• Journal of the Korean Mathematical Society
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• v.46 no.5
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• pp.919-947
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• 2009

In this paper, we give a recursive formula for the Jones polynomial of a 2-bridge knot or link with Conway normal form C($-2n_1$, $2n_2$, $-2n_3$, ..., $(-1)_r2n_r$) in terms of $n_1$, $n_2$, ..., $n_r$. As applications, we also give a recursive formula for the Jones polynomial of a 3-periodic link $L^{(3)}$ with rational quotient L = C(2, $n_1$, -2, $n_2$, ..., $n_r$, $(-1)^r2$) for any nonzero integers $n_1$, $n_2$, ..., $n_r$ and give a formula for the span of the Jones polynomial of $L^{(3)}$ in terms of $n_1$, $n_2$, ..., $n_r$ with $n_i{\neq}{\pm}1$ for all i=1, 2, ..., r.

• Journal of the Korean Mathematical Society
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• v.41 no.3
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• pp.479-487
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• 2004

Let G be a finite group and N be a normal subgroup of G. We denote by ncc(N) the number of conjugacy classes of N in G and N is called n-decomposable, if ncc(N) = n. Set $K_{G}\;=\;\{ncc(N)$\mid$N{\lhd}G\}$. Let X be a non-empty subset of positive integers. A group G is called X-decomposable, if KG = X. In this paper we characterise the {1, 3, 4}-decomposable finite non-perfect groups. We prove that such a group is isomorphic to Small Group (36, 9), the $9^{th}$ group of order 36 in the small group library of GAP, a metabelian group of order $2^n{2{\frac{n-1}{2}}\;-\;1)$, in which n is odd positive integer and $2{\frac{n-1}{2}}\;-\;1$ is a Mersenne prime or a metabelian group of order $2^n(2{\frac{n}{3}}\;-\;1)$, where 3$\mid$n and $2\frac{n}{3}\;-\;1$ is a Mersenne prime. Moreover, we calculate the set $K_{G}$, for some finite group G.

• Journal of the Korean Chemical Society
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• v.35 no.6
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• pp.707-712
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• 1991

N'-phenyl-N-(2-chloroethyl)-N-aminourea has been prepared from N'-phenyl-N-(2-chloroethyl)-N-nitrosourea by means of the electrochemical reduction with the mercury pool electrolytic cell. In order to find out the optimum condition of the reaction, the voltammetric behaviors for N'-aryl-N-(2-chloroethyl)-N-nitrosourea derivatives have been investigated by the cyclic voltammetry and polarography. The peak potentials was shifted to the negative direction as the pH value of the solution decrease. The substituent effects of phenyl ring on the peak potential were not observed in this case. (5:3) EtOH/4 N-HCl mixed solution was employed for the electrolysis. The applied potential was -0.7 V vs. Ag/AgCl/4 N-HCl electrode. The number of electrons participated to the reduction process was 4, respectively. The product was identified by FT-IR, NMR, mass and/or elemental analysis data.

• Korean Journal of Animal Reproduction
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• v.6 no.1
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• pp.31-35
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• 1982

A study of 188 lactations of Holstein cows in Gwangju area was undertaken to establish the shape of lactation curve during the period from October in 1980 to January in 1982. The Gammafunction described by Wood(1967) was fitted to the lactations observed. The results obtained in the present study were summarized as follows; 1. The lactation curve of the 188 lactations was expressed by the equation based on Wood's model (1967) as follows; Yn=24.5m0.0762e-0.0944n(R2=0.99) 2. The lactation curves by parity were represented by the equations as follows; Yn=18.81n0.1486e-0.0741n(R2=0.98)……………parity 1 Yn=26.51n0.1161e-0.1200n(R2=0.96)……………parity 2 Yn=26.95n0.2804e-0.1703n(R2=0.99)……………parity 3 Yn=27.92n0.1429e-0.1427n(R2=0.98)……………parity 4 Yn=22.61n0.1985e-0.1211n(R2=0.94)……………parity 5 3. The lactation curves by calving seasons were represented by the equationes as follows; Yn=27.05n0.0739e-0.1005n(R2=0.98)……………spring Yn=23.08n0.2040e-0.1202n(R2=0.98)……………summer Yn=26.81n0.0460e-0.1134n(R2=0.98)……………autumn Yn=23.40n0.1299e-0.1101n(R2=0.95)……………winter

• Journal of the Korean Mathematical Society
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• v.45 no.4
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• pp.993-1005
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• 2008

Let {$X,\;X_n;n{\geq}1$} be a sequence of i.i.d. random variables. Set $S_n=X_1+X_2+{\cdots}+X_n,\;M_n=\max_{k{\leq}n}|S_k|,\;n{\geq}1$. Then we obtain that for any -1$\lim\limits_{{\varepsilon}{\searrow}0}\;{\varepsilon}^{2b+2}\sum\limits_{n=1}^\infty\;{\frac {(log\;n)^b}{n^{3/2}}\;E\{M_n-{\varepsilon}{\sigma}\sqrt{n\;log\;n\}+=\frac{2\sigma}{(b+1)(2b+3)}\;E|N|^{2b+3}\sum\limits_{k=0}^\infty\;{\frac{(-1)^k}{(2k+1)^{2b+3}$ if and only if EX=0 and $EX^2={\sigma}^2<{\infty}$.

