• 한국광물학회지
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• 제15권2호
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• pp.95-103
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• 2002

본 연구는 일라이트-스멕타이트 혼합층광물(I-S)의 구조를 MacEwan 결정자 모델과 기본입자 모델을 통하여 살펴봄으로써, 팽창성(% $S_{XRD}$), MacEwan 결정자두께( $N_{CSD}$), 평균기본입자두께( $N_{F}$ ) 간의 관계를 정량적으로 해석하고자 하였다. 두 모델에 대한 비교를 통하여, % $S_{XRD}$, $N_{CSD}$, $N_{F}$ 는 서로 독립된 변수들이 아니고 I-S 구조 내에서 특정한 기하학적 관계를 가지고 있음을 알 수 있었다. % $S_{XRD}$는 단범위적층효과에 의해 $N_{CSD}$에 영향을 받고, $N_{F}$ 및 스멕타이트 층간개수( $N_{S}$ )와 $N_{s}$ =( $N_{F-}$1)/(100%/% $S_{XRD-}$ $N_{F}$ ) 관계가 성립함을 알 수 있었다. 특히, 이 관계로부터 % $S_{XRD}$와 $N_{F}$ 는 물리적으로 제한된 조건인 1< $N_{F}$ <100%/ % $S_{XRD}$를 만족해야 한다는 결과를 도출할 수 있었다. 본 연구는 이러한 물리적 제한조건을 이용하여, % $S_{XRD}$, $N_{F}$ , $N_{s}$ , 질서도 등을 종합적으로 해석하는데 유용할 것으로 사료되는 다이어그램을 제시하였으며, 금성산화 산암복합체에서 산출되는 I-S에 대한 XRD 자료를 이용하여, 이를 검증하였다. 또한, 자연상 I-S는 % $S_{XRD}$가 감소할수록, $N_{F}$ 는 물리적 상한조건인 $N_{F}$ =100%/% $S_{XRD}$에서 점차 멀어지게 됨을 알 수 있었으며, 이러한 결과는 기본입자가 두꺼워질수록 적층능력이 감소하는 것에서 기인한 것으로 사료된다.다.하는 것에서 기인한 것으로 사료된다.다.

• 한국항해학회지
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• 제14권2호
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• pp.1-14
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• 1990

The Radio Navigation System(R. N. S.) has been progressed consistantly with the development of electric-electronic engineering techniques since the R. D. E had been developed in 1910. The R. N. S. mostly depends on either Hyperbolic Navigation System(H. N. S.) or Spherical Navigation System(S. N. S.) in the ocean, and on Rectangular Navigation System (R. N. S.) in the air near the airport or an a combinations of the above systems in both area. Another effective R. N. S may be the Ellipse-Hyperbola Navigation System(E-H N. S.), which is proposed and named such in this paper. The equations calculating GDOP are derived and the GDOP values are calculated in the case of H. N. S., S. N. S, and E-H. N. S., respectively, for the specified case that four transmitting stations are arranged on the apex of a square, Then the GDOP diagrams of above navigation systems are presented for qualitative comparison in this paper. To measure the distances from the receiver to the stations in S. N. S., and/or the sum of distances to two stations in E-H N. S., the time synchronization between the transmitter clocks and the receiver clock is a major premise. The author has proposed the algorithm for getting this synchronmization utilizing the by S. N. S. or E-H N. S while GDOPs of those are relatively good. Even though clock synchronization error is a voidable due to the fix error used, the simulated results shows that the position accuracy of S. N. S. and E-H N. S. by the proposed method is far upgraded compared with that determined by H. N. S. directly, as far as the outer region of transmitter arrangement is concerned.

