• Kyungpook Mathematical Journal
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• v.47 no.1
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• pp.119-125
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• 2007

In this paper, we investigate the following: Let A be a semisimple Banach algebra. Suppose that there exists a linear derivation $f:A{\rightarrow}A$ such that the functional equation $<f(x),x>^2=0$ holds for all $x{\in}A$. Then we have $f=0$ on A.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.3
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• pp.443-451
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• 2016

In this paper, we introduce the concept of a symmetric bi-f-multiplier in incline algebras and give some properties of incline algebras. Also, we characterize Ker(D) and $Fix_a(D)$ by symmetric bi-f-multipliers in incline algebras.

• The Pure and Applied Mathematics
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• v.22 no.4
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• pp.383-387
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• 2015

In [1], the definition of C*-Lie ternary (σ,τ,ξ)-derivation is not well-defined and so the results of [1, Section 4] on C*-Lie ternary (σ,τ,ξ)-derivations should be corrected.

• Kyungpook Mathematical Journal
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• v.53 no.4
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• pp.497-505
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• 2013

The noncommutative Singer-Wermer conjecture states that every derivation on a Banach algebra (possibly noncommutative) leaves primitive ideals of the algebra invariant. This conjecture is still an open question for more than thirty years. In this note, we approach this question via some sufficient conditions for the separating ideal of ${\phi}$-derivations to be nilpotent. Moreover, we show that the spectral boundedness of ${\phi}$-derivations implies that they leave each primitive ideal of Banach algebras invariant.

• Bulletin of the Korean Chemical Society
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• v.30 no.2
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• pp.315-318
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• 2009

Some particular bound state energies of an electron, under Coulomb potential field, confined in a two-dimensional circle and a three-dimensional sphere are analytically derived. The derivation shows that the electron cannot be bound in a negative energy state when the circle (or sphere) is smaller than a certain critical size. The critical size dependency on the strength of Coulomb potential and the angular momentum of the electron is also analytically derived. This system mimics quantum dots. Therefore the derivation provides new information on a minimum critical size of quantum dots with hydrogenic impurity.

• Honam Mathematical Journal
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• v.40 no.2
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• pp.227-237
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• 2018

There are various papers on finding all the derivations of a non-associative algebra and an anti-symmetrized algebra. We find all the derivations of a growing algebra in the paper. The dimension of derivations of the growing algebra is one and every derivation of the growing algebra is outer. We show that there is a class of purely outer algebras in this work.

• Journal of applied mathematics & informatics
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• v.9 no.1
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• pp.381-387
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• 2002

Our main goal is to show that if there Jordan derivation D, G on a noncommutative (n+1)!-torsion free prime ring R such that D($\chi$)$\chi$$^n$+$\chi$$^n$G($\chi$) $\in$ C(R) for all $\chi$ $\in$ R, then we have D=0 and G=0.

• Korean Journal of Crystallography
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• v.9 no.1
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• pp.39-43
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• 1998

The well-known geometries showing the relation between the angular coordinates of a plane normal and a Laue diffraction spot have been improved. The Bernalte's algebraic equations for the lines in the Greninger and Leonhardt charts have been alternatively derived in more intuitive and perspicuous ways than his original derivation.

• Kyungpook Mathematical Journal
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• v.56 no.2
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• pp.343-347
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• 2016

Posner's first theorem states that if R is a prime ring of characteristic different from two, $d_1$ and $d_2$ are derivations on R such that the iterate $d_1d_2$ is also a derivation of R, then at least one of $d_1$, $d_2$ is zero. In the present paper we extend this result to *-prime rings of characteristic different from two.

• The Pure and Applied Mathematics
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• v.15 no.3
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• pp.259-296
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• 2008

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