• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.441-452
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• 2006

We introduce the counting function ${\pi}^*_{2.8}(x)$ of the primes with difference 8 between consecutive primes ($p_n,\;p_{n+l}=p_n+8$) can be approximated by logarithm integral $Li^*_{2.8}$. We calculate the values of ${\pi}^*_{2.8}(x)$ and the sum $C_{2,8}(x)$ of reciprocals of primes with difference 8 between consecutive primes $p_n,\;p_{n+l}=p_n+8$ where x is counted up to $7{\times}10^{10}$. From the results of these calculations. we obtain ${\pi}^*_{2.8}(7{\times}10^{10}$)= 133295081 and $C_{2.8}(7{\times}10^{10}) = 0.3374{\pm}2.6{\times}10^{-4}$.

• Journal of the Korean Crystal Growth and Crystal Technology
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• v.6 no.4
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• pp.600-608
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• 1996

Specific structural properties of Li intercalation reaction into the spinel relatedmanganese dioxide, $Li_{x}Mn_{2}O_{4}(0.2{\leq}x{\leq}2.0)$, are investigated by X-ray diffractional and electrochemical studies of Li/1M $LiClO_{4}$-propylene carbonate solution/$Li_{x}Mn_{2}O_{4}$ cell. The effect of the chemical composition and the reaction temperature on electrochemical parameter of $Li_{x}Mn_{2}O_{4}$ are studied by the phenomena of phase-transition, analysis of crystal lattice, fine structure, and thermal analysis. Treatment of the spinel $Li_{x}Mn_{2}O_{4}$ with aqueous acid was found to result in conversiton of $Li_{x}Mn_{2}O_{4}$ to nearly pure $MnO_{2}$, as evidenced by a reduction in the lattice constant $a_{c}$ from 8.255 to $8.031\;{\AA}$. At a composition range of $0.2{\leq}x{\leq}0.6$ in $Li_{x}Mn_{2}O_{4}$ the reduction proceeded in a homogeneous phase, which was characterized by a constant voltage of 3.9~3.7 V together with a lattice constant of $8.255\;{\AA}$.

• Korean Journal of Materials Research
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• v.5 no.6
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• pp.723-731
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• 1995

P $b_2$S $r_2$( $Y_{1-x}$ C $a_{x}$)C $u_3$ $O_{8+}$$\delta$/ samples were prepared with x=0.4~0.6 and small $\delta$. To minimize the extent of oxidative decomposition reaction which occurs during the preparation of this phase, two annealing steps were adopted : First, sintered samples of P $b_2$S $r_2$( $Y_{1-x}$ C $a_{x}$)C $u_3$ $O_{8+}$$\delta$/ are oxygenated under 100% $O_2$, which leads to a large $\delta$(e.g., $\delta$=1.8). Second, the resulting samples are deoxygenated under 0.1~1.0% $O_2$in $N_2$, lowering $\delta$ to desired values. This two-step annealing procedure minimized the extent of oxidative decomposition. However, even with the two-step annealing procedure, the oxidative decomposition of P $b_2$S $r_2$( $Y_{1-x}$ C $a_{x}$)C $u_3$ $O_{8+}$$\delta$/ cannot be completely suppressed if $\delta$ is to be reduced to maximize $T_{c}$. Electrical resistivity data show that $T_{c}$(onset) is a function of hole concentration in the Cu $O_2$layer, and the optimum hole concentration for the maximum $T_{c}$ is achieved when $Ca^{2+}$is substituted for $Y^{3+}$between 0.5 and 0.6 A $T_{c}$(onset)=80K has been observed for one such sample, and this is the highest $T_{c}$(onset) yet reported for this compound.ed for this compound.nd.

• Journal of the Korean Institute of Telematics and Electronics
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• v.21 no.2
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• pp.36-46
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• 1984

The Ga1-xInxSe single crystals for 0.0 < x < 0.1 and 0.8 < 1.0 were grown by the Bridgman method. The crystal structure of Ga1-xInxSe is found to be hexagonal for 0.0 < X < 1.0. The Ga1-xInxSesingle crystals have indirect energy gap with a temperature coefficient dEg/dT= -(2.4 - 4.3) $\times$ 10-4 eV/K in the range 60-250K. The temperature dependence of the energy gap can be explained by the electron-Phonos interaction model.

