• Bulletin of the Korean Mathematical Society
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• v.33 no.2
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• pp.303-310
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• 1996

The Gottlieb group of a compact connected ANR X, G(X), consists of all $\alpha \in \prod_{1}(X)$ such that there is an associated map $A : S^1 \times X \to X$ and a homotopy commutative diagram $$ S^1 \times X \longrightarrow^A X $$ $$incl \uparrow \nearrow \alpha \vee id $$ $$ S^1 \vee X $$.

• Journal of the Korean Mathematical Society
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• v.31 no.4
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• pp.609-618
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• 1994

F. Rhodes [2] introduced the fundamental group $\sigma(X, x_0, G)$ of a transformation group (X,G) as a generalization of the fundamental group $\pi_1(X, x_0)$ of a topological space X and showed a sufficient condition for $\sigma(X, x_0, G)$ to be isomorphic to $\pi_1(X, x_0) \times G$, that is, if (G,G) admits a family of preferred paths at e, $\sigma(X, x_0, G)$ is isomorphic to $\pi_1(X, x_0) \times G$. B.J.Jiang [1] introduced the Jiang subgroup $J(f, x_0)$ of the fundamental group of X which depends on f and showed a condition to be $J(f, x_0)$ = Z(f_\pi(\pi_1(X, x_0)), \pi_1(X, f(x_0)))$.

• Journal of the korean academy of Pediatric Dentistry
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• v.39 no.3
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• pp.257-266
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• 2012

The objective of this in vitro study was to monitor the amount of remineralization of decalcified enamel according to the number of fluoride varnish application using quantitative light-induced fluorescence-D and polarizing microscope. Artificial white lesion induced on the sound 72 teeth, $CavityShield^{TM}$ (Group I), $FluroDose^{TM}$ (Group II) and $Flor-Opal^{(R)}$ Varnish (Group III) were applied 1, 2 or 3 times every two weeks. The following results was obtained: 1. In group I, II and III, ${\Delta}L$ were increased. From regression analysis of ${\Delta}L$ by the number of application, the equation was y = 3.878x + 90.612 in group I, y = 3.133x + 37.168 in group II, and y = 3.509x + 82.322 in group III(p < 0.05). 2. In group I, II and III, ${\Delta}D$ were decreased. From regression analysis of ${\Delta}D$ by the number of application, the equation was y = -2.336x + 107.235 in group I, y = -2.158x + 101.620 in group II, and y = -1.940x + 94.806 in group III(p < 0.05). 3. The Pearson correlation value between the ${\Delta}L$ and ${\Delta}D$ was -0.673 in group I, -0.574 in group II, and -0.431 in group III(p < 0.05).

• Bulletin of the Korean Mathematical Society
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• v.27 no.2
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• pp.113-120
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• 1990

In this paper we introduce S(X, $x_{0}$) which is a generalization of Ellis group G(X, $x_{0}$), and S-sets in S(X, $x_{0}$). In particular we cind the sufficient condition for the group A(I) of all automorphisms of I and K=Iu to be isomorphic, where I is a minimal right ideal and u is an idempotent of I.f I.

• Bulletin of the Korean Mathematical Society
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• v.42 no.4
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• pp.807-815
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• 2005

Let R be a ring with identity, X the set of all nonzero, nonunits of Rand G the group of all units of R. We will consider two group actions on X by G, the regular action and the conjugate action. In this paper, by investigating two group actions we can have some results as follows: First, if G is a finitely generated abelian group, then the orbit O(x) under the regular action on X by G is finite for all nilpotents x $\in$ X. Secondly, if F is a field in which 2 is a unit and F $\backslash\;\{0\}$ is a finitley generated abelian group, then F is finite. Finally, if G in a unit-regular ring R is a torsion group and 2 is a unit in R, then the conjugate action on X by G is trivial if and only if G is abelian if and only if R is commutative.

• Journal of the Korean Mathematical Society
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• v.43 no.5
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• pp.1047-1063
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• 2006

Let $\varepsilon_#(X)$ be the subgroups of $\varepsilon(X)$ consisting of homotopy classes of self-homotopy equivalences that fix homotopy groups through the dimension of X and $\varepsilon_*(X) $ be the subgroup of $\varepsilon(X)$ that fix homology groups for all dimension. In this paper, we establish some connections between the homotopy group of X and the subgroup $\varepsilon_#(X)\cap\varepsilon_*(X)\;of\;\varepsilon(X)$. We also give some relations between $\pi_n(W)$, as well as a generalized Gottlieb group $G_n^f(W,X)$, and a subset $M_{#N}^f(X,W)$ of [X, W]. Finally we establish a connection between the coGottlieb group of X and the subgroup of $\varepsilon(X)$ consisting of homotopy classes of self-homotopy equivalences that fix cohomology groups.

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.657-663
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• 2005

In this paper, we consider groups of permutations S on a set A acting on subsets X of A. In particular, we show that if $X_2{\subseteq}X_1{\subseteq}A$ and Y is an S-normal extension of $X_2 in X_1$, then the Galois group $G_{S}(X_1/Y){\;}of{\;}X_1{\;}over{\;}X_2$ relative to S is an S-closed subgroup of $G_{S}(X_1/X_2)$ in the setting of a Galois theory (correspondence) for this situation.

• Bulletin of the Korean Mathematical Society
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• v.38 no.1
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• pp.143-148
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• 2001

First, we show the finiteness property of the homotopy fixed point set of p-discrete toral group. Let $G_\infty$ be a p-discrete toral group and X be a finite complex with an action of $G_\infty such that X^K$ is nilpotent for each finit p-subgroup K of $G_\infty$. Assume X is $F_\rho-complete$. Then X(sup)hG$\infty$ is F(sub)p-finite. Using this result, we give the condition so that X$^{hG}$ is $F_\rho-finite for \rho-compact$ toral group G.

• Applied Biological Chemistry
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• v.36 no.5
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• pp.381-386
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• 1993

New twenty five Imazethapyr derivatives, [2-(4-isopropyl-4-methyl-5-oxo-2-imidazolin -2-yl)-3-(N-methyl-N-X(sub.)-phenylaminooxoacetyl)-5-methylpyridine] were synthesized. and The quantitative structure activity relationships (QSARs) between their post-emergence herbicidal activity$(pI_{50})$ values in vivo against Barnyard grass (Echinochloa crus-galli) and physicochemical parameters of substituents(X) of 3-(N-methyl-N-X(sub.)-phenylaminooxoacetyl) group have been studied. From the basis on the findings, in case of post-emergence, the activities were dependent on the steric constant$(E_s<0)$ and electron donating $(\sigma<0)$ effect by subsitituents(X) of 3-(N-methyl-N-X(sub.)phenylaminooxoacetyl) group. Therefore, The most effective compound,15 (4-t-butyl group) and 20 (3,5-dimethyl group) were examined in this study. And the conditions on the compounds predicted to show higher herbicidal activity were also discussed.

• Bulletin of the Korean Mathematical Society
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• v.52 no.4
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• pp.1353-1363
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• 2015

Let D be a division ring and w($x_1,\;x_2,\;{\ldots},\;x_m$) be a generalized group monomial over $D^*$. In this paper, we investigate subnormal subgroups and maximal subgroups of $D^*$ which satisfy the identity $w(x_1,\;x_2,\;{\ldots},\;x_m)=1$.