• Kyungpook Mathematical Journal
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• v.53 no.4
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• pp.565-571
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• 2013

In this paper, we investigate the commutativity of a semiprime ring R admitting a generalized derivation F with associated derivation D satisfying any one of the properties: (i) $F(x){\circ}D(y)=[x,y]$, (ii) $D(x){\circ}F(y)=F[x,y]$, (iii) $D(x){\circ}F(y)=xy$, (iv) $F(x{\circ}y)=[F(x) y]+[D(y),x]$, and (v) $F[x,y]=F(x){\circ}y-D(y){\circ}x$ for all x, y in some appropriate subsets of R.

• Communications of the Korean Mathematical Society
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• v.23 no.4
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• pp.469-477
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• 2008

We introduce the notion of two-sided $\Gamma$-$\alpha$-derivation of a $\Gamma$-near-ring and give some generalizations of [1, 2].

• Communications of the Korean Mathematical Society
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• v.17 no.4
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• pp.607-618
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• 2002

Let A be a noncommutative Banach algebra. Suppose there exists a continuous linear Jordan derivation D : A \longrightarrowA such that D($\chi$)[D($\chi$),$\chi$]D($\chi$) $\in$ rad(A) for all $\chi$ A. In this case, we have D(A) ⊆ rad(A).

• Bulletin of the Korean Mathematical Society
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• v.42 no.4
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• pp.671-678
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• 2005

Let R be a noncommutative semi prime ring. Suppose that there exists a derivation d : R $\to$ R such that for all x $\in$ R, either [[d(x),x], d(x)] = 0 or $\langle$$\langle(x),\;x\rangle,\;d(x)\rangle$ = 0. In this case [d(x), x] is nilpotent for all x $\in$ R. We also apply the above results to a Banach algebra theory.

• Honam Mathematical Journal
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• v.36 no.4
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• pp.885-893
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• 2014

In this paper, we introduce the concept of a right f-derivation in incline algebras and give some properties of incline algebras. Also, the concept of d-ideal is introduced in an incline algebra with respect to right f-derivations.

• 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.

• Honam Mathematical Journal
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• v.45 no.4
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• pp.678-681
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• 2023

Let G be a cyclic group of prime power order p^k, and let I be the augmentation ideal of the integral group ring ℤ[G]. We define a derivation on ℤ/p^kℤ[G], and show that for 2 ≤ n ≤ p, an element α ∈ I is in Iⁿ if and only if the i-th derivative of the image of α in ℤ/p^kℤ[G] vanishes for 1 ≤ i ≤ (n - 1).

• Proceedings of the Korean Society of Developmental Biology Conference
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• 2003.02a
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• pp.4-4
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• 2003

No Abstract, See Full Text

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 2019.11a
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• pp.249-251
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• 2019

In the ongoing standardization of Versatile Video Coding (VVC), DCT-2, DST-7 and DCT-8 are designated as the vital primary transform kernels. Due to the effectiveness of DST-4 and DCT-4 in smaller resolution sequences, DST-4 and DCT-4 transform kernel can also be used as the replacement of the DST-7 and DCT-8 transform kernel respectively. While storing all of those transform kernels, ROM memory storage is considered as the major issue. So, to deal with this scenario, a unified DST-3 based transform kernel derivation method is proposed in this paper. The transform kernels used in this paper is DCT-2, DST-4 and DCT-4 transform kernels. The proposed ROM memory required to store the matrix elements is 1368 bytes each of 8-bit precision.

• Kyungpook Mathematical Journal
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• v.53 no.2
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• pp.233-245
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• 2013

Let $\mathcal{A}$ be a Banach ternary algebra over a scalar field R or C and $\mathcal{X}$ be a ternary Banach $\mathcal{A}$-module. A quartic mapping $D\;:\;(\mathcal{A},[\;]_{\mathcal{A}}){\rightarrow}(\mathcal{X},[\;]_{\mathcal{X}})$ is called a $4^{th}$- order ternary derivation if $D([x,y,z])=[D(x),y^4,z^4]+[x^4,D(y),z^4]+[x^4,y^4,D(z)]$ for all $x,y,z{\in}\mathcal{A}$. In this paper, we prove Ulam stability generalizations of $4^{th}$- order ternary derivations associated to the following JMRassias quartic functional equation on fr$\acute{e}$che algebras: $$f(kx+y)+f(kx-y)=k^2[f(x+y)+f(x-y)]+2k^2(k^2-1)f(x)-2(k^2-1)f(y)$$.