• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.10 no.5
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• pp.113-119
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• 2010

In this paper, the considered cognitive radio system has a pair of PT-PR and a pair of ST-SR. In first time slot(1 Phase), PT broadcast signal $x_p$ to PR, ST and SR. Then, each receivers(PR, ST, SR) decode received signal $x_p$. In second time slot(2 Phase), ST combine decoded signal ${x_p}^{\prime}$ and signal $x_s$, and it broadcast combined signal to PR and SR. PR and SR decode combined signal. At this time, PR can achieve diversity gain, due to using MRC, it combine 'received and decoded signal ${x_p}^{\prime}$ at 1 phase' and 'detected signal $x_p$ at 2 phase'. SR use linear combining technique and it can obtain $x_s$.

• Communications of the Korean Mathematical Society
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• v.27 no.3
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• pp.557-564
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• 2012

This study concerns the existence of positive solution for the following nonlinear system $$\{-div(|x|^{-ap}|{\nabla}u|^{p-2}{\nabla}u)=|x|^{-(a+1)p+c_1}({\alpha}_1f(v)+{\beta}_1h(u)),x{\in}{\Omega},\\-div(|x|^{-bq}|{\nabla}v|q^{-2}{\nabla}v)=|x|^{-(b+1)q+c_2}({\alpha}_2g(u)+{\beta}_2k(v)),x{\in}{\Omega},\\u=v=0,x{\in}{\partial}{\Omega}$$, where ${\Omega}$ is a bounded smooth domain of $\mathbb{R}^N$ with $0{\in}{\Omega}$, 1 < $p,q$ < N, $0{{\leq}}a<\frac{N-p}{p}$, $0{{\leq}}b<\frac{N-q}{q}$ and $c_1$, $c_2$, ${\alpha}_1$, ${\alpha}_2$, ${\beta}_1$, ${\beta}_2$ are positive parameters. Here $f,g,h,k$ : $[0,{\infty}){\rightarrow}[0,{\infty})$ are nondecresing continuous functions and $$\lim_{s{\rightarrow}{\infty}}\frac{f(Ag(s)^{\frac{1}{q-1}})}{s^{p-1}}=0$$ for every A > 0. We discuss the existence of positive solution when $f,g,h$ and $k$ satisfy certain additional conditions. We use the method of sub-super solutions to establish our results.

• Journal of the Korean Mathematical Society
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• v.55 no.2
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• pp.373-390
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• 2018

In this paper we study the small-data scattering of the d dimensional fractional $Schr{\ddot{o}}dinger$ equations with d = 2, 3, $L{\acute{e}}vy$ index 1 < ${\alpha}$ < 2 and Hartree type nonlinearity $F(u)={\mu}({\mid}x{\mid}^{-{\gamma}}{\ast}{\mid}u{\mid}^2)u$ with max(${\alpha}$, ${\frac{2d}{2d-1}}$) < ${\gamma}{\leq}2$, ${\gamma}$ < d. This equation is scaling-critical in ${\dot{H}}^{s_c}$, $s_c={\frac{{\gamma}-{\alpha}}{2}}$. We show that the solution scatters in $H^{s,1}$ for any s > $s_c$, where $H^{s,1}$ is a space of Sobolev type taking in angular regularity with norm defined by ${\parallel}{\varphi}{\parallel}_{H^{s,1}}={\parallel}{\varphi}{\parallel}_{H^s}+{\parallel}{\nabla}_{{\mathbb{S}}{\varphi}}{\parallel}_{H^s}$. For this purpose we use the recently developed Strichartz estimate which is $L^2$-averaged on the unit sphere ${\mathbb{S}}^{d-1}$ and utilize $U^p-V^p$ space argument.

• Bulletin of the Korean Chemical Society
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• v.9 no.3
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• pp.115-117
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• 1988

The addition of L-cysteine without blocking amino and carboxyl groups to${\beta},{\beta}$-dinitrostyrene derivatives(11a-e) were investigated. ${\beta},{\beta}$ -Dinitrostyrene derivatives(11a-e) easily undergo addition reactions with L-cysteine to from s-(2,2-dinitro-1-phenylethyl)-L-cysteine(12a), s-[2,2-dinitro-1-(p-methyl)phenylethyl]-L-cysteine (12b), s-[2,2-dinitro-1-(p-methoxy)phenylethyl]-L-cystein e(12c), s-[2,2-dinitro-1-(p-chloro)phenylethyl]-L-cysteine (12d) and s-[2,2-dinitro-1-(p-nitro)phenylethyl]-L-cysteine( 12a), respectively. The structure of adducts were confirmed by means of spectral data, molecular weight measurement and elemental analysis.