• Journal of the Korean Mathematical Society
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• v.57 no.3
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• pp.707-719
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• 2020

In this article we study almost contact manifolds admitting weakly Einstein metrics. We first prove that if a (2n + 1)-dimensional Sasakian manifold admits a weakly Einstein metric, then its scalar curvature s satisfies -6 ⩽ s ⩽ 6 for n = 1 and -2n(2n + 1) ${\frac{4n^2-4n+3}{4n^2-4n-1}}$ ⩽ s ⩽ 2n(2n + 1) for n ⩾ 2. Secondly, for a (2n + 1)-dimensional weakly Einstein contact metric (κ, μ)-manifold with κ < 1, we prove that it is flat or is locally isomorphic to the Lie group SU(2), SL(2), or E(1, 1) for n = 1 and that for n ⩾ 2 there are no weakly Einstein metrics on contact metric (κ, μ)-manifolds with 0 < κ < 1. For κ < 0, we get a classification of weakly Einstein contact metric (κ, μ)-manifolds. Finally, it is proved that a weakly Einstein almost cosymplectic (κ, μ)-manifold with κ < 0 is locally isomorphic to a solvable non-nilpotent Lie group.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.13 no.3
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• pp.27-34
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• 2003

Recently, an efficient hardware development for a cryptosystem is concerned. The efficiency of a multiplier for GF($2^n$)is directly related to the efficiency of some cryptosystem. This paper, considering the trade-off between time complexity andsize complexity, proposes a new multiplier architecture having n[n/2] AND gates and n([n/2]+1)- $$\Delta$_n$ = XOR gates, where $$\Delta$_n$=1 if n is even, $$\Delta$_n$=0 otherwise. This size complexity is less than that of existing ${multipliers}^{[5][12]}$which are $n^2$ AND gates and $n^2$-1 XOR gates. While a new multiplier is a serial-parallel multiplier to output a result of multiplication of two elements of GF($2^n$) after 2 clock cycles, the suggested multiplier is more suitable for some cryptographic device having space limitations.

• Clean Technology
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• v.17 no.2
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• pp.134-141
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• 2011

The effects of the compounds and concentrations of nitrogenous electron acceptor, the ratio of electron donor/electron acceptor (C/N), and the complexity of electron donor on the emission of $N_2O$ during wastewater denitrification were quantitatively investigated in this study. The higher ${NO_3}^-$ and ${NO_2}^-$ concentrations, the more $N_2O$ emission was observed. ${NO_2}^-$ has strong effect on $N_2O$ emission as it emitted morc $N_2O$ than ${NO_3}^-$, 50 mg/L of ${NO_2}^-$-N gave the highest conversion (9.3%) and yield (9.8%) of $N_2O$ while ${NO_3}^-$-N (50 mg/L) gave 5.6% conversion and 11.0% yield. Lower C/N ratio decreases nitrogen removal efficiency, but it increases the conversion of $N_2O$ because of the incomplete denitrification by the limited organic carbon. When real domestic wastewater is used as the electron donor of the denitrification, $N_2O$ emission is reduced to 1/10 of the emission when single carbon (acetate) is used. It is thought that multiple carbon source utilizes many denitrification pathways and it seems to be helpful for the reduction of $N_2O$ emission.

• Bulletin of the Korean Chemical Society
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• v.20 no.10
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• pp.1200-1204
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• 1999

The reactions of Ru(tpy)Cl3 (tpy = 2,2';6',2"-terpyridine) with new N,N,C-terdentate ligands, 3,2'-annulated-6-(2"-pyridyl)-2-phenylpyridines (1, HL) and the properties of their Ru(II) complexes are described. The distribution ratio of the two possible Ru(II) complexes, a pentaaza-coordinated complex [Ru(tpy)(1-N,N')Cl]+ and a cycloruthenated complex [Ru(tpy)(La-N,N',C)]+ are highly dependent on the length of the polymethylene unit. The trimethylene bridge of the N,N,C-terdentate in pentaaza-coordinated complex is rigid enough to induce an asymmetry in the complex.

• Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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• v.16 no.1
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• pp.106-113
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• 2002

In this paper, breakdown characteristics of pure Kr, Ar and $N_2$gas with gas pressure range were investigated, and the measured values were compared with those in Ar/$N_2$and Kr/$N_2$gas mixtures with pressure varying. Also, various characteristics with gas mixtures in practical incandescent lamps were investigated. Summarizing the experimental results, the breakdown voltages of $N_2$gas were increased than those of Kr and Ar gas with large molecular weight, and the breakdown voltage increased with gas pressure increasing. The breakdown voltages of Ar/$N_2$and Ar/$N_2$gas mixtures were decreased with decreasing the mixtures ratio of $N_2$gas, and corona inception voltage of Kr/$N_2$gas mixtures under non-uniform fields were increased than those of Ar/$N_2$gas mixtures. In case of tactical incandescent lamps, luminous and lifetime of Kr(70%)/$N_2$(30%) gas mixtures were increased about 94[lm] and 380[hr] than those of Ar(70%)/$N_2$(30%) gas mixtures. and injection pressure of gas mixtures with cooling temperature of 20[$^{\circ}C$] in incandescent lamps were increased about 13[%] than those with cooling temperature of 40[$^{\circ}C$].