• The Pure and Applied Mathematics
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• v.21 no.1
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• pp.23-38
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• 2014

In this paper, we introduce the concept of w¡compatibility and weakly commutativity for hybrid pair of mappings $F:X{\times}X{\times}X{\rightarrow}2^X$ and $g:X{\rightarrow}X$ and establish a common tripled fixed point theorem under generalized nonlinear contraction. An example is also given to validate our result. We improve, extend and generalize various known results.

• The Pure and Applied Mathematics
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• v.23 no.1
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• pp.35-51
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• 2016

We establish coincidence point theorem for g-nondecreasing mappings satisfying generalized nonlinear contraction on partially ordered metric spaces. We also obtain the coupled coincidence point theorem for generalized compatible pair of mappings F, G : X² → X by using obtained coincidence point results. Furthermore, an example is also given to demonstrate the degree of validity of our hypothesis. Our results generalize, modify, improve and sharpen several well-known results.

• Honam Mathematical Journal
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• v.30 no.1
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• pp.197-203
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• 2008

We show the existence of the unique solution of the following system of the nonlinear wave equations with Dirichlet boundary conditions and periodic conditions under some conditions $U_{tt}-U_{xx}+av^+=s{\phi}_{00}+f$ in $(-{\frac{\pi}{2},{\frac{\pi}{2}}){\times}R$, ${\upsilon}_{tt}-{\upsilon}_{xx}+bu^+=t{\phi}_{00}+g$ in $(-{\frac{\pi}{2},{\frac{\pi}{2}}){\times}R$, where $u^+$ = max{u, 0}, s, t ${\in}$ R, ${\phi}_{00}$ is the eigenfunction corresponding to the positive eigenvalue ${\lambda}_{00}$ of the wave operator. We first show that the system has a positive solution or a negative solution depending on the sand t, and then prove the uniqueness theorem by the contraction mapping principle on the Banach space.

• 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.

• East Asian mathematical journal
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• v.32 no.3
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• pp.333-354
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• 2016

We present coincidence point theorem for g-non-decreasing mappings satisfying generalized nonlinear contraction on partially ordered metric spaces. We show how multidimensional results can be seen as simple consequences of our unidimensional coincidence point theorem. We also obtain the coupled coincidence point theorem for generalized compatible pair of mappings $F,G:X^2{\rightarrow}X$ by using obtained coincidence point results. Furthermore, an example and an application to integral equation are also given to show the usability of obtained results. Our results generalize, modify, improve and sharpen several well-known results.

• The Journal of Korean Physical Therapy
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• v.22 no.2
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• pp.25-30
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• 2010

Purpose: Behavior and movement are accomplished by voluntary contractions of skeletal muscles. There are three types of muscle contractions: concentric, isometric and eccentric. The aim of our study was to determine whether there is a difference in the cortical activation pattern between concentric contraction and eccentric contraction of the wrist extensor muscle. Methods: Four healthy right-handed volunteers without any previous history of physical or neurological illness were recruited. fMRI scanning was done during 4 repeated blocks of concentric and eccentric exercise of the wrist joint. Subjects exercised for 12 seconds and then rested for 12 seconds before beginning the second set of exercises. To determine the excitability of cortical neurons during exercise, voxel count and intensity index were analyzed. Results: For right hand movements, when concentric contractions of the right wrist were done, only the left primary motor area was activated. In contrast, during eccentric contraction, both the primary motor area and secondary motor area were activated. For left hand movements, both concentric and eccentric contractions induced only the supplementary motor cortex and the contralateral primary motor cortex. Conclusion: During eccentric contractions, both the primary motor area and secondary motor area are activated in ipsilateral and contralateral brain areas. Thus, eccentric contractions require more complex and difficult movements than concentric contractions do.

• International Journal of Highway Engineering
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• v.14 no.4
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• pp.63-72
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• 2012

PURPOSES : Hot-mix asphalt(HMA) concretes show a trend of strength increase at low temperature due to binder stiffness increase, but strength decrease below a ceratin low temperature. This is due to the differential thermal contraction(DTC) which is induced by a significant difference in coefficients of thermal contraction between aggregate and asphalt which is coated around the aggregate. This DTC damage is well known to occur in HMA concrete, but is not yet investigated in warm-mix asphalt(WMA) concretes. METHODS : To evaluate DTC damage on WMA in this study, the flexural strength($S_f$) of WMA concretes, which were produced at $30{\sim}40^{\circ}C$ lower temperature, was evaluated in comparison with that of HMA at -5, -15 and $-25^{\circ}C$. RESULTS : Most of WMA and HMA mixtures showed flexural strength increase down to $-15^{\circ}C$ and decrease below $-15^{\circ}C$. this type of strength reduction below $-15^{\circ}C$ can e explained as the effect of differential thermal contraction that is a consequence of the large difference in coefficients of thermal contraction between aggregate and asphalt. the property reduction of WMA is similar the result of previous works dealt with HMA mixtures. CONCLUSIONS : Even though there is some differences by materials used, the WMA concretes showed a significantly lower DTC damage than HMA concrete at low temperature at ${\alpha}$=0.05 level.

