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GENERALIZED STABILITIES OF CAUCHY'S GAMMA-BETA FUNCTIONAL EQUATION

  • Lee, Eun-Hwi;Han, Soon-Yi
    • Honam Mathematical Journal
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    • v.30 no.3
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    • pp.567-579
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    • 2008
  • We obtain generalized super stability of Cauchy's gamma-beta functional equation B(x, y) f(x + y) = f(x)f(y), where B(x, y) is the beta function and also generalize the stability in the sense of R. Ger of this equation in the following setting: ${\mid}{\frac{B(x,y)f(x+y)}{f(x)f(y)}}-1{\mid}$ < H(x,y), where H(x,y) is a homogeneous function of dgree p(0 ${\leq}$ p < 1).

Analysis of the Mean Uranium Valence of $U_{1-y}Er_{y}O_{2{\pm}x}$ Solid Solutions in terms of Lattice Parameter and Oneen Potential (격자상수 및 산소포텐샬에 의한 $U_{1-y}Er_{y}O_{2{\pm}x}$ 고용체의 평균우라늄원자가 분석)

  • Kim, Han-Soo;Sohn, Dong-Seong
    • Nuclear Engineering and Technology
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    • v.28 no.2
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    • pp.118-128
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    • 1996
  • The lattice parameters of stoichiometric $UO_2$ and $U_{1-y}Er_{y}O_2$ in the range of y=0.01 to y =0.33 were determined with use of X-ray diffraction data. Oxygen potentials have been measured by means of a thermogravimetric method in the range of 1200~$1500^{\circ}C$ and $10^{-14}$ $\leq$ $Po_2$ $\leq$ $10^{-3}$ for pure $UO_2$ and $U_{1-y}Er_{y}O_{2{\pm}x}$ solid solutions with y=0.02, y=0.06 and y=0.20, respectively. Their oxygen partial pressures were maintained by controlling $CO_2$/CO mixture atmosphere, and the $Po_2$ values corresponding to x of $U_{1-y}Er_{y}O_{2{\pm}x}$ solid solutions were measured with an electrolyte oxygen sensor. The lattice parameter decreases linearly with an increase in the erbium content. The change of the lattice parameter can be expressed in a linear equation of y as a($\AA$) =5.4695-0.220y for 0 $\leq$y$\leq$0.33. The experimental coefficient of y -0.220 in $U_{1-y}Er_{y}O_2$ was an intermediate value between the calculated values -0.273 and -0.156 in the case of $U^{5+}$ and $U^{6+}$, respectively. The (equation omitted) has been found to undergo abrupt increase in the range of -360 to -270 kJ/mole for y=0.06 and -320 to -220 H/mole for y=0.20, respectively, in the temperature range of 1200-$1500^{\circ}C$. (equation omitted) increases with erbium content, but the effect of the dopant for x =0.01 is less significant than that for stoichiometry. The oxygen potentials for $UO_2$ and $U_{0.98}Er_{0.02}O_{2+x}$ can be approximately represented by the $U^{5+}$/$U^{4+}$ model but those for y$\geq$ 0.06 in $U_{1-y}Er_{y}O_{2{\pm}x}$ solid solutions cannot be interpreted by the mean uranium valence model.

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QUADRATIC ρ-FUNCTIONAL INEQUALITIES IN NON-ARCHIMEDEAN NORMED SPACES

  • Cui, Yinhua;Hyun, Yuntak;Yun, Sungsik
    • The Pure and Applied Mathematics
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    • v.24 no.2
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    • pp.109-127
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    • 2017
  • In this paper, we solve the following quadratic ${\rho}-functional$ inequalities ${\parallel}f({\frac{x+y+z}{2}})+f({\frac{x-y-z}{2}})+f({\frac{y-x-z}{2}})+f({\frac{z-x-y}{2}})-f(x)-f(y)f(z){\parallel}$ (0.1) ${\leq}{\parallel}{\rho}(f(x+y+z)+f(x-y-z)+f(y-x-z)+f(z-x-y)-4f(x)-4f(y)-4f(z)){\parallel}$, where ${\rho}$ is a fixed non-Archimedean number with ${\mid}{\rho}{\mid}$ < ${\frac{1}{{\mid}4{\mid}}}$, and ${\parallel}f(x+y+z)+f(x-y-z)+f(y-x-z)+f(z-x-y)-4f(x)-4f(y)-4f(z){\parallel}$ (0.2) ${\leq}{\parallel}{\rho}(f({\frac{x+y+z}{2}})+f({\frac{x-y-z}{2}})+f({\frac{y-x-z}{2}})+f({\frac{z-x-y}{2}})-f(x)-f(y)f(z)){\parallel}$, where ${\rho}$ is a fixed non-Archimedean number with ${\mid}{\rho}{\mid}$ < ${\mid}8{\mid}$. Using the direct method, we prove the Hyers-Ulam stability of the quadratic ${\rho}-functional$ inequalities (0.1) and (0.2) in non-Archimedean Banach spaces and prove the Hyers-Ulam stability of quadratic ${\rho}-functional$ equations associated with the quadratic ${\rho}-functional$ inequalities (0.1) and (0.2) in non-Archimedean Banach spaces.

A Study on Characteristic of Superconductivity and Microstructure of $Y_1Ba_2Cu_3O_{7-y}$-Ag ($Y_1Ba_2Cu_3O_{7-y}$-Ag의 초전도성과 미세구조의 특성 연구)

  • Kim, Chae-Ok;Park, Jeong-Su;Yu, Deok-Su
    • Korean Journal of Materials Research
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    • v.5 no.7
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    • pp.786-793
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    • 1995
  • Ag-doped $Y_1$Ba$_2$Cu$_3$O$_{7-y}$ samples have been prepared by solid state reaction. High-Tc super conductivity, microstructure and mechanical property of the Ag-doped $Y_1$Ba$_2$Cu$_3$O$_{7-y}$ samples have been studied. As the Ag content increased, the grain size of $Y_1$Ba$_2$Cu$_3$O$_{7-y}$, increased and connectivity between the grains was improved, and the sample becomed denser and harder than the undoped. From the result, it is concluded that Ag addition reduced weak link and weak coupling between grains and led to the strong coupling. Furthermore, the anisotropy of crytstal structure was decreased and thermal stability, mechanical property of $Y_1$Ba$_2$Cu$_3$O$_{7-y}$-Ag were improved.mproved.

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The Electrochemical Characterization of $LiMn_{2-y}M_{y}O_4$ Cathode Material - I. Crystal Structure and AC Impedance Properties of $LiMn_{2-y}Mg_{y}O_4$ ($LiMn_{2-y}M_{y}O_4$ 정극 활물질의 전기화학적 특성 - I. $LiMn_{2-y}Mg_{y}O_4$의 결정 구조 및 AC Impedance 특성)

  • 정인성;김종욱;구할본;김형곤;손명모
    • Journal of the Korean Institute of Electrical and Electronic Material Engineers
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    • v.14 no.4
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    • pp.309-315
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    • 2001
  • Crystallized $LiMn_{2-y}Mg_{y}O_4$ powder was prepared by calcing the mixture of LiOH.$H_2O$, $MnO_2$ and MgO at $800^{\circ}C$ for 36h in an air atmosphere. The structure of $LiMn_{2-y}Mg_{y}O_4$ crystallites was analyzed from powder X-ray diffraction data as a cubic spinel, space group Fd3m. Though all cathode material showed spinel phase based on cubic phase in X-ray diffraction, other peaks gradually exhibited and became intense with increasing y value in $LiMn_{2-y}Mg_{y}O_4$. However, ununiform which calculated by (111) face and (222) face was constant in spite of the increase of y value, except pure $LiMn_2O_4$. AC impedance of Li/$LiMn_{2-y}Mg_{y}O_4$ cells revealed the similar resistance of about $70\Omega$ before cycling. In addition, The impedance of Li/$LiMn_{1.9}Mg_{0.1}O_4$ cell changed during charge and discharge or after cycling.

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A Study on Public Key Knapsack Cryptosystem for Security in Computer Communication Networks (컴퓨터 통신 네트워크의 보안성을 위한 공개키 배낭 암호시스템에 대한 연구)

  • Yang Tae-Kyu
    • The Journal of Information Technology
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    • v.5 no.4
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    • pp.129-137
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    • 2002
  • In this paper, a public key knapsack cryptosystem algorithm is based on the security to a difficulty of polynomial factorization in computer communication networks is proposed. For the proposed public key knapsack cryptosystem, a polynomial vector Q(x,y,z) is formed by transform of superincreasing vector P, a polynomial g(x,y,z) is selected. Next then, the two polynomials Q(x,y,z) and g(x,y,z) is decided on the public key. The enciphering first selects plaintext vector. Then the ciphertext R(x,y,z) is computed using the public key polynomials and a random integer $\alpha$. For the deciphering of ciphertext R(x,y,z), the plaintext is determined using the roots x, y, z of a polynomial g(x,y,z)=0 and the increasing property of secrety key vector. Therefore a public key knapsack cryptosystem is based on the security to a difficulty of factorization of a polynomial g(x,y,z)=0 with three variables. The propriety of the proposed public key cryptosystem algorithm is verified with the computer simulation.

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A Study on the Solution of Y2K Problem (Y2k 문제 해결 방안)

  • 박민수;최수길
    • Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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    • 1999.11a
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    • pp.270-273
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    • 1999
  • Y2k will be able to enormous disaster. The many make an effort to find a solution to problem of Y2k. Problem of Y2k must solution to as follow. First, problem of Y2k solution organization must constructed. Second, in step with each stage-the first, developing and complete stage, stage of Y2k solution must be constructed. Third, solution of Y2k must construct to hierarchy. hierarchy structure constructed form six stage to first stage, first stage is investigation resources, second stage is estimation influence, third stage is planing conversion, fourth stage is working conversion, fifte spot, sixth stage is diffusion on the spot.

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Isolation and purification of chicken egg yolk immunoglobulin against Edwardsiella tarda (Edwardsiella tarda에 대한 계란난황항체의 분리와 정제)

  • Kim, Yeong-Dae;O, Myeong-Ju;Jeong, Tae-Seong;Jeong, Seong-Ju
    • Journal of fish pathology
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    • v.17 no.1
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    • pp.11-20
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    • 2004
  • The present study compared purification methods of hen egg yolk immunoglobulin (IgY) from the hen immunized with Edwardsiella tarda. The purification of anti-E. tarda IgY was performed by four different methods, polyethylene glycol (PEG), chloroform polyethylene glycol (Chloroform-PEG), ammonium sulfate and purification kit. Purified IgY had heavy chain of 64 kDa and light chain of 27 kDa size. IgY purified from the hen immunized with E. tarda showed higher ELISA values and agglutination titers than those with IgY purified from the non-immunized hen as a negative control. In addition, purified IgY recognized similar E. tarda proteins to those with anti-E. tarda rabbit serum by western blotting. Purified IgY had an agglutination titer of 1:512 by PEG method and ammonium sulfate method, and 1:128 by chloroform-PEG method and purification kit. Moreover, PEG method was the most rapid method among the four different IgY purification methods. These results indicate that PEG method is effective purification method maintaining biological activity of the IgY.

Evaluating internal exposure due to intake of 131I at a nuclear medicine centre of Dhaka using bioassay methods

  • Sharmin Jahan;Jannatul Ferdous;Md Mahidul Haque Prodhan;Ferdoushi Begum
    • Nuclear Engineering and Technology
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    • v.56 no.6
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    • pp.2050-2056
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    • 2024
  • Handling of radioisotopes may cause external and internal contamination to occupational workers while using radiation for medical purposes. This research aims to monitor the internal hazard of occupational workers who handle 131I. Two methods are used: in vivo or direct method and in vitro or indirect method. The in vivo or direct method was performed by assessing thyroid intake with a thyroid uptake monitoring machine. The in vitro or indirect method was performed by assessing urine samples with the help of a gamma-ray spectroscopy practice using a High-Purity Germanium (HPGe) Detector. In this study, fifty-nine thyroid counts and fifty-nine urine samples were collected from seven occupational workers who were in charge of 131I at the National Institute of Nuclear Medicine and Allied Sciences (NINMAS), Dhaka. The result showed that the average annual effective dose of seven workforces from thyroid counts were 0.0208 mSv/y, 0.0180 mSv/y, 0.0135 mSv/y, 0.0169 m Sv/y, 0.0072 mSv/y, 0.0181 mSv/y, 0.0164 mSv/y and in urine samples 0.0832 mSv/y, 0.0770 mSv/y, 0.0732 mSv/y, 0.0693 mSv/y, 0.0715 mSv/y, 0.0662 mSv/y, 0.0708 mSv/y.The total annual effective dose (in vivo and in vitro method) was found among seven workers in average 0.1039 mSv/y, 0.0950 mSv/y, 0.0868 mSv/y, 0.0862 mSv/y, 0.0787 mSv/y, 0.0843 mSv/y, 0.0872 mSv/y. Following the rules of the International Commission on Radiological Protection (ICRP), the annual limit of effective dose for occupational exposure is 20 mSv per year and the finding values from this research work are lesser than this safety boundary.

A Study on the Modification of NH4+Y-zeolite for Improving Adsorption/Desorption Performance of Benzene (NH4+Y-zeolite의 개질을 통한 벤젠 흡·탈착 성능 증진 연구)

  • Jang, Young Hee;Noh, Young Il;Lee, Sang Moon;Kim, Sung Su
    • Clean Technology
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    • v.25 no.1
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    • pp.33-39
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    • 2019
  • A.C (activated carbon) is mainly used to remove VOCs (volatile organic compounds), however, it has many problems such as fire risk due to increasing of adsorbent surface temperature during VOCs ad/desorption, increased cost by frequent replacement cycles requirement and performance degradation when containing moisture. In order to solve these problems, many researches, hydrophobic zeolite adsorbents, have been reported. In this study, $NH_4{^+}Y$-zeolite was synthesized with Y-zeolite through steam treatment and acid treatment, which is one of the hydrophobic modification methods, to secure high surface area, thermal stability and humidity resistance. The Y, Y-550-HN, Y-600-HN and Y-650-HN had adsorption capacities of $23mg\;g^{-1}$, $38mg\;g^{-1}$, $77mg\;g^{-1}$, $61mg\;g^{-1}$. The change of Si/Al ratio, which is an index to confirm the degree of modification, was confirmed by XRF (X-ray fluorescence spectrometer) analysis. As a result, the adsorbtion performance was improved when Y-zeolite modified, and the Si/Al ratio of Y, Y-550-HN, Y-600-HN, Y-650-HN were increased to 3.1765, 6.6706, 7.3079, and 7.4635, respectively. Whereas it was confirmed that structural crystallization due to high heat treatment temperature affected performance degradation. Therefore, there is an optimal heat treatment temperature of Y-zeolite, optimum modification condition study could be a substitute for activated carbon as a condition for producing an adsorbent having high durability and stability.