• Kyungpook Mathematical Journal
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• v.51 no.2
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• pp.125-138
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• 2011

We give some characterizations of non-existence of lightlike hypersurfaces of an indefinite space form. Some geometric objects for the induced Ricci tensor to be symmetric are studied.

• Bulletin of the Korean Mathematical Society
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• v.60 no.6
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• pp.1539-1553
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• 2023

We show the asymptotics of the volume density function in the class of central harmonic manifolds can be specified arbitrarily and do not determine the geometry.

• Geophysics and Geophysical Exploration
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• v.23 no.1
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• pp.50-54
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• 2020

Herein, the closed-form expressions of the magnetic field due to an axially symmetric body such as a right cylinder, are derived. The magnetic field due to a right cylinder is converted from the gravity gradient tensor using Poisson's relation; the magnetic field induced by a constant magnetization can be obtained from the gravity gradient tensor with a constant density. Because of the axial symmetry of the cylinder, the expressions of gravity gradient tensor are derived in cylindrical coordinate and then transformed into Cartesian coordinates for the three components of the magnetic field using an arbitrary magnetization direction.

• Progress in Superconductivity and Cryogenics
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• v.26 no.1
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• pp.10-13
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• 2024

We performed angle-resolved Raman spectroscopy experiments on lead-doped and undoped Bi₂Sr₂CaCu₂O_8+δ(Bi2212) samples using a 660 nm laser and analyzed the Raman tensor of the phonon modes. The phonon mode was clearly observed at the 60, 103, and 630 cm^-1 Raman shifts. The 60, 630 cm^-1 peaks were only clearly observed when the incident and scattered light polarizations were configured to be parallel. The polarization angle dependence of the amplitude of the 60, 630 cm^-1 peak on the parallel configuration shows a twofold symmetry; therefore, both peaks originate from Ag phonons and the crystal structure of Bi2212 should be considered orthorhombic. On the other hand, the 103 cm^-1 peak is clearly observed in both parallel and perpendicular configurations. Remarkably, the off-diagonal component of the Raman tensor of the 103 cm^-1 peak showed an anti-symmetry that could not be realized within the known crystal structure of Bi2212. The implications of our findings are discussed.

• Structural Engineering and Mechanics
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• v.63 no.2
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• pp.161-169
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• 2017

In this paper, using consistent couple stress theory and Hamilton's principle, the free vibration analysis of Euler-Bernoulli nano-beams made of bi-directional functionally graded materials (BDFGMs) with small scale effects are investigated. To the best of the researchers' knowledge, in the literature, there is no study carried out into consistent couple-stress theory for free vibration analysis of BDFGM nanostructures with arbitrary functions. In addition, in order to obtain small scale effects, the consistent couple-stress theory is also applied. These models can degenerate into the classical models if the material length scale parameter is taken to be zero. In this theory, the couple-tensor is skew-symmetric by adopting the skew-symmetric part of the rotation gradients as the curvature tensor. The material properties except Poisson's ratio are assumed to be graded in both axial and thickness directions, which it can vary according to an arbitrary function. The governing equations are obtained using the concept of Hamilton principle. Generalized differential quadrature method (GDQM) is used to solve the governing equations for various boundary conditions to obtain the natural frequencies of BDFG nano-beam. At the end, some numerical results are presented to study the effects of material length scale parameter, and inhomogeneity constant on natural frequency.

• Honam Mathematical Journal
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• v.43 no.4
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• pp.613-626
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• 2021

The aim of the present work is to study the properties of three-dimensional Lorentzian para-Kenmotsu manifolds equipped with a Yamabe soliton. It is proved that every three-dimensional Lorentzian para-Kenmotsu manifold is Ricci semi-symmetric if and only if it is Einstein. Also, if the metric of a three-dimensional semi-symmetric Lorentzian para-Kenmotsu manifold is a Yamabe soliton, then the soliton is shrinking and the flow vector field is Killing. We also study the properties of three-dimensional Ricci symmetric and 𝜂-parallel Lorentzian para-Kenmotsu manifolds with Yamabe solitons. Finally, we give a non-trivial example of three-dimensional Lorentzian para-Kenmotsu manifold.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.19 no.3
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• pp.173-178
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• 2019

To analyze the diffraction properties of optical signals by periodic blazed 2D diffraction gratings, Toeplitz dielectric tensor is first defined and formulated by 2D spatial Fourier expansions associated with asymmetric blazed grating profile. The characteristic modes in each layer is then based on eigenvalue problem, and the complete solution is found rigorously in terms of modal transmission-line theory (MTLT) to address the pertinent boundary-value problems. Toeplitz matrix of symmetric and sawtooth profiles is derived from that of asymmetric blazed grating profile, and the diffraction properties for each profile are numerically simulated. The numerical results reveal that the asymmetric and symmetric profiles behave as anti-reflection GMR filter while the sawtooth profile works better as anti-transmission one rather than anti-reflection filter.

