• Journal of the Korean Mathematical Society
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• v.45 no.2
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• pp.393-404
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• 2008

Biharmonic Legendre curves in a Sasakian space form are studied. A non-existence result in a 7-dimensional 3-Sasakian manifold is obtained. Explicit formulas for some biharmonic Legendre curves in the 7-sphere are given.

• Bulletin of the Korean Mathematical Society
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• v.59 no.1
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• pp.227-239
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• 2022

In this paper, we consider Legendre trajectories of trans-S-manifolds. We obtain curvature characterizations of these curves and give a classification theorem. We also investigate Legendre curves whose Frenet frame fields are linearly dependent with certain combination of characteristic vector fields of the trans-S-manifold.

• Journal of applied mathematics & informatics
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• v.40 no.3_4
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• pp.587-601
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• 2022

We find the characterizations of the curvatures of Legendre curves and magnetic curves in Kenmotsu manifolds with C-parallel and C-proper mean curvature vector fields in the tangent and normal bundles. Finally, an illustrative example is presented.

• The Pure and Applied Mathematics
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• v.27 no.2
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• pp.83-96
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• 2020

In this paper we study Biharmonic curves, Legendre curves and Magnetic curves in three dimensional f-Kenmotsu manifolds. We also study 1-type curves in a three dimensional f-Kenmotsu manifold by using the mean curvature vector field of the curve. As a consequence we obtain for a biharmonic helix in a three dimensional f-Kenmotsu manifold with the curvature κ and the torsion τ, κ² + τ² = -(f² + f'). Also we prove that if a 1-type non-geodesic biharmonic curve γ is helix, then λ = -(f² + f').

• Structural Engineering and Mechanics
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• v.41 no.5
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• pp.605-615
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• 2012

In this paper, guided circumferential wave propagating in an orthotropic viscoelastic cylindrical curved plate subjected to traction-free conditions is investigated in the frame of the Kelvin-Voight viscoelastic theory. The obtained three wave equations are decoupled into two groups, Lamb-like wave and SH wave. They are separately solved by the Legendre polynomial series approach. The availability of the method is confirmed through the comparison with the published data of the SH wave for a viscoelastic flat plate. The dispersion curves and attenuation curves for the carbon fiber and prepreg cylindrical plates are illustrated and the viscous effect on dispersion curves is shown. The influences of the ratio of radius to thickness are analyzed.

• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.485-489
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• 2006

In this paper, we slightly improve the Baby-step Giant-step for certain elliptic curves. This method gives the running time improvement of $200\%$ in precomputation (Baby-step) and requires half as much storage as the original Baby-step Giant-step method.

• Advances in nano research
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• v.14 no.5
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• pp.463-474
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• 2023

The purpose of this paper is to present the analysis of propagating and evanescent waves in functionally graded (FG) nanoplates with the consideration of nonlocal effect. The analytical integration nonlocal stress expansion Legendre polynomial method is proposed to obtain complete dispersion curves in the complex domain. Unlike the traditional Legendre polynomial method that expanded the displacement, the presented polynomial method avoids employing the relationship between local stress and nonlocal stress to construct boundary conditions. In addition, the analytical expressions of numerical integrations are presented to improve the computational efficiency. The nonlocal effect, inhomogeneity of medium and their interactions on wave propagation are studied. It is found that the nonlocal effect and inhomogeneity of medium reduce the frequency bandwidth of complex evanescent Lamb waves, and make complex evanescent Lamb waves have a higher phase velocity at low attenuation. The occurrence of intersections of propagating Lamb wave in the nonlocal homogeneous plate needs to satisfy a smaller Poisson's ratio condition than that in the classical elastic theory. In addition, the inhomogeneity of medium enhances the nonlocal effect. The conclusions obtained can be applied to the design and dynamic response evaluation of composite nanostructures.

• Communications of the Korean Mathematical Society
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• v.35 no.3
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• pp.967-977
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• 2020

In this article, we find the necessary and sufficient condition for a proper biharmonic Frenet curve in the Lorentzian Sasakian space forms 𝓜³₁(H) except the case constant curvature -1. Next, we find that for a slant curve in a 3-dimensional Sasakian Lorentzian manifold, its ratio of "geodesic curvature" and "geodesic torsion -1" is a constant. We show that a proper biharmonic Frenet curve is a slant pseudo-helix with 𝜅² - 𝜏² = -1 + 𝜀₁(H + 1)𝜂(B)² in the Lorentzian Sasakian space forms x1D4DC³₁(H) except the case constant curvature -1. As example, we classify proper biharmonic Frenet curves in 3-dimensional Lorentzian Heisenberg space, that is a slant pseudo-helix.

• Journal of Astronomy and Space Sciences
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• v.31 no.3
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• pp.199-204
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• 2014

This paper intends to highlight the effect of the third-body in an inclined orbit on a spacecraft orbiting the primary mass. To achieve this goal, a new origin of coordinate is introduced in the primary and the X-axis toward the node of the spacecraft. The disturbing function is expanded up to the second order using Legendre polynomials. A double-averaged analytical model is exploited to produce the evolutions of mean orbital elements as smooth curves.

• Bulletin of the Korean Mathematical Society
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• v.53 no.3
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• pp.723-732
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• 2016

We characterize proper biharmonic anti-invariant surfaces in 3-dimensional generalized (${\kappa}$, ${\mu}$)-manifolds with constant mean curvature by means of the scalar curvature of the ambient space and the mean curvature. In addition, we give a method for constructing infinity many examples of proper biharmonic submanifolds in a certain 3-dimensional generalized (${\kappa}$, ${\mu}$)-manifold. Moreover, we determine 3-dimensional generalized (${\kappa}$, ${\mu}$)-manifolds which admit a certain kind of proper biharmonic foliation.