• Journal of applied mathematics & informatics
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• 제9권1호
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• pp.239-252
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• 2002

A sort sequence $S_n$ is sequence of all unordered pairs of indices in $I_n$={1,2,…n}. With a sort sequence $S_n$ = ($s_1,S_2,...,S_{\frac{n}{2}}$),one can associate a predictive sorting algorithm A($S_n$). An execution of the a1gorithm performs pairwise comparisons of elements in the input set X in the order defined by the sort sequence $S_n$ except that the comparisons whose outcomes can be inferred from the results of the preceding comparisons are not performed. A sort sequence is said to be extremal if it maximizes a given objective function. First we consider the extremal sort sequences with respect to the objective function $\omega$($S_n$) - the expected number of tractive predictions in $S_n$. We study $\omega$-extremal sort sequences in terms of their prediction vectors. Then we consider the objective function $\Omega$($S_n$) - the minimum number of active predictions in $S_n$ over all input orderings.

• 한국통계학회:학술대회논문집
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• 한국통계학회 2002년도 춘계 학술발표회 논문집
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• pp.49-54
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• 2002

For arbitrary random variables {$X_{n},n{\geq}1$}, the order of growth of the series. $S_{n}\;=\;{\sum}_{j=1}^n\;X_{j}$ is studied in this paper. More specifically, when the series S_{n}$ diverges almost surely, the strong law of large numbers $S_{n}/g_{n}^{-1}$($A_{n}{\psi}(A_{n}))\;{\rightarrow}\;0$ a.s. is constructed by extending the results of Petrov (1973). On the other hand, if the series $S_{n}$ converges almost surely to a random variable S, then the tail series $T_{n}\;=\;S\;-\;S_{n-1}\;=\;{\sum}_{j=n}^{\infty}\;X_{j}$ is a well-defined sequence of random variables and converges to 0 almost surely. For the almost surely convergent series $S_{n}$, a tail series strong law of large numbers $T_{n}/g_{n}^{-1}(B_{n}{\psi}^{\ast}(B_{n}^{-1}))\;{\rightarrow}\;0$ a.s., which generalizes the result of Klesov (1984), is also established by investigating the duality between the limiting behavior of partial sums and that of tail series. In particular, an example is provided showing that the current work can prevail despite the fact that previous tail series strong law of large numbers does not work.

• 대한수학회보
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• 제30권2호
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• pp.213-221
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• 1993

In this paper, we will show that the multiplicative group G in a finite ring R with identity 1 has a (B, N)-pair satisfying the following conditions; (1) G=BNB where B and N are subgroups of G. (2) B.cap.N is a normal subgroup of N and W = N/(B.cap.N), is generated by a set S = { $s_{1}$, $s_{2}$, .., $s_{k}$} where $s_{i}$.mem.N/(B.cap.N), $s_{i}$$^{2}$.iden.1 and $s_{i}$.neq.1. (3) For any s.mem.S and w.mem.W, we have sBw.contnd.BwB.cup.BswB. (4) We have sBs not .subeq. B for any s.mem.S. When G, B, N and S satisfy the above conditions, we say that the quadruple (G, B, N, S) is a Tits system. The group W is called the Weyl gorup of the Tits system.ystem.m.

• 한국수학사학회지
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• 제21권4호
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• pp.1-10
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• 2008

이 논문은 홍길주(洪吉周)$(1786{\sim}1841)$의 기하신설(幾何新說)에 들어 있는 대수학 분야를 조사하여 홍길주(洪吉周)의 대수학을 구조적으로 분석한다. 쌍추억산(雙推臆算)은 수리정온(數理精蘊)의 첩차호징(疊借互徵)으로 이에 대한 문제를 추가한 것이고, 개방몽구(開方蒙求)에서 완전제곱수부터 완전다섯제곱수를 급수로 나타내는 등식(等式)을 얻어내었다. 잡쇄수초에서, 정수환(整數環) Z의 상환(商環) Z/(9)를 도입하여 합동방정식을 해결하고, 마지막으로 황금비(黃金比)의 성질을 기하적으로 규명하였다.

• 대한수학회보
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• 제60권4호
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• pp.915-931
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• 2023

Let F_n be the Farey sequence of order n. For S ⊆ F_n, let 𝓠(S) be the set of rational numbers x/y with x, y ∈ S, x ≤ y and y ≠ 0. Recently, Wang found all subsets S of F_n with |S| = n + 1 for which 𝓠(S) ⊆ F_n. Motivated by this work, we try to determine the structure of S ⊆ F_n such that |S| = n and 𝓠(S) ⊆ F_n. In this paper, we determine all sets S ⊆ F_n satisfying these conditions for n ∈ {p, 2p}, where p is prime.

