• Kyungpook Mathematical Journal
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• v.56 no.3
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• pp.979-991
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• 2016

The object of the present paper is to study N(k)-quasi-Einstein manifolds. We study an N(k)-quasi-Einstein manifold satisfying the curvature conditions $R({\xi},X){\cdot}Z=0$, $Z(X,{\xi}){\cdot}R=0$, and $P({\xi},X){\cdot}Z=0$, where R, P and Z denote the Riemannian curvature tensor, the projective curvature tensor and Z tensor respectively. Next we prove that the curvature condition $C{\cdot}Z=0$ holds in an N(k)-quasi-Einstein manifold, where C is the conformal curvature tensor. We also study Z-recurrent N(k)-quasi-Einstein manifolds. Finally, we construct an example of an N(k)-quasi-Einstein manifold and mention some physical examples.

• Journal of the Korean Mathematical Society
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• v.42 no.5
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• pp.883-892
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• 2005

We classify N($\kappa$)-contact metric manifolds which satisfy $Z(\xi,\;X)\cdotZ\;=\;0,\;Z(\xi,\;X)\cdotR\;=\;0\;or\;R(\xi,\;X)\cdotZ\;=\;0$.

• The Pure and Applied Mathematics
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• v.28 no.2
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• pp.143-153
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• 2021

In this paper, we study some curvature properties of Sasakian 3-manifolds associated to Ƶ-tensor. It is proved that if a Sasakian 3-manifold (M, g) satisfies one of the conditions (1) the Ƶ-tensor is of Codazzi type, (2) M is Ƶ-semisymmetric, (3) M satisfies Q(Ƶ, R) = 0, (4) M is projectively Ƶ-semisymmetric, (5) M is Ƶ-recurrent, then (M, g) is of constant curvature 1. Several consequences are drawn from these results.

• Bulletin of the Korean Chemical Society
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• v.33 no.9
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• pp.3039-3042
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• 2012

Pressure tensors at the planar surface of liquid-vapor argon are evaluated from the virial theorem, Irving-Kirkwood, and Harasima versions using a test-area molecular dynamics simulation method through a Lennard-Jones intermolecular potential at two temperatures. We found that the normal and transverse components of the pressure tensor, $p_N(z)$ and $p_T(z)$, obtained from the virial theorem and Harasima version are essentially the same. The normal component of the pressure tensor from Irving-Kirkwood version, $p_N^{IK}(z)$, is shown to be a nearly constant at the lower temperature, independent of z, as agreed in a previous study, but not for $p_N^H$(z), while the transverse components, $p_T^{IK}(z)$ and $p_T^H(z)$, are almost the same. The values of surface tension for both versions computed from $p_N(z)-p_T(z)$ are also the same and are fully consistent with the experimental data.

• Kyungpook Mathematical Journal
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• v.58 no.4
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• pp.761-779
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• 2018

The object of the present paper is to study weakly Z symmetric spacetimes $(WZS)_4$. At first we prove that a weakly Z symmetric spacetime is a quasi-Einstein spacetime and hence a perfect fluid spacetime. Next, we consider conformally flat $(WZS)_4$ spacetimes and prove that such a spacetime is infinitesimally spatially isotropic relative to the unit timelike vector field ${\rho}$. We also study $(WZS)_4$ spacetimes with divergence free conformal curvature tensor. Moreover, we characterize dust fluid and viscous fluid $(WZS)_4$ spacetimes. Finally, we construct an example of a $(WZS)_4$ spacetime.

• Journal of the Korean Magnetics Society
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• v.25 no.4
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• pp.129-137
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• 2015

The Cu(radius ra = $95{\mu}m$)/$Ni_{80}Fe_{20}$(outer radius $r_b$ = $120{\mu}m$) core/shell composite wire is fabricated by electrodeposition. The two diagonal components of impedance tensor for the Cu/$Ni_{80}Fe_{20}$ core/shell composite wire in cylindrical coordinates, $Z_{zz}$ and $Z_{{\theta}{\theta}}$, are measured as a function of frequency in 10 kHz~10 MHz and external static magnetic field in 0 Oe~200 Oe. The equations expressing the diagonal $Z_{zz}$ and $Z_{{\theta}{\theta}}$ in terms of diagonal components of complex permeability tensor, ${\mu}^*_{zz}$ and ${\mu}^*_{{\theta}{\theta}}$, are derived from Maxwell's equations. The real and imaginary parts of ${\mu}^*_{zz}$(f) and ${\mu}^*_{{\theta}{\theta}}$(f) spectra are extracted from the measured $Z_{zz}$(f) and $Z_{{\theta}{\theta}}$(f) spectra, respectively. It is presened that the extraction of ${\mu}^*_{zz}$(f) and ${\mu}^*_{{\theta}{\theta}}$(f) spectra from the diagonal impedance spectra can be a versatile tool to investigate dymanic magnetization process in the core/shell composite wire.

• Journal of the Korean Mathematical Society
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• v.46 no.2
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• pp.249-256
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• 2009

Let $G{\otimes}G$ be the tensor square of a group G. The set of all elements a in G such that $a{\otimes}g\;=\;1_{\otimes}$, for all g in G, is called the tensor centre of G and denoted by $Z^{\otimes}^$(G). In this paper some properties of the tensor centre of G are obtained and the capability of the pair of groups (G, G') is determined. Finally, the structure of $J_2$(G) will be described, where $J_2$(G) is the kernel of the map $\kappa$ : $G{\otimes}\;{\rightarrow}\;G'$.

• Journal of applied mathematics & informatics
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• v.39 no.5_6
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• pp.751-760
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• 2021

We study in this paper the right Rényi mean for a quantum divergence induced from the α - z Rényi relative entropy. Many properties including homogeneity, invariance under permutation, repetition and unitary congruence transformation, and determinantal inequality have been presented. Moreover, we give the identity of two right Rényi means with respect to tensor product.

• Bulletin of the Korean Mathematical Society
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• v.32 no.2
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• pp.221-231
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• 1995

Let $Z_1, Z_2, \ldots, Z_l$ be random set functions or intergrals. Then it is possible to discuss their products. In the case of random integrals, $Z_i$ is a random set function indexed y a family, $G_i$ say, of real valued functions g on $S_i$ for which the integrals $Z_i(g) = \smallint gdZ_i$ are well defined. If $g_i = \in g_i (i = 1, 2, \ldots, l) and g_1 \otimes \cdots \otimes g_l$ denotes the tensor product $g(s) = g_1(s_1)g_2(s_2) \cdots g_l(s_l) for s = (s_1, s_2, \ldots, s_l) and s_i \in S_i$, then we can defined $Z(g) = (Z_1 \times Z_2 \times \cdots \times Z_l)(g) = Z_1(g_1)Z_2(g_2) \cdots Z_l(g_l)$.

• Communications of the Korean Mathematical Society
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• v.35 no.3
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• pp.935-951
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• 2020

The aim of the paper is to study some geometric properties of weakly Z-symmetric manifolds. Weakly Z-symmetric manifolds with Codazzi type and cyclic parallel Z tensor are studied. We consider Einstein weakly Z-symmetric manifolds and conformally flat weakly Z-symmetric manifolds. Next, it is shown that a totally umbilical hypersurface of a conformally flat weakly Z-symmetric manifolds is of quasi constant curvature. Also, decomposable weakly Z-symmetric manifolds are studied and some examples are constructed to support the existence of such manifolds.