• East Asian mathematical journal
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• v.25 no.4
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• pp.433-440
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• 2009

Let R be a ring with unity, X the set of all nonzero, nonunits of R and G the group of all units of R. We will consider some group actions on X by G, the left (resp. right) regular action and the conjugate action. In this paper, by investigating these group actions we can have some results as follows: First, if E(R), the set of all nonzero nonunit idempotents of a unit-regular ring R, is commuting, then $o_{\ell}(x)\;=\;o_r(x)$, $o_c(x)\;=\;\{x\}$ for all $x\;{\in}\;X$ where $o_{\ell}(x)$ (resp. $o_r(x)$, $o_c(x)$) is the orbit of x under the left regular (resp. right regular, conjugate) action on X by G and R is abelian regular. Secondly, if R is a unit-regular ring with unity 1 such that G is a cyclic group and $2\;=\;1\;+\;1\;{\in}\;G$, then G is a finite group. Finally, if R is an abelian regular ring such that G is an abelian group, then R is a commutative ring.

• The korean journal of orthodontics
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• v.16 no.2
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• pp.53-67
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• 1986

The physical tooth movement by orthodontic force is based upon alveolar bone resorption at compression site and new bone formation at tension site of the alveolar socket. The function of the cyclic AMP is to participate not only in initial action of bone cells by mechanical forces but also in the continuous cellular response leading to bone remodelling. This experiment was performed to clarify the role of cyclic AMP in bone remodelling by mechanical force in the NORMAL group, the DIABETES group and the INSULIN TREATED group. The 72 rats were divided into the NORMAL group, the DIABETES group and the INSULIN TREATED group. The same orthodontic forces were applied to the rats of 3 groups. These rats were treated for periods of time ranging from 1 hour, 1 day, 7 days, 14 days, 21 days and 28 days. The samples of alveolar bones were obtained from compression and tension sites surrounding the tipping teeth from NORMAL, DIABETE and INSULIN TREATED rats. The samples were assayed for cyclic AMP by the cyclic AMP RIA kit. The results were as follows: 1. The cyclic AMP levels of alveolar bone in compression and tension sites showed initial decrease, then increased and .remained elevated by the time consuming. 2. The highest cyclic AMP level showed in the DIABETES group and the lowest level was in the NORMAL group. 3. The cyclic AMP levels in the INSULIN TREATED group was similar with the NORMAL group in control and tension sites, but in the compression sites it was similar with the DIABETES group.

• Journal of applied mathematics & informatics
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• v.30 no.3_4
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• pp.455-462
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• 2012

The cyclic group $Cn={\langle}(12{\cdots}n){\rangle}$ acts on the set ($^{[n]}_k$) of all $k$-subsets of [$n$]. In this action of $C_n$ the number of orbits of size $d$, for $d|n$, is $$O^{n,k}_d=\frac{1}{d}\sum_{\frac{n}{d}|s|n}{\mu}(\frac{ds}{n})(^{n/s}_{k/s})$$. Stanton and White[7] generalized the above identity to construct the orbit polynomials $$O^{n,k}_d(q)=\frac{1}{[d]_{q^{n/d}}}\sum_{\frac{n}{d}|s|n}{\mu}(\frac{ds}{n})[^{n/s}_{k/s}]{_q}^s$$ and conjectured that $O^{n,k}_d(q)$ have non-negative coefficients. In this paper we give a combinatorial proof for the positivity of coefficients of the orbit polynomial $O^{n,3}_d(q)$.

• Korean Journal of Mathematics
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• v.25 no.3
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• pp.349-358
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• 2017

The cyclic group $C_n={\langle}(12{\cdots}n){\rangle}$ acts on the set $(^{[n]}_k)$ of all k-subsets of [n]. In this action of $C_n$ the number of orbits of size d, for d | n, is $$O^{n,k}_d={\frac{1}{d}}{\sum\limits_{{\frac{n}{d}}{\mid}s{\mid}n}}{\mu}({\frac{ds}{n}})(^{n/s}_{k/s})$$. Stanton and White [6] generalized the above identity to construct the orbit polynomials $$O^{n,k}_d(q)={\frac{1}{[d]_{q^{n/d}}}}{\sum\limits_{{\frac{n}{d}}{\mid}s{\mid}n}}{\mu}({\frac{ds}{n}})[^{n/s}_{k/s}]_{q^s}$$ and conjectured that $O^{n,k}_d(q)$ have non-negative coefficients. In this paper we give a constructive proof for the positivity of coefficients of the orbit polynomial $O^{n,2}_d(q)$.

• Journal of the Chungcheong Mathematical Society
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• v.13 no.2
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• pp.71-79
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• 2001

We study only free actions of finite abelian groups G on the 3-dimensional nilmanifold, up to topological conjugacy. we shall deal with only one out of 15 distinct almost Bieberbach groups up to Seifert local invariant.

