• Journal of the Institute of Convergence Signal Processing
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• v.8 no.3
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• pp.178-184
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• 2007

The EEG signal in general can be categorized as the Alpha wave, the Beta wave, the Theta wave, and the Delta wave. The alpha wave, showed in stable state, is the dominant wave for a human EEG and the beta wave displays the excited state. The subject of this paper was to recognize the stable state of EEG quantitatively using wavelet transform and power spectrum analysis. We decomposed EEG signal into the alpha wave and the beta wave in the process of wavelet transform, and calculated each power spectrum of EEG signal, using Fast Fourier Transform. And then we calculated the stable state quantitatively by stable state ratio, defined as the power spectrum of the alpha wave over that of the beta wave. The study showed that it took more than 10 minutes to reach the stable state from the normal activity in 69 % of the subjects, 5 -10 minutes in 9%, and less than 5 minutes in 16 %.

• Proceedings of the IEEK Conference
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• 2006.06a
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• pp.879-880
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• 2006

The subject of this paper is to recognize the stable state of EEG using wavelet transform and power spectrum analysis. An alpha wave, showed in stable state, is dominant wave for a human EEG and a beta wave displayed excited state. We decomposed EEG signal into an alpha wave and a beta wave in the process of wavelet transform. And we calculated each power spectrum of EEG signal, an alpha wave and a beta wave using Fast Fourier Transform. We recognized the stable state by making a comparison between power spectrum ratios respectively.

• Bulletin of the Korean Mathematical Society
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• v.56 no.5
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• pp.1117-1127
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• 2019

Let ${\mathcal{L}}_2=(-{\Delta})^2+V^2$ be the $Schr{\ddot{o}}dinger$ type operator, where nonnegative potential V belongs to the reverse $H{\ddot{o}}lder$ class $RH_s$, s > n/2. In this paper, we consider the operator $T_{{\alpha},{\beta}}=V^{2{\alpha}}{\mathcal{L}}^{-{\beta}}_2$ and its conjugate $T^*_{{\alpha},{\beta}}$, where $0<{\alpha}{\leq}{\beta}{\leq}1$. We establish the $(L^p,\;L^q)$-boundedness of operator $T_{{\alpha},{\beta}}$ and $T^*_{{\alpha},{\beta}}$, respectively, we also show that $T_{{\alpha},{\beta}}$ is bounded from Hardy type space $H^1_{L_2}({\mathbb{R}}^n)$ into $L^{p_2}({\mathbb{R}}^n)$ and $T^*_{{\alpha},{\beta}}$ is bounded from $L^{p_1}({\mathbb{R}}^n)$ into BMO type space $BMO_{{\mathcal{L}}1}({\mathbb{R}}^n)$, where $p_1={\frac{n}{4({\beta}-{\alpha})}}$, $p_2={\frac{n}{n-4({\beta}-{\alpha})}}$.

• The Pure and Applied Mathematics
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• v.5 no.2
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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.

• Korean Journal of Microbiology
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• v.29 no.2
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• pp.111-116
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• 1991

Rhizopus nigricans produces 11.alpha.-hydroxyprogesternoe with a unidentified byproduct, which is hardly separated. Results of chromatography, IR and NMR spectroscopy identified the byproduct to be 11.alpha.-hydroxy-allopregnane-3,20-dione. R. nigricans was found to transform progesternoe into a monoform intermediate, 11.alpha.-hydroxyprogesterone, from which 11.alpha.-hydroxy-allopregnane-3,20-dione and 6.betha., 11.alpha. - dihydroxyprogesterone were formed respectively by 5.alpha.-reduction and 6.betha.-hydroxylation.

