• Kyungpook Mathematical Journal
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• v.48 no.1
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• pp.45-61
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• 2008

We investigate the generalized Hyers-Ulam-Rassias stability in p-Banach spaces for the following functional equation which is two types, that is, either cubic or quadratic: 2f(x+3y) + 6f(x-y) + 12f(2y) = 2f(x - 3y) + 6f(x + y) + 3f(4y). The concept of Hyers-Ulam-Rassias stability originated essentially with the Th. M. Rassias' stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72 (1978), 297-300.

• Economic and Environmental Geology
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• v.4 no.4
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• pp.225-234
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• 1971

With the advance of civilization and steadily increasing population rivalry and competition for the use of the sewage, culverts, farm irrigation and control of various types of flood discharge have developed and will be come more and more keen in the future. The author has tried to calculated a formula that could adjust these conflicts and bring about proper solutions for many problems arising in connection with these conditions. The purpose of this study is to find out effective sewage, culvert, drainage, farm irrigation, flood discharge and other engineering needs in the Taegu area. If demands expand further a new formula will have to be calculated. For the above the author estimated methods of control for the probable expected rainfall using a formula based on data collected over a long period of time. The formula is determined on the basis of the maximum daily rainfall data from 1921 to 1971 in the Taegu area. 1. Iwai methods shows a highly significant correlation among the variations of Hazen, Thomas, Gumbel methods and logarithmic normal distribution. 2. This study obtained the following major formula: ${\log}(x-2.6)=0.241{\xi}+1.92049{\cdots}{\cdots}$(I.M) by using the relation $F(x)=\frac{1}{\sqrt{\pi}}{\int}_{-{\infty}}^{\xi}e^{-{\xi}^2}d{\xi}$. ${\xi}=a{\log}_{10}\(\frac{x+b}{x_0+b}\)$ ($-b<x<{\infty}$) ${\log}(x_0+b)=2.0448$ $\frac{1}{a}=\sqrt{\frac{2N}{N-1}}S_x=0.1954$. $b=\frac{1}{m}\sum\limits_{i=1}^{m}b_s=-2.6$ $S_x=\sqrt{\frac{1}{N}\sum\limits^N_{i=1}\{{\log}(x_i+b)\}^2-\{{\log}(x_0+b)\}^2}=0.169$ This formule may be advantageously applicable to the estimation of flood discharge, sewage, culverts and drainage in the Taegu area. Notation for general terms has been denoted by the following. Other notations for general terms was used as needed. $W_{(x)}$ : probability of occurranec, $W_{(x)}=\int_{x}^{\infty}f_{(n)}dx$ $S_{(x)}$ : probability of noneoccurrance. $S_{(x)}=\int_{-\infty}^{x}f_(x)dx=1-W_{(x)}$ T : Return period $T=\frac{1}{nW_{(x)}}$ or $T=\frac{1}{nS_{(x)}}$ $W_n$ : Hazen plot $W_n=\frac{2n-1}{2N}$ $F_n=1-W_x=1-\(\frac{2n-1}{2N}\)$ n : Number of observation (annual maximum series) P : Probability $P=\frac{N!}{{t!}(N-t)}F{_i}^{N-t}(1-F_i)^t$ $F_n$ : Thomas plot $F_n=\(1-\frac{n}{N+1}\)$ N : Total number of sample size $X_l$ : $X_s$ : maximum, minumum value of total number of sample size.

• The Korean Journal of Zoology
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• v.39 no.1
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• pp.75-88
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• 1996

OTF9-63 (OTF9) and P19S1O1A1 (P19) embryonal carcinoma (EC) cells were examined for their ability to produce the readivation of inactive X chromosomes from somatic cells. They were hybridized with various somatic cells and resulting HATr EC-somatic cell clones were analysed for their morphology, chromosomal replication pafterns and expression proffies of X-linked and distantiy located genes, Hprt and Pgk-1. The results demonstrated that 0RF9 cells could reactivate the inactive X chromosome whereas P19 cells could not. In adition, EC-somatic cell hybrids tended to reduce the number of sex chromosomes in long-term culture, resulting m 1:2 ratio of sex chromosomes to autosomes The use of EC cell hybrids provides an experimental system for studying the mechanism(s) of the X-reactivatio that is initiated and maintained from meiotic prophase of oogenesis to early embryogenesis.

