• The Pure and Applied Mathematics
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• v.13 no.4 s.34
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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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• v.24 no.4
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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.

• Journal of the Chungcheong Mathematical Society
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• v.35 no.2
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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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• v.30 no.2
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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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• v.28 no.1
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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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• v.46 no.4
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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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• v.50 no.3
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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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• v.55 no.1
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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.

• Journal of the Korean earth science society
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• v.33 no.1
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• pp.11-31
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• 2012

Kaula's theory of satellite orbit and Kepler's law are re-visited. All the mathematical steps of derivation are thoroughly shown including the ones, which had been omitted in Kaula's original publication. Particularly in evaluations of the 15 independent Lagrange brackets, simplicity and clarity are attained by using orthogonal property of transformation matrix. Explanations of important physical concepts are included as well in the midway of derivation. One conceptual blunder of Kaula's is corrected.

• Wind and Structures
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• v.30 no.6
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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.