• Honam Mathematical Journal
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• v.6 no.1
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• pp.1-12
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• 1984

Let(X, $\Im$) be a probabilistic metric space with a t-norm. Common fixed point theorems and convergence theorems generalizing the results of Ćirić, Fisher, Sehgal, Istrătescu-Săcuiu and others are proved for three mappings P,S,T on X satisfying $F_{Pu, Pv}(qx){\geq}min\left{F_{Su,Tv}(x),F_{Pu,Su}(x),F_{Pv,Tv}(x),F_{Pu,Tv}(2x),F_{Pv,Su}(2x)\right}$ for every $u, v {\in}X$, all x>0 and some $q{\in}(0, 1)$. One of the main results is extended to uniform spaces. Mathematics Subject Classification (1980): 54H25.

• Korea-Australia Rheology Journal
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• v.21 no.1
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• pp.59-69
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• 2009

The prediction of pressure drop for a droplet flow in a confined micro channel is presented using FE-FTM (Finite Element - Front Tracking Method). A single droplet is passing through 5:1:5 contraction - straight narrow channel - expansion flow domain. The pressure drop is investigated especially when the droplet flows in the straight narrow channel. We explore the effects of droplet size, capillary number (Ca), viscosity ratio ($\chi$) between droplet and medium, and fluid elasticity represented by the Oldroyd-B constitutive model on the excess pressure drop (${\Delta}p^+$) against single phase flow. The tightly fitted droplets in the narrow channel are mainly considered in the range of $0.001{\leq}Ca{\leq}1$ and $0.01{\leq}{\chi}{\leq}100$. In Newtonian droplet/Newtonian medium, two characteristic features are observed. First, an approximate relation ${\Delta}p^+{\sim}{\chi}$ observed for ${\chi}{\geq}1$. The excess pressure drop necessary for droplet flow is roughly proportional to $\chi$. Second, ${\Delta}p^+$ seems inversely proportional to Ca, which is represented as ${\Delta}p^+{\sim}Ca^m$ with negative m irrespective of $\chi$. In addition, we observe that the film thickness (${\delta}_f$) between droplet interface and channel wall decreases with decreasing Ca, showing ${\delta}_f{\sim}Ca^n$ Can with positive n independent of $\chi$. Consequently, the excess pressure drop (${\Delta}p^+$) is strongly dependent on the film thickness (${\delta}_f$). The droplets larger than the channel width show enhancement of ${\Delta}p^+$, whereas the smaller droplets show no significant change in ${\Delta}p^+$. Also, the droplet deformation in the narrow channel is affected by the flow history of the contraction flow at the entrance region, but rather surprisingly ${\Delta}p^+$ is not affected by this flow history. Instead, ${\Delta}p^+$ is more dependent on ${\delta}_f$ irrespective of the droplet shape. As for the effect of fluid elasticity, an increase in ${\delta}_f$ induced by the normal stress difference in viscoelastic medium results in a drastic reduction of ${\Delta}p^+$.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.9 no.2
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• pp.137-140
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• 2009

In this paper, we introduce and formulate the definitions of Banach operator type k and Banach operator pair on intuitionistic fuzzy metric space. Thereafter we prove some properties and theorems on intuitionistic fuzzy metric space.

• Honam Mathematical Journal
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• v.40 no.4
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• pp.719-732
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• 2018

In this manuscript, hybrid fixed point results for four maps using (E.A) and tangential properties in the setting of metric space are studied. Application to system of functional equations is also studied.

• Korea-Australia Rheology Journal
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• v.21 no.4
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• pp.225-233
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• 2009

In various attempts to relate the behaviour of highly-elastic liquids in complex flows to their rheometrical behaviour, obvious candidates for study have been the variation of shear viscosity with shear rate, the two normal stress differences $N_1$ and $N_2$, especially $N_1$, and the extensional viscosity $\eta_E$. In this paper, we shall be mainly interested in 'constant-viscosity' Boger fluids, and, accordingly, we shall limit attention to $N_1$ and $\eta_E$. We shall concentrate on two important flows - axisymmetric contraction flow and "splashing" (particularly that which arises when a liquid drop falls onto the tree surface of the same liquid). Modern numerical techniques are employed to provide the theoretical predictions. It is shown that the two obvious manifestations of viscoelastic rheometrical behaviour can sometimes be opposing influences in determining flow characteristics. Specifically, in an axisymmetric contraction flow, high $\eta_E$ can retard the flow, whereas high $N_1$ can have the opposite effect. In the splashing experiment, high $\eta_E$ can certainly reduce the height of the so-called Worthington jet, thus confirming some early suggestions, but, again, other rheometrical influences can also have a role to play and the overall picture may not be as clear as it was once envisaged.

