• Bulletin of the Korean Mathematical Society
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• v.50 no.3
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• pp.983-991
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• 2013

For each real number $n$ > 6, we prove that there is a sequence $\{pk(n,z)\}^{\infty}_{k=1}$ of fourth degree self-reciprocal polynomials such that the zeros of $p_k(n,z)$ are all simple and real, and every $p_{k+1}(n,z)$ has the largest (in modulus) zero ${\alpha}{\beta}$ where ${\alpha}$ and ${\beta}$ are the first and the second largest (in modulus) zeros of $p_k(n,z)$, respectively. One such sequence is given by $p_k(n,z)$ so that $$p_k(n,z)=z^4-q_{k-1}(n)z^3+(q_k(n)+2)z^2-q_{k-1}(n)z+1$$, where $q_0(n)=1$ and other $q_k(n)^{\prime}s$ are polynomials in n defined by the severely nonlinear recurrence $$4q_{2m-1}(n)=q^2_{2m-2}(n)-(4n+1)\prod_{j=0}^{m-2}\;q^2_{2j}(n),\\4q_{2m}(n)=q^2_{2m-1}(n)-(n-2)(n-6)\prod_{j=0}^{m-2}\;q^2_{2j+1}(n)$$ for $m{\geq}1$, with the usual empty product conventions, i.e., ${\prod}_{j=0}^{-1}\;b_j=1$.

• Korean Journal of Fisheries and Aquatic Sciences
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• v.17 no.1
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• pp.1-8
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• 1984

The author carried out an experiment to determine the resistance of trawl net aboard M/S Saebada, training ship of National Fisheries University of Pusan, 2,275 G/T and 3,600ps. Total tension loaded on warp were measured by the recording tension meter. Resistance of the net is estimated by subtracting the resistance of otter boards and warps from the total tension. Coefficient k and exponent n of the formula on the trawl net deduced by Koyama, $R_N=k\frac{d}{l}abv^n$ were calculated from the resistance of the net obtained. The results obtained are can be summarized as follows : 1. Six seamed net with two net pendant k=11, n=1.8 2. Eight seamed net with three net pendant k=11, n=1.8 3. Ten seamed net with three net pendant k=9, n=1.9 4. Ten seamed net with four net pendant k=9, n=1.9

• Journal of KIISE:Computer Systems and Theory
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• v.29 no.12
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• pp.665-679
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• 2002

The fault diameter of a graph G is the maximum of lengths of the shortest paths between all two vertices when there are $\chi$(G) - 1 or less faulty vertices, where $\chi$(G) is connectivity of G. In this paper, we analyze the fault diameter of recursive circulant $G(2^m,2^k)$ with $k{\geq}3$. Let $ dia_{m.k}$ denote the diameter of $G(2^m,2^k)$. We show that if $2{\leq}m,2{\leq}k, the fault diameter of $G(2{\leq}m,2{\leq}k)$ is equal to $2^m-2$, and if m=k+1, it is equal to $2^k-1$. It is also shown that for m>k+1, the fault diameter is equal to di a_$m{\neq}1$(mod 2k); otherwise, it is less than or equal to$dia_{m.k+2}$.

• 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.

• Bulletin of the Korean Chemical Society
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• v.18 no.5
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• pp.523-527
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• 1997

Apparent second-order rate constants (kapp) have been measured spectrophotometrically for the reaction of 2,4-dinitrophenyl benzoate (DNPB) with 6 secondary cyclic amines in H2O containing 20 mole% DMSO at 25.0±0.1 ℃. The Bronsted-type plot (log kapp vs. pKa) shows a break at pKa near 9.1, e.g. two straight lines with βapp values of 0.67 and 0.44 for the low basic (pKa < 9.1) and the highly basic (pKa > 9.1) amines, respectively. Using an estimated k2 value of 3×109 sec-1, all the other microconstants (k1, k-1 and K) involved in the present aminolysis have been calculated. The k value decreases with increasing the basicity of amines while k1 and K values increase with increasing the amine basicity, as expected. Good linear Bronsted-type plots have been obtained for these microconstants of the present aminolysis of DNPB. The magnitudes of the slope of the Bronsted-type plots, k1 and k-1 have been calculated to be 0.43 and - 0.24, respectively, indicating the k-1 step is about two folds less sensitive than the k1 step to the amine basicity. The K value has been calculated to be 0.66, which appears to be much smaller than the one for other aminolyses showing general base catalysis. The small K value has been attributed to the absence of general base catalysis in the present aminolysis of DNPB.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.33 no.9C
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• pp.669-675
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• 2008

