• 대한화학회지
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• 제37권7호
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• pp.648-654
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• 1993

$[M(cyclam)X_2]Y(M=Co^{3+},\;Fe^{3+},\;Mn^{3+}\;:\;X=Cl-^,\;Br^-,\;NCS^-\;:\;Y=Cl^-,\;Br^-,\;NCS^-),\;[Co(trans-14-diene)X_2]Y(X=Cl^-,\;Br^-\;:\;Y= ClO_4^-)$ 및 $[Co(trans-14-diene)](ClO_4)_2$ 착이온은 sodium borohydride 하에서 산소를 활성화시킬 수 있었다. 활성화된 산소에 의한 2,4-di-tert-butylphenol 과 2,6-di-tert-butylphenol 산화반응의 생성물질을 각각 2,4-tert-butyl-1,6-benzoquinone(BQ) 와 3,5,3',5'-tetra-tert-butyldiphenoquinone(DPQ) 이었다. BQ와 DPQ 생성반응에서 포화 거대고리 리간드 착물인 $[Co(cyclam)X_2]Y$은 불포화 거대고리착물 $[Co(trans-14-diene)X_2]Y$에 비하여 더 효과적인 촉매제이었다. 촉매로 작용한 Co(III)-거대고리착물과 산소간의 몰 결합비$(O_2/M)$는 1/1이었고, $[M(cyclam)Cl_2]Cl(M=Fe(III)$, Mn(III))에서는 이들 비가 1/2이었다. 반응(10)과 (2)에서 산소분자의 활성종은 Co(III) 거대고리착물이온과 $[M(cyclam)Cl_2]Cl(M=Fe(III)$, Mn(III))에서 각각 superoxolike$({O_2}^-)$와 peroxolike$({O_2}^{2-})$로 가정하였다.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제11권1호
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• pp.41-56
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• 2007

A 3-partite 2-digraph is an orientation of a 3-partite multi-graph that is without loops and contains at most two edges between any pair of vertices from distinct parts. Let D(X, Y, Z) be a 3-partite 2-digraph with ${\mid}X{\mid}=l,\;{\mid}Y{\mid}=m,\;{\mid}Z{\mid}=n$. For any vertex v in D(X, Y, Z), let $d^+_{\nu}\;and\;d^-_{\nu}$ denote the outdegree and indegree respectively of v. Define $p_x=2(m+n)+d^+_x-d^-_x,\;q_y=2(l+n)+d^+_y-d^-_y\;and\;r_z=2(l+m)+d^+_z-d^-_z$ as the marks (or 2-scores) of x in X, y in Y and z in Z respectively. In this paper, we characterize the marks of 3-partite 2-digraphs and give a constructive and existence criterion for sequences of non-negative integers in non-decreasing order to be the mark sequences of some 3-partite 2-digraph.

• 대한수학회논문집
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• 제12권2호
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• pp.393-401
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• 1997

Let $A_1,A_2,\cdots,A_m$ and $B_1,B_2,\cdots,B_n$ be two sequences of events on a given probability space. Let $X_m$ and $Y_n$, respectively, be the number of those $A_i$ and $B_j$, which occur we establish new upper and lower bounds on the probability $P(X=r, Y=t)$ which improve upper bounds and classical lower bounds in terms of the bivariate binomial moment $S_{r,t},S_{r+1,t},S_{r,t+1}$ and $S_{r+1,t+1}$.

• Bulletin of the Korean Chemical Society
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• 제18권3호
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• pp.311-316
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• 1997

The synthesis and characterization of the mononuclear group 13 heterocyclic carboxaldehyde methyldithiocarbazate complexes Me2M[NC5H4CRNNC(S)SCH3] (M=Al, R=H(1); M=Ga, R=H(2); M=Al, R=CH3(3); M-Ga, R=CH3(4); M=In, R=CH3(5)) are described. Compounds 1-5 were prepared by the reaction of MMe3 (M=Al, Ga, In) with 2-formy or 2-acetylpyridine-S-methyldithiocarbazate in toluene. These compounds 1-5 have been characterized by microanalysis, NMR (1H, 13C) spectroscopy, mass spectra, and single-crystal X-ray diffraction. X-ray single-crystal diffraction analyses reveal that 4-5 are mononuclear metal compounds with coordination number of 5 and N,N,S coordination mode.