• Applied Biological Chemistry
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• v.38 no.5
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• pp.455-462
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• 1995

The new six herbicidal N-[(pyrimidin-2-yl)aminocarbonyl]-2-substituted-6-(1-hydroxy-2-fluoroethyl)benzenesulfonamide derivatives(S) were synthesized and rate constants for the hydrolysis of thier in the range of pH $1.0{\sim}10.0$ have been studied in 15%(v/v) aqueous acetonitrile solution at $45^{\circ}C$. From the basis of the results, pH-effect, solvent effect, ortho-substituent effect, thermodynamic parameters(${\Delta}H^{\neq}$ & ${\Delta}S^{\neq}$), pKa constant(4.80), rate equation, analysis of hydrolysis products(2-(1-hydroxy-2-fluoroethyl)benzenesulfonamide & 4,6-dimethoxyaminopyrimidine), it may be concluded that the general acid catalyzed hydrolysis through $A-S_E2$ mechanism and specific acid catalyzed hydrolysis through A-2 type(or $A_{AC}2$) mechanism proceeds via conjugate acid($SH^+$) and tetrahedral intermediate(I) below pH 8.0, whereas, above pH 9.0, the general base catalyzed hydrolysis by water molecules(B) through $(E_1)_{anion}$ mechanism proceeds via conjugate base(CB). In the range between $pH\;7.0{\sim}pH\;9.0$, these two reactions occur competitively.

• YAKHAK HOEJI
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• v.46 no.5
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• pp.313-319
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• 2002

Synthesis of 7$\beta$-[(Z)-2-(2-aminothiazol-4-yl)-2-(1-carboxy-1-methylethoxyimino)acetamido]-3-[[(3S, 5S)-5-[4-phenyl-5-(4-methylphenyl or 2-thiophenyl)-4H-l, 2, 4- triazol-3-yl]thiomethylpyrrolidin-3-yl]]thiomethyl-3-cephem-4-carboxylic acids (7a, 7b) were described. (2S, 4S)-4-acethylthio-2-[4-phenyl-5-(4-methylphenyl or 2-thiophenyl)-4 H-1, 2, 4-triazol-3-yl]thiomethyl-1-tert-butoxycarbonylpyrrolidines (4a, 4b) were prepared from trans-4-hydroxy-L-proline with (2S, 4R)-absolute configuration as starting material. 4-Phenyl-5-(4-methylphenyl or 2-thiophenyl)-4 H-l, 2, 4-triazol-3-thiols (2a, 2b) were prepared from p-toluic anhydride and 2-thiophene carboxylic acid hydrazide, respectively. p-Methoxybenzyl 7$\beta$-(Z)-2-(2-for-mamidothiazol-4-yl)-2-(1-tert-butoxycarbonylisopropylimino]acetamido-3-[[ (3S, 5S)-5-[4-phenyl-5-(4-methylphenyl or 2-thio phenyl)-4H-1, 2, 3-triazol-3-yl]thiomethyl-1- tert-butoxycarbonylpyrrolidin-3-yl]]thiomethyl-3-cephem-4-carboxylates (6a, 6b) were achieved by using p-methoxybenzyl ]7P-(Z)-2-(2-formamidothiazol-4-yl)-2-(tert-butoxycarbonylisopropylimino] acetamido-3-chloromethyl-3-cephem-4-carboxylate (5) and (2S, 4S)-4-acethylthio-2-[4-phenyl-5-(4-methyl phenyl or 2-thiophenyl)-4H-1, 2, 4-triazol-3-yl]thiomethyl-1-tert-butoxycarbonyl pyrrolidines (4a, 4b). Removal of formyl, Boc, and p-methoxybenzyl protecting groups were carried out by triflu oroacetic acid and anisole to give the target compounds.

• The Journal of Engineering Geology
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• v.11 no.2
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• pp.215-227
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• 2001

The Okchon Formation and the Mesozoic granite of the Boeun, Chungbuk are compared in terms of seismic wave velocities estimated from the field experiment, and seismic wave velocities in 3-D measured from the rock specimen. P-wave velocity for the field data ranges from 861 m/s (Guryongsan-2 Formation) to 2697m/s (Bulguksa Granite). P-wave anisotropy also ranges from 46% (Changri Formation) to 81% (Bulguksa Granite), with an average value of 68.5%. P-wave velocities for the rock specimens from Guryongsan-1, Guryongsan-2, Changri, and Munjuri Formations are greater than 5000m/s. S-wave velocities for those specimens are approximately 3500m/s, which is 3-5 times grater than the ones estimated from the field experimental data. P-wave anisotropy for the specimens from Bulguksa Granite and Guryongsan-1 Formation exceeds 60%, which is compared to 30% for the other specimens. This value is much smaller than average P-wave anisotropy (69.5%) for the field data. It is suggested that velocity difference, associated with the propagation direction, is much greater for the field data than for the specimens.

