• Journal of the Korean Mathematical Society
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• v.51 no.5
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• pp.881-895
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• 2014

In a recent paper [10] we introduced the notion of Levi harmonic map f from an almost contact semi-Riemannian manifold (M, ${\varphi}$, ${\xi}$, ${\eta}$, g) into a semi-Riemannian manifold $M^{\prime}$. In particular, we compute the tension field ${\tau}_H(f)$ for a CR map f between two almost contact semi-Riemannian manifolds satisfying the so-called ${\varphi}$-condition, where $H=Ker({\eta})$ is the Levi distribution. In the present paper we show that the condition (A) of Rawnsley [17] is related to the ${\varphi}$-condition. Then, we compute the tension field ${\tau}_H(f)$ for a CR map between two arbitrary almost contact semi-Riemannian manifolds, and we study the concept of Levi pluriharmonicity. Moreover, we study the harmonicity on quasicosymplectic manifolds.

• Journal of the Chungcheong Mathematical Society
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• v.6 no.1
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• pp.65-69
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• 1993

In this paper, we show that the module derivation D is continuous on the Banach algebra and the Silov algebra, and also that the derivation restricted by separating space and the radical on the semi prime Banach algebra is continuous.

• Communications of the Korean Mathematical Society
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• v.8 no.4
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• pp.579-585
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• 1993

• Bulletin of the Korean Mathematical Society
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• v.49 no.3
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• pp.511-515
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• 2012

We first show that the semiprimeness, primeness, and reducedness can go up to up-monoid rings. By these results we can compute the lower nilradicals of up-monoid rings, from which the well-known fact of Amitsur and McCoy for the polynomial rings can be extended to up-monoid rings.

• The Pure and Applied Mathematics
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• v.16 no.2
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• pp.227-241
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• 2009

Let A be a Banach algebra. Suppose there exists a continuous linear Jordan derivation D : A $\rightarrow$ A such that $[D(x),\;x]D(x)^2[D(x),\;x]\;{\in}\;rad(A)$ for all $x\;{\in}\;A$. Then we have D(A) $\subseteq$ rad(A).

• Journal of applied mathematics & informatics
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• v.42 no.1
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• pp.199-206
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• 2024

The goal of this study is to bring out the following conclusion: Let 𝓡 be a non-commutative prime ring of characteristic not two and 𝓓 be a bi-semiderivation on 𝓡 with a function 𝖋 (surjective). If 𝓓 acts as an endomorphism or as an anti-endomorphism, then 𝓓 = 0 on 𝓡.

• Ocean and Polar Research
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• v.36 no.1
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• pp.59-69
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• 2014

The long-term mooring performed at a KOGA station, located at about $30^{\circ}20^{\prime}N$, $126^{\circ}12^{\prime}E$ in the East China Sea shelf, shows some different behaviors between "semi-diurnal" and "diurnal currents" defined as the currents with periods around, respectively, a half day and a day. They appear to be predominantly tidal having significant coherences with sea level changes around the semi-diurnal and diurnal frequencies. The "semi-diurnal current" is strongly barotropic all year round. However, contrastingly, it is largely baroclinic in summer in the area about 70 km nearer to the continental slope, referred to as the "slope-area", as was found in previous current observations. The "diurnal current" of tidal origin is strongly barotropic in winter. In spring and summer, however, it becomes more baroclinic although it still remains largely barotropic, also showing more of its barotropic nature than in the "slope-area". The inertial oscillation contributing to the "diurnal current" appears to be more prominent when the current is baroclinic, indicating the important role played by stratification in generation of inertial oscillations. Downward energy propagation of inertial oscillation is not observed, suggesting that it is not created at the surface by wind. Considering that the study area is both near a critical latitude and proximity to the continental slope, it is suggested that parametric subharmonic instability (PSI) plays a significant role in creating the baroclinic inertial oscillation.

• Bulletin of the Korean Mathematical Society
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• v.46 no.5
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• pp.857-866
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• 2009

Let n be a fixed positive integer, R be a 2n!-torsion free prime ring and $\mu$, $\nu$ be a pair of generalized derivations on R. If < $\mu^2(x)+\nu(x),\;x^n$ > = 0 for all x $\in$ R, then $\mu$ and $\nu$ are either left multipliers or right multipliers. Let n be a fixed positive integer, R be a noncommutative 2n!-torsion free prime ring with the center $C_R$ and d, g be a pair of derivations on R. If < $d^2(x)+g(x)$, $x^n$ > $\in$ $C_R$ for all x $\in$ R, then d = g = 0. Then we apply these purely algebraic techniques to obtain several range inclusion results of pair of (generalized-)derivations on a Banach algebra.

• Bulletin of the Korean Mathematical Society
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• v.60 no.5
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• pp.1281-1293
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• 2023

The purpose of this paper is to study the relationship between the structure of a factor ring R/P and the behavior of some derivations of R. More precisely, we establish a connection between the commutativity of R/P and derivations of R satisfying specific identities involving the prime ideal P. Moreover, we provide an example to show that our results cannot be extended to semi-prime ideals.

• Bulletin of the Korean Mathematical Society
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• v.51 no.4
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• pp.943-948
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• 2014

Suppose that G is a finite group and H is a subgroup of G. H is said to be an ss-quasinormal subgroup of G if there is a subgroup B of G such that G = HB and H permutes with every Sylow subgroup of B; H is said to be semi-p-cover-avoiding in G if there is a chief series 1 = $G_0$ < $G_1$ < ${\cdots}$ < $G_t=G$ of G such that, for every i = 1, 2, ${\ldots}$, t, if $G_i/G_{i-1}$ is a p-chief factor, then H either covers or avoids $G_i/G_{i-1}$. We give the structure of a finite group G in which some subgroups of G with prime-power order are either semi-p-cover-avoiding or ss-quasinormal in G. Some known results are generalized.