• 한국수학교육학회지시리즈A:수학교육
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• 제23권1호
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• pp.51-52
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• 1984

• 호남수학학술지
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• 제22권1호
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• pp.17-20
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• 2000

• Journal of applied mathematics & informatics
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• 제6권3호
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• pp.937-942
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• 1999

In this paper we will show that if [G($\chi$),$\chi$] D($\chi$) and [D($\chi$), G($\chi$)] lie in the nil radical of A for all $\chi$$\in$A, then either D or G maps A into the radical where D and G are derivations on a Banach algebra A.

• 호남수학학술지
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• 제27권3호
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• pp.431-443
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• 2005

We investigate the equation Ax = y, where the vectors x and y are given and the operator A is normal and required to lie in CSL-algebra $AlG{\mathcal{L}}$. We desire a necessary and sufficient condition for the existence of a solution A.

• 호남수학학술지
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• 제29권2호
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• pp.213-222
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• 2007

A Weyl type algebra is defined in the paper (see [2],[4], [6], [7]). A Weyl type non-associative algebra $\bar{WN_{m,n,s}}$ and its restricted subalgebra $\bar{WN_{m,n,s_r}}$ are defined in the papers (see [1], [14], [16]). Several authors find all the derivations of an associative (Lie or non-associative) algebra (see [3], [1], [5], [7], [10], [16]). We find Der($\bar_{WN_{0,0,1_n}}$) of the algebra $\bar_{WN_{0,0,1_n}}$ and show that the algebras $\bar_{WN_{0,0,1_n}}$ and $\bar_{WN_{0,0,s_1}}$ are not isomorphic in this work. We show that the associator of $\bar_{WN_{0,0,1_n}}$ is zero.

• 대한수학회보
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• 제48권1호
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• pp.17-21
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• 2011

Let A be a co-Poisson Hopf algebra with Poisson co-bracket $\delta$. Here it is shown that the Hopf dual $A^{\circ}$ is a Poisson Hopf algebra with Poisson bracket {f, g}(x) = < $\delta(x)$, $f\;{\otimes}\;g$ > for any f, g $\in$ $A^{\circ}$ and x $\in$ A if A is an almost normalizing extension over the ground field. Moreover we get, as a corollary, the fact that the Hopf dual of the universal enveloping algebra U(g) for a finite dimensional Lie bialgebra g is a Poisson Hopf algebra.

• Kyungpook Mathematical Journal
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• 제60권4호
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• pp.683-710
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• 2020

Let ℕ be the set of nonnegative integers and 𝕬 be a 2-torsion free triangular algebra over a commutative ring ℛ. In the present paper, under some lenient assumptions on 𝕬, it is proved that if Δ = {𝛿_n}_n∈ℕ is a sequence of ℛ-linear mappings 𝛿_n : 𝕬 → 𝕬 satisfying ${\delta}_n([[x,\;y],\;z])\;=\;\displaystyle\sum_{i+j+k=n}\;[[{\delta}_i(x),\;{\delta}_j(y)],\;{\delta}_k(z)]$ for all x, y, z ∈ 𝕬 with xy = 0 (resp. xy = p, where p is a nontrivial idempotent of 𝕬), then for each n ∈ ℕ, 𝛿_n = d_n + 𝜏_n; where d_n : 𝕬 → 𝕬 is ℛ-linear mapping satisfying $d_n(xy)\;=\;\displaystyle\sum_{i+j=n}\;d_i(x)d_j(y)$ for all x, y ∈ 𝕬, i.e. 𝒟 = {d_n}_n∈ℕ is a higher derivation on 𝕬 and 𝜏_n : 𝕬 → Z(𝕬) (where Z(𝕬) is the center of 𝕬) is an ℛ-linear map vanishing at every second commutator [[x, y], z] with xy = 0 (resp. xy = p).

• Korean Journal of Mathematics
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• 제27권4호
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• pp.969-976
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• 2019

Let ℬ(ℋ) be the algebra of all bounded linear operators on a complex Hilbert space ℋ and 𝒨 ⊆ ℬ(ℋ) be a von Neumann algebra without central abelian projections. Let ξ be a non-zero scalar. In this paper, it is proved that a mapping φ : 𝒨 → ℬ(ℋ) satisfies φ([A, B]^ξ_⁎)= [φ(A), B]^ξ_⁎+[A, φ(B)]^ξ_⁎ for all A, B ∈ 𝒨 if and only if φ is an additive ⁎-derivation and φ(ξA) = ξφ(A) for all A ∈ 𝒨.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 2002년도 ITC-CSCC -2
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• pp.1141-1144
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• 2002

The research on computer graphics(CG) has been actively studied and developed. Namely, many surface/solid models have been proposed in the field of computer aided geometric design as well as the one of CG. Since it is difficult to visualize the complex shape exactly, an approximation by generating a set of meshes is usually used. Therefore it is important to guarantee the quality of the approximation in consideration of the computational cost. In this paper, a mesh generation algorithm will be proposed for a surface defined by Lie algebra. The proposed algorithm considers the quality in the meaning of validation of invariants obtained by the mesh, using automatic differentiation.

• 대한수학회논문집
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• 제5권2호
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• pp.165-170
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• 1990