• Journal of the Korean Mathematical Society
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• v.35 no.4
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• pp.1045-1060
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• 1998

Recently, Chung and et al. ([11], 1991c) introduced a new concept of a manifold, denoted by ＊g-SE $X_{n}$ , in Einstein's n-dimensional ＊g-unified field theory. The manifold ＊g-SE $X_{n}$ is a generalized n-dimensional Riemannian manifold on which the differential geometric structure is imposed by the unified field tensor ＊ $g^{λν}$ through the SE-connection which is both Einstein and semi-symmetric. In this paper, they proved a necessary and sufficient condition for the unique existence of SE-connection and presented a beautiful and surveyable tensorial representation of the SE-connection in terms of the tensor ＊ $g^{λν}$. This paper is the first part of the following series of two papers: I. The SE-curvature tensor of ＊g-SE $X_{n}$ II. The contracted SE-curvature tensors of ＊g-SE $X_{n}$ In the present paper we investigate the properties of SE-curvature tensor of ＊g-SE $X_{n}$ , with main emphasis on the derivation of several useful generalized identities involving it. In our subsequent paper, we are concerned with contracted curvature tensors of ＊g-SE $X_{n}$ and several generalized identities involving them. In particular, we prove the first variation of the generalized Bianchi's identity in ＊g-SE $X_{n}$ , which has a great deal of useful physical applications.tions.

• Bulletin of the Korean Mathematical Society
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• v.35 no.4
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• pp.641-652
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• 1998

Chung and et al. ([2].1991) introduced a new concept of a manifold, denoted by $^{\ast}g-SEX_n$, in Einstein's n-dimensional $^{\ast}g$-unified field theory. The manifold $^{\ast}g-SEX_n$ is a generalized n-dimensional Riemannian manifold on which the differential geometric structure is imposed by the unified field tensor $^{\ast}g^{\lambda \nu}$ through the SE-connection which is both Einstein and semi-symmetric. In this paper, they proved a necessary and sufficient condition for the unique existence of SE-connection and sufficient condition for the unique existence of SE-connection and presented a beautiful and surveyable tensorial representation of the SE-connection in terms of the tensor $^{\ast}g^{\lambda \nu}$. Recently, Chung and et al.([3],1998) obtained a concise tensorial representation of SE-curvature tensor defined by the SE-connection of $^{\ast}g-SEX_n$ and proved deveral identities involving it. This paper is a direct continuations of [3]. In this paper we derive surveyable tensorial representations of constracted curvature tensors of $^{\ast}g-SEX_n$ and prove several generalized identities involving them. In particular, the first variation of the generalized Bianchi's identity in $^{\ast}g-SEX_n$, proved in theorem (2.10a), has a great deal of useful physical applications.

• Bulletin of the Korean Mathematical Society
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• v.26 no.2
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• pp.159-164
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• 1989

Let M be a hypersurface of dimension n(.geq.2) in an (n+1)-dimensional real space form over bar M(c) with constant curvature c and H the second fundamental tensor of M. M is said to be birecurrent if here exists a covariant tensor field .alpha. of order 2 such that .del.$^{2}$H=H .alpha., where .del. is the connection of M. Also, M is said to be recurrent if there exists a 1-form .betha. such that .del.H=H .betha.. Matsuyama [2] recently proved that a recurrent hypersurface M in a real space form is locally symmetric and a complete irreducible birecurrent hypersurface M in a real space form is recurrent. The main purpose of this paper is to characterize the birecurrent or recurrent hypersurface M of a Riemannian manifold with constant curvature c and to prove that M is classified as a cylinder, $M^{n}$ (c) or ( $c_{1}$)* $M^{n-r}$ ( $c_{2}$) where 1/ $c_{1}$+1/ $c_{2}$=1/c.