• Journal of the Chungcheong Mathematical Society
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• v.17 no.1
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• pp.85-101
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• 2004

Let A be a Hopf algebra with a linear form ${\sigma}:k{\rightarrow}A{\otimes}A$, which is convolution invertible, such that ${\sigma}_{21}({\Delta}{\otimes}id){\tau}({\sigma}(1))={\sigma}_{32}(id{\otimes}{\Delta}){\tau}({\sigma}(1))$. We define Hopf algebras, ($A_{\sigma}$, m, u, ${\Delta}_{\sigma}$, ${\varepsilon}$, $S_{\sigma}$). If B and C are opposite skew copaired Hopf algebras and $A=B{\otimes}_kC$ then we find Hopf algebras, ($A_{[{\sigma}]}$, $m_B{\otimes}m_C$, $u_B{\otimes}u_C$, ${\Delta}_{[{\sigma}]}$, ${\varepsilon}B{\otimes}{\varepsilon}_C$, $S_{[{\sigma}]}$). Let H be a finite dimensional commutative Hopf algebra with dual basis $\{h_i\}$ and $\{h_i^*\}$, and let $A=H^{op}{\otimes}H^*$. We show that if we define ${\sigma}:k{\rightarrow}H^{op}{\otimes}H^*$ by ${\sigma}(1)={\sum}h_i{\otimes}h_i^*$ then ($A_{[{\sigma}]}$, $m_A$, $u_A$, ${\Delta}_{[{\sigma}]}$, ${\varepsilon}_A$, $S_{[{\sigma}]}$) is the dual space of Drinfeld double, $D(H)^*$, as Hopf algebra.

• Journal of the Korean Chemical Society
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• v.46 no.6
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• pp.495-501
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• 2002

The critical micelle concentration(CMC) and the counterion binding constant(B) for the mixed micel-lization of sodium n-octanoate(SOC) with n-octylammonium chloride(OAC) were determined as a function of the overall mole fraction of $SOC({\alpha}_1).$ Various thermodynamic parameters($x_i$, $Y_i$, $C_i$, $${\alpha}_i^M$$, and $\Delta$$H_{mix}$) for the mixed micellization of the SOC/OAC systems have been calculated and analyzed by means of the equations derived from the nonideal mixed micellar model. The results show that there are great deviations from the ideal behavior for the mixed micellization of these systems. And other thermodynamic parameters(${\Delta}$$G^0_m$, ${\Delta}$$H^0_m$, and ${\Delta}$$S^0_m$) associated with the micellization of SOC,OAC, and their $mixture({\alpha}_1=0.5)$ have been also estimated from the temperature dependence of CMC and B values, and the significance of these parameters and their relation to the theory of the micelle formation have been considered and analyzed by comparing each other.

• Biomedical Science Letters
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• v.6 no.2
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• pp.83-91
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• 2000

Subconfluent neonatal human epidermal keratinocytes were treated with a concentration 200 ng/$m\ell$ of human recombinant epidermal growth factor (hrEGF), human recombinant insulin-like growth factor-1 (hrIGF-1), and with a combination of hrEGF and hrIGF-1. Cytoplasmic and membrane-associated proteins were extracted and assayed. Proteins were separated by SDS-PAGE, and subjected to the western blot analysis. In the cytoplasmic fraction, the PKC concentration of keratinocyte treated with hrIGF-1 was higher than the control group, but the concentration of control group was the highest than the others in the membrane fraction. In the cytoplasmic fraction, EGF stimulated PKC-$\beta$II, -$\delta$, -$\theta$, and also stimulated PKC-$\alpha$, -$\beta$I, -$\delta$, -$\Im$ and -$\theta$ in the membrane fraction. IGF-1 stimulated PKC-$\beta$I, -$\Im$ and -$\theta$ in the cytoplasmic, PKC-$\alpha$, -$\beta$I, -$\delta$, -$\Im$, - $\varepsilon$ and -$\theta$ in the membrane. In the cells treated with a combination of EGF and IGF-1, PKC-$\alpha$, -$\beta$I, -$\Im$ and -$\theta$ in the cytoplasmic fraction, PKC-$\alpha$, -$\delta$, -$\Im$, -$\varepsilon$ and -$\theta$ in the membrane fraction were stimulated.