• The Korean Journal of Pharmacology
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• v.19 no.1
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• pp.93-99
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• 1983

Hydrocortisone 5 mg/kg which exerts minimal effect on the renal function and furosemide 1 mg/kg which induces moderate amount of diuresis were injected intraperitoneally to study their effects on the renal cyclic nucleotides content in rats. 1) The renal tissue levels of cAMP were significantly increased by administration of hydrocortisone, but there was no significant change in the furosemide group compared with that of saline treated control group. Moderate elevation in renal cAMP level was noted by the combined administration of hydrocortisone and furosemide, but this elevation was less than that of hvdrocortisone treated group. 2) The renal cGMP level did not show nay remarkable change after the administration of hydrocortisone, however, there were a significant increase by the administration of furosemide alone or combination of both drugs. The level of renal cGMP was higher and maintained longer in the combined treated group than furosemide treated group. The result of this experiment indicates that the potentiating effect of hydrocortisone on the diuretic action of furosemide nay be related to the renal levels of cGMP rather than that of cAMP.

• Journal of Plant Biology
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• v.21 no.1_4
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• pp.13-21
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• 1978

The effect of cyclic-AMP on the induction of acid phosphatase activity in barley aleurone layers was examined. Tannic acid was used as a inhibitor. Decursinol and coumarin were also used as a comparison. Maxiumu promotion of the enzyme activity was obtained with 10-5M cyclic-AMP, but this promotion was lower than that of 10-5M GAS induced enzyme activity in incubation medium. The inhibition rate in the addition of tannic acid was shown 17% and 63% at a ratio to GAs (by weight) of 10 : 1, and 58% and 94% at a ratio of 100 : 1 treated with GAs, and cyclic-AMP, respectively. The most potentiation of 10-6M GAS effect was induced by the additiion of suboptimal concentration (10-6M) of cyclic-AMP. Additional GAs and cyclic-AMP were shown the recovery of the enzyme activity inhibited by tannic acid. The combination with cyclic-AMP and theophylline enhanced the enzyme activity, too. Any other nucleotides tested except cyclic-AMP didn't show the action. There were no differences in acid phosphatase isozyme patterns by polyacrylamide disc electrophoresis, in conjunction with the different additions but the size of bands showed great differences. Especially, the 3rd band and the 5th band group were remarkable.

• Bulletin of the Korean Mathematical Society
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• v.54 no.5
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• pp.1725-1741
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• 2017

For a complex smooth projective surface M with an action of a finite cyclic group G we give a uniform proof of the isomorphism between the invariant $H^1(G,\;H^2(M,\;{\mathbb{Z}}))$ and the first cohomology of the divisors fixed by the action, using G-equivariant cohomology. This generalizes the main result of Bogomolov and Prokhorov [4].

• Bulletin of the Korean Mathematical Society
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• v.25 no.2
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• pp.179-183
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• 1988

In this paper we study a $C^{*}$-dynamical system (A, G, .alpha.) where A is a UHF-algebra, G is a finite abelian group and .alpha. is a *-automorphic action of product type of G on A. In [2], A. Kishimoto considered the case G= $Z_{n}$, the cyclic group of order n and investigated a condition in order that the fixed point algebra $A^{\alpha}$ of A under the action .alpha. is UHF. In later N.J. Munch studied extremal tracial states on $A^{\alpha}$ by employing the method of A. Kishimoto [3], where G is a finite abelian group. Generally speaking, when G is compact (not necessarily discrete and abelian), $A^{\alpha}$ is an AF-algebra and its ideal structure was well analysed by N. Riedel [4]. Here we obtain some conditions for $A^{\alpha}$ to be UHF, where G is a finite abelian group, which is an extension of the result of A. Kishimoto.oto.

• Bulletin of the Korean Mathematical Society
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• v.38 no.2
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• pp.347-355
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• 2001

Let ($X, \omega$) be a closed symplectic 4-manifold. Let a finite cyclic group G act semifreely, holomorphically on X as isometries with fixed point set $\Sigma$(may be empty) which is a 2-dimension submanifold. Then there is a smooth structure on the quotient X'=X/G such that the projection $\pi$:X$\rightarrow$X' is a Lipschitz map. Let L$\rightarrow$X be the Spin$^c$ -structure on X pulled back from a Spin$^c$-structure L'$\rightarrow$X' and b_2^$+(X')>1. If the Seiberg-Witten invariant SW(L')$\neq$0 of L' is non-zero and $L=E\bigotimesK^-1\bigotimesE$ then there is a G-invariant pseudo-holomorphic curve u:$C\rightarrowX$,/TEX> such that the image u(C) represents the fundamental class of the Poincare dual $c_1$(E). This is an equivariant version of the Taubes' Theorem.