• Smart Media Journal
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• v.7 no.2
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• pp.9-14
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• 2018

The k-ary n-cube $Q^k_n$ is widely used in the design and implementation of parallel and distributed processing architectures. It consists of $k^n$ identical nodes, each node having degree 2n is connected through bidirectional, point-to-point communication channels to different neighbors. On $Q^k_n$ we would like to transmit packets from a source node to 2n destination nodes simultaneously along paths on this network, the $i^{th}$ packet will be transmitted along the $i^{th}$ path, where $0{\leq}i{\leq}2n-1$. In order for all packets to arrive at a destination node quickly and securely, we present an $O(n^3)$ routing algorithm on $Q^k_n$ for generating a set of one-to-many node-disjoint and nearly shortest paths, where each path is either shortest or nearly shortest and the total length of these paths is nearly minimum since the path is mainly determined by employing the Hungarian method.

• Journal of Environmental Science International
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• v.16 no.8
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• pp.913-920
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• 2007

Hydrochloride acid salts of new $N_2O_2$ tetradentate ligands containing amine and phenol N,N'-bis(2-hydroxybenzyl)-o-phenylenediamine(H-BHP), N,N'-bis(5-bromo-2-hydroxybenzyl)-o-phenylenediamine(Br-BHP), N,N'-bis(5-chloro-2-hydroxybenzyl)-o-phenylene-diamine(Cl-BHP), N,N'-bis(5-methyl-2-hydroxybenzyl)-o-phenylene-diamine (Me-BHP) and N,N'-bis(5-methoxy-2-hydroxybenzyl)-o-phenylenediamine(MeO-BHP) were synthesized. The ligands were characterized by elemental analysis, mass and NMR spectroscopy. The elemental analysis showed that the ligands were isolated as dihydrochloride salt. The potentiometry study revealed that the proton dissociation constants$(logK_n{^H})$ of ligands and stability constants $(logK_{ML})$ of transition and heavy metals complexes. The order of the stability constants of each metal ions for ligands was Br-BHP < Cl-BHP > H-BHP < MeO-BHP < Me-BHP.

• Journal for History of Mathematics
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• v.21 no.4
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• pp.1-10
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• 2008

In this paper, we investigate the part dealing with algebra in Hong Gil Ju's GiHaSinSul to analyze his algebraic structure. The book consists of three parts. In the first part SangChuEokSan, he just renames Die jie hu zheng(疊借互徵) in Shu li jing yun to SangChuEokSan and adds a few examples. In the second part GaeBangMongGu, he obtains the following identities: $$n^2=n(n-1)+n=2S_{n-1}^1+S_n^0;\;n^3=n(n-1)(n+1)+n=6S_{n-1}^2+S_n^0$$; $$n^4=(n-1)n^2(n+1)+n(n-1)+n=12T_{n-1}^2+2S_{n-1}^1+S_n^0$$; $$n^5=2\sum_{k=1}^{n-1}5S_k^1(1+S_k^1)+S_n^0$$ where $S_n^0=n,\;S_n^{m+1}={\sum}_{k=1}^nS_k^m,\;T_n^1={\sum}_{k=1}^nk^2,\;and\;T_n^2={\sum}_{k=1}^nT_k^1$, and then applies these identities to find the nth roots $(2{\leq}n{\leq}5)$. Finally in JabSwoeSuCho, he introduces the quotient ring Z/(9) of the ring Z of integers to solve a system of congruence equations and also establishes a geometric procedure to obtain golden sections from a given one.

• Communications for Statistical Applications and Methods
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• v.16 no.5
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• pp.841-849
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• 2009

Let {$X_n$, n ${\ge}$ 1} be a negatively associated sequence of identically distributed random variables with mean zeros and positive finite variances. Set $S_n$ = ${\Sigma}^n_{i=1}\;X_i$. Suppose that 0 < ${\sigma}^2=EX^2_1+2{\Sigma}^{\infty}_{i=2}\;Cov(X_1,\;X_i)$ < ${\infty}$. We prove that, if $EX^2_1(log^+{\mid}X_1{\mid})^{\delta}$ < ${\infty}$ for any 0< ${\delta}{\le}1$, then $\lim_{{\epsilon}\downarrow0}{\epsilon}^{2{\delta}}\sum_{{n=2}}^{\infty}\frac{(logn)^{\delta-1}}{n^2}ES^2_nI({\mid}S_n{\mid}\geq{\epsilon}{\sigma}\sqrt{nlogn}=\frac{E{\mid}N{\mid}^{2\delta+2}}{\delta}$, where N is the standard normal random variable. We also prove that if $S_n$ is replaced by $M_n=max_{1{\le}k{\le}n}{\mid}S_k{\mid}$ then the precise rate still holds. Some results in Fu and Zhang (2007) are improved to the complete moment case.

