• Journal of Korean Ophthalmic Optics Society
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• v.6 no.2
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• pp.65-70
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• 2001

We obtained the sum of two curvature ($C_x+C_y$) in toric lens which two toroidal surface is the right angle each other. $$C_x+C_y=\frac{x^2+y^2}{2r_1}+\frac{x^2}{2}(\frac{1}{r_2}-\frac{1}{r_1})$$ and the sum of two curvature ($C_a+C_b$) in toric lens about the cross angle. $$(C_a+C_b)=\frac{x^2cos^2{\alpha}_1}{2r_1}+\frac{x^2cos^2{\alpha}_2}{2r_2}+\frac{y^2sin^2{\alpha}_1}{2r_1}+\frac{y^2sin^2{\alpha}_2}{2r_2}$$ and claculated the parameter S, C, ${\theta}$ of a combination power in toric lens of the cross angle including surface curvature ($C_x$, $C_y$) values. $$S=(n-1)\[\frac{C_x}{x^2}+\frac{C_y}{y^2}\]-\frac{C}{2},\;C=-\frac{2(n-1)}{sin2{\theta}}\[\frac{C_x}{x^2}+\frac{C_y}{y^2}\]$$ $${\theta}=\frac{1}{2}tan^{-1}\[-\frac{{C_xy^2sin2{\theta}_1}+{C_yx^2sin2{\theta}_2}}{{C_xy^2cos2{\theta}_1}+{C_yx^2cos2{\theta}_2}}\]$$.

• Journal of the Korean Crystal Growth and Crystal Technology
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• v.23 no.1
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• pp.14-19
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• 2013

We have successfully synthesized $Bi_{4-x}La_xTi_3O_{12}$ (x~2) having Aurivillius-type layered perovskite structure from exfoliated layered perovskite oxide of $K_2La_2Ti_3O_{10}$ with Ruddlesden-Popper structure. The reaction between the exfoliated lanthanum titanate nanosheets and BiOCl nanocrystal resulted in the formation of polycrystalline $Bi_{4-x}La_xTi_3O_{12}$ (x~2) after heating above $700^{\circ}C$. Colloidal suspension of the nanosheets could be obtained by intercalating ethylamine (EA) into the protonated lanthanum titanate, $H_2La_2Ti_3O_{10}$, derived from $K_2La_2Ti_3O_{10}$. Transmission electron microscopic (TEM) analysis show that the exfoliated lanthanium titanate nanosheets have a thickness of a few nano meters. According to X-ray diffraction (XRD) analysis, the exfoliated lanthanium titanate was found to be transformed into $Bi_{4-x}La_xTi_3O_{12}$ (x~2) after restacking with BiOCl and subsequent thermal treatment at > $700^{\circ}C$.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 1999.11a
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• pp.248-251
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• 1999

The microwave dielectric properties of The Dielectric Properties of $Ba_{1-x}$A$_{x}$(Mg$_{1}$3/Nb$_{2}$3/)O$_3$ (A = Sr, Ca, x = 0, 0.2 ,0.4 ,0.6, 0.8, 1.0) were investigated. In composition of $Ba_{1-x}$A$_{x}$(Mg$_{1}$3/Nb$_{2}$3/)O, densities are decreased with increasing x values. Grain sizes are decreased with Sr content and Increased with Ca content. The hexagonally ordered superstructure was observed in $Ba_{1-x}$Sr$_{x}$(Mg$_{1}$3/Nb$_{2}$3/)O$_3$(BSMN) systems, the intensity of superlattice increased with x value. In $Ba_{1-x}$Cr$_{x}$(Mg$_{1}$3/Nb$_{2}$3/)O$_3$(BSMN) systems, the additional diffraction patterns were shown. The highest value of $\varepsilon$$_{r}$ was shown in x=0.2 of BCMN systems and the value was 41.9. The highest Q$\times$f was shown in x=0.2 of BSMN systems and the value was 68,000. $\tau$$_{f}$ were shown 0 ppm/$^{\circ}C$ near x=0.8.TEX> near x=0.8.0.8.

• Korean Journal of Plant Taxonomy
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• v.42 no.4
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• pp.307-315
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• 2012

Somatic chromosome numbers for 10 taxa and karyotypes analysis for 6 taxa of Korean Vicia were investigated. Somatic chromosome numbers of treated taxa were 2n = 12, 14 or 24 and therefore they proved to be diploid or tetraploid with basic chromosome numbers of x = 6 or 7. The chromosome number of V. hirticalycina (2n = 2x = 12) was reported for the first time in this study. The chromosome numbers of nine taxa were the same as in previous studies; V. angustifolia (2n = 2x = 12), V. cracca (2n = 4x = 24), V. hirsuta (2n = 2x = 14), V. tetrasperma (2n = 2x = 14 + 2B), V. amurensis (2n = 2x = 12), V. chosenensis (2n = 2x = 12, 12 + 2B), V. unijuga (2n = 4x = 24), V. unijuga f. minor (2n = 4x = 24), V. venosa var. cuspidata (2n = 4x = 24). The karyotypes of V. cracca, V. amurensis, V. hirticalycina, V. unijuga, V. unijuga f. minor, V. venosa var. cuspidata were observed as 2 m + 8 sm + 2 st, 2 m + 2 sm + 2 st, 3 m + 1 sm + 2 st, 4 m + 6 sm + 2 st, 4 m + 6 sm + 2 st, 4 m + 8 sm, respectively.

• Korean Journal of Mathematics
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• v.19 no.2
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• pp.171-180
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• 2011

In this paper, we study the superstability problem bounded by two-variables of Th. M. Rassias type for the generalized sine functional equations $$g(x+y)f(x-y)=f(x)^2-f(y)^2 \\ f(x+y)g(x-y)=f(x)^2-f(y)^2 \\ g(x+y)g(x-y)=f(x)^2-f(y)^2$$, which does not use his iteration method.

