• Title/Summary/Keyword: orthogonal derivation

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SEMIPRIME NEAR-RINGS WITH ORTHOGONAL DERIVATIONS

  • Park, Kyoo-Hong;Jung, Yong-Soo
    • 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.

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ON ORTHOGONAL REVERSE DERIVATIONS OF SEMIPRIME 𝚪-SEMIRINGS

  • Kim, Kyung Ho
    • 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.

ORTHOGONAL PEXIDER HOM-DERIVATIONS IN BANACH ALGEBRAS

  • Vahid Keshavarz;Jung Rye Lee;Choonkil Park
    • 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.

An Asymmetric Fuglede-Putnam's Theorem and Orthogonality

  • Ahmed, Bachir;Segres, Abdelkder
    • 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.

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Range Kernel Orthogonality and Finite Operators

  • Mecheri, Salah;Abdelatif, Toualbia
    • 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.

Detailed Re-derivation of Keplerian Orbit and Kaula's Satellite Orbit Perturbation Theory (케플러궤도운동과 카울라의 인공위성궤도 섭동이론의 상세한 재유도)

  • Na, Sung-Ho;Bae, Tae-Seok;Jo, Jung-Hyun;Park, Jong-Uk
    • 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.

POD Analysis for modeling wind pressures and wind effects of a cylindrical shell roof

  • Li, Fanghui;Chen, Xinzhong
    • 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.