• Korean Journal of Mathematics
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• v.16 no.2
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• pp.215-231
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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 $T:C{\rightarrow}{\mathcal{K}}(E)$ a multivalued nonself-mapping such that $P_T$ is nonexpansive, where $P_T(x)=\{u_x{\in}Tx:{\parallel}x-u_x{\parallel}=d(x,Tx)\}$. For $f:C{\rightarrow}C$ a contraction and $t{\in}(0,1)$, let $x_t$ be a fixed point of a contraction $S_t:C{\rightarrow}{\mathcal{K}}(E)$, defined by $S_tx:=tP_T(x)+(1-t)f(x)$, $x{\in}C$. It is proved that if C is a nonexpansive retract of E and $\{x_t\}$ is bounded, then the strong ${\lim}_{t{\rightarrow}1}x_t$ exists and belongs to the fixed point set of T. Moreover, we study the strong convergence of $\{x_t\}$ with the weak inwardness condition on T in a reflexive Banach space with a uniformly $G{\hat{a}}teaux$ differentiable norm. Our results provide a partial answer to Jung's question.

• Women's Health Nursing
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• v.8 no.4
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• pp.538-549
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• 2002

This study was designed to test the effects of a full body massage on uterine contraction, length of labor, type of delivery, and drug intervention for primipara during labor. Data were collected using a quasi-experiment method (nonequivalent control group, pre-post test design) from November 1, 2001 to July 31, 2002. The subjects of this experiment consisted of 28 women in the experimental group and 29 in the control group, out of 57 primipara hospitalized at the U OB & GYN hospital in Inchon. The experimental group was given a 20 minute full body massage for each of the three delivery phases (latent, active, and transition). The control group was given conventional delivery care. Three (3) parameters were analyzed in this experiment. (1) The interval, duration, and strength of uterine contraction, using an electric tocodynamometer (2) The elapsed time for stage 1 and stage 2 labor. (3) The types of deliveries and drug interventions, using postpartum medical records The data collected were analyzed using the repeated measures analysis of variance (ANOVA), t-test, and $x^2$ test of the SPSS program. The results of the experiment are as follows: 1) Uterine contraction interval was significantly reduced (F=3.210, p=.050). Duration of uterine contraction showed significant increase only during the transition phase (t=-2.319, p=.023). Strength of uterine contraction showed no significant difference. 2) Total length of labor was significantly shortened (t=-5.245, p=.000). The length of 1st stage labor was significantly shortened (t=-5.164, p=.000), with latent phase showing (t=-4.709, p=.000), active phase (t=-2.973, p=.005), and transition phase (t=-2.031, p=.047). The length of 2nd stage labor showed no significant difference. 3) The number of natural deliveries were significantly increased ($x^2$=13.127, p=.004). 4) The number of drug interventions were significantly fewer ($x^2$= 4.493, p=.034). In conclusion, this study shows that a full body massage has a significantly positive effect on uterine contraction interval, length of labor, type of delivery, and drug intervention. Therefore, this study suggests that a full body massage be used clinically to help primipara during labor.

• Journal of Pharmaceutical Investigation
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• v.16 no.1
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• pp.18-23
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• 1986

Anemarrhenae Rhizoma has been clinically used as a sedative drug in oriental medicine. We observed the sedative action and effect on the movement of isolated-ileum with each water extract of Anemarrhenae Rhizoma (F-I), saline solution treated preparation (F-II) and 25% ethanol treated preparation (F-III). The results obtained were summerized as follows; 1) Sedative actions were recognized with F-I, F-II and F-III. 2) Prolonged effect of sleeping time was recognized significantly with F-I, F-II and F-III. 3) Each fraction of Anemarrhenae Rhizoma showed the released action on the isolated-ileum of the mouse, rat, rabbit and guinea pig, and antagonic action against contraction induced by acetylcholine, barium chloride and histamine. Thus the mechanism in the released action of the smooth muscle was partly considered as the direct dependence of the smooth muscle.

• Bulletin of the Korean Chemical Society
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• v.12 no.2
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• pp.182-188
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• 1991

The reactions of aniline with benzyl and phenacyl compounds are studied by the AM1 method. Two types of modeling were adopted: Cation-neutral, in which a proton is attached to the leaving group F and anion-neutral model, in which aniline was replaced by phenoxide with Cl as the leaving group. The cation-neutral model represented the reactvery well, reproducing the various solution-phase experimental results. In the benzyl system, the ${\pi}$-electrons of the two rings (X-ring in the nucleophile and Y-ring in the substrate) interact conjugatively in the transition state (TS) resulting in a bond contraction of the $C_{\alpha}-C_{Y1}$ bond (benzylic effect), whereas in the phenacyl system the ${\pi}$ electrons of the X-ring delocalizes more efficiently into the carbonyl group than into the Y-ring (resonance shunt effect) with a bond contraction of the $C_{\alpha}-C_{\beta}$ bond. The bond contraction in the benzylic effect was substantially greater than that in the resonance shunt effect. The TS was rather loose for benzyl while it was tighter for phenacyl system. Various bond length changes with substituents in the TS were, however, found to be irregular.

• The Pure and Applied Mathematics
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• v.23 no.1
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• pp.73-96
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• 2016

We establish a coupled coincidence point theorem for generalized com-patible pair of mappings under generalized nonlinear contraction on a partially or-dered metric space. We also deduce certain coupled fixed point results without mixed monotone property of F : X × X → X . An example supporting to our result has also been cited. As an application the solution of integral equations are obtained here to illustrate the usability of the obtained results. We improve, extend and generalize several known results.