• Journal of the Korean Statistical Society
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• v.12 no.2
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• pp.100-109
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• 1983

Let ${X_i}$ be a process with stationary and independent increments whose log characteristic function is expressed as $ibut-2^{-1}\sigma^2u^2t+t\int_{{0 }^c}{(exp(iux)-1-iux(i+x^2)^{-1})dv(x)}$. Our main result is taht $x^2(\int_{\y\>x}{dv(y)})/(\int_{$\mid$y$\mid$\leqx}{y^2dv(y)+\sigma^2}) \to 1$ as $x \to 0 (resp. x \to \infty)$ is necessary, and sufficient for ${X-i}$ to have ${A_t}$ and ${B_t}$ such that $(X_t-A_t)/B_t \to^D n(0,1)$ as $t \to 0 (resp. t \to \infty)$.

• The Pure and Applied Mathematics
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• v.25 no.3
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• pp.219-227
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• 2018

In this paper, we solve the additive ${\rho}$-functional equations $$(0.1)\;f(x+y)+f(x-y)-2f(x)={\rho}\left(2f\left({\frac{x+y}{2}}\right)+f(x-y)-2f(x)\right)$$, where ${\rho}$ is a fixed non-Archimedean number with ${\mid}{\rho}{\mid}$ < 1, and $$(0.2)\;2f\left({\frac{x+y}{2}}\right)+f(x-y)-2f(x)={\rho}(f(x+y)+f(x-y)-2f(x))$$, where ${\rho}$ is a fixed non-Archimedean number with ${\mid}{\rho}{\mid}$ < |2|. Furthermore, we prove the Hyers-Ulam stability of the additive ${\rho}$-functional equations (0.1) and (0.2) in non-Archimedean Banach spaces.

• Bulletin of the Korean Chemical Society
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• v.22 no.3
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• pp.298-302
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• 2001

A site preference of niobium atom in Rb2-xLa2Ti3-xNbxO10 (0.0 $\leq$ x $\leq1.0)$ and RbLa2-xCaxTi2-xNb1+xO10 (0.0 $\leq$ x $\leq2.0)$, which are the solid-solutions between Rb2La2Ti3O10 and RbCa2Nb3O10, has been investigated by Raman spectroscopy. The Raman spectra of Rb2-xLa2Ti3-xNbxO10 (0.0 $\leq$ x $\leq1.0)$ gave an evidence that niobium atoms substituted for titanium atoms preferably occupy the highly distorted outer octahedral sites rather than the central ones in triple-octahedral perovskite layers. In contrast, the Raman spectra of RbLa2-xCaxTi2-xNb1+xO10 (0.0 $\leq$ x $\leq2.0)$ showed no clear information for the cationic arrangement in perovskite slabs. This difference indicated that a site preference of niobium atoms is observed only when the linear Rb-O-Ti linkage can be replaced by much stronger terminal Nb-O bond with double bond character. From comparison with the Raman spectroscopic behavior of CsLa2-xA’xTi2-xNb1+xO10 (A’ = Ca and Ba; 0.0 $\leqx\leq2.0)$, it is also proposed that a local difference in arrangement of interlayer atoms causes a significantly different solid acidity and photocatalytic activity of the layered perovskite oxides, despite their crystallographically similar structures.

• Progress in Superconductivity
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• v.13 no.3
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• pp.163-168
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• 2012

The effects of Ta substitution on the superconducting and magnetic properties of the $(Ru_{1-x}Ta_x)Sr_2(Gd_{1.4}Ce_{0.6})Cu_2O_z(0{\leq}x{\leq}0.5)$ system have been investigated. The X-ray diffraction measurements indicate that the Ta ion replaces Ru sites up to x = 0.4. It is found that the Ta substitution for Ru significantly reduces the weak-ferromagnetic component of the field-cooled magnetic susceptibility without an appreciable change of room temperature thermopower at lower Ta doping level below x = 0.2. The resistive transition temperature tends to decrease monotonically from 27 K for the x = 0 sample to 16 K (9 K) for the x = 0.4 (x = 0.5) sample. These results suggest that superconductivity of the $(Ru_{1-x}Ta_x)Sr_2(Gd_{1.4}Ce_{0.6})Cu_2O_z$ compound is not significantly affected by the magnetic state of the Ru sublattice. The experimental results are discussed in connection with previous reports on the effects of Nb substitution.

• 한국생물공학회:학술대회논문집
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• 2003.04a
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• pp.439-444
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• 2003

The major factors related in enzymatic hydrolysis of food waste using cellulolytic enzymes of Trichoderma harzianum FJ1 were optimized by response surface analysis. The factors largely affecting to the reducing sugar concentration and enzymatic saccharification rate of food waste such as substrate concentration ($X_1$, %), enzyme concentration ($X_2$, U/ml), and reaction time ($X_3$, hr) were employed. A quadratic polynominal expressing the reducing sugar (RS) concentration relating with the above factors was as follows : RS (g/l) = -17.80 + $5.04X_1$ + $51.37X_2$ + $1.21X_3$ - $0.11X_1\;^2$ - $38.86X_2\;^2$ - $0.03X_3\;^2$ + $1.64X_1X_2$ + $0.04X_1X_3$ - $0.70X_2X_3$ ($R^2$=0.9939). The maximum value of the reducing sugar concentration and saccharification rate were obtained in the conditions of substrate concentration of 18.2%, enzyme concentration of 0.78 U/ml, and reaction time of 19 hr, respectively. The predicated reducing sugar concentration and saccharification rate by the response surface methodology were 95.13 g/l and 47.27%, respectively.