• The Journal of the Korean Society for Microbiology
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• v.15 no.1
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• pp.71-75
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• 1980

Antisera to ox red blood cell were prepared by intraperitoneal hypermultiple injections without adjuvant in outbred white rabits. Purified IgG fraction from these rabbits anti-ox red blood cell antiserum for T subset assay was obtained by precipitation with 50% saturated ammonium sulphate followed by DEAE-cellulose chromatography and Sephadex G-150 gel filtration. These purified IgG fraction was compared with Cappel company standard IgG fraction for $T_G$ subpopulation assay. We used home-made IgG fraction and obtained favorable results in $T_G$ subopulation assay as Cappel company standard IgG fraction.

• Journal of the Korean Mathematical Society
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• v.45 no.5
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• pp.1393-1404
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• 2008

Let K be a nonempty closed convex subset of a Banach space E. Suppose $\{T_{n}\}$ (n = 1,2,...) is a uniformly asymptotically regular sequence of nonexpansive mappings from K to K such that ${\cap}_{n=1}^{\infty}$ F$\(T_n){\neq}{\phi}$. For $x_0{\in}K$, define $x_{n+1}={\lambda}_{n+1}x_{n}+(1-{\lambda}_{n+1})T_{n+1}x_{n},n{\geq}0$. If ${\lambda}_n{\subset}[0,1]$ satisfies $lim_{n{\rightarrow}{\infty}}{\lambda}_n=0$, we proved that $\{x_n\}$ weakly converges to some $z{\in}F\;as\;n{\rightarrow}{\infty}$ in the framework of reflexive Banach space E which satisfies the Opial's condition or has $Fr{\acute{e}}chet$ differentiable norm or its dual $E^*$ has the Kadec-Klee property. We also obtain that $\{x_n\}$ strongly converges to some $z{\in}F$ in Banach space E if K is a compact subset of E or there exists one map $T{\in}\{T_{n};n=1,2,...\}$ satisfy some compact conditions such as T is semi compact or satisfy Condition A or $lim_{n{\rightarrow}{\infty}}d(x_{n},F(T))=0$ and so on.

• The Journal of the Korean Society for Microbiology
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• v.18 no.1
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• pp.67-71
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• 1983

Antisera to ox red blood cells were prepared by injection of ox red blood cell stroma without adjuvant in outbred white rabbits. Purified IgM fraction for T-cell subset assay was obtained from these rabbit anti-ox red blood cell stroma antisera by precipitation with 50% saturated ammonium sulphate followed by DEAE-Cellulose chromatography and Sephadex G-200 gel filtration. The serological identification of purified IgM fraction was achieved by immunoelectrophoresis with guinea pig antiserum against rabbit anti-ox red blood cell IgM antibody.

• 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.44 no.4
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• pp.731-742
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• 2007

Let X be a Banach space, $A:D(A){\subset}X{\rightarrow}X$ the generator of a compact $C_0-semigroup\;S(t):X{\rightarrow}X,\;t{\geq}0$, D a locally closed subset in X, and $f:(a,b){\times}C([-q,0];X){\rightarrow}X$ a function of Caratheodory type. The main result of this paper is that a necessary and sufficient condition in order that D be a viable domain of the semi linear differential equation of retarded type $$u#(t)=Au(t)+f(t,u_t),\;t{\in}[t_0,\;t_0+T],{u_t}_0={\phi}{\in}C([-q,0];X)$$ is the tangency condition $$\limits_{h{\downarrow}0}^{lim\;inf\;h^{-1}d(S(h)v(0)+hf(t,v);D)=0}$$ for almost every $t{\in}(a,b)$ and every $v{\in}C([-q,0];X)\;with\;v(0){\in}D$.

