• East Asian mathematical journal
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• v.40 no.1
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• pp.37-50
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• 2024

We establish the existence, multiplicity and uniqueness of positive solutions to nonlocal boundary value systems with strongly coupled integral boundary condition by using the global continuation theorem and Banach's contraction principle.

• Journal of Power System Engineering
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• v.21 no.6
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• pp.5-12
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• 2017

The steady-state, incompressible and three-dimensional numerical analysis was carried out to investigate the internal flow fields characteristics according to wind tunnel contraction type. The turbulence model used in this study is a realizable $k-{\varepsilon}$ modified from the standard $k-{\varepsilon}$ model. As a results, the distribution of the axial mean velocity components along the central axis of the flow model is very similar to the ASME and BE types, and the cubic and cosine types. When the flow passes through the interior space of the analytical models, the flow resistance at the inlet of the plenum chamber is the largest at BS type contraction, but the smallest at cubic type contraction. The boundary layer thickness is the smallest in the cosine type contraction as the axial distance increases. The maximum turbulent kinetic energy in the test section is the smallest in the order of the contraction of cubic type and cosine type. Comprehensively, cubic type contraction is the best choice for wind tunnel performance, and cosine type contraction can be the next best solution.

• The Pure and Applied Mathematics
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• v.27 no.4
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• pp.207-229
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• 2020

We establish fixed point and multidimensional fixed point results satisfying generalized (𝜓, 𝜃, 𝜑)-contraction on partially ordered non-Archimedean fuzzy metric spaces. By using this result we obtain the solution for periodic boundary value problems and give an example to show the degree of validity of our hypothesis. Our results generalize, extend and modify several well-known results in the literature.

• Korean Journal of Mathematics
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• v.30 no.2
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• pp.375-389
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• 2022

In this paper, we prove some fixed-point theorems in partially ordered fuzzy metric spaces for (𝜙, 𝜓, 𝛽)-Geraghty contraction type mappings which are generalization of mappings with Geraghty contraction type condition. Application of the derived results are shown in proving the existence of unique solution to some boundary value problems.

• The Pure and Applied Mathematics
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• v.30 no.3
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• pp.289-307
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• 2023

We prove some common fixed point theorems for β-non-decreasing mappings under contraction mapping principle on partially ordered metric spaces. We study the existence of solution for periodic boundary value problems and also give an example to show the degree of validity of our hypothesis. Our results improve and generalize various known results.

• The Pure and Applied Mathematics
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• v.14 no.4
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• pp.283-287
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• 2007

An extension of the contraction mapping theorem is provided in a Banach space setting to approximate fixed points of operator equations. Our approach is justified by numerical examples where our results apply whereas the classical contraction mapping principle cannot.

• Korean Journal of Mathematics
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• v.16 no.4
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• pp.545-551
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• 2008

We investigate the multiple solutions for a parabolic boundary value problem with jumping nonlinearity crossing no eigenvalues. We show the existence of the unique solution of the parabolic problem with Dirichlet boundary condition and periodic condition when jumping nonlinearity does not cross eigenvalues of the Laplace operator $-{\Delta}$. We prove this result by investigating the Lipschitz constant of the inverse compact operator of $D_t-{\Delta}$ and applying the contraction mapping principle.

• Journal of the Korea Society of Computer and Information
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• v.12 no.4
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• pp.61-68
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• 2007

Two experiments examined the visual memory distortion by presenting 170 subjects with wide-angle views of four scenes on monitor screen. Retention interval of 0, 1 and 48 hours tested in reproduction and recognition experiment. The results of reproduction showed that the subjects tend to magnify the foreground and background of scenes compared to the real input (scene) for all retention intervals. The viewers recognized mure wide-angle views for the same scenes at the retention interval of 1 and 48 hours. These results demonstrated boundary extension is not a robust and unidirectional phenomenon but boundary contraction can be occurred with wide-angle views. The results also suggested that boundary contraction is the product of the activation of a memory schema hypothesis: In memory the representation moves toward a prototypical view and prototypical object size.

• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1445-1460
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• 2010

In this paper, a second-order system of multi-point boundary value problems in Banach spaces is investigated. Based on a specially constructed cone and the fixed point theorem of strict-set-contraction operators, the criterion of the existence and multiplicity of positive solutions are established. And two examples demonstrating the theoretic results are given.

• Korea-Australia Rheology Journal
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• v.19 no.4
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• pp.211-219
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• 2007

Here we demonstrate complex transient behavior of viscoelastic liquid described numerically with the Leonov model in straight and contraction channel flow domains. Finite element and implicit Euler time integration methods are employed for spatial discretization and time marching. In order to stabilize the computational procedure, the tensor-logarithmic formulation of the constitutive equation with SUPG and DEVSS algorithms is implemented. For completeness of numerical formulation, the so called traction boundaries are assigned for flow inlet and outlet boundaries. At the inlet, finite traction force in the flow direction with stress free condition is allocated whereas the traction free boundary is assigned at the outlet. The numerical result has illustrated severe forward-backward fluctuations of overall flow rate in inertial straight channel flow ultimately followed by steady state of forward flow. When the flow reversal occurs, the flow patterns exhibit quite complicated time variation of streamlines. In the inertialess flow, it takes much more time to reach the steady state in the contraction flow than in the straight pipe flow. Even in the inertialess case during startup contraction flow, quite distinctly altering flow patterns with the lapse of time have been observed such as appearing and vanishing of lip vortices, coexistence of multiple vortices at the contraction comer and their merging into one.