• Bulletin of the Korean Chemical Society
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• v.10 no.6
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• pp.582-585
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• 1989

Two crystal structures of dehydrated $Sr^{2+}\;and\;Tl^+$ exchanged zeolite A, $Sr_xTl_{12-2x}-A$ (x = 1.6 and 5.45), have been determined by single-crystal X-ray diffraction techniques. Their structures were solved and refined in the cubic space group Pm3m at $21(1)^{\circ}C.$ Both crystals were ion exchanged in flowing streams of mixed $Sr(NO_3)_2\;and\;TlNO_3$ aqueous solution, followed by dehydration at $360^{\circ}C\; and\; 2${\times}$10^{-6}$ Torr for 2 days. Full-matrix least-squares refinements of the dehydrated $Sr_{1.6}Tl_{8.8}-A (a = 12.214(2){\AA})\; and\;Sr_{5.45}Tl{1.1}-A (a=12.291(2){\AA})$ have converged to final error indices, $R_1=0.055\; and\;R_2=0.061$ with 286 reflections, and R1 = 0.072 and R2 = 0.090 with 217 reflections, respectively, for which$\;I\;{>}\;3{\sigma}(I)$. In both structures, all Sr(II) ions are coordinated by three framework oxygens; Sr(II) to O(3) distances are $2.21(2){\AA}\;for\;Sr_{1.6}Tl_{8.8}-A \;and\;2.31(1){\AA} \;for\;Sr_{5.45}Tl_{1.1}-A,$and Tl(I) to O(3) distances are $2.657(6){\AA}\;for\;Sr_{1.6}Tl_{8.8}-A\;and\;2.845(8){\AA}\;for\;Sr_{5.45}Tl_{1.1}-A,$ respectively. In each structure, the angle subtended at Sr(II), O(3)-Sr(II)-O(3) is $118.7(4)^{\circ}\;for\; Sr_{1.6}Tl_{8.8}-A \;and\;120.0(4)^{\circ}\;for\;Sr_{5.45}Tl_{1.1}-A.\;Sr^{2+}$ ions prefer to 6-ring sites and $Tl^+$ ions to 8-ring sites when total number of ions per unit cell is more than 8.

• Journal of Bio-Environment Control
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• v.17 no.2
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• pp.124-131
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• 2008

To investigate main air temperature factors correlated to difference of fruit characteristics according to cultivating areas, fruit and air temperature characteristics of eight cultivating areas of 'Fuyu' persimmon were analyzed by principle components and multiple regression analysis. The first principal components extracted from 16 air temperature factors was annual mean temperature, mean temperature during October, annual mean minimum extreme temperature, mean temperature during growing period, and so forth. The second principal components was mean temperature during May and June and so forth. And cumulative contribution was 91.4%. The five of eight cultivating area had clearly the difference of main factors or the correlated direction among cultivating areas. In multiple regression analysis between the extracted main factors and fruit characteristics, fruit hight were highly correlated with mean temperature during growing period ($X_8$) and cumulative temperature ($X_6$), and the regression equation was $Y=150.55-5.375X_8+ 0.014X_6(r^2=0.843)$. Also this regression equation was affected by mean minimum temperature during growing period, cumulative temperature, and mean temperature during August. Fruit diameter was negatively correlated with mean temperature during growing period, flesh browning rate and Hunter a value of peel color were positively correlated with mean minimum temperature during growing period and annual minimum air temperature, respectively.

• Bulletin of the Korean Mathematical Society
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• v.26 no.2
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• pp.139-149
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• 1989

pp.Hartman and G. Stampacchia [6] proved the following theorem in 1966: If f:X.rarw. $R^{n}$ is a continuous map on a compact convex subset X of $R^{n}$ , then there exists $x_{0}$ ..mem.X such that $x_{0}$ , $x_{0}$ -x>.geq.0 for all x.mem.X. This remarkable result has been investigated and generalized by F.E. Browder [1], [2], W. Takahashi [9], S. Park [8] and others. For example, Browder extended this theorem to a map f defined on a compact convex subser X of a topological vector space E into the dual space $E^{*}$; see [2, Theorem 2]. And Takahashi extended Browder's theorem to closed convex sets in topological vector space; see [9, Theorem 3]. In Section 2, we obtain some variational inequalities, especially, generalizations of Browder's and Takahashi's theorems. The generalization of Browder's is an earlier result of the first author [8]. In Section 3, using Theorem 1, we improve and extend some known fixed pint theorems. Theorems 4 and 8 improve Takahashi's results [9, Theorems 5 and 9], respectively. Theorem 4 extends the first author's fixed point theorem [8, Theorem 8] (Theorem 5 in this paper) which is a generalization of Browder [1, Theroem 1]. Theorem 8 extends Theorem 9 which is a generalization of Browder [2, Theorem 3]. Finally, in Section 4, we obtain variational inequalities for multivalued maps by using Theorem 1. We improve Takahashi's results [9, Theorems 21 and 22] which are generalization of Browder [2, Theorem 6] and the Kakutani fixed point theorem [7], respectively.ani fixed point theorem [7], respectively.