For an odd prime p, n=4k and $d=((p^2k+1)/2)^2$, there are $(p^{2k}+1)/2$ distinct decimated sequences, s(dt+1), $0{\leq}l<(p^{2k}+1)/2$, of a p-ary m-sequence, s(t) of period $p^n-1$. In this paper, it is shown that the cross-correlation function between s(t) and s(dt+l) takes the values in $\{-1,-1{\pm}\sqrt{p^n},-1+2\sqrt{p^n}\}$ and their, cross-correlation distribution is also derived.

• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.445-452
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• 2004

In [8], Rosenfeld's digital ($k_0,\;k_1$)-continuity was introduced and another was also established in terms of the preservation of ${k_i}-connectedness,\;i\;{\in}\;\{0,\;1\}$ [2, 3]. In this paper a new version of digital ($k_0,\;k_1$)-continuity for images in $Z^n$ is referred, which is proved to be an extended version of the formers [2, 3, 8]. The current digital ($k_0,\;k_1$)-continuity is derived from the notion of n kinds of digital neighborhoods with some radius without any difficulties on the dimension and adjacency of an image in $Z^n$. The aim of this paper is to compare among Rosenfeld's digital continuity, the current digital continuity and Boxer's digital ($k_0,\;k_1$)-continuity.

• BMB Reports
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• v.45 no.11
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• pp.653-658
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• 2012

After the outbreak of the swine-origin influenza A H1N1 virus in April 2009, World Health Organization declared this novel H1N1 virus as the first pandemic influenza virus (2009 pH1N1) of the $21^{st}$ century. To elucidate the characteristics of 2009 pH1N1, the growth properties of A/Korea/01/09 (K/09) was analyzed in cells. Interestingly, the maximal titer of K/09 was higher than that of a seasonal H1N1 virus isolated in Korea 2008 (S/08) though the RNP complex of K/09 was less competent than that of S/08. In addition, the NS1 protein of K/09 was determined as a weak interferon antagonist as compared to that of S/08. Thus, in order to confine genetic determinants of K/09, activities of two major surface glycoproteins were analyzed. Interestingly, K/09 possesses highly reactive NA proteins and weak HA cell-binding avidity. These findings suggest that the surface glycoproteins might be a key factor in the features of 2009 pH1N1.

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.447-452
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• 2005

Given operators X and Y on a Hilbert space H, an interpolating operator is a bounded operator A such that AX = Y. In this article, we investigate compact interpolation problems for vectors in a tridiagonal algebra. Let L be a subspace lattice acting on a separable complex Hilbert space H and Alg L be a tridiagonal algebra. Let X = $(x_{ij})\;and\;Y\;=\;(y_{ij})$ be operators acting on H. Then the following are equivalent: (1) There exists a compact operator A = $(x_{ij})$ in AlgL such that AX = Y. (2) There is a sequence {$\alpha_n$} in $\mathbb{C}$ such that {$\alpha_n$} converges to zero and $$y_1\;_j=\alpha_1x_1\;_j+\alpha_2x_2\;_j\;y_{2k}\;_j=\alpha_{4k-1}x_{2k\;j}\;y_{2k+1\;j}=\alpha_{4k}x_{2k\;j}+\alpha_{4k+1}x_{2k+1\;j}+\alpha_{4k+2}x_{2k+2\;j\;for\;all\;k\;\epsilon\;\mathbb{N}$$.

• Proceedings of the Korean Magnestics Society Conference
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• 2008.12a
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• pp.172.1-172.1
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• 2008