• Bulletin of the Korean Mathematical Society
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• v.49 no.5
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• pp.1027-1040
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• 2012

The aim of this paper is to study the Weyl type-theorems for the orthogonal direct sum $S{\oplus}T$, where S and T are bounded linear operators acting on a Banach space X. Among other results, we prove that if both T and S possesses property ($gb$) and if ${\Pi}(T){\subset}{\sigma}_a(S)$, ${\PI}(S){\subset}{\sigma}_a(T)$, then $S{\oplus}T$ possesses property ($gb$) if and only if ${\sigma}_{SBF^-_+}(S{\oplus}T)={\sigma}_{SBF^-_+}(S){\cup}{\sigma}_{SBF^-_+}(T)$. Moreover, we prove that if T and S both satisfies generalized Browder's theorem, then $S{\oplus}T$ satis es generalized Browder's theorem if and only if ${\sigma}_{BW}(S{\oplus}T)={\sigma}_{BW}(S){\cup}{\sigma}_{BW}(T)$.

• East Asian mathematical journal
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• v.24 no.1
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• pp.81-95
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• 2008

Let E be a uniformly convex Banach space with a uniformly $G{\hat{a}}teaux$ differentiable norm, C a nonempty closed convex subset of E, and $T\;:\;C\;{\rightarrow}\;E$ a nonexpansive mapping satisfying the weak inwardness condition. Assume that every weakly compact convex subset of E has the fixed point property. For $f\;:\;C\;{\rightarrow}\;C$ a contraction and $t\;{\in}\;(0,\;1)$, let $x_t$ be a unique fixed point of a contraction $T_t\;:\;C\;{\rightarrow}\;E$, defined by $T_tx\;=\;tf(x)\;+\;(1\;-\;t)Tx$, $x\;{\in}\;C$. It is proved that if {$x_t$} is bounded, then $x_t$ converges to a fixed point of T, which is the unique solution of certain variational inequality. Moreover, the strong convergence of other implicit and explicit iterative schemes involving the sunny nonexpansive retraction is also given in a reflexive and strictly convex Banach space with a uniformly $G{\hat{a}}teaux$ differentiable norm.

• Journal of the Korean Mathematical Society
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• v.49 no.6
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• pp.1259-1271
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• 2012

We consider a tournament T = (V,A). For each subset X of V is associated the subtournament T(X) = (X,$A{\cap}(X{\times}X)$) of T induced by X. We say that a tournament T' embeds into a tournament T when T' is isomorphic to a subtournament of T. Otherwise, we say that T omits T'. A subset X of V is a clan of T provided that for a, $b{\in}X$ and $x{\in}V{\backslash}X$, $(a,x){\in}A$ if and only if $(b,x){\in}A$. For example, ${\emptyset}$, $\{x\}(x{\in}V)$ and V are clans of T, called trivial clans. A tournament is indecomposable if all its clans are trivial. In 2003, B. J. Latka characterized the class ${\tau}$ of indecomposable tournaments omitting a certain tournament $W_5$ on 5 vertices. In the case of an indecomposable tournament T, we will study the set $W_5$(T) of vertices $x{\in}V$ for which there exists a subset X of V such that $x{\in}X$ and T(X) is isomorphic to $W_5$. We prove the following: for any indecomposable tournament T, if $T{\notin}{\tau}$, then ${\mid}W_5(T){\mid}{\geq}{\mid}V{\mid}$ -2 and ${\mid}W_5(T){\mid}{\geq}{\mid}V{\mid}$ -1 if ${\mid}V{\mid}$ is even. By giving examples, we also verify that this statement is optimal.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.22 no.2
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• pp.9-14
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• 2022

This paper presents a subset sum problem (SSP) algorithm which takes the time complexity of O(nlogn). The SSP can be classified into either super-increasing sequence or random sequence depending on the element of Set S. Additive algorithm that runs in O(nlogn) has already been proposed to and utilized for the super-increasing sequence SSP, but exhaustive Brute-Force method with time complexity of O(n2ⁿ) remains as the only viable algorithm for the random sequence SSP, which is thus considered NP-complete. The proposed subtractive algorithm basically selects a subset S comprised of values lower than target value t, then sets the subset sum less the target value as the Residual r, only to remove from S the maximum value among those lower than t. When tested on various super-increasing and random sequence SSPs, the algorithm has obtained optimal solutions running less than the cardinality of S. It can therefore be used as a general algorithm for the SSP.

• Journal of Periodontal and Implant Science
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• v.12 no.1
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• pp.51.1-51.1
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• 1982