Results 31 to 40 of about 3,505,093 (295)
Higher Order Automatic Differentiation with Dual Numbers
Periodica Polytechnica Electrical Engineering and Computer Science, 2020 In engineering applications, we often need the derivatives of functions defined by a program. The approach chosen for derivative computation must be algebraic to allow computer implementation.
László Szirmay-Kalos
semanticscholar +1 more source
Introduction to Third-Order Jacobsthal and Modified Third-Order Jacobsthal Hybrinomials
Discussiones Mathematicae - General Algebra and Applications, 2021 The hybrid numbers are generalization of complex, hyperbolic and dual numbers. In this paper, we introduce and study the third-order Jacobsthal and modified third-order Jacobsthal hybrinomials, i.e., polynomials, which are a generalization of the ...
Cerda-Morales Gamaliel
doaj +1 more source
JSIAM Letters, 2020 Hyper-dual numbers (HDN) are numbers de(cid:12)ned by using nilpotent elements that differ from each other. The introduction of an operator to extend the domain of functions to HDN space based on Taylor expansion allows higher-order derivatives to be ...
Y. Imoto +5 more
semanticscholar +1 more source
Vanishing Properties of Dual Bass Numbers [PDF]
Algebra Colloquium, 2014 Let R be a Noetherian ring, M an Artinian R-module, and 𝖒 ∈ Cos RM. Then cograde R𝔭 Hom R (R𝔭,M) = inf {i | πi(𝔭,M) > 0} and [Formula: see text] where πi(𝔭,M) is the i-th dual Bass number of M with respect to 𝔭, cograde R𝔭 Hom R (R𝔭,M) is the common length of any maximal Hom R (R𝔭, M)-quasi co-regular sequence contained in 𝔭 R𝔭, and fd R𝔭 Hom R (R𝔭,
openaire +3 more sources
A Note on Generalized Hybrid Tribonacci Numbers
Discussiones Mathematicae - General Algebra and Applications, 2020 In this paper, we introduce the generalized hybrid Tribonacci numbers. These numbers can be considered as a generalization of the generalized complex Tribonacci, generalized hyperbolic Tribonacci and generalized dual Tribonacci numbers.
Yaǧmur Tülay
doaj +1 more source
On the group of automorphisms of the algebra of plural numbers
Дифференциальная геометрия многообразий фигур, 2023 The algebra of dual numbers was first introduced by V. K. Clifford in 1873. The algebras of plural and dual numbers are analogous to the algebra of complex numbers. Dual numbers form an algebra, but not a field, because only dual numbers with a real part
A. Ya. Sultanov +2 more
doaj +1 more source
A Study on Dual Hyperbolic Fibonacci and Lucas Numbers
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2019 In this study, the dual-hyperbolic Fibonacci and dual-hyperbolic Lucas numbers are introduced. Then, the fundamental identities are proven for these numbers.
Cihan Arzu +3 more
doaj +1 more source
Mathematics and Poetry • Unification, Unity, Union
Sci, 2020 We consider a multitude of topics in mathematics where unification constructions play an important role: the Yang–Baxter equation and its modified version, Euler’s formula for dual numbers, means and their inequalities, topics in differential geometry ...
Florin Felix Nichita
doaj +1 more source
One-Parameter Generalization of Dual-Hyperbolic Jacobsthal Numbers
Annales Mathematicae Silesianae, 2023 In this paper, we introduce one-parameter generalization of dual-hyperbolic Jacobsthal numbers – dual-hyperbolic r-Jacobsthal numbers. We present some properties of them, among others the Binet formula, Catalan, Cassini, and d’Ocagne identities. Moreover,
Bród Dorota +2 more
doaj +1 more source
AIMS Mathematics, 2023 <abstract><p>This paper introduced the concept of dual Leonardo numbers to generalize the earlier studies in harmony and establish key formulas, including the Binet formula and the generating function. Both were employed to obtain specific elements from the sequence. Moreover, we presented a range of identities that provided deeper insights
openaire +3 more sources