• Journal of the Korean Institute of Telematics and Electronics A
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• v.31A no.9
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• pp.128-138
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• 1994

In 1.55.mu.m DFB lasers with two non-AR mirrors, I have analyzed the effect of the sturctures of indes and/or gain gratings and mirror positions on the threshold gains, the lasing frequencies, and the beam profiles in longitudinal direction of lasers. I have obtained the optimum condition of static characteristics that ${\Delta}{\Omega}$(the phase difference betweeen index grating and gain grating is 3${\pi}$/4, $({\kappa}L)_{i}$=4~6 in case of $({\kappa}L)_{i}$=0.9 and $({\kappa}L)_{i}$=3~5 in case of $({\kappa}L)_{i}$=0.7. The modal selectivity and intensity uniformity of this optimum condition are 2~2.5 times better than those of the gain-coupled DFB lasers ${\Delta}{\Omega}$=0). The gain-coupled DFB lasers${\Delta}{\Omega}$=0) have 10$^{10) times better modal selectivity and intensity uniformity than the loss-coupled DFB lasers(TEX>${\Delta}{\Omega}$=${\pi}$).

• Bulletin of the Korean Chemical Society
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• v.2 no.4
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• pp.142-147
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• 1981

A blend polymeric system composed of poly(methyl methacrylate) (PMMA or PM) and polystyrene (PS) dissolved in chloroform was rheologically studied. The viscosities ${\eta}_{bl}$ of the blend system with various blending ratios ${\chi}$ changing from zero (pure PS solution) to unity (pure PMMA solution) were measured at $25{\circ}C$ as a function of shear rates ${\dot{s}}$ by using a Couette type viscometer. ${\eta}_{bl}$ at a given ${\dot{s}}$ decreased exponentially with ${\chi}$ reaching asymptotic constant value of ${\eta}_{bl}$ ; ${\eta}_{bl}$ at a given ${\chi}$ is greater at a smaller ${\dot{s}}$. These results are explained by using Ree-Erying's theory of viscosity, ${\eta}_{bl}=(x_1{\beta}_1/{\alpha}_1)_{b}_1＋ (x_2{\beta}_2/{\alpha}_2)_{bl}[sinh^{-1}{\beta}_2(bl) {\dot{s}}]/{\beta}_2(bl){\dot{s}}$. The Gibbs activation energy ${\Delta}G_i^\neq$(i = 2 for non-Newtonian units) entering into the intrinsic relaxation time ${\beta}$ is represented by a linear combination ${\Delta}G_i^\neq(bl) ={\chi}{\Delta}G_i^{\neq}_{iPM}+(1-{\chi}){\Delta}G_i^{\neq}_{iPS}$;the intrinsic shear modulus$[[\alpha}_i]^{-1}$ is also represented by $[{\alpha}_i(bl)]^{-1}={\chi}[{\alpha}_{iPM}]^{-1}+(1-{\chi})[{\alpha}_{iPS}]^{-1}$ and the fraction of area on a shear surface occupied by the ith flow units $x_i(bl)$ is similarly represented, i.e., $x_i(bl) = {\chi}x_{iPM}+(1-{\chi})x_{iPS}$. By using these ideas the Ree-Eyring equation was rewritten which explained the experimental results satisfactorily.

• Economic and Environmental Geology
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• v.28 no.4
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• pp.351-367
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• 1995

The elemental geochemistry and oxygen isotopes of illite/smectite (I/S) have been studied in relationship to the mineralogical trend in the Reindeer D-27 well, Beaufort-Mackenzie Basin. The increase in concentrations of $K_2O$, Rb and rare earth elements (REE), the decrease in concentrations of tetrahedral elements such as Mg, Ti, Sc, Zn and Zr, and the increase in concentrations of tetrahedral elements such as Be and V can be related to I/S compositions that vary systematically with depth. Layer formulae of S- and I-layers are estimated as $[Al_{1.57}Fe_{.19}Mg_{.31}Ti_{.07}][Si_{3.84}Al_{.16}]O_{10}(OH)_2$ and $[Al_{1.84}Mg_{.16}][Si_{3.33}Al_{.67}]O_{10}(OH)_2$, respectively. The mobilization of REE appears to occur during illitization. The increase in concentrations of REE, especially La and Ce, with depth is probably linked to incorporation of ions with high valency (e.g. $V^{5+}$) in tetrahedral sites. The excess valency due to V is partly counter-balanced by ions with low valency (e.g. $Be^{2+}$) and, in turn, the local valency deficiency caused by $Be^{2+}$ could be compensated by high-charge interlayer cations such as REE (＋3). ${\delta}^{18}O$ values of I/S range from 2.91 to 15.72‰ (SMOW), and increase with depth, contrasting to trends observed in the Gulf Coast and elsewhere. The increase in ${\delta}^{18}O$ of I/S results from the rapid increase in ${\delta}^{18}O$ of pore water that overcomes the decrease in temperature-dependent fractionation values with increasing burial depth (${\delta}^{18}O_{pore\;water}>-d{\Delta}/_{I/S-water};\;d{\delta}^{18}O_{I/S}>0$). Calculated ${\delta}^{18}O$ values of pore water in equilibrium with I/S suggest that the original water was probably meteoric water. The stratification of pore water is postulated from the presence of an isotopically light interval, about 450m thick. The depth range of the isotopically light zone overlaps, but does not coincide with the interval of lowered I-content and $K_2O$ concentrations, suggesting that oxygens may have been exchanged independently of mineralogical and geochemical reactions.

