• Journal of the Mineralogical Society of Korea
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• v.15 no.2
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• pp.95-103
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• 2002

The object of this study was to interpret the ralationship between expandability (% $S_{XRD}$), MacEwan crystallite thickness ( $N_{CSD}$), and mean fundamental particle thickness ( $N_{F}$ ) in illite-semctite mixed layer (I-S), quantitatively. This interpretation was extracted from comparison of two structural models (MacEwan crystallite model and fundamental particle model) of I-S mixed layers. In I-S structure, % $S_{XRD}$, $N_{CSD}$, and $N_{F}$ are not independent parameters but are related to each others by particular geometric relations. % $S_{XRD}$ is dependent on $N_{CSD}$ by short-stack effect, whereas, % $S_{XRD}$ and $N_{F}$ have relation to smectite interlayer number (Ns)=( $N_{F-}$1)/(100%/% $S_{XRD-}$ $N_{F}$ . Therefore, % $S_{XRD}$ and $N_{F}$ should satisfy a specific physical condition, 1< $N_{F}$ <100%/% $S_{XRD}$, because $N_{s}$ is positive. Based on this condition, this study suggested % $S_{XRD}$ vs $N_{F}$ diagram which can be used to interpret % $S_{XRD}$, $N_{F}$ , $N_{S}$ , and ordering, quantitatively. The diagram was examined by XRD data for I-S samples from Ceumseongsan volcanic complex, Korea. I-S samples showed that $N_{F}$ departs from the physical upper-limit ( $N_{F}$ =100%/% $S_{XRD}$) with decrease in % $S_{XRD}$. This phenomenon may happen due to decrease of stacking-capability of fundamental particles with their thickening.g.s with their thickening.g.

• Journal of the Korean Institute of Navigation
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• v.14 no.2
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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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• v.9 no.1
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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.

• Proceedings of the Korean Statistical Society Conference
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• 2002.05a
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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.

• Bulletin of the Korean Mathematical Society
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• v.30 no.2
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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.

• 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.

• Bulletin of the Korean Mathematical Society
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• v.60 no.4
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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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• v.23 no.6
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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.

• Journal of the Chungcheong Mathematical Society
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• v.31 no.3
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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.

• Honam Mathematical Journal
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• v.26 no.4
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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 $\Large{E\;\left.{\frac{X^{r+1}_{u(m)}}{X^s_{u(n)}}}\right)=\frac{1}{(r+2)}E\;\left.{\frac{X^{r+2}_{u(m)}}{X^s_{u(n-1)}}}\right)-\frac{1}{(r+2)}E\;\left.{\frac{X^{r+2}_{u(m-1)}}{X^s_{u(n-1)}}}\right)}$.