• Bulletin of the Korean Chemical Society
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• v.5 no.6
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• pp.215-218
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• 1984

A series of S-(2,2-diethoxycarbonyl-1-phenylethyl)-L-cysteine derivatives (10a-e) were synthesized from the reaction of $\beta$$\beta$-diethoxycarbonylstyrene with L-cysteine in 1:1 aqueous methanol. Thus, S-(2,2-diethoxycarbonyl-1-phenylethyl)-L-cysteine( 10a), S-[2,2-diethoxycarbonyl-1-(3',4'-methylendioxy)ph enylethyl]-L-cysteine (10b), S-[2,2-diethoxycarbonyl-1-(3',4',5'-trimethoxy)phe nylethyl]-L-cyseine (10c), S-[2,2-diethoxycarbonyl-1-(p-hydroxy)phenylethyl] -L-cysteine (10d), S-[2,2-diethoxycarbonyl-1-(p-methoxy)phenylethyl] -L-cysteine (10e) were obtained in moderate to excellent yields. The structure of the adducts was characterized by analytical and spectral data. The effects of pH upon the product yields were also briefly examined.

• Journal of the Korean Mathematical Society
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• v.46 no.1
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• pp.187-213
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• 2009

For a positive integer k and an arbitrary integer h, the classical Dedekind sums s(h,k) is defined by $$S(h,\;k)=\sum\limits_{j=1}^k\(\(\frac{j}{k}\)\)\(\(\frac{hj}{k}\)\),$$ where $$((x))=\{{x-[x]-\frac{1}{2},\;if\;x\;is\;not\;an\;integer; \atop \;0,\;\;\;\;\;\;\;\;\;\;if\;x\;is\;an\;integer.}\$$ J. B. Conrey et al proved that $$\sum\limits_{{h=1}\atop {(h,k)=1}}^k\;s^{2m}(h,\;k)=fm(k)\;\(\frac{k}{12}\)^{2m}+O\(\(k^{\frac{9}{5}}+k^{{2m-1}+\frac{1}{m+1}}\)\;\log^3k\).$$ For $m\;{\geq}\;2$, C. Jia reduced the error terms to $O(k^{2m-1})$. While for m = 1, W. Zhang showed $$\sum\limits_{{h=1}\atop {(h,k)=1}}^k\;s^2(h,\;k)=\frac{5}{144}k{\phi}(k)\prod_{p^{\alpha}{\parallel}k}\[\frac{\(1+\frac{1}{p}\)^2-\frac{1}{p^{3\alpha+1}}}{1+\frac{1}{p}+\frac{1}{p^2}}\]\;+\;O\(k\;{\exp}\;\(\frac{4{\log}k}{\log\log{k}}\)\).$$. In this paper we give some formulae on the mean value of the Dedekind sums and and Hardy sums, and generalize the above results.

• Korean Journal of Poultry Science
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• v.32 no.1
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• pp.15-21
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• 2005

This Study was conducted to investigate the effects of microbial phytase in low phosphirus and calcium level diet on the performance and nutrient digestibility in laying hens. One hundred ninety two, 50 wks old, ISA brown commerical layers were used for 12 weeks feeding trial after 7-d adjustment period. Four dietary treatments included CON(control; Co.), P2 ($0.06\%$ Natuphos, BASF) and P3 ($0.06\%$ PHOSMAX, GENOFOCUS). Ca and available P concentrations of P1, P2 and P3 were 90 and $50\%$ of NRC recommecdations to accentuate difference in response to phytase availability. In whole period, egg production was not affected by treatments. At 12 weeks, egg weight was significantly increased in adding phytase treatments (P<0.05). Egg shell thickness was increased in P1, P2 and P3 treatments compared with control (P<0.05) at 9 weeks. Ca concentration of serum tended to decrease in P1 treatment without significant difference (P>0.05). Ca and P concentrations of tibia were higher in layers fed dietary phyrase than those fed control diet without significant difference (P>0.05). Digestibilities of DM, N and ash were improved in P1 treatment compared with P2 and P3 treatments (P<0.05). Ca and P digestibilities were the highest in P2 treatment (P>0.05), but was not significant difference between control and P1 treatments.