• Journal of the Korean Mathematical Society
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• v.46 no.5
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• pp.919-947
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• 2009

In this paper, we give a recursive formula for the Jones polynomial of a 2-bridge knot or link with Conway normal form C($-2n_1$, $2n_2$, $-2n_3$, ..., $(-1)_r2n_r$) in terms of $n_1$, $n_2$, ..., $n_r$. As applications, we also give a recursive formula for the Jones polynomial of a 3-periodic link $L^{(3)}$ with rational quotient L = C(2, $n_1$, -2, $n_2$, ..., $n_r$, $(-1)^r2$) for any nonzero integers $n_1$, $n_2$, ..., $n_r$ and give a formula for the span of the Jones polynomial of $L^{(3)}$ in terms of $n_1$, $n_2$, ..., $n_r$ with $n_i{\neq}{\pm}1$ for all i=1, 2, ..., r.

• The KIPS Transactions:PartA
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• v.14A no.5
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• pp.263-268
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• 2007

In this paper, we analyze some topological properties of Folded Hyper-Star FHS(2n,n). First, we prove that FHS(2n,n) has maximal fault tolerance, and broadcasting time using double rooted spanning tree is 2n-1. Also we show that FHS(2n,n) can be embedded into Folded hypercube with dilation 1, and Folded hypercube can be embedded into FHS(2n,n) ith dilation 2 and congestion 1.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.247-262
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• 2006

The main objective of this paper is to study the boundedness character, the periodic character and the global stability of the positive solutions of the following difference equation $x_{n+1}=\frac{{\alpha}x_n+{\beta}x_{n-1}+{\gamma}x_{n-2}+{\delta}x_{n-3}}{Ax_n+Bx_{n-1}+Cx_{n-2}+Dx{n-3}}$, n=0, 1, 1, ... where the coefficients A, B, C, D, ${\alpha},\;{\beta},\;{\gamma},\;{\delta}$ and the initial conditions x-3, x-2, x-1, x0 are arbitrary positive real numbers.

• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.753-762
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• 2010

Let K be a nonempty closed convex subset of a real Hilbert space H. Let T : K $\rightarrow$ K be a nonexpansive mapping with a nonempty fixed point set Fix(T). Let f : K $\rightarrow$ K be a contraction mapping. Let {$\alpha_n$} and {$\beta_n$} be sequences in (0, 1) such that $\lim_{x{\rightarrow}0}{\alpha}_n=0$, (0.1) $\sum_{n=0}^{\infty}\;{\alpha}_n=+{\infty}$, (0.2) 0 < a ${\leq}\;{\beta}_n\;{\leq}$ b < 1 for all $n\;{\geq}\;0$. (0.3) Then it is proved that the modified Krasnoselski-Mann iterative sequence {$x_n$} given by {$x_0\;{\in}\;K$, $y_n\;=\;{\alpha}_{n}f(x_n)+(1-\alpha_n)x_n$, $n\;{\geq}\;0$, $x_{n+1}=(1-{\beta}_n)y_n+{\beta}_nTy_n$, $n\;{\geq}\;0$, (0.4) converges strongly to a point p $\in$ Fix(T} which satisfies the variational inequality

$\leq$ 0, z $\in$ Fix(T). (0.5) This result improves and extends the corresponding results of Yao et al[Y.Yao, H. Zhou, Y. C. Liou, Strong convergence of a modified Krasnoselski-Mann iterative algorithm for non-expansive mappings, J Appl Math Com-put (2009)29:383-389.

• Korean Journal of Environmental Agriculture
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• v.42 no.4
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• pp.389-395
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• 2023

This study evaluated the effects of gibberellic acid (GA₃) on the growth and quality of creeping bentgrass (Agrostis palustris Huds.). Experimental treatments included a No application of fertilizer and GA₃ (NFG) Control [3 N active ingredient (a.i.) g/m²], 0.3GA₃ (GA₃ 0.3 a.i. mg/m²/200 mL), 0.6GA₃ (GA₃ 0.6 a.i. mg/m²/200 mL), 1.2GA₃ (GA₃ 1.2 a.i. mg/m²/200 mL), and 2.4GA₃ (GA₃ 2.4 a.i. mg/m²/200 mL). Additionally, the study included a 1.5N+GA₃ experiment with similar GA₃ treatments combined with 1.5N a.i. g/m² : NFG, Control (3N a.i. g/m²), 1.5N+ 0.3GA₃ (1.5N a.i. g/m²+GA₃ 0.3 a.i. mg/m²/200 mL), 1.5N+0.6GA₃ (1.5N a.i. g/m²+GA₃ 0.6 a.i. mg/m²/200 mL), 1.5N+1.2GA₃ (1.5N a.i. g/m²+GA₃ 1.2 a.i. mg/m²/ 200 mL), and 1.5N+2.4GA₃ (1.5N a.i. g/m²+GA₃ 2.4 a.i. mg/m²/200 mL). Compared to the NFG, turf color index chlorophyll content was not significantly different (p< 0.05). However, shoot length in 1.2GA₃, 2.4GA₃, 1.5N+0.3GA₃, 1.5N+0.6GA₃, 1.5N+1.2GA₃, and 1.5N+2.4GA₃ treatments increased by 0.8%, 10.6%, 5.15%, 8.3%, 13.5 %, and 21.6%, respectively, compared to the control. As compared to the control, clipping yield in 1.5N+1.2GA₃ and 1.5N+2.4GA₃ treatments increased by 7.1% and 14.3 %, respectively. These results indicated that GA₃ application increased shoot length, with the 1.2GA₃ treatment showing shoot length similar to the control (3N a.i. g /m² ).