• Journal of the Korean Chemical Society
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• v.55 no.3
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• pp.502-508
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• 2011

Synthesis of $Nd_{2x}Cd_{2-3x}SiO_4$ ($0.01{\leq}x{\leq}0.21$) [S1-S3: x=0.01, 0.11 and 0.21] solid solutions were prepared by solgel method. Powder x-ray diffraction (XRD) results show monoclinic unit cell with space group P21/m. The average crystallite sizes are found to be 20 to 45 nm. The Scanning Electron Microcopy (SEM) images show morphology of the sample is in globular nature. The energy dispersive analysis of x-rays (EDX) and X-ray mapping results confirmed that all the constituent elements of the composites were present and that were distributed in uniformly. The optical absorption band at ~750 nm was due to $^4I_{9/2}{\rightarrow}^4F_{7/2}+^4S_{3/2}$ transition optically active $Nd^{3+}$ ions. Electron Paramagnetic Resonance (EPR) lineshapes of S1-S3 at 10, 40, 77 and 300 K show a broad unresolved isotropic lineshapes were observed due to rapid spin lattice relaxation of $Nd^{3+}$.

• Journal of the Chungcheong Mathematical Society
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• v.13 no.1
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• pp.71-78
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• 2000

The main goal of this paper is to prove the following theorem ; Let (X, ${\rho}_1$) be a fuzzy normed linear space over K and (Y, ${\rho}_2$) be a fuzzy Banach space over K. If ${\chi}_{B_{{\parallel}{\cdot}{\parallel}}}{\supseteq}{\rho}*$, then (CF(X,Y), ${\rho}*$) is a fuzzy Banach space, where ${\rho}*(f)={\vee}{\lbrace}{\theta}{\wedge}\frac{1}{t({\theta},f)}\;{\mid}\;{\theta}{\in}(0,1){\rbrace}$, $f{\in}CF(X,Y)$, $B_{{\parallel}{\cdot}{\parallel}}$ is the closed unit ball on (CF(X, Y), ${\parallel}{\cdot}{\parallel}$ and ${\parallel}f{\parallel}={\vee}{\lbrace}P^2_{{\alpha}^-}(f(x))\;{\mid}\;P^1_{{\alpha}^-}(x)=1,\;x{\in}X{\rbrace}$, $f{\in}CF(X,Y)$, ${\alpha}{\in}(0,1)$.

• Journal of Surface Science and Engineering
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• v.52 no.4
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• pp.187-193
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• 2019

Electroless Ni-P coatings are widely used in the chemical, mechanical, and electronic industries because of their excellent wear and abrasion resistance. In this study, the effect of $TiO_2$ particles of composite coating was investigated. To improve the corrosion resistance, electroless $Ni-P-TiO_2$composite coating was studied by varying the $TiO_2$ content. The morphology and phase structure of $Ni-P-TiO_2$ composite coatings were analyzed by scanning electron microscopy(SEM), X-ray diffractometry(XRD) and X-ray photoelectron spectroscopy(XPS). The result showed that $Ni-P-TiO_2$composite coating is composed of Ni, P, Ti and O. It exhibits an amorphous structure, high hardness and good corrosion resistance to the substrate. $Ni-P-TiO_2$ composite coatings have higher open circuit potential than that of the substrate, which obtained at $TiO_2$ content of 5.0 g/L optimal integrated properties.

• The Transactions of the Korean Institute of Electrical Engineers C
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• v.52 no.7
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• pp.293-297
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• 2003

Silicon dioxide (SiO$_2$) layers were fabricated on Si$_3$N$_4$/SiO$_2$/Si layer structures by low pressure chemical vapor deposition (LPCVD). Potassium and aluminum were then coimplanted by implanting potassium ions with the energy of 100 ［keY］ and dose of 5x10$^{16}$ [cm￣$^2$］ and 1x10$^{17}$ [cm￣$^2$］ into an aluminum buffer layer on the SiO$_2$Si$_3$N4/SiO$_2$/Si structure. The pH, pNa, and pK ion sensitivities of the resulting layers were investigated and compared to those of as-deposited silicon dioxide layer. The pK-sensitivity of the silicon dioxide was enhanced by the K and Al coimplantation. On the contrary, the pH and pNa-sensitivities of the coimplanted silicon dioxides were quite lower than that of the as-deposited silicon dioxide.

