortex. Such a meridional influence was revealed to be associated with the beta gyre and the Rossby wave, which are formed around the vortex due to the beta effect. In the case of the basic zonal state of climatological mean, the meridional translation speed reached the maximum value when the vortex underwent recurving.

• 대한수학회보
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• 제60권6호
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• pp.1555-1566
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• 2023

A Hilbert space operator A ∈ B(H) is a generalised n-projection, denoted A ∈ (G-n-P), if A^*n = A. (G-n-P)-operators A are normal operators with finitely countable spectra σ(A), subsets of the set $\{0\}\,{\cup}\,\{\sqrt[n+1]{1}\}.$ The Aluthge transform à of A ∈ B(H) may be (G - n - P) without A being (G - n - P). For doubly commuting operators A, B ∈ B(H) such that σ(AB) = σ(A)σ(B) and ${\parallel}A{\parallel}\,{\parallel}B{\parallel}\;{\leq}\;{\parallel}{\tilde{AB}}{\parallel},$ ${\tilde{AB}}\;{\in}\;(G\,-\,n\,-\,P)$ if and only if $A\;=\;{\parallel}{\tilde{A}}{\parallel}\,(A_{00}\,{\oplus}\,(A_0\,{\oplus}\,A_u))$ and $B\;=\;{\parallel}{\tilde{B}}{\parallel}\,(B_0\,{\oplus}\,B_u),$ where A₀₀ and B₀, and A₀ ⊕ A_u and B_u, doubly commute, A₀₀B₀ and A₀ are 2 nilpotent, A_u and B_u are unitaries, A^*n_u = A_u and B^*n_u = B_u. Furthermore, a necessary and sufficient condition for the operators αA, βB, αà and ${\beta}{\tilde{B}},\;{\alpha}\,=\,\frac{1}{{\parallel}{\tilde{A}}{\parallel}}$ and ${\beta}\,=\,\frac{1}{{\parallel}{\tilde{B}}{\parallel}},$ to be (G - n - P) is that A and B are spectrally normaloid at 0.

• Bulletin of the Korean Chemical Society
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• 제35권8호
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• pp.2487-2493
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• 2014

Dimeric ${\beta}$-cyclodextrin linked by a thioether bridge was synthesized from a reaction of mono-6-iodo-6-deoxy-${\beta}$-cyclodextrin with sodium sulfide, and the structure was analyzed using nuclear magnetic resonance spectroscopy and matrix-assisted laser desorption/ionization time-of-flight mass spectrometry. The effects of thioether-bridged dimeric ${\beta}$-CD on the aqueous solubility of flavonols (myricetin, quercetin, and kaempferol) were investigated by ultraviolet-visible spectroscopy. The aqueous solubility of myricetin, quercetin, and kaempferol were enhanced 33.6-, 12.4-, and 10.5-fold following the addition of 9 mM of thioether-bridged dimeric ${\beta}$-CD. In comparison, the aqueous solubility of myricetin, quercetin, and kaempferol were enhanced 5.4-, 3.3-, and 2.7-fold using the same concentration of monomeric ${\beta}$-cyclodextrin. Furthermore, the formation of flavonol/thioether-bridged dimeric ${\beta}$-CD inclusion complexes was confirmed with nuclear magnetic resonance, Fourier-transform infrared spectroscopy, differential scanning calorimetry, and scanning electron microscopy. The results showed that the nature of the complexes significantly differed from that of free flavonols. Herein, we suggest that the thioether-bridged dimeric ${\beta}$-CD can act as an effective complexing agent for flavonols.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제5권2호
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• pp.123-132
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• 1998

Let F and G denote the distribution functions of the failure times and the censoring variables in a random censorship model. Susarla and Van Ryzin(1978) verified consistency of $F_{\alpha}$, he NPBE of F with respect to the Dirichlet process prior D($\alpha$), in which they assumed F and G are continuous. Assuming that A, the cumulative hazard function, is distributed according to a beta process with parameters c, $\alpha$, Hjort(1990) obtained the Bayes estimator $A_{c,\alpha}$ of A under a squared error loss function. By the theory of product-integral developed by Gill and Johansen(1990), the Bayes estimator $F_{c,\alpha}$ is recovered from $A_{c,\alpha}$. Continuity assumption on F and G is removed in our proof of the consistency of $A_{c,\alpha}$ and $F_{c,\alpha}$. Our result extends Susarla and Van Ryzin(1978) since a particular transform of a beta process is a Dirichlet process and the class of beta processes forms a much larger class than the class of Dirichlet processes.