• Bulletin of the Korean Mathematical Society
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• v.26 no.1
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• pp.35-42
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• 1989

Let .ohm.$_{n}$ and Pm $t_{n}$ denote the sets of all n*n doubly stochastic matrices and the set of all n*n permutation matrices respectively. For m*n matrices A=[ $a_{ij}$ ], B=[ $b_{ij}$ ] we write A.leq.B(A$a_{ij}$ .leq. $b_{ij}$ ( $a_{ij}$ < $b_{ij}$ ) for all i=1,..,m; j=1,..,n. Let $I_{n}$ denote the identity matrix of order n, let $J_{n}$ denote the n*n matrix all of whose entries are 1/n, and let $K_{n}$=n $J_{n}$. For a complex square matrix A, the permanent of A is denoted by per A. Let $E_{ij}$ denote the matrix of suitable size all of whose entries are zeros except for the (i,j)-entry which is one.hich is one.

• Bulletin of the Korean Mathematical Society
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• v.33 no.1
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• pp.119-126
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• 1996

In this paper we study the asymptotic behavior of the edge independence number of a random (n,n)-tree. The tools we use include the matrix-tree theorem, the probabilistic method and Hall's theorem. We begin with some definitions. An (n,n)_tree T is a connected, acyclic, bipartite graph with n light and n dark vertices (see [Pa92]). A subset M of edges of a graph is called independent(or matching) if no two edges of M are adfacent. A subset S of vertices of a graph is called independent if no two vertices of S are adjacent. The edge independence number of a graph T is the number $\beta_1(T)$ of edges in any largest independent subset of edges of T. Let $\Gamma(n,n)$ denote the set of all (n,n)-tree with n light vertices labeled 1, $\ldots$, n and n dark vertices labeled 1, $\ldots$, n. We give $\Gamma(n,n)$ the uniform probability distribution. Our aim in this paper is to find bounds on $\beta_1$(T) for a random (n,n)-tree T is $\Gamma(n,n)$.

• Bulletin of the Korean Mathematical Society
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• v.30 no.1
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• pp.25-27
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• 1993

In our paper [4] we showed that over bar $A_{n-1}$ is a split extension of (n-1) copies of Z by the symmetric group S$_{n}$ of degree n. We show in this paper how over bar $A_{n-1}$ appears naturally as a subgroup of the natural wreath product W=ZS$_{n}$.TEX> n/.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.1
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• pp.7-10
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• 2009

With the introduction of a new parameter $n{\geq}1$, Kim generalized an upper bound for the exponential function that implies the inequality between the arithmetic and geometric means. By a change of variable, this generalization is equivalent to exp $(\frac{n(x-1)}{n+x-1})\;\leq\;\frac{n-1+x^n}{n}$ for real ${n}\;{\geq}\;1$ and x > 0. In this paper, we show that this inequality is true for real x > 1 - n provided that n is an even integer.

• Journal of Microbiology and Biotechnology
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• v.28 no.2
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• pp.218-226
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• 2018

Nanometric Lactobacillus plantarum nF1 (nLp-nF1) is a biogenics consisting of dead L. plantarum cells pretreated with heat and a nanodispersion process. In this study, we investigated the immune-enhancing effects of nLp-nF1 in vivo and in vitro. To evaluate the immunostimulatory effects of nLp-nF1, mice immunosuppressed by cyclophosphamide (CPP) treatment were administered with nLp-nF1. As expected, CPP restricted the immune response of mice, whereas oral administration of nLp-nF1 significantly increased the total IgG in the serum, and cytokine production (interleukin-12 (IL-12) and tumor necrosis factor alpha (TNF-${\alpha}$)) in bone marrow cells. Furthermore, nLp-nF1 enhanced the production of splenic cytokines such as IL-12, TNF-${\alpha}$, and interferon gamma (IFN-${\gamma}$). In vitro, nLp-nF1 stimulated the immune response by enhancing the production of cytokines such as IL-12, TNF-${\alpha}$, and IFN-${\gamma}$. Moreover, nLp-nF1 given a food additive enhanced the immune responses when combined with various food materials in vitro. These results suggest that nLp-nF1 could be used to strengthen the immune system and recover normal immunity in people with a weak immune system, such as children, the elderly, and patients.