• 한국수학교육학회지시리즈B:순수및응용수학
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• 제21권1호
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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.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제23권1호
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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.

• 호남수학학술지
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• 제30권1호
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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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• 제24권1호
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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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• 제32권3호
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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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• 제22권2호
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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.

• Journal of applied mathematics & informatics
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• 제42권4호
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• pp.749-759
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• 2024

In this manuscript, we formulate the notion of Ω(H, θ)-contraction on a self mapping f : W → W, this contraction based on the concept of Ω-distance mappings equipped on G-metric spaces together with the concept of H-simulation functions and the class of Θ-functions, we employ our new contraction to unify the existence and uniqueness of some new fixed point results. Moreover, we formulate a numerical example and a significant application to show the novelty of our results; our application is based on the significant idea that the solution of an equation in a certain condition is similar to the solution of a fixed point equation. We are utilizing this idea to prove that the equation, under certain conditions, not only has a solution as the Intermediate Value Theorem says but also that this solution is unique.

• 한국도로학회논문집
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• 제14권4호
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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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• 제17권2호
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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.

• 한국진공학회지
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• 제5권4호
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• pp.315-326
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• 1996

광전자분광 실험방법을 이용하여 희토류(Sm, Eu, Gd, 및 Tb) 화합물 부도체들의 희토류 원소의 3d와 4d 전자의 내각준위의 스펙트럼들을 연구했다. $La_2O_3,\;Ce_2O_3$ 등과 같은 가벼운 희토류 화합물 부도체의 경우와는 달리 Sm 이상의 무거운 희토류 화합물들의 경우는 란탄족 수축(lantanide contraction) 현상에 의한 희토류 원소의 f 전자와 음이온의 p 전자사이의 혼성의 크기가 줄어들면서 이 혼성에 의한 위성구조가 존재하지 않는 것을 알 수 있었다. 또한 Eu 부도체의 안정된 +3가의 화합물들에서 보이는 위성구조는 표면의 전자구조가 덩어리와는 다른 +2가의 전자가를 갖기 때문이라는 것을 밝혔다. 그리고 Eu 3d 전자의 내각준위의 주요 피크에 대하여 대략 10eV보다 큰 결합에너지 영역에 존재하는 위성구조는 $\underline{3d}4f^6$ 전자구조의 여러겹 효과에 의한 것으로 추정된다. 이러한 여러겹 효과는 Gd 부도체 화합물에서도 역시 발견할 수 있는데, Gd 3d 전자의 내각준위의 스펙트럼에의 위성구조는 $\underline{3d}4f^6$ 전자구조의 여러겹 효과에 의한 것이다. 모든 희토류 부도체 화합물들의 3d 전자의 내각준위의 스펙트럼에서 주요 피크에 대하여 대략 15eV보다 큰 결합에너지 영역에서 보이는 위성구조는 플라즈몬을 생성해서 에너지를 잃는 과정에서 발생하는 것이다.