Results 41 to 50 of about 1,451,548 (325)
Hyper-Dual Leonardo Quaternions
Journal of New TheoryIn this paper, hyper-dual Leonardo quaternions are defined and studied. Some basic properties of the hyper-dual Leonardo quaternions, including their relationships with the hyper-dual Fibonacci quaternions and hyper-dual Lucas quaternions, are analyzed ...
Tülay Yağmur
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Smooth affine group schemes over the dual numbers [PDF]
Épijournal de Géométrie Algébrique, 2019 We provide an equivalence between the category of affine, smooth group schemes over the ring of generalized dual numbers $k[I]$, and the category of extensions of the form $1 \to \text{Lie}(G, I) \to E \to G \to 1$ where G is an affine, smooth group ...
Matthieu ROMAGNY, Dajano Tossici
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Self-Dual Conformal Supergravity and the Hamiltonian Formulation
, 2000 In terms of Dirac matrices the self-dual and anti-self-dual decomposition of a conformal supergravity is given and a self-dual conformal supergravity theory is developed as a connection dynamic theory in which the basic dynamic variabes include the self ...
A. Ashtekar +23 more
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Large branes in AdS and their field theory dual [PDF]
, 2000 Recently it was suggested that a graviton in $AdS_5 \times S^5$ with a large momentum along the sphere can blow up into a spherical D-brane in $S^5$. In this paper we show that the same graviton can also blow up into a spherical D-brane in $AdS_5$ with ...
Hashimoto, Akikazu +2 more
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Transmathematica, 2019 The class of dual number meadows is introduced. By definition this class is a quasivariety. Dual number meadows contain a non-zero element the square of which is zero. These structures are non-involutive and coregular. Some properties of the equational theory of dual number meadows are discussed and an initial algebra specification is given for the ...
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Dual-Numbers Reverse AD, Efficiently
, 2022 Where dual-numbers forward-mode automatic differentiation (AD) pairs each scalar value with its tangent derivative, dual-numbers /reverse-mode/ AD attempts to achieve reverse AD using a similarly simple idea: by pairing each scalar value with a backpropagator function. Its correctness and efficiency on higher-order input languages have been analysed by
Smeding, Tom, Vákár, Matthijs
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Journal of Innovative Applied Mathematics and Computational SciencesMotivated by the definition of Tribonacci quaternions, we define hyper-dual numbers whose components involve Tribonacci and Tribonacci-Lucas numbers. We refer to these new numbers as hyper-dual Tribonacci numbers and hyper-dual Tribonacci-Lucas numbers,
Ahmad Ali Mehrad, Mansoor Kakar Mirwais
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Some properties and Vajda theorems of split dual Fibonacci and split dual Lucas octonions
AIMS Mathematics, 2022 In this paper, we introduce split dual Fibonacci and split dual Lucas octonions over the algebra $ \widetilde{\widetilde{O}}\left(a, b, c\right) $, where $ a, b $ and $ c $ are real numbers. We obtain Binet formulas for these octonions.
Ümit Tokeşer +2 more
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An Introduction to The Dual Symbolic 3-Plithogenic And 4-Plithogenic Numbers [PDF]
Neutrosophic Sets and Systems, 2023 The objective of this paper is to use dual numbers with symbolic 3-plithogenic and 4-plithogenic numbers in one numerical system called dual symbolic 3-plithogenic/4-plithogenic numbers.
Khadija Ben Othman +2 more
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Geometry of the line space associated to a given dual ruled surface
AIMS Mathematics, 2022 As a continuation to our results in [1], we study the dual ruled surface defined on the set of dual numbers. The idea of the dual part are defined similar to quaternion space. The dual part of this represents a ruled dual submanifold.
Rawya A. Hussein, Ali A. Ali
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