• Title/Summary/Keyword: U.J.S.

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Signed degree sequences in signed 3-partite graphs

  • Pirzada, S.;Dar, F.A.
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.11 no.2
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    • pp.9-14
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    • 2007

  • A signed 3-partite graph is a 3-partite graph in which each edge is assigned a positive or a negative sign. Let G(U, V, W) be a signed 3-partite graph with $U\;=\;\{u_1,\;u_2,\;{\cdots},\;u_p\},\;V\;=\;\{v_1,\;v_2,\;{\cdots},\;v_q\}\;and\;W\;=\;\{w_1,\;w_2,\;{\cdots},\;w_r\}$. Then, signed degree of $u_i(v_j\;and\;w_k)$ is $sdeg(u_i)\;=\;d_i\;=\;d^+_i\;-\;d^-_i,\;1\;{\leq}\;i\;{\leq}\;p\;(sdeg(v_j)\;=\;e_j\;=\;e^+_j\;-\;e^-_j,\;1\;{\leq}\;j\;{\leq}q$ and $sdeg(w_k)\;=\;f_k\;=\;f^+_k\;-\;f^-_k,\;1\;{\leq}\;k\;{\leq}\;r)$ where $d^+_i(e^+_j\;and\;f^+_k)$ is the number of positive edges incident with $u_i(v_j\;and\;w_k)$ and $d^-_i(e^-_j\;and\;f^-_k)$ is the number of negative edges incident with $u_i(v_j\;and\;w_k)$. The sequences ${\alpha}\;=\;[d_1,\;d_2,\;{\cdots},\;d_p],\;{\beta}\;=\;[e_1,\;e_2,\;{\cdots},\;e_q]$ and ${\gamma}\;=\;[f_1,\;f_2,\;{\cdots},\;f_r]$ are called the signed degree sequences of G(U, V, W). In this paper, we characterize the signed degree sequences of signed 3-partite graphs.

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Best simultaneous approximations from a convex subset

  • Park, Sung-Ho;Rhee, Hyang-Joo
    • Bulletin of the Korean Mathematical Society
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    • v.33 no.2
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    • pp.193-204
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    • 1996

  • Let U and V be nonempty compact subsets of two Hausdorff topological vector spaces. Suppose that a function $J : U \times V \to R$ is such that for each $\upsilon \in V, J(\cdot, \upsilon)$ is lower semi-continuous and convex on U, and for each $ u \in U, J(u, \cdot)$ is upper semi-continuous and concave on V.

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AT LEAST FOUR SOLUTIONS TO THE NONLINEAR ELLIPTIC SYSTEM

  • Jung, Tacksun;Choi, Q-Heung
    • Korean Journal of Mathematics
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    • v.17 no.2
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    • pp.197-210
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    • 2009

  • We prove the existence of multiple solutions (${\xi},{\eta}$) for perturbations of the elliptic system with Dirichlet boundary condition $$(0.1)\;\begin{array}{lcr}A{\xi}+g_1({\xi}+ 2{\eta})=s{\phi}_1+h\;in\;{\Omega},\\A{\xi}+g_2({\xi}+ 2{\eta})=s{\phi}_1+h\;in\;{\Omega},\end{array}$$ where $lim_{u{\rightarrow}{\infty}}\frac{gj(u)}{u}={\beta}_j$, $lim_{u{\rightarrow}-{\infty}}\frac{gj(u)}{u}={\alpha}_j$ are finite and the nonlinearity $g_1+2g_2$ crosses eigenvalues of A.

