• 한국수학교육학회지시리즈B:순수및응용수학
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• 제13권4호
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• pp.303-310
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• 2006

M. $Bre\v{s}ar$ and J. Vukman obtained some results concerning orthogonal derivations in semiprime rings which are related to the result that is well-known to a theorem of Posner for the product of two derivations in prime rings. In this paper, we present orthogonal generalized derivations in semiprime near-rings.

• East Asian mathematical journal
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• 제24권4호
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• pp.389-398
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• 2008

In this paper, some results of [6] concerning orthogonal ($\sigma$, $\tau$)-derivations and generalized ($\sigma$, $\tau$)-derivations are generalized for a nonzero ideal of a semiprime ring.

• 충청수학회지
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• 제35권2호
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• pp.115-124
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• 2022

In this paper, we introduce the notion of orthogonal reserve derivation on semiprime 𝚪-semirings. Some characterizations of semiprime 𝚪-semirimgs are obtained by means of orthogonal reverse derivations. We also investigate conditions for two reverse derivations on semiprime 𝚪-semiring to be orthogonal.

• Korean Journal of Mathematics
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• 제30권2호
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• pp.341-349
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• 2022

In this paper, we introduce the notion of orthogonal reserve derivation on semiprime semirings. Some characterizations of semiprime semirimgs are obtained by means of orthogonal reverse derivations. We also investigate conditions for two reverse derivations on semiring to be orthogonal.

• Nonlinear Functional Analysis and Applications
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• 제28권1호
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• pp.95-105
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• 2023

In the present paper, we introduce a new system of functional equations, known as orthogonal Pexider hom-derivation and Pexider hom-Pexider derivation (briefly, (Pexider) hom-derivation). Using the fixed point method, we investigate the stability of Pexider hom-derivations and (Pexider) hom-derivations on Banach algebras.

• Kyungpook Mathematical Journal
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• 제46권4호
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• pp.497-502
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• 2006

An asymmetric Fuglede-Putnam theorem for $p$-hyponormal operators and class ($\mathcal{Y}$) is proved, as a consequence of this result, we obtain that the range of the generalized derivation induced by the above classes of operators is orthogonal to its kernel.

• Kyungpook Mathematical Journal
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• 제50권3호
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• pp.379-387
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• 2010

In this paper, we present some results concerning orthogonal generalized (${\sigma},{\tau}$)-derivations in semiprime near-rings. These results are a generalization of result of Bresar and Vukman, which are related to a theorem of Posner for the product of two derivations in prime rings.

• Kyungpook Mathematical Journal
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• 제55권1호
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• pp.63-71
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• 2015

Let H be a separable infinite dimensional complex Hilbert space, and let $\mathcal{L}(H)$ denote the algebra of all bounded linear operators on H into itself. Let $A,B{\in}\mathcal{L}(H)$ we define the generalized derivation ${\delta}_{A,B}:\mathcal{L}(H){\mapsto}\mathcal{L}(H)$ by ${\delta}_{A,B}(X)=AX-XB$, we note ${\delta}_{A,A}={\delta}_A$. If the inequality ${\parallel}T-(AX-XA){\parallel}{\geq}{\parallel}T{\parallel}$ holds for all $X{\in}\mathcal{L}(H)$ and for all $T{\in}ker{\delta}_A$, then we say that the range of ${\delta}_A$ is orthogonal to the kernel of ${\delta}_A$ in the sense of Birkhoff. The operator $A{\in}\mathcal{L}(H)$ is said to be finite [22] if ${\parallel}I-(AX-XA){\parallel}{\geq}1(*)$ for all $X{\in}\mathcal{L}(H)$, where I is the identity operator. The well-known inequality (*), due to J. P. Williams [22] is the starting point of the topic of commutator approximation (a topic which has its roots in quantum theory [23]). In [16], the author showed that a paranormal operator is finite. In this paper we present some new classes of finite operators containing the class of paranormal operators and we prove that the range of a generalized derivation is orthogonal to its kernel for a large class of operators containing the class of normal operators.

• 한국지구과학회지
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• 제33권1호
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• pp.11-31
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• 2012

카울라에 의해 완성되었던 인공위성궤도이론과 케플러의 법칙을 다시 다루었다. 카울라의 원문에서는 생략되었던 부분을 포함한 모든 수식유도과정을 상세히 기술하였다. 특히 15개의 독립적인 라그랑지 괄호들을 계산하는 데에 변환행렬의 직교성을 사용하여, 간결성과 명확성을 이루었다. 여러 중간단계에서 중요한 물리적인 개념들에 대한 설명도 추가하였다. 카울라의 개념적 오류 한 개를 정정하였다.

• Wind and Structures
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• 제30권6호
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• pp.559-573
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• 2020

This paper presents a study on the effectiveness of the proper orthogonal decomposition (POD) technique for reconstruction of wind pressure field as applied to a cylindrical shell roof based on simultaneously measured wind pressure data. The influence of wind loading mode truncation on the statistics of dynamic pressures and wind load effects are investigated. The results showed that truncation of higher wind loading modes can have more noticeable influence on the maximum and minimum pressures that the standard derivation (STD) values. The truncation primarily affects the high-frequency content of the pressures. Estimation of background response using wind loading modes is more effective than the use of traditional structural modal analysis.