• Journal of Surface Science and Engineering
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• v.24 no.1
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• pp.1.2-1.2
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• 1991

The formation of managanese ferrite has been performed to investigate some properties according to the variation of compositions, pH, current density by electrolysis. It has been found that the amount of oxidized weight of anode were increased with increasing current density. The amount of oxidized weight of anode were most in pH10. As the result of X-ray diffraction Mn Fe2O4 crystal composition in pH13. When the particles of Mnx Fe3-x O4 were heated at 30$0^{\circ}C$, it has been shown typical MnFe2O4(JCPDS Card No. 10-319) in X-1 composition. As the result of SEM observation, the size of MnFe2O4 particles were about 0.1$\mu\textrm{m}$, the shape of particles were spherical type. According to the above mentioned experimental condition, 0.1-0.5$\mu\textrm{m}$ sub-micron particles of manganese ferrite were formed from the wasted manganese dry cell, through washing longrightarrow reduction longrightarrow electrloysis.

• Radiation Oncology Journal
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• v.20 no.3
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• pp.246-252
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• 2002

Purpose : It has been recognized that interaction of the Fas : Fas ligand plays an important role in radiation-induced apoptosis. The purpose of this study was to investigate the role of Fas mutation in radiation-induced apoptosis in vivo. Materials and Method : Mice with mutations in Fas, $MRL/Mpj-Fas^{Ipr}$, and its normal control, MRL/Mpj, were used in this study. Eight-week old male mice were given whole body radiation. After irradiation, the mice were killed and their spleens were collected at different time intervals. Tissue samples were stained with hematoxylin-eosin and the numbers of apoptotic cells were scored. Regulating molecules of apoptosis including p53, Bcl-2, Bax, $Bcl-X_L,\;and\;Bcl-X_S$ were also analyzed by Western blotting. Results : At 25 Gy irradiation, the level of apoptosis reached the peak value at 8 hr after radiation and recovered to the normal value at 24 hr after radiation in MRL/Mpj mice. In contrast, the peak apoptosis level appeared at 4 hr after radiation in $MRL/Mpj-Fas^{Ipr}$. At 8 hr after radiation, the levels of apoptosis in MRL/Mpj mice and $MRL/Mpj-Fas^{Ipr}$ mice were $52.3{\pm}7.8\%\;and\;8.0{\pm}8.6\%$, respectively (p<0.05). The expression of apoptosis regulating molecules, p53, $Bcl-X_L\;and\;Bcl-X_S$, increased in MRL/Mpj mice in response to radiation; p53 with a peak level of 3-fold at 8 h, $Bcl-X_L$ with a peak level of 3.3-fold at 12 h, and $Bcl-X_S$ with a peak level of 3-fold at 12 h after 25 Gy radiation. Bcl-2 and Bax did not show significant change in MRL/Mpj mice. However in $MRL/Mpj-Fas^{Ipr}$ mice, the expression levels of p53, Bcl-2, Bax, $BCl-X_L\;and\;BCl-X_S$ showed no significant change. Conclusion : The level of radiation-induced apoptosis was lower in Fas mutated mice, Ipr, than in control mice. This seemed to be related to the lack of radiation-induced p53 activation in the Ipr mice. This result suggests that Fas plays an important role in radiation-induced apoptosis in vivo.

• Journal of the Korean Chemical Society
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• v.50 no.1
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• pp.46-52
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• 2006

studies of olefin oxidation using Al(III)-porphyrin complexes as catalyst are investigated in CH2Cl2, in which NaClO is used as terminal oxidant. Porphyrins are TPP(5,10,15,20-Tetraphenylporphyrin) and (p-X)TPP(X=CH3O, CH3, F, Cl). Olefins are styrene and (p-X)styrene (X=CH3O, CH3, Cl, Br). The values of Km and Vmax are calculated from the Michaelis-Menten equation. According to the substituents of substrate and catalyst, kinetic parameters will be measured. Investigating the correlation between the Michaelis-Menten rate parameters and the substituent constants, we were able to analyze the influence on the changes of catalytic activity or the rate determining step during the process of the formation and the dissociation of the M-oxo-olefin.