• Kyungpook Mathematical Journal
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• 제56권3호
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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.

• 대한수학회지
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• 제42권5호
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• pp.883-892
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• 2005

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

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제28권2호
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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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• 제33권9호
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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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• 제58권4호
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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.

• 한국자기학회지
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• 제25권4호
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• pp.129-137
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• 2015

Cu(반경 $r_a$ = $95{\mu}m$)/$Ni_{80}Fe_{20}$(외경 $r_b$ = $120{\mu}m$)의 코어/쉘 복합 와이어를 전기도금방법으로 제작하였다. 제작 된 복합 와이어에 대해 원통 좌표계에서 임피던스 텐서의 두 대각 성분 $Z_{{\theta}{\theta}}$와 $Z_{zz}$를 10 kHz~10 MHz 범위의 주파수(f)와 0 Oe~200 Oe 범위의 외부 정지 자기장의 함수로 측정하였다. Maxwell 방정식으로부터 코어/쉘 복합 와이어의 두 대각 임피던스 $Z_{{\theta}{\theta}}$와 $Z_{zz}$를 각각 복소 투자율 텐서의 두 대각 성분 ${\mu}^*_{zz}$와 ${\mu}^*_{{\theta}{\theta}}$로 표현하는 식을 유도하였다. 유도된 식을 이용하여 측정된 $Z_{{\theta}{\theta}}$(f)와 $Z_{zz}$(f) 스펙트럼으로부터 ${\mu}^*_{zz}$(f)와 ${\mu}^*_{{\theta}{\theta}}$(f) 스펙트럼을 각각 뽑아낼 수 있었다. 뽑아낸 두 대각 투자율 스펙트럼을 자벽이동과 자화회전의 완화과정으로 해석하면 Cu/NiFe 코어/쉘 복합 와이어의 동적 자화과정을 규명하는 유용한 도구가 될 수 있다는 것을 제시하였다.

• 대한수학회지
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• 제46권2호
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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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• 제39권5_6호
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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.

• 대한수학회보
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• 제32권2호
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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 $Z(g) = (Z_1 \times Z_2 \times \cdots \times Z_l)(g) = Z_1(g_1)Z_2(g_2) \cdots Z_l(g_l)$.

• 대한수학회논문집
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• 제35권3호
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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.