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- 주제어 : Generalized derivative (검색결과 175 건)
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A STUDY OF THE RIGHT LOCAL GENERAL TRUNCATED M-FRACTIONAL DERIVATIVE
Chauhan, Rajendrakumar B.,Chudasama, Meera H. Korean Mathematical Society 2022 대한수학회논문집 Vol.37 No.2
We introduce a new type of fractional derivative, which we call as the right local general truncated M-fractional derivative for α-differentiable functions that generalizes the fractional derivative type introduced by Anastassiou. This newly defined operator generalizes the standard properties and results of the integer order calculus viz. the Rolle's theorem, the mean value theorem and its extension, inverse property, the fundamental theorem of calculus and the theorem of integration by parts. Then we represent a relation of the newly defined fractional derivative with known fractional derivative and in context with this derivative a physical problem, Kirchoff's voltage law, is generalized. Also, the importance of this newly defined operator with respect to the flexibility in the parametric values is described via the comparison of the solutions in the graphs using MATLAB software.
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朴準元 慶一大學校 1999 論文集 Vol.16 No.5
For generalized derivations g₁, g₂, g₁+g₂and [ g₁, g₂]are generalized derivations. If Ι is ideal in R and g is a generalized derivation, than Ι+g(Ι) and Ι∩g-¹(Ι) are ideals in R. Moreover, a generalized derivation g in M?( R) is characterized by g=g(Ι)+d?+ad?.
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LEFT JORDAN DERIVATIONS ON BANACH ALGEBRAS AND RELATED MAPPINGS
Jung, Yong-Soo,Park, Kyoo-Hong Korean Mathematical Society 2010 대한수학회보 Vol.47 No.1
In this note, we obtain range inclusion results for left Jordan derivations on Banach algebras: (i) Let $\delta$ be a spectrally bounded left Jordan derivation on a Banach algebra A. Then $\delta$ maps A into its Jacobson radical. (ii) Let $\delta$ be a left Jordan derivation on a unital Banach algebra A with the condition sup{r$(c^{-1}\delta(c))$ : c $\in$ A invertible} < $\infty$. Then $\delta$ maps A into its Jacobson radical. Moreover, we give an exact answer to the conjecture raised by Ashraf and Ali in [2, p. 260]: every generalized left Jordan derivation on 2-torsion free semiprime rings is a generalized left derivation.
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Pair of (generalized-)derivations on rings and Banach algebras
Feng Wei,Zhankui Xiao 대한수학회 2009 대한수학회보 Vol.46 No.5
Let n be a fixed positive integer, R be a 2n!-torsion free prime ring and μ, be a pair of generalized derivations on R. If (μ2(x)+ v(x), x^n = 0 for all x ∈ R, then μ and 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 CR and d, g be a pair of derivations on R. If (d^2(x) + g(x), x^n)∈ CR for all x ∈ 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. Let n be a fixed positive integer, R be a 2n!-torsion free prime ring and μ, be a pair of generalized derivations on R. If (μ2(x)+ v(x), x^n = 0 for all x ∈ R, then μ and 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 CR and d, g be a pair of derivations on R. If (d^2(x) + g(x), x^n)∈ CR for all x ∈ 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.
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INFLUENCE ANALYSIS FOR GENERALIZED ESTIMATING EQUATIONS
Jung Kang-Mo The Korean Statistical Society 2006 Journal of the Korean Statistical Society Vol.35 No.2
We investigate the influence of subjects or observations on regression coefficients of generalized estimating equations using the influence function and the derivative influence measures. The influence function for regression coefficients is derived and its sample versions are used for influence analysis. The derivative influence measures under certain perturbation schemes are derived. It can be seen that the influence function method and the derivative influence measures yield the same influence information. An illustrative example in longitudinal data analysis is given and we compare the results provided by the influence function method and the derivative influence measures.
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On generalized derivations of $BE$-algebras
김경호 충청수학회 2014 충청수학회지 Vol.27 No.2
In this paper, we introduce the notion of a generalized derivation in a BE-algebra, and consider the properties of gen- eralized derivations. Also, we characterize the fixed set Fixd(X) and Kerd by generalized derivations. Moreover, we prove that if d is a generalized derivation of a BE-algebra, every filter F is a d-invariant.
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ON GENERALIZED DERIVATIONS OF BE-ALGEBRAS
Kim, Kyung Ho Chungcheong Mathematical Society 2014 충청수학회지 Vol.27 No.2
In this paper, we introduce the notion of a generalized derivation in a BE-algebra, and consider the properties of generalized derivations. Also, we characterize the fixed set $Fix_d(X)$ and Kerd by generalized derivations. Moreover, we prove that if d is a generalized derivation of a BE-algebra, every filter F is a d-invariant.
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τ-CENTRALIZERS AND GENERALIZED DERIVATIONS
Zhou, Jiren Korean Mathematical Society 2010 대한수학회지 Vol.47 No.3
In this paper, we show that Jordan $\tau$-centralizers and local $\tau$-centralizers are $\tau$-centralizers under certain conditions. We also discuss a new type of generalized derivations associated with Hochschild 2-cocycles and introduce a special local generalized derivation associated with Hochschild 2-cocycles. We prove that if $\cal{L}$ is a CDCSL and $\cal{M}$ is a dual normal unital Banach $alg\cal{L}$-bimodule, then every local generalized derivation of above type from $alg\cal{L}$ into $\cal{M}$ is a generalized derivation.
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γ-CENTRALIZERS AND GENERALIZED DERIVATIONS
Jiren Zhou 대한수학회 2010 대한수학회지 Vol.47 No.3
In this paper, we show that Jordan γ-centralizers and local γ-centralizers are γ-centralizers under certain conditions. We also discuss a new type of generalized derivations associated with Hochschild 2-cocycles and introduce a special local generalized derivation associated with Hochschild 2-cocycles. We prove that if L is a CDCSL and M is a dual normal unital Banach algL-bimodule, then every local generalized derivation of above type from algL into M is a generalized derivation.
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Konstantina Panagiotidou,Juan de Dios Perez 대한수학회 2015 대한수학회보 Vol.52 No.5
In this paper the notion of Lie derivative of a tensor field T of type (1,1) of real hypersurfaces in complex space forms with respect to the generalized Tanaka-Webster connection is introduced and is called generalized Tanaka-Webster Lie derivative. Furthermore, three dimensional real hypersurfaces in non-flat complex space forms whose generalized Tanaka-Webster Lie derivative of 1) shape operator, 2) structure Jacobi operator coincides with the covariant derivative of them with respect to any vector field X orthogonal to ξ are studied.
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