• Bulletin of the Korean Mathematical Society
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• v.53 no.2
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• pp.365-371
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• 2016

Let f be a transcendental meromorphic function in the complex plane $\mathbb{C}$, and a be a nonzero constant. We give a quantitative estimate of the characteristic function T(r, f) in terms of $N(r,1/(f^2(f^{\prime})^n-a))$, which states as following inequality, for positive integers $n{\geq}2$, $$T(r,f){\leq}\(3+{\frac{6}{n-1}}\)N\(r,{\frac{1}{af^2(f^{\prime})^n-1}}\)+S(r,f)$$.

• Journal of the Korea Society of Computer and Information
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• v.16 no.8
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• pp.103-108
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• 2011

Generally, Miller-Rabin method has been the most popular primality test. This method arbitrary selects m at k-times from m=[2, n-1] range and (m,n)=1. Miller-Rabin method performs $k{\times}r$ times and reports prime as $m^d\;{\equiv}\;1(mod\;n)$ or $m^{2^rd}\;{\equiv}\;-1(mod n)$ such that n-1=$2^sd$, $0\;{\leq}\;r\;{\leq}\;s-1$. This paper suggests more simple primality test than Miller-Rabin method. This test method computes c=$p^{\frac{n-1}{2}}(mod\;n)$ for k times and reports prime as c=-1. The proposed primality test method reduces $k{\times}r$ times of Miller-Rabin method to k times.

• Communications of the Korean Mathematical Society
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• v.34 no.1
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• pp.1-16
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• 2019

Let a, b, P, and Q be real numbers with $PQ{\neq}0$ and $(a,b){\neq}(0,0)$. The Horadam sequence $\{W_n\}$ is defined by $W_0=a$, $W_1=b$ and $W_n=PW_{n-1}+QW_{n-2}$ for $n{\geq}2$. Let the sequence $\{X_n\}$ be defined by $X_n=W_{n+1}+QW_{n-1}$. In this study, we obtain some new identities between the Horadam sequence $\{W_n\}$ and the sequence $\{X_n\}$. By the help of these identities, we show that Diophantine equations such as $$x^2-Pxy-y^2={\pm}(b^2-Pab-a^2)(P^2+4),\\x^2-Pxy+y^2=-(b^2-Pab+a^2)(P^2-4),\\x^2-(P^2+4)y^2={\pm}4(b^2-Pab-a^2),$$ and $$x^2-(P^2-4)y^2=4(b^2-Pab+a^2)$$ have infinitely many integer solutions x and y, where a, b, and P are integers. Lastly, we make an application of the sequences $\{W_n\}$ and $\{X_n\}$ to trigonometric functions and get some new angle addition formulas such as $${\sin}\;r{\theta}\;{\sin}(m+n+r){\theta}={\sin}(m+r){\theta}\;{\sin}(n+r){\theta}-{\sin}\;m{\theta}\;{\sin}\;n{\theta},\\{\cos}\;r{\theta}\;{\cos}(m+n+r){\theta}={\cos}(m+r){\theta}\;{\cos}(n+r){\theta}-{\sin}\;m{\theta}\;{\sin}\;n{\theta},$$ and $${\cos}\;r{\theta}\;{\sin}(m+n){\theta}={\cos}(n+r){\theta}\;{\sin}\;m{\theta}+{\cos}(m-r){\theta}\;{\sin}\;n{\theta}$$.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.471-477
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• 2007

In this paper we establish some recurrence relations satisfied by the quotient moments of the upper record values from the Weibull distribution. Suppose $X{\in}WEI({\lambda})\;then\;E(\frac {X^\tau_U(m)} {X^{s+1}_{U(n)}})=\frac{1}{(s-\lambda+1)}E(\frac {X^\tau_U(m)}{X^{s-\lambda+1}_{U(n-1)}})-\frac{1}{(s-\lambda+1)}+E(\frac{X^\tau_U(m)}{X^{s-\lambda+1}_{U(n)}})\;and\;E(\frac {X^{\tau+1}_{U(m)}}{X^s_{U(n)}})=\frac{1}{(r+\lambda+1)}E(\frac{X^{\tau+\lambda+1}_{U(m)}}{X^s_{U(n-1)}})-\frac{1}{(\tau+\lambda+1)}E(\frac{X^{\tau+\lambda+1}_{U(m-1)}}{X^s_{U(n-1)}})$.

• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.13-30
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• 2010

Let C be a nonempty closed convex subset of a real Hilbert space H. Consider the following iterative algorithm given by $x_0\;{\in}\;C$ arbitrarily chosen, $x_{n+1}\;=\;{\alpha}_n{\gamma}f(W_nx_n)+{\beta}_nx_n+((1-{\beta}_n)I-{\alpha}_nA)W_nP_C(I-s_nB)x_n$, ${\forall}_n\;{\geq}\;0$, where $\gamma$ > 0, B : C $\rightarrow$ H is a $\beta$-inverse-strongly monotone mapping, f is a contraction of H into itself with a coefficient $\alpha$ (0 < $\alpha$ < 1), $P_C$ is a projection of H onto C, A is a strongly positive linear bounded operator on H and $W_n$ is the W-mapping generated by a finite family of nonexpansive mappings $T_1$, $T_2$, ${\ldots}$, $T_N$ and {$\lambda_{n,1}$}, {$\lambda_{n,2}$}, ${\ldots}$, {$\lambda_{n,N}$}. Nonexpansivity of each $T_i$ ensures the nonexpansivity of $W_n$. We prove that the sequence {$x_n$} generated by the above iterative algorithm converges strongly to a common fixed point $q\;{\in}\;F$ := $\bigcap^N_{i=1}F(T_i)\;\bigcap\;VI(C,\;B)$ which solves the variational inequality $\langle({\gamma}f\;-\;A)q,\;p\;-\;q{\rangle}\;{\leq}\;0$ for all $p\;{\in}\;F$. Using this result, we consider the problem of finding a common fixed point of a finite family of nonexpansive mappings and a strictly pseudocontractive mapping and the problem of finding a common element of the set of common fixed points of a finite family of nonexpansive mappings and the set of zeros of an inverse-strongly monotone mapping. The results obtained in this paper extend and improve the several recent results in this area.

