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Dual Numbers and Operational Umbral Methods [PDF]
Axioms, 2019 Dual numbers and their higher-order version are important tools for numerical computations, and in particular for finite difference calculus. Based on the relevant algebraic rules and matrix realizations of dual numbers, we present a novel point of view,
Nicolas Behr +3 more
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On tertions and dual numbers [PDF]
Notes on Number Theory and Discrete MathematicsIn a previous author's paper [1], the mathematical object called "tertion" was discussed. Some operations over tertions were introduced and their properties were studied. There, it was showed that the complex numbers and quaternions can be represented by
Krassimir T. Atanassov
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Dual Numbers Approach in Multiaxis Machines Error Modeling [PDF]
Journal of Applied Mathematics, 2014 Multiaxis machines error modeling is set in the context of modern differential geometry and linear algebra. We apply special classes of matrices over dual numbers and propose a generalization of such concept by means of general Weil algebras.
Jaroslav Hrdina, Petr Vašík
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Parallel dual-numbers reverse AD
Journal of Functional Programming, 2022 Abstract Where dual-numbers forward-mode automatic differentiation (AD) pairs each scalar value with its tangent value, dual-numