• Bulletin of the Korean Mathematical Society
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• v.43 no.3
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• pp.635-644
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• 2006

For a lower niltriangular matrix ring $A=NT_n(K)(n{\geq}3)$, we show that every derivation of A is a sum of certain diagonal, trivial extension and strongly nilpotent derivation. Moreover, a strongly nilpotent derivation is a sum of an inner derivation and an uaz-derivation.

• Bulletin of the Korean Mathematical Society
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• v.52 no.4
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• pp.1123-1132
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• 2015

In this paper, we investigate derivations on the noncommutative Banach algebra $L^{\infty}_0({\omega})^*$ equipped with an Arens product. As a main result, we prove the Singer-Wermer conjecture for the noncommutative Banach algebra $L^{\infty}_0({\omega})^*$. We then show that a derivation on $L^{\infty}_0({\omega})^*$ is continuous if and only if its restriction to rad($L^{\infty}_0({\omega})^*$) is continuous. We also prove that there is no nonzero centralizing derivation on $L^{\infty}_0({\omega})^*$. Finally, we prove that the space of all inner derivations of $L^{\infty}_0({\omega})^*$ is continuously homomorphic to the space $L^{\infty}_0({\omega})^*/L^1({\omega})$.

• Journal of Power Electronics
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• v.16 no.4
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• pp.1565-1577
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• 2016

For grid-connected LCL-filtered inverters, dual-loop current control with an inner-loop active damping (AD) based on capacitor current feedback is generally used for the sake of current quality. However, existing studies on capacitor current feedback AD with a control delay do not reveal the mathematical relation among the dual-loop stability, capacitor current feedback factor, delay time and LCL parameters. The robustness was not investigated through mathematical derivations. Thus, this paper aims to provide a systematic study of dual-loop current control in a digitally-controlled inverter. At first, the stable region of the inner-loop AD is derived. Then, the dual-loop stability and robustness are analyzed by mathematical derivations when the inner-loop AD is stable and unstable. Robust design principles for the inner-loop AD feedback factor and the outer-loop current controller are derived. Most importantly, ensuring the stability of the inner-loop AD is critical for achieving high robustness against a large grid impedance. Then, several improved approaches are proposed and synthesized. The limitations and benefits of all of the approaches are identified to help engineers apply capacitor current feedback AD in practice.

• East Asian mathematical journal
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• v.30 no.3
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• pp.259-270
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• 2014

For a generalized triangular matrix ring $$T=\[\array{R\;M\\0\;S}]$$, over rings R and S having only the idempotents 0 and 1 and over an (R, S)-bimodule M, we characterize all homomorphisms ${\alpha}$'s and all ${\alpha}$-derivations of T. Some of the homomorphisms are compositions of an inner homomorphism and an extended or a twisted homomorphism.

• Journal of applied mathematics & informatics
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• v.5 no.3
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• pp.889-893
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• 1998

In this paper we show that $\sigma$a maps into the radical if and only if for every irreducible representation $\pi$,$\pi$(a) is scalar and obtain that every inner derivation corresponding to $\sigma$-quasi central elements in some Banach algebra maps into the radical.

• Communications of the Korean Mathematical Society
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• v.32 no.4
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• pp.827-833
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• 2017

In this paper, we define a set including of all $f_a$ with $a{\in}R$ generalized derivations of R and is denoted by $f_R$. It is proved that (i) the mapping $g:L(R){\rightarrow}f_R$ given by g (a) = f-a for all $a{\in}R$ is a Lie epimorphism with kernel $N_{{\sigma},{\tau}}$ ; (ii) if R is a semiprime ring and ${\sigma}$ is an epimorphism of R, the mapping $h:f_R{\rightarrow}I(R)$ given by $h(f_a)=i_{{\sigma}(-a)}$ is a Lie epimorphism with kernel $l(f_R)$ ; (iii) if $f_R$ is a prime Lie ring and A, B are Lie ideals of R, then $[f_A,f_B]=(0)$ implies that either $f_A=(0)$ or $f_B=(0)$.

• Bulletin of the Korean Mathematical Society
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• v.35 no.3
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• pp.583-590
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• 1998

The purpose of this paper is to prove the following results: Let A be a noncommutative semisimple Banach algebra. (1) Suppose that a linear derivation D : A $\to A$ is such that [D(x),x]x=0 holds for all $x \in A$. Then we have D=0. (2) Suppose that a linear derivation $D:A\to A$ is such that $D(x)x^2 + x^2D(x)=0$ holds for all $x \in A$. Then we have C=0.

• Communications of the Korean Mathematical Society
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• v.35 no.3
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• pp.891-906
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• 2020

In this paper, the commutative module amenable Banach algebras are characterized. The hereditary and permanence properties of module amenability and the relations between module amenability of a Banach algebra and its ideals are explored. Analogous to the classical case of amenability, it is shown that the projective tensor product and direct sum of module amenable Banach algebras are again module amenable. By an application of Ryll-Nardzewski fixed point theorem, it is shown that for an inverse semigroup S, every module derivation of 𝑙¹(S) into a reflexive module is inner.

• Journal of Power Electronics
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• v.17 no.4
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• pp.1027-1036
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• 2017

The brushless doubly-fed induction generator (BDFIG) is a new type of dual stator winding induction generator. In such a generator, both the power winding (PW) and the control winding (CW) are housed in the stator. This paper presents the performance characteristics of a stand-alone BDFIG operation system. A new T-type steady-state model of a BDFIG is proposed. This model is more suitable for the performance analysis of stand-alone BDFIGs than the conventional Π-type steady-state model and the simplified inner core steady-state model. The characteristics of the power flow and CW current are analyzed by detailed mathematical derivations on the basis of the proposed T-type steady-state model. The analysis results are verified by experiments, which are carried out on a prototype BDFIG. The results of the performance analysis contribute to simplifying the control circuit, improving the control performance, and selecting an appropriate BDFIG for actual industrial applications.