• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1211-1220
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• 2009

In this paper, we consider the multipoint boundary value problem for the one-dimensional p-Laplacian $({\phi}_p(u'))'$(t)+q(t)f(t,u(t),u'(t))=0, t $\in$ (0, 1), subject to the boundary conditions: $u(0)=\sum\limits_{i=1}^{n-2}{\alpha}_iu({\xi}_i),\;u(1)=\sum\limits_{i=1}^{n-2}{\beta}_iu({\xi}_i)$ where $\phi_p$(s) = $|s|^{n-2}s$, p > 1, $\xi_i$ $\in$ (0, 1) with 0 < $\xi_1$ < $\xi_2$ < $\cdots$ < $\xi{n-2}$ < 1 and ${\alpha}_i,\beta_i{\in}[0,1)$, 0< $\sum{\array}{{n=2}\\{i=1}}{\alpha}_i,\sum{\array}{{n=2}\\{i=1}}{\beta}_i$<1. Using a fixed point theorem due to Bai and Ge, we study the existence of at least three positive solutions to the above boundary value problem. The important point is that the nonlinear term f explicitly involves a first-order derivative.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.4
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• pp.1102-1115
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• 1995

An experimental study on the flow over the axisymmetric backward-facing step was carried out. The purpose of the present study is to investigate the effect of the boundary layer thickness at the separation point on the reattachment length and to understand the structure of the recirculating flows. Local mean and fluctuating velocity components were measured in the separating and reattaching axisymmetric turbulent boundary layer over the wall of convex cylinder placed in a water tunnel by using 2-color 4-beam fiber optics laser Doppler velocimetry. The study demonstrated that the reattachment length increases with increasing boundary layer thickness. It was also observed that the reverse flow velocity and turbulent kinetic energy decrease with an increase in the momentum thickness at the separation point. The measured velocity field suggests that the boundary layer thickness at the separation can affect definitely on the formation of corner eddy.

• 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.

• Bulletin of the Korean Mathematical Society
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• v.48 no.5
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• pp.1047-1061
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• 2011

In this paper, a class of second-order boundary value problems with Sturm-Liouville boundary conditions or multi-point conditions is considered. Some existence and uniqueness theorems of positive solutions of the problem are obtained by using monotone iterative technique, the iterative sequences yielding approximate solutions are also given. The results are illustrated with an example.

• Journal of the Korean Institute of Telematics and Electronics
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• v.27 no.1
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• pp.96-104
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• 1990

In this paper, a novel method of jig-saw puzzle matching is proposed using a modifided boundary matching algorithm without a priori knowledge for the matched puzzle. Specifically, a boundary tracking algorithm is utilised to segment each puzzle from low-resolution image data. Segmented puzzle is described via corner point, angle and distance between two adjacent coner point, and convexity and/or concavity of corner point. Proposed algorithm is implemented and tested in IBM PC and PC version vision system, and applied successfully to real jig-saw puzzles.

• 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.

• 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.

• Journal of applied mathematics & informatics
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• v.27 no.1_2
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• pp.183-194
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• 2009

In this paper, we considered the following four-point boundary value problem $\{{x"(t)+h(t)f(t,x(t),x'(t))=0,\;0<t<1\atop%20x'(0)=ax(\xi),\;x'(1)=bx(\eta)}\$. where $0\;<\;{\xi}\;<\;{\eta}\;<\;1,\;{\delta}\;=\;ab{\xi}\;-\;ab{\eta}\;+\;a\;-\;b\;<\;0,\;0\;<\;a\;<\;\frac{1}{\xi},\;0\;<\;b\;<\;\frac{1}{\eta}$. After the discussion of the Green function of the corresponding homogeneous system, we establish some criteria for the existence of positive solutions by using the generalized Leggett-William's fixed point theorem. The interesting point is the expression of the Green function, which is a difficulty for multi-point BVP.

• Korean Journal of Computational Design and Engineering
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• v.7 no.2
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• pp.75-80
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• 2002

This paper details a robust and efficient algorithm for point classification with respect to a polygon in 2D real number domain. The concept of tolerance makes this algorithm robust and consistent. It enables to define‘on-boundary’ , which can be interpreted as either‘in-’or‘out-’side region, and to manage rounding errors in floating point computation. Also the tolerance is used as a measure of reliability of point classifications. The proposed algorithm is based on a ray-intersection technique known as the most efficient, in which intersections between a ray originating from a given test point and the boundary of a region are counted. An odd number of intersections indicates that the point is inside region. For practical examples the algorithm is most efficient because most edges of the polygon region are processed by simple bit operations.

• Journal of computational fluids engineering
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• v.4 no.2
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• pp.17-30
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• 1999

The unsteady transitional boundary layer due to rotor-stator interaction was studied at two operation points, the design and one off design points. The off design point leads to lower blade loading and lower Reynolds number. A Navier-Stokes code developed in the previous study was parallelized to expedite computations. A low Reynolds number turbulence model was used to close the momentum equations. All computations show good agreement with experimental data. The wake induced transitional strip on the suction side of the stator is clearly captured at design point operation. There is no noticeable change in shape and phase angle of the wake induced strip even in the laminar sublayer. The wake induced transitional strip at off design point shows more complex structure. The wake induced transitional strip is observed only in the turbulent layer, and becomes obscure in the laminar sublayer and buffer layer. This behavior is probably consequent upon that the transition is governed by both wake induced strip and natural transition mechanism by Tollmien-Schlichting wave.