• 대한수학회지
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• 제50권4호
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• pp.755-770
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• 2013

One of the interesting nonlinear matrix equations is the quadratic matrix equation defined by $$Q(X)=AX^2+BX+C=0$$, where X is a $n{\times}n$ unknown real matrix, and A, B and C are $n{\times}n$ given matrices with real elements. Another one is the matrix polynomial $$P(X)=A_0X^m+A_1X^{m-1}+{\cdots}+A_m=0,\;X,\;A_i{\in}\mathbb{R}^{n{\times}n}$$. Newton's method is used to find the symmetric and bisymmetric solvents of the nonlinear matrix equations Q(X) and P(X). The method does not depend on the singularity of the Fr$\acute{e}$chet derivative. Finally, we give some numerical examples.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제12권2호
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• pp.55-68
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• 2008

One of well known and much studied nonlinear matrix equations is the matrix polynomial which has the form $P(X)=A_0X^m+A_1X^{m-1}+{\cdots}+A_m$, where $A_0$, $A_1$, ${\cdots}$, $A_m$ and X are $n{\times}n$ complex matrices. Newton's method was introduced a useful tool for solving the equation P(X)=0. Here, we suggest an improved approach to solve each Newton step and consider how to incorporate line searches into Newton's method for solving the matrix polynomial. Finally, we give some numerical experiment to show that line searches reduce the number of iterations for convergence.

• 한국세라믹학회지
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• 제38권8호
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• pp.693-697
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• 2001

고상반응법으로 이론 밀도의 약 92%의 소결 밀도를 갖는 입방정계의 새로운 이온전도체 L $a_{2-x}$S $r_{x}$M $o_{2-y}$C $r_{y}$ $O_{9-{\delta}}$(x=0, 0.05, y=0, 0.1)를 제조하였다. 교류 복소임피던스는 3$50^{\circ}C$~90$0^{\circ}C$의 온도범위에서 공기중에서 측정하여, EQUIVCRT 모델링 소프트웨어로 해석하였다. 상 전이온도인 58$0^{\circ}C$ 전.후로 임피던스 스펙트럼에 큰 차이가 있었으며, 전기전도도는 L $a_2$M $o_2$ $O_{9}$ 시편의 경우 7$50^{\circ}C$에서 3$\times$$10^{-2}$ S$cm^{-1}$ /로 우수하였으며, 활성화 에너지는 고온 상 영역에서는 0.89 eV, 저온 상 영역에서는 1.12 eV이었다. 순수한 L $a_2$M $o_2$ $O_{9}$과 비교하여 Cr 치환효과는 크지 않았으나, Sr 치환 시에는 상 전이온도의 감소와 전기전도도의 증가 현상을 보였으며, 전이온도 부근에서의 전기전도도 변화 폭은 작았다.다.

• 대한수학회보
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• 제26권2호
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• pp.185-190
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• 1989

In [4], J. Leray introduced the notion of partial hyperbolicity to characterize the operators for which the non-characteristic Cauchy problem is solvable in the Geverey class for any data which are holomorphic in a part of variables x"=(x$_{2}$,..,x$_{l}$ ) in the initial hyperplane x$_{1}$=0. A linear partial differential operator is called partially hyperbolic modulo the linear subvarieties S:x"=constant if the equation P$_{m}$(x, .zeta.$_{1}$, .xi.')=0 for .zeta.$_{1}$ has only real roots when .xi.'is real and .xi."=0, where P$_{m}$ is the principal symbol of pp. Limiting to the case of operators with constant coefficients, A. Kaneko proposed a new sharper condition when S is a hyperplane [3]. In this paper, we generalize this condition to the case of general linear subvariety S and show that it is sufficient for the solvability of Cauchy problem for the hyperfunction Cauchy data which contains variables parallel to S as holomorphic parameters.blem for the hyperfunction Cauchy data which contains variables parallel to S as holomorphic parameters.

• 대한수학회논문집
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• 제34권4호
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• pp.1105-1115
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• 2019

For positive integers n and k, let $S_k(n)$ and $S^{\prime}_k(n)$ be the sums of the elements in the finite sets {$x^k:1{\leq}x{\leq}n$, (x, n) = 1} and {$x^k:1{\leq}x{\leq}n/2$, (x, n) = 1}respectively. The formulae for both $S_k(n)$ and $S^{\prime}_k(n)$ are established. The explicit formulae when k = 1, 2, 3 are also given.

• 충청수학회지
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• 제26권2호
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• pp.275-285
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• 2013

In this paper a nonlinear matrix equation is considered which has the form $$P(X)=A_0X^m+A_1X^{m-1}+{\cdots}+A_{m-1}X+A_m=0$$ where X is an $n{\times}n$ unknown real matrix and $A_m$, $A_{m-1}$, ${\cdots}$, $A_0$ are $n{\times}n$ matrices with real elements. Newtons method is applied to find the skew-symmetric solvent of the matrix polynomial P(X). We also suggest an algorithm which converges the skew-symmetric solvent even if the Fr$\acute{e}$echet derivative of P(X) is singular.