• Restorative Dentistry and Endodontics
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• v.17 no.2
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• pp.331-341
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• 1992

The purpose of this study was to measure the polymerization contraction stress of two types of composite resins; chemical cured type(Cliarfil F II, Kuraray, Japan) and photo-cured type(Photo-Clearfil Bright, Kuraray, Japan). The stresses of composite resin by contraction measured with specially designed measuring device(Fig. 1). The stresses caused by shrinkage during hardening of specimens were measured according to the type of composite resins, thickness of specimen(0.65, 1.30 and 1.95mm), and ratio of catalyst to base in case of only chemical cured composite resin(0.5, 1.0 and 1.5). As the composite resin specimen shrank on hardening, the load cell recorded force vs time automatically on pen-recorder(Toa, Japan) with a cross-head speed 60mm/hr at 0~10 voltages up to 2 hours. The experiments were conducted in a room maintained at $23{\pm}2^{\circ}C$ and relative humidity $50{\pm}10%$. The results were as follows. 1. The contraction stress during hardening was higher in photo cured composite resin than in chemical cured composite resin. 2. The contraction stress during hardening was increased with thickness of composite resin specimen. 3. In chemical cured composite resin, the polymerization contraction stress was decreased with ratio of catalyst and base. 4. The contraction stress during polymerization was higher in early time after insertion of photo cured composite resin and chemical cured composite resin.

• Journal of the Korean Vacuum Society
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• v.5 no.4
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• pp.315-326
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• 1996

The electronic structures of 3d and 4d core-levels of rare-earth atoms in the insulating rare-earth (Sm, Eu, Gd, and Tb) compounds were studied with x-ray photoelectron spectroscopy(XPS). It is shown that the intrinsic satellite structure due to the hybridization disappears for chemically stable-earth trivalent heavy rare-earth insulating compounds as the hybridization between f electrons of rare-earth atoms and p electrons of anion atoms decreases due to the lanthanide contraction. Eu atoms at the surface of the stable insulating trivalent Eu compounds are found to be divalent. The satellite peak of Eu 3d core-level spectra at about 10eV higher binding energy side relative the main peak comes from the multiplet structures of $\underline{3d}4f^6$ configuration. The satellite structure appearing at about 15 eV higher binding energy side relative to the main peak in all insulating rare-earth compounds is due to an energy loss process of creating a plasmon.

• BMB Reports
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• v.34 no.6
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• pp.573-577
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• 2001

The mammalian heart is known to undergo significant mechanical changes during fetal and neonatal development. The objective of this study was to define the ontogeny of the ryanodine receptor/$Ca^{2+}$ release channel and SERCA that play the major roles in excitation-contraction coupling. Whole ventricular homogenates of fetal (F) (19 and 22 days in gestation), postnatal (N) (1 and 7 days postnatal), and adult (A) (5 weeks postnatal) Sprague-Dawley rat hearts were used to study [$^3H$]ryanodine binding and oxalate-supported $^{45}Ca^{2+}$ uptake. For the ryanodine receptor, the major findings were: (1) The ryanodine receptor density, as determined by maximal [$^3H$]ryanodine binding ($B_{max}$), increased 3 fold between the F22 and A periods ($0.26{\pm}0.1$ vs. $0.73{\pm}0.07$ pmoles/mg protein, p<0.01), whereas there was no significant change during the F22 and N1 development phases ($0.26{\pm}0.1$ vs. $0.34{\pm}0.01$). (2) Affinity of the ryanodine receptor to ryanodine did not significantly change, as suggested by the lack of change in the $K_d$ during the development and maturation. For SERCA, changes started early with an increased rate of $Ca^{2+}$ uptake in the fetal periods (F19: $8.1{\pm}1.1$ vs. F22: $19.3{\pm}2.2$ nmoles/g protein/min; p<0.05) and peaked by 7 days (N7) of the postnatal age ($34.9{\pm}2.1$). Thus, we conclude that the quantitative changes occur in the ryanodine receptor during myocardial development. Also, the maturation of the $Ca^{2+}$ uptake appears to start earlier than that of the $Ca^{2+}$ release.