• Journal of The Korean Astronomical Society
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• v.16 no.2
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• pp.55-63
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• 1983

From UBVRI photometry and space motion data of 232 late type dwarf stars, it is found that for the stars of (R-I)<0.5, $\Delta$(U-B) and $\Delta$(B-V) color excesses are correlated with their orbital eccentricities. Therefore, $\Delta$(U-B) and $\Delta$(B-V) color excesses can be used as possible photometric abundance indicators for the stars of (R-I)<0.5. For the stars of (R-I)${\geq}$0.5, the correlation between color excess and orbital eccentricity is not clear. However, it is interesting to note that the high orbital eccentricity stars show some blue deficiencies and these blue deficiencies seem to be correlated with orbital eccentricity.

• Journal of the Korean Chemical Society
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• v.21 no.6
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• pp.395-403
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• 1977

Significant structure theory was applied to some liquid mixture systems ranging from simple monatomic molecule systems to polyatomic molecule systems, and the activity coefficients ${\gamma}$ of the liquid mixture systems were calculated over whole mole fractions using the following thermodynamic relation $RTln_{{\gamma}i} = (\frac{{\partial A}^E}{{\partial N}_i})_{T,V,N_i} $ where $A^E$ represents the excess Helmholtz free energy, and $N_i$ is the number of molecules of component i. The activity coefficients of the solutions such as monatomic molecule systems (Ar-Kr, Kr-Xe) and diatomic molecule systems $(Ar-O_2,\;N_2-CO)$ and $CH_4-Kr$ systems whose components have similar shapes for intermolecular potential curves were calculated successfully only with the ${\delta}E_s$, correction parameter for energy $E_s$, for mixture systems. For other systems such as $Ar-N_2,\;O_2-N_2\;and\;CH_4-C_3H_8$ whose components have dissimilar intermolecular potential curve shapes an additional correction parameters ${\delta}$V and even one more parameter ${\delta}$n were necessary [see Eqs.(10)∼(12)].

• Journal of the Korea Institute of Information and Communication Engineering
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• v.11 no.1
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• pp.89-94
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• 2007

High duality BiSrCaCuO thin films fabricated by using the i-beam sputtering method at various substrate temperatures, $T_{sub}$ and oxidation gas pressures, $pO_3$. The correlation diagrams of the BiSrCaCuO phases with Tsub and $pO_3$ are established in the 2212 and 2223 compositional films. In spite of 2212 compositional sputtering, Bi2201 and Bi2223 as well as Bi2212 phases come out as stable phases depending on $T_{sub}$ and $pO_3$. From these results, the thermodynamic evaluation of ${\Delta}H$ and${\Delta}S$, which are related with Gibbs' free energy change for single Bi2212 or Bi2223 phase, was performed.

• East Asian mathematical journal
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• v.34 no.5
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• pp.643-649
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• 2018

Let M be a connected n-dimensional submanifold of a Euclidean space $E^{n+k}$ equipped with the induced metric and ${\Delta}$ its Laplacian. If the position vector x of M is decomposed as a sum of three vectors $x=x_1+x_2+x_0$ where two vectors $x_1$ and $x_2$ are non-constant eigenvectors of the Laplacian, i.e., ${\Delta}x_i={\lambda}_ix_i$, i = 1, 2 (${\lambda}_i{\in}R$) and $x_0$ is a constant vector, then, M is called a 2-type submanifold. In this paper we proved that a connected 2-type hypersurface M in $E^{n+1}$ whose postion vector x satisfies ${\langle}{\Delta}x,x-x_0{\rangle}=c$ for a constant c, where ${\langle}$, ${\rangle}$ is the usual inner product in $E^{n+1}$, is of null 2-type and has constant mean curvature and scalar curvature.