• 대한수학회보
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• 제37권3호
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• pp.429-435
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• 2000

Our main goal is to show that if there exist Jordan derivations D, E and G on a noncommutative 2-torsion free prime ring R such that$(G^2(x)+E(x))D(x)=0\ or\ D(x)(G^2(x)+E(x))=0\ for\ all\ x\inR$, then we have D=o or E=0, G=0.

• 대한수학회보
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• 제46권5호
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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.

• Korean Journal of Mathematics
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• 제24권3호
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• pp.345-367
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• 2016

The concept of derivations of BCI-algebras was first introduced by Jun and Xin. In this paper, we introduce the notions of (l, r)-derivations, (r, l)-derivations and derivations of UP-algebras and investigate some related properties. In addition, we define two subsets $Ker_d(A)$ and $Fix_d(A)$ for some derivation d of a UP-algebra A, and we consider some properties of these as well.

• 대한수학회지
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• 제42권3호
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• pp.573-597
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• 2005

A continuous linear operator T, on the space of entire functions in d variables, is PDE-preserving for a given set $\mathbb{P}\;\subseteq\;\mathbb{C}|\xi_{1},\ldots,\xi_{d}|$ of polynomials if it maps every kernel-set ker P(D), $P\;{\in}\;\mathbb{P}$, invariantly. It is clear that the set $\mathbb{O}({\mathbb{P}})$ of PDE-preserving operators for $\mathbb{P}$ forms an algebra under composition. We study and link properties and structures on the operator side $\mathbb{O}({\mathbb{P}})$ versus the corresponding family $\mathbb{P}$ of polynomials. For our purposes, we introduce notions such as the PDE-preserving hull and basic sets for a given set $\mathbb{P}$ which, roughly, is the largest, respectively a minimal, collection of polynomials that generate all the PDE-preserving operators for $\mathbb{P}$. We also describe PDE-preserving operators via a kernel theorem. We apply Hilbert's Nullstellensatz.

• 대한수학회보
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• 제55권4호
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• pp.1109-1124
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• 2018

For a metric space (X, d) and ${\alpha}$ > 0. We study the structure and properties of vector-valued Lipschitz algebra $Lip{\alpha}(X,E)$ and $lip{\alpha}(X,E)$ of order ${\alpha}$. We investigate the approximate and Character amenability of vector-valued Lipschitz algebras.

• 충청수학회지
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• 제32권2호
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• pp.179-189
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• 2019

In this paper, we introduce the notion of symmetric bi-generalized derivation of lattice implication algebra L and investigated some related properties. Also, we prove that a map $F:L{\times}L{\rightarrow}L$ is a symmetric bi-generalized derivation associated with symmetric bi-derivation D on L if and only if F is a symmetric map and it satisfies $F(x{\rightarrow}y,z)=x{\rightarrow}F(y,z)$ for all $x,y,z{\in}L$.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제18권3호
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• pp.235-235
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• 2014

• 대한수학회지
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• 제41권6호
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• pp.945-955
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• 2004

In this paper, we establish a number system in $R^n$ which arises from a Haar wavelet basis in connection with decompositions of certain Cuntz algebra representations on $L^2$( $R^n$). Number systems in $R^n$ are also of independent interest [9]. We study radix-representations of $\chi$ $\in$ $R^n$: $\chi$:$\alpha$$_{ι}$ $\alpha$$_{ι-1}$…$\alpha$$_1$$\alpha$$_{0}$ ㆍ$\alpha$$_{-1}$ $\alpha$$_{-2}$ … as $\chi$= $M^{ι}$$\alpha$$_{ι}$ $\alpha$＋…M$\alpha$$_1$＋$\alpha$$_{0}$ ＋ $M^{-1}$ $\alpha$$_{-1}$ ＋ $M^{-2}$ $\alpha$$_{-2}$ ＋… where each $\alpha$$_{k}$ $\in$ D, and D is some specified digit set. Our analysis uses iteration techniques of a number-theoretic flavor. The view-point is a dual one which we term fractals in the large vs. fractals in the small,illustrating the number theory of integral lattice points vs. fractions.s vs. fractions.

• 대한수학회보
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• 제38권4호
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• pp.709-718
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• 2001

In this paper we show that if D and G are continuous linear Jordan derivations on a Banach algebra A satisfying [D(x), x]x - x[G(x),x] $\epsilon$ rad(A)for all $\epsilon$ A, then both D and G map A into rad(A).

• 충청수학회지
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• 제10권1호
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• pp.105-108
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• 1997

In this paper we prove that if D is a continuous derivation on a noncommutative complex Banach algebra A and [D(x),x] is idempotent for every $x{\in}A$, then D maps A into its radical.