• Clean Technology
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• v.25 no.1
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• pp.40-45
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• 2019

In this study, nitrous oxide ($N_2O$) emission concentration was measured 3 times continuously for 24 hours from August 27, 2018 to October 22, 2018 and non-dispersive infrared (NDIR) spectrometer was used to calculate $N_2O$ concentration of exhaust gas from municipal solid waste (MSW) incinerator. As a result of $N_2O$ emission characteristics, it is estimated that $N_2O$ emission concentration is due to the difference of furnace temperature, oxygen concentration rather than the chemical component of waste. The measured $N_2O$ emission concentration of MSW incinerator was obtained in the range of 53.6 ~ 59.5 ppm and the total average concentration was measured 55.6 ppm. Therefore, the amount of $N_2O$ emissions calculated from the $N_2O$ concentration was $98.05kg\;day^{-1}$ on average and the amount of $N_2O$ distribution in the range of $90.41{\sim}108.44kg\;day^{-1}$ was obtained. As a result, the $N_2O$ emission factor of the MSW incinerator was estimated to be $1,066.13g_{N_2O}\;ton_{waste^{-1}}$. The estimated $N_2O$ emission factor of the MSW incinerator was 20 times higher than calculated emission factor used in the Tier 2 method. Consequently, it is considered that the method of calculating the amount of $N_2O$ emission in the MSW incineration facilities using waste type and incineration amount needs to be supplemented to ensure accuracy.

• Journal of the Korean Chemical Society
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• v.27 no.4
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• pp.294-301
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• 1983

Six new compounds of p-acetamidobenzenesulfonamides which contain O, O'-diethyl-1-aminobenzylphosphonate and their derivatives were prepared: O, O'-diethyl N-(p-acetamidobenzenesulfonyl) aminobenzylphosphonate, N-(p-acetamidobenzenesulfonyl) aminobenzylphosphonic acid, O,O'-diethyl N-[N-(p-acetamidobenzenesulfonyl) glycyl] aminobenzylphosphonate, O,O'-diethyl N-[N-(p-acetamidobenzenesulfonyl)-DL-alanyl] aminobenzylphosphonate, O,O'-diethyl N-[N-(p-acetamidobenzenesulfonyl)-L-leucyl] aminobenzylphosphonate, and O,O'-diethyl N-[N-(p-acetamidobenzenesulfonyl)-L-phenylalanyl]aminobenzylphosphonate. All the compounds were obtained as white crystals and characterized by means of elemental analysis and infrared spectroscopy.

• Journal of the Korean Chemical Society
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• v.24 no.6
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• pp.463-468
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• 1980

Tris(hydroxyethyl) phosphate, ethylphosphoramidic dichloride, N,N-diethylphosphoramidic dichloride, bis(hydroxyethyl) N-ethylphosphoramidate and bis(hydroxyethyl) N,N-diethylphosphoramidate were synthesized and characterized. Phosphate and phosphoramidates were polymerized with the elimination of ethylene glycol when heated under reduced pressure and they gave no molecular ion peaks in their mass spectra. And also ethylphosphoramidic dichloride gave polymeric products at 180$^{\circ}C$ with the evolution of HCl. IR spectra showed characteristic P=O streching bands in the range of 1,300 to$ 1,200 cm^{-1}.$

• Microbiology and Biotechnology Letters
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• v.21 no.2
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• pp.181-186
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• 1993

The functions of n-alkane inducible genes, ALI1 and POX18Cm isolated from Canida maltosa were investigated, using it's distruptants. As a result, it is suggested that ALI1 is essential for n-alkane assimilation in C. mltosa and it regulates genes related to assimilation of n-alkane (ALI1, P450alk POX18Cm) at transcriptional level. Nuclear localization experiments indicated that ALI1 was located and functioned in the nucleus. POX18Cm is considered as a peroxisomal nonspecific lipid transfer protein gene related to n-alkane assimilation in C. maltosa also regulated by ALI1. But it had no significant effect on n-alkane assimilation in C. maltosa.

• The Korean Journal of Applied Statistics
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• v.18 no.3
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• pp.689-699
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• 2005

We usually use $S^2=\frac{{\Sigma}^n_{i=1}(X_i-\={X})^2}{n-1}$ as sample variance. Korean high school text-books use $S^2_n=\frac{{\Sigma}^n_{i=1}(X_i-\={X})^2}{n}$as sample variance. We can compare the above two definitions of sample variance through their theoretical relationship and simulation.