• Journal of applied mathematics & informatics
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• v.42 no.1
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• pp.85-92
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• 2024

In this work we give the necessary and sufficient conditions for f-biharmonic curves in three-dimensional generalized symmetric spaces.

• Proceedings of the Jangjeon Mathematical Society
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• v.20 no.2
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• pp.183-191
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• 2017

We get one theorem that there exist solutions for the fourth order semi- linear elliptic Dirichlet boundary value problem with fully nonlinear term. We prove this result by the critical point theory and the variation of linking method.

• Korean Journal of Mathematics
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• v.20 no.1
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• pp.125-135
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• 2012

We obtain the multiple solutions for the fourth order elliptic problem with a variable coefficient and a jumping semilinear term. We have a result that there exist at least two solutions if the variable coefficient of the semilinear term crosses some number of the eigenvalues of the biharmonic eigenvalue problem. We obtain this multiplicity result by applying the Leray-Schauder degree theory.

• Korean Journal of Mathematics
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• v.25 no.3
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• pp.455-468
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• 2017

We prove the existence of multiple solutions for the fourth order nonlinear elliptic problem with fully nonlinear term. Our method is based on the critical point theory; the variation of linking method and category theory.

• Communications of the Korean Mathematical Society
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• v.38 no.4
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• pp.1281-1298
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• 2023

Let (M^2m, 𝜑, g) be a B-manifold. In this paper, we introduce a new class of metric on (M^2m, 𝜑, g), obtained by a non-conformal deformation of the metric g, called a generalized Berger-type deformed metric. First we investigate the Levi-Civita connection of this metric. Secondly we characterize the Riemannian curvature, the sectional curvature and the scalar curvature. Finally, we study the proper biharmonicity of the identity map and of a curve on M with respect to a generalized Berger-type deformed metric.

• Tribology and Lubricants
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• v.17 no.5
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• pp.391-398
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• 2001

Two dimensional slow viscous flow around two counter-rotating equal cylinders is investigated based on Stokes'approximation. An exact formal expression of the stream function is obtained by using the bipolar cylinder coordinates and Fourier series expansion. From the stream function obtained, the streamline patterns around the cylinders are shown and the pressure distribution in the flow field is determined. By integrating the stress distributions on the cylinder, the force and the moment exerted on the cylinder are calculated. The flow rate through the gap between the two cylinders is also determined as the distance between two cylinders varies. Special attention is directed to the case of very small distance between two cylinders concerned with the lubrication theory and the minimum pressure is calculated to explain a possible cavitation.

• Proceedings of the Korean Society of Tribologists and Lubrication Engineers Conference
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• 2000.06a
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• pp.142-149
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• 2000

Two dimensional slow viscous flow around two counter-rotating equal cylinders is Investigated based on Stokes' approximation. An exact formal expression of the stream function is obtained by using the bipolar cylinder coordinates and Fourier series expansion. From the stream function obtained, the streamline patterns around the cylinders are shown and the pressure distribution In the flow field is determined. By Integrating the stress distribution on the cylinder, the force and the moment exerted on the cylinder are calculated. The flow rate through the gap between the two cylinders is determined as the distance between two cylinders vary. It Is also revealed that the velocity at the far field has finite non-zero value. Special attention is directed to the case of very small distances between two cylinders by way of the lubrication theory.

• Communications of the Korean Mathematical Society
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• v.20 no.3
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• pp.563-578
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• 2005

In [Z. Cai and B. C. Shin, SIAM J. Numer. Anal. 40 (2002), 307-318], we developed the discrete first-order system least squares method for the second-order elliptic boundary value problem by directly approximating $H(div){\cap}H(curl)-type$ space based on the Helmholtz decomposition. Under general assumptions, error estimates were established in the $L^2\;and\;H^1$ norms for the vector and scalar variables, respectively. Such error estimates are optimal with respect to the required regularity of the solution. In this paper, we study solution methods for solving the system of linear equations arising from the discretization of variational formulation which possesses discrete biharmonic term and focus on numerical results including the performances of multigrid preconditioners and the finite element accuracy.

• Transactions of the Korean Society of Mechanical Engineers
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• v.15 no.2
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• pp.396-403
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• 1991

A solution is presented for the computation of the elastic-creep stresses in a hollow cylinder subjected to nonaxisymmetric temperature distribution. The creep problem is treated by the Maxwell creep model. Laplace transformation is used for reformation of the governing equation of elastic problem and Hooke's law in a function of .gamma. , .theta. , and creep constant. The governing equation is set up using the Airy stress function which leads to the biharmonic equation. The solution is obtained by using Fourer series method and Laplace inverse method used to obtain the stress components which include the variation of time. This solution shows excellent agreement with Lamkin's and Boley & Weiner's solution. The viscoelastic stresses are also obtained for the fuel rob tube subjecting nonaxisymmetric thermal load.

• International Journal of Aeronautical and Space Sciences
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• v.17 no.1
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• pp.64-72
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• 2016

The coverage area of a GNSS regional ionospheric delay model is mainly determined by the distribution of GNSS ground monitoring stations. Extrapolation of the ionospheric model data can extend the coverage area. An extrapolation algorithm, which combines observed ionospheric delay with the environmental parameters, is proposed. Neural network and least square regression algorithms are developed to utilize the combined input data. The bi-harmonic spline method is also tested for comparison. The IGS ionosphere map data is used to simulate the delays and to compute the extrapolation error statistics. The neural network method outperforms the other methods and demonstrates a high extrapolation accuracy. In order to determine the directional characteristics, the estimation error is classified into four direction components. The South extrapolation area yields the largest estimation error followed by North area, which yields the second-largest error.