• Bulletin of the Korean Chemical Society
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• 제23권6호
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• pp.851-856
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• 2002

The Reaction of S-methyl-S-cysteine(L-Smc) with racemic $s-cis-[Co(demba)Cl_2]-1$ (Hydmedba = $NN'-dimethylethylenediamine-NN'-di-\alpha-butyric$, acid) yields ${\Delta}$-s-cis-[Co(dmedba)(L-Smc)] 2 with N, O-chelation. Oxidation of sulfur of 2 with $H_2O_2$ in a 1 : 1 mole ratio gives ${\Delta}$-s-cis[Co(dmedba)(L-S(O)mc)] 3 having an uncoordinated sulfenate group. Oxidation of sulfur of L-Sm with $H_2O_2in$ a 1: 1 mole ratio produces S-methyl-L-cysteinesulfenate (L-S(O)me) 5. Direct reaction of 1 with 5 in basic medium gives an N.O-chelated ${\Delta}$s-cis[Co(dmedba)(L-S(O)mc)-N.O], which turmed out be same as obtained by oxidation of 2, while an N, S-chelated ${\Delta}$-s-cis-[Co(dmedba)(S-S(O)mc)-N,O] complex 4 is obtained in acidic medium from the reaction of 1 with 5. This is one of the rare $[$Co^{III}$(N_2O_2-type$ ligand)(amino acid)] type complex preparations, where the reaction conditions determine which mode of N, O and N, S caelation modes is favored.

• 충청수학회지
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• 제31권3호
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• pp.281-285
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• 2018

Let $S_k(N)$ be the space of cusp forms of weight k for ${\Gamma}_0(N)$. We show that $S_k(N)$ is the direct sum of subspaces $S_k^+(N)$ and $S_k^-(N)$. Where $S_k^+(N)$ is the vector space of cusp forms of weight k for the group ${\Gamma}_0^+(N)$ generated by ${\Gamma}_0(N)$ and $W_N$ and $S_k^-(N)$ is the subspace consisting of elements f in $S_k(N)$ satisfying $f{\mid}_kW_N=-f$. We find generators spanning the space $S_k^-(N)$ from $Poincar{\acute{e}}$ series and give all linear relations among such generators.

• 호남수학학술지
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• 제26권4호
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• pp.463-469
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• 2004

In this paper we establish some recurrence relations satisfied by quotient moments of upper record values from the exponential distribution. Let $\{X_n,\;n{\geq}1\}$ be a sequence of independent and identically distributed random variables with a common continuous distribution function F(x) and probability density function(pdf) f(x). Let $Y_n=max\{X_1,\;X_2,\;{\cdots},\;X_n\}$ for $n{\geq}1$. We say $X_j$ is an upper record value of $\{X_n,\;n{\geq}1\}$, if $Y_j>Y_{j-1}$, j > 1. The indices at which the upper record values occur are given by the record times {u(n)}, $n{\geq}1$, where u(n)=min\{j{\mid}j>u(n-1),\;X_j>X_{u(n-1)},\;n{\geq}2\} and u(1) = 1. Suppose $X{\in}Exp(1)$. Then $\Large{E\;\left.{\frac{X^r_{u(m)}}{X^{s+1}_{u(n)}}}\right)=\frac{1}{s}E\;\left.{\frac{X^r_{u(m)}}{X^s_{u(n-1)}}}\right)-\frac{1}{s}E\;\left.{\frac{X^r_{u(m)}}{X^s_{u(n)}}}\right)}$ and $\Large{E\;\left.{\frac{X^{r+1}_{u(m)}}{X^s_{u(n)}}}\right)=\frac{1}{(r+2)}E\;\left.{\frac{X^{r+2}_{u(m)}}{X^s_{u(n-1)}}}\right)-\frac{1}{(r+2)}E\;\left.{\frac{X^{r+2}_{u(m-1)}}{X^s_{u(n-1)}}}\right)}$.