• Journal of the Korean Magnetics Society
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• v.8 no.5
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• pp.271-274
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• 1998

Spin reorientation and magnetocrystalline anisotropy of magnetically aligned $(Nd_{1-x}R_x)_2Fe_{14}B$ (R=Y, Pr) power were studied. The spin reorientation temperature $(T_{SR})$ of $(Nd_{1-x}R_x)_2Fe_{14}B$ decreases linearly by increasing Pr-substitution with the ratio of ${\Delta}T_{SR}=-1.35$ K/Pr at.% in composition range of 0$\leq$x$\leq$0.75. The spin reorientation temperature of $(Nd_{1-x}R_x)_2Fe_{14}B$ decreases by increasing Pr-substitution to 118 K (x=0.5) then increases to 122 K (x=0.75). The spin reorientation angle at 4.2 K decreases by increasing rare earth substitution with the ratio of $\Delta$SRA=-0.073$^{\circ}$/Y at.% and $\Delta$SRA=-0.258$^{\circ}$/Pr at.% in composition range of 0$\leq$x$\leq$0.5. The spin reorientation is expected to disappear at x$\geq$0.9 in case of $(Nd_{1-x}R_x)_2Fe_{14}B$ and at x$\geq$0.8 in case of $(Nd_{1-x}R_x)_2Fe_{14}B$.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• v.13 no.12
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• pp.989-995
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• 2000

G $e_{1-x}$ S $n_{x}$G $e_{1-y}$S $n_{y}$ is a very promising material for the high-speed device due to the fact that electron and hole mobilities for the strained G $e_{1-x}$ S $n_{x}$G $e_{1-y}$S $n_{y}$ are greatly enhanced. Because G $e_{1-x}$ S $n_{x}$G $e_{1-y}$S $n_{y}$ has a direct band gap for the proper combination of x and y, it can be applied to the optoelectronic device. Therefore, the study of the electrical property for G $e_{1-x}$ S $n_{x}$G $e_{1-y}$S $n_{y}$(001) with a direct energy gap is needed. G $e_{1-x}$ S $n_{x}$ layer can not be grown thickly due to the large difference of lattice constants. This fact prefers the structure of the device where electrons and holes move in the plane direction. The transverse mobilities of electron and hole for G $e_{0.8}$S $n_{0.2}$Ge(001) are 2~3 times larger than those for Ge/Ge/ sub0.8/S $n_{0.2}$(001). Therefore, G $e_{0.8}$S $n_{0.2}$Ge(001) is expected to be better than Ge/G $e_{0.8}$S $n_{0.2}$(001) for the development of the high-speed device.h-speed device.device.h-speed device. device.

• Journal of the Korean Society for Heat Treatment
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• v.15 no.2
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• pp.76-81
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• 2002

The melt-spun amorphous $Fe_{77-X}P_{13}C_4B_4Al_2Mo_X$(x=4~10) and $Fe_{82-X}P_XC_4B_4Al_2Mo_8$(x=9~15) alloys were found to exhibit a large supercooled liquid region(${\Delta}T_x$) exceeding 40 K before crystallization. The largest ${\Delta}T_x$ for the glassy alloys containing Mo reaches as large as 65 K for the $Fe_{69}P_{13}C_4B_4Al_2Mo_8$ alloy. The corrosion behavior of the amorphous $Fe_{77-X}P_{13}C_4B_4Al_2Mo_X$(x=4~15) and $Fe_(82-X)P_XC_4B_4Al_2Mo_8$ (x=9~17) alloys were examined by electrochemical measurements in 9M $H_2SO_4$ solution at 303 K. The addition of Mo(or P) for replacing some portion of Fe is effective in improving the corrosion resistance of the investigated Fe-based glassy alloys. They are spontaneously passivated and have a wide passive region with low passive current density.