• 한국전기전자재료학회논문지
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• 제29권11호
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• pp.712-715
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• 2016

In this paper, we fabricated flexible CNT/PVDF piezoelectric composite device by introducing CNTs (carbon nanotubes) into PVDF (poly-vinylidene fluoride) solution using spray coating technique. Flexible PEDOT:PSS conducting polymer was used as electrodes. We tried to improve the piezoelectric performance from the CNT/PVDF composite film by increasing the portion of the ${\beta}$-phase PVDF in the film. We confirmed the structural conformation of the CNT/PVDF composite film as a function of CNT concentration by using FT-IR (fourier transform infra-red). As increasing CNT concentration, portion of the ${\beta}$-phase PVDF and resulting piezoelectric performance increased in the CNT/PVDF composite film. We found that CNTs introduced were played as seeds for formation of the ${\beta}$-phase PVDF in the CNT/PVDF composite film and resulting improvement of the piezoelectric performance.

• 한국표면공학회지
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• 제36권2호
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• pp.200-205
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• 2003

Thermoelectric p-type $Fe_{0.98}$ $Mn_{ 0.02}$$Si_2$ bulk specimens have been produced by mechanical alloying and consolidation by vacuum hot pressing. The subsequent isothermal annealing was not able to fully transform the mestastable as -milled powders into the $\beta$ $-FeSi_2$ phase, so that the obtained matrix consisted of not only thermoelectric semiconducting $\beta$-FeSi$_2$ but also some residual, untransformed metallic $\alpha$ $- Fe_2$$Si_{ 5}$ and $\varepsilon$-FeSi mixtures. Interestingly, $\beta$ - $FeSi_2$ was more easily obtained in the low density specimen when compared to the high density specimen. The oxidation at 700 and $800^{\circ}C$ in air led to the phase transformation of the above described iron - silicides and the formation of a thin silica surface layer.

• 신재생에너지
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• 제9권3호
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• pp.5-13
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• 2013

In the previous research, dynamic results have been analyzed in the time and frequency regions. Time and frequency region can be transformed by the Fourier transform. This transform is very useful about analyzing system behaviors. However, because of coupling, it cannot give clear results in the real system including lots of defects. In this paper, we introduced the analysis based on quefrency region to represent physical means clearly from complicated results. We simulated the drive train system which has defects, and compared between frequency and quefrency region to show its excellence. To do this process, We established mathematical model. The equation of motion was derived by the Lagrange equation and constraint equations. The constraint equation included relationships about gear mesh, flexibility of shaft. About numerical analysis, the Newmark beta method was used to get results. And FFT (Fast Fourier Transform) which converts results from time domain to frequency, qufrequency was used.

• 펄프종이기술
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• 제32권5호
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• pp.14-25
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• 2000

In this investigation, a wavelet transform analysis was used to decompose beta-radiographic formation images into spectral and spatial components. Conventional formation analysis may use spectral analysis, based on Fourier transformation or variance vs. zone size, to describe the grammage distribution of features such as flocs, streaks and mean fiber orientation. However, these methods have limited utility for the analysis of statistically stationary data sets where variance is not uniform with position, e.g. paper machine CD profiles (especially those that contain streaks). A continuous wavelet transform was used to analyze formation data arrays obtained from radiographic imaging of handsheets and cross machine paper samples. The response of the analytical method to grammage, floc size distribution, mean fiber orientation an sensitivity to feature localization were assessed. From wavelet analysis, the change in scale of grammage variation as a function of position was used to demonstrate regular and isolated differences in the formed structure.