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Training Effect on the Perception and Production of English Grapheme by Korean Learners of English (한국 학생들의 영어 철자 인지와 발화에 대한 훈련효과)

  • Cho, Mi-Hui
    • The Journal of the Korea Contents Association
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    • v.19 no.11
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    • pp.226-233
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    • 2019

  • Given that English grapheme is realized as five different American English vowels [ʌ, ju, ʊ, u, ə], the purpose of the current study is to examine Korean learners' perception and production of English grapheme and training effect on words with . Thus, the current study conducted pretest, training, and posttest for 31 Korean university students on 24 English words with . The overall results showed that the participants' perception and production accuracy was significantly improved in the posttest, thus indicating training effect on both perception and production. However, it was not the case that all five different vowels demonstrated training effect. In perception the accuracy rates of [ʌ], [ju], and [ə] were improved after training whereas those of [ʊ] and [u] were not. In production [ʌ], [ʊ], and [u] did not show training effect. These results indicate that the Korean participants had difficulty distinguishing between tense [u] and lax [ʊ] both in perception and production. In particular, the Korean participants tended to replace lax [ʊ] with tense [u] in production. This is because tense [u] is the best match to Korean [u] in acoustic measurements, so that tense [u] is easy for the Korean participants to pronounce than lax [ʊ]. Also, English [ʌ] tended to be mispronounced as [u]-quality vowels such as [u] and [ju], which is due to the spelling . The Korean participants also showed errors which insert [j] after alveolars [t, d, n, s], which runs against yod-dropping in American English. They also deleted [j] after labials and velars, which is due to the absence of orthography in the target words. Finally, pedagogical implications were discussed based on the findings of the current study.

  • https://doi.org/10.5392/JKCA.2019.19.11.226 인용 PDF KSCI

CHARACTERIZATIONS OF THE EXPONENTIAL DISTRIBUTION BY ORDER STATISTICS AND CONDITIONAL

  • Lee, Min-Young;Chang, Se-Kyung;Jung, Kap-Hun
    • Communications of the Korean Mathematical Society
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    • v.17 no.3
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    • pp.535-540
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    • 2002

  • Let X$_1$, X$_2$‥‥,X$\_$n/ be n independent and identically distributed random variables with continuous cumulative distribution function F(x). Let us rearrange the X's in the increasing order X$\_$1:n/ $\leq$ X$\_$2:n/ $\leq$ ‥‥ $\leq$ X$\_$n:n/. We call X$\_$k:n/ the k-th order statistic. Then X$\_$n:n/ - X$\_$n-1:n/ and X$\_$n-1:n/ are independent if and only if f(x) = 1-e(equation omitted) with some c > 0. And X$\_$j/ is an upper record value of this sequence lf X$\_$j/ > max(X$_1$, X$_2$,¨¨ ,X$\_$j-1/). We define u(n) = min(j|j > u(n-1),X$\_$j/ > X$\_$u(n-1)/, n $\geq$ 2) with u(1) = 1. Then F(x) = 1 - e(equation omitted), x > 0 if and only if E[X$\_$u(n+3)/ - X$\_$u(n)/ | X$\_$u(m)/ = y] = 3c, or E[X$\_$u(n+4)/ - X$\_$u(n)/|X$\_$u(m)/ = y] = 4c, n m+1.

  • https://doi.org/10.4134/CKMS.2002.17.3.535 인용 PDF KSCI

LU-FACTORIZATION OF THE SQUARE-TYPE MATRIX OF THE STIRLING MATRIX

  • Ji-Hwan Jung
    • East Asian mathematical journal
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    • v.39 no.5
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    • pp.523-528
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    • 2023

  • Let Sn = [S(i, j)]1≤i,j≤n and S*n = [S(i + j, j)]1≤i,j≤n where S(i, j) is the Stirling number of the second kind. Choi and Jo [On the determinants of the square-type Stirling matrix and Bell matrix, Int. J. Math. Math. Sci. 2021] obtained the diagonal entries of matrix U in the LU-factorization of S*n for calculating the determinant of S*n, where L = Sn. In this paper, we compute the all entries of U in the LU-factorization of matrix S*n. This implies the identities related to Stirling numbers of both kinds.

  • https://doi.org/10.7858/eamj.2023.038 인용 PDF