• 충청수학회지
• /
• 제15권2호
• /
• pp.67-72
• /
• 2003

The purpose of this paper is to prove flow induced by a covering map. Lee and Park had studied semiflows induced by a covering map in 1997 [1]. This proof differs from the proof of Lee and Park. Notice that for the proof of this paper, we use the fact that $\mathbb{R}$ is connected space.

• 대한수학회논문집
• /
• 제27권4호
• /
• pp.733-743
• /
• 2012

In the present paper, we prove common fixed point theorems for single-valued and set-valued occasionally weakly compatible mappings in Menger spaces. Our results improve and extend the results of Chen and Chang [Chi-Ming Chen and Tong-Huei Chang, Common fixed point theorems in Menger spaces, Int. J. Math. Math. Sci. 2006 (2006), Article ID 75931, Pages 1-15].

• 대한수학회보
• /
• 제36권4호
• /
• pp.717-722
• /
• 1999

The set of continuous maps of a space X to real usual space R equipped with the toplogy of pointwise convergence will be denoted by $C_p$(X). In this paper, we prove that; $C_p$(X) is hereditarily separable and hereditary Lindelof if and only if $X^n$ is hereditarily separable and hereditary Lindelof.

• Journal of applied mathematics & informatics
• /
• 제30권1_2호
• /
• pp.265-278
• /
• 2012

In this work we have considered several common fixed point results in metric spaces for weak compatible mappings. By applications of these results we establish some fixed point theorems in fuzzy metric spaces.

• 대한수학회보
• /
• 제55권5호
• /
• pp.1317-1332
• /
• 2018

In this paper, we introduce the D-ratio of a rational map $f:{\mathbb{P}}^n{\dashrightarrow}{\mathbb{P}}^n$, defined over ${\bar{\mathbb{Q}}}$, whose indeterminacy locus is contained in a hyperplane H on ${\mathbb{P}}^n$. The D-ratio r(f; ${\bar{V}}$) characterizes endomorphisms and provides a useful height inequality on ${\mathbb{P}}^n({\bar{\mathbb{Q}}}){\backslash}H$. We also provide a dynamical application: preperiodic points of dynamical systems of small D-ratio are of bounded height.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제2권2호
• /
• pp.157-162
• /
• 1995

Let I be the interval, $S^1$ the circle and let X be a compact metric space. And let $C^{circ}(X,\;X)$ denote the set of continuous maps from X into itself. For any f$f\in\;C\circ(X,\;X),\;let\;P(f),\;R(f),\;\Gamma(f),\;\Lambda(f)\;and\;\Omega(f)$ denote the collection of the periodic points, recurrent points, ${\gamma}-limit{\;}points,{\;}{\omega}-limit$ points and nonwandering points, respectively.(omitted)

• 통합자연과학논문집
• /
• 제9권2호
• /
• pp.128-135
• /
• 2016

5-hydroxytryptamine (serotonin) receptor ($5-HT_7R$) 7 is one of G-Protein coupled receptors, which is activated by the neurotransmitter Serotonin. After activation by serotonin, $5-HT_7$ activates the production of the intracellular signaling molecule cyclic AMP. $5-HT_7$ receptor has been found to be involved in the pathophysiology of various disorders. It is reported that $5-HT_7$ receptor antagonists can be used as antidepressant agents. In this study, we report the important structural and chemical parameters for 2-methoxyphenylpiperazinylakanamides as $5-HT_7R$ inhibitors. A 3D QSAR study based on comparative molecular field analysis (CoMFA) was performed. The best predictions were obtained for the best CoMFA model with $q^2$ of 0.594 with 6 components, $r^2$ of 0.986, Fisher value as 60.607, and an estimated standard error of 0.043. The predictive ability of the test set was 0.602. Results obtained the CoMFA models suggest that the data are well fitted and have high predictive ability. The contour maps are generated and studied. The contour analyses may serve as tool in the future for designing of novel and more potent $5-HT_7R$ derivatives.

• 약학회지
• /
• 제54권4호
• /
• pp.288-294
• /
• 2010

Three dimensional quantitative-structure relationships (3D-QSARs) models between structures of phenoxy, phenylthio or benzyloxy substituted quinolone analogues and their antitrypanosomal activity against Chagas disease (Trypanosoma cruzi) were derived and discussed quantitatively using comparative molecular field analysis (CoMFA) and comparative molecular similarity indices analysis (CoMSIA) methods. The optimized CoMFA 1 model ($q^2$=0.528 and $r^2$=0.964) showed the best statistical results. According to the optimized CoMFA 1 model, the antitrypanosomal activities were dependent on the steric (60.0%) and electrostatic (36.2%) factors of quinolone derivatives. From the contour maps, it is predicted that the activity will be increased when sterically favored groups were located in $R_4$ and $R_5$ position and sterically disfavored groups were located in $R_2$ position. Also, the positively charged groups on $R_2$ would be able to increase the antitrypanosomal activities.

• 약학회지
• /
• 제55권2호
• /
• pp.98-105
• /
• 2011

To search the minimum structural requirement of tricyclic isoxazole analogues (1~30) as new class potent antidepressant, thee-dimensional quanti- tative-structure relationship (3D-QSAR) models between substituents ($R_1{\sim}R_5$) of tricyclic isoxazoles and their antidepressant activity against medetomidine-induced loss of righting were performed and discussed quantitatively using comparative molecular field analysis (CoMFA) and comparative molecular similarity indies analysis (CoMSIA) methods. The correlativity and predictability ($r^2$=0.484 and $q^2$=0.947) of CoMSIA-2 model were higher than those of the rest models. The inhibitory activity against medetomidine-induced loss of righting was dependent on electrostatic field (43.4%), hydrophobic field (35.3%), and steric field (21.2%) of tricyclic isoxazoles. From the CoMSIA-2 contour maps, it is predicted that the antidepressant activity of potent antidepressants against medetomidine-induced loss of righting will be able to increase by the substituents ($R_1{\sim}R_5$) which were in accord with CoMSIA field.

• 농업과학연구
• /
• 제35권1호
• /
• pp.33-40
• /
• 2008

The structural characteristics that influence on the fungicidal activities of N-phenylbenzenesulfonamide (1~24) and N-phenyltheinylsulfonamide (25~30) derivatives against Dampping-off (Pythium ultimum) were discussed quantitatively using the models of molecular holographic quantitative structure-activity relationships (HQSAR). From the based on these findings, the statistical results of the optimized HQSAR F-3 model showed better predictablity ($r^2_{cv.}$ or $q^2=0.581$) and correlation coefficient ($r^2_{ncv.}=0.963$). And, from the analytical results of the atomic contribution maps on the fungicidal activities, the most active compound is $R_1=2-fluoro-4-chloro$ substituent (4) and the most inactive one is $R_1=4-methoxy$ substituent (20). It was found that the 2-fluoro-4-chlorophenyl group as a $R_1$-group was an important structure and a characteristic factor not only for herbicidal activity but also for fungicidal activity.