• Journal of the Korean Institute of Telematics and Electronics
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• v.26 no.2
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• pp.140-146
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• 1989

An efficient quantization and encoding of BTC (Block Truncation Coding) parameters {($Y_{\alpha},\;Y_{\beta}),\;P_{{\beta}/{\beta}}$} are investigated, In our algorithm 4${\times}$4 blocks are classified into flat or edge block. While edge block is represented by two approximation level $Y_{\alpha},\;Y_{\beta}$ with label plane $P_{{\beta}/{\beta}}$, flat block is represented by single approximation level Y. The approximation levels Y, $Y_{\alpha}$ and $Y_{\beta}$ are encoded by predictive quatization specially designed, and the label plane $P_{{\beta}/{\beta}}$ is tried to be encoded using stored 32 reference plantes. The performance of the proposed scheme has appeared comparable to much more complex transform coding in terms of SNR, although it requires more study on the representation of small slope in background.

• Bulletin of the Korean Mathematical Society
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• v.58 no.1
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• pp.235-251
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• 2021

We consider the Schrödinger type operator ��k = (-∆)k+Vk on ℝn(n ≥ 2k + 1), where k = 1, 2 and the nonnegative potential V belongs to the reverse Hölder class RHs with n/2 < s < n. In this paper, we establish the (Lp, Lq)-boundedness of the higher order Riesz transform T��,�� = V2��∇2��-��2 (0 ≤ �� ≤ 1/2 < �� ≤ 1, �� - �� ≥ 1/2) and its adjoint operator T∗��,�� respectively. We show that T��,�� is bounded from Hardy type space $H^1_{\mathcal{L}_2}({\mathbb{R}}_n)$ into Lp2 (ℝn) and T∗��,�� is bounded from ��p1 (ℝn) into BMO type space $BMO_{\mathcal{L}_1}$ (ℝn) when �� - �� > 1/2, where $p_1={\frac{n}{4({\beta}-{\alpha})-2}}$, $p_2={\frac{n}{n-4({\beta}-{\alpha})+2}}$. Moreover, we prove that T��,�� is bounded from $BMO_{\mathcal{L}_1}({\mathbb{R}}_n)$ to itself when �� - �� = 1/2.

• Kyungpook Mathematical Journal
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• v.49 no.1
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• pp.155-166
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• 2009

We give a necessary and sufficient condition that a square integrable functional F(x) on Yeh-Wiener space has an integral transform $\hat{F}_{{\alpha},{\beta}}F(x)$ which is also square integrable. This extends the result by Kim and Skoug for functional F(x) in $L_2(C_0[0,T])$.

• Asian-Australasian Journal of Animal Sciences
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• v.29 no.8
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• pp.1159-1165
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• 2016

The nutritional value of feed proteins and their utilization by livestock are related not only to the chemical composition but also to the structure of feed proteins, but few studies thus far have investigated the relationship between the structure of feed proteins and their solubility as well as digestibility in monogastric animals. To address this question we analyzed soybean meal, fish meal, corn distiller's dried grains with solubles, corn gluten meal, and feather meal by Fourier transform infrared (FTIR) spectroscopy to determine the protein molecular spectral band characteristics for amides I and II as well as ${\alpha}$-helices and ${\beta}$-sheets and their ratios. Protein solubility and in vitro digestibility were measured with the Kjeldahl method using 0.2% KOH solution and the pepsin-pancreatin two-step enzymatic method, respectively. We found that all measured spectral band intensities (height and area) of feed proteins were correlated with their the in vitro digestibility and solubility ($p{\leq}0.003$); moreover, the relatively quantitative amounts of ${\alpha}$-helices, random coils, and ${\alpha}$-helix to ${\beta}$-sheet ratio in protein secondary structures were positively correlated with protein in vitro digestibility and solubility ($p{\leq}0.004$). On the other hand, the percentage of ${\beta}$-sheet structures was negatively correlated with protein in vitro digestibility (p<0.001) and solubility (p = 0.002). These results demonstrate that the molecular structure characteristics of feed proteins are closely related to their in vitro digestibility at 28 h and solubility. Furthermore, the ${\alpha}$-helix-to-${\beta}$-sheet ratio can be used to predict the nutritional value of feed proteins.

• Communications of the Korean Mathematical Society
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• v.27 no.4
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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.