• Honam Mathematical Journal
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• v.30 no.2
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• pp.233-246
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• 2008

In this paper, we obtain the general solution of the following cubic type functional equation and establish the stability of this equation (0.1) $kf({{\sum}\limits^{n-1}_{j=1}}x_j+kx_n)+kf({{\sum}\limits^{n-1}_{j=1}}x_j-kx_n)+2{{\sum}\limits^{n-1}_{j=1}}f(kx_j)+(k^3-1)(n-1)[f(x_1)+f(-x_1)]=2kf({\sum\limits^{n-1}_{j=1}}x_j)=K^3{\sum\limits^{n-1}_{j=1}[f(x_j+x_n)+f(x_j-x_n)]$ for any integers k and n with k ${\geq}$ 2 and n ${\geq}$ 3.

• Journal of the Korean Chemical Society
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• v.36 no.2
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• pp.191-196
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• 1992

Reaction of N,N-dimethylaniline(N,N-DMA) and iodine in $CHCl_3,\;CH_2Cl_2 : CHCl_3$(1:1), $CH_2Cl_2$(1:1), and CH2Cl2 has been studied kinetically by using conductivity method. Pseudo first-order rate constants ($k_{obs}$) and second-order rate constants ($k_{obs}$/[N,N-DMA]) are dependent on the N,N-DMA concentration. Second-order rate constants obtained were decreased with increasing N,N-DMA concentration. We analysed these results on the basis of formation of charge transfer complex as a reaction intermediate. From the construction of reaction scheme and activation parameters for the formation and transformation of charge transfer complex. The equilibrium constants decreased when the dielectric constant of solvent was increased, and the value is 1.9${\sim}$4.2$M^{-1}$. The rate of transformation are markedly affected by the solvent polarity.${\Delta}H^{\neq}$ is 6.3-12.6kJ/mol, and ${\Delta}S^{\neq}$ is large negative value of -234J/mol K.

• Journal of the Korean Mathematical Society
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• v.54 no.4
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• pp.1149-1161
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• 2017

An ($n_1,\;n_2,\;{\ldots},\;n_k$)-colored permutation is a permutation of $n_1+n_2+{\cdots}+n_k$ in which $1,\;2,\;{\ldots},\;n_1$ have color 1, and $n_1+1,\;n_1+2,\;{\ldots},\;n_1+n_2$ have color 2, and so on. We give a bijective proof of Steinhardt's result: the number of colored permutations with no monochromatic cycles is equal to the number of permutations with no fixed points after reordering the first $n_1$ elements, the next $n_2$ element, and so on, in ascending order. We then find the generating function for colored permutations with no monochromatic cycles. As an application we give a new proof of the well known generating function for colored permutations with no fixed colors, also known as multi-derangements.

• Journal of the Korean Chemical Society
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• v.16 no.6
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• pp.369-372
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• 1972

The dissociation constants of dibasic carboxylic acids $(HOOC(CH_2)_nCOOH$, n = 0~4] in methanol, N, N-dimethylformamide and acetonitrile have been determined by the potentiometric method with a glass electrode. The difference between over-all dissociation constants in each other solvent is found to be of the same order of magnitude, and the $K_1/K_2$ ratios in aprotic dimethylformamide and acetonitrile are much greater than those in protic methanol and water.

• Kyungpook Mathematical Journal
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• v.49 no.2
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• pp.283-288
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• 2009

Let N be a zero-symmetric near-ring with identity and let ${\Gamma}(N)$ be a graph with vertices as elements of N, where two different vertices a and b are adjacent if and only if + = N, where is the ideal of N generated by x. Let ${\Gamma}_1(N)$ be the subgraph of ${\Gamma}(N)$ generated by the set {n ${\in}$ N : = N} and ${\Gamma}_2(N)$ be the subgraph of ${\Gamma}(N)$ generated by the set $N{\backslash}{\upsilon}({\Gamma}_1(N))$, where ${\upsilon}(G)$ is the set of all vertices of a graph G. In this paper, we completely characterize the diameter of the subgraph ${\Gamma}_2(N)$ of ${\Gamma}(N)$. In addition, it is shown that for any near-ring, ${\Gamma}_2(N){\backslash}M(N)$ is a complete bipartite graph if and only if the number of maximal ideals of N is 2, where M(N) is the intersection of all maximal ideals of N and ${\Gamma}_2(N){\backslash}M(N)$ is the graph obtained by removing the elements of the set M(N) from the vertices set of the graph ${\Gamma}_2(N)$.