Results 241 to 250 of about 543,884 (273)

COHOMOLOGY AND DEFORMATIONS OF GENERALIZED REYNOLDS OPERATORS ON LEIBNIZ ALGEBRAS

Rocky Mountain Journal of Mathematics
The authors consider generalized Reynolds operators on Leibniz algebras and give some examples of such operators. They are Leibniz analogues of twisted Poisson structures. They show that these operators induce a new Leibniz algebra structure. Its cohomology is the Leibniz analogue of the cohomology of twisted Poisson structures.
Apurba Das
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An Operator Equation Generalizing the Leibniz Rule for the Second Derivative

Lecture Notes in Mathematics, 2012
We determine all operators \(T : {C}^{2}(\mathbb{R}) \rightarrow C(\mathbb{R})\) and \(A : {C}^{1}(\mathbb{R}) \rightarrow C(\mathbb{R})\) which satisfy the equation $$T(f \cdot g) = (Tf) \cdot g + f \cdot (Tg) + (Af) \cdot (Ag)\ ;\quad f,g \in {C}^{2}(\mathbb{R}).$$ (1) This operator equation models the second order Leibniz rule for (f ⋅g ...
Vitali Milman, Milman Vitali, KÖNIG Hermann   +2 more
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Leibniz’s Rule and Fubini’s Theorem Associated with a General Quantum Difference Operator

Springer Optimization and Its Applications, 2020
In this paper, we derive Leibniz’s rule and Fubini’s theorem associated with a general quantum difference operator Dβ which is defined by \(D_\beta f(t)=\frac {f(\beta (t))-f(t)}{\beta (t)-t}\), β(t) ≠ t. Here β is a strictly increasing continuous function defined on a set \(I\subseteq \mathbb R\) that has only one fixed point s0 ∈ I and satisfies the ...
Enas Shehata, P Agarwal, Shehata Enas M   +2 more
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Extended Rota-Baxter Operators on Leibniz Algebras

Frontiers of Mathematics
Dingguo Wang, Wang Dingguo
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Twisted relative Rota-Baxter operators on Leibniz conformal algebras

Communications in Algebra
Shengxiang Wang
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Relative Rota--Baxter operators of arbitrary weight on Leibniz algebras and post-Leibniz algebra structures

Publicationes Mathematicae Debrecen, 2023
The author defines cohomology of relative Rota-Baxter operators of arbitrary weight on Leibniz algebras and studies their deformations. This is done by generalizing the operators of weight 0 developed by \textit{R. Tang} et al. [Int. J. Geom. Methods Mod. Phys. 17, No. 12, Article ID 2050174, 21 p. (2020; Zbl 1550.17003)].
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Erratum: Weighted Fractional Leibniz-type Rules for Bilinear Multiplier Operators

Potential Analysis, 2023
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Brummer, Joshua, Naibo, Virginia
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Leibniz-Type Rules for Bilinear Fourier Multiplier Operators with Besov Regularity

Results in Mathematics, 2021
The main result of the paper is a Leibniz-type estimate for the bilinear Fourier multiplier operator \[ T_m(f,g)(x) = \int_{\mathbb{R}^{2n}} m(\xi,\eta)e^{i(\xi+\eta)\cdot x}\widehat{f}(\xi)\widehat{g}(\eta) d\xi d\eta \] under Besov regularity assumptions on the symbol \(m\).
Zongguang Liu, Xinfeng Wu, Jiexing Yang
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Characterizing Equivalential and Algebraizable Logics by the Leibniz Operator

Studia Logica, 1997
In this paper the author characterizes the hierarchy of protoalgebraic, equivalential, finitely equivalential, possibly infinitely algebraizable and finitely algebraizable logics by properties of the Leibniz operator. The author gives a new short proof of the main result of \textit{W. J. Blok} and \textit{D. Pigozzi} [Algebraizable logics, Mem.
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Weighted Fractional Leibniz-Type Rules for Bilinear Multiplier Operators

Potential Analysis, 2018
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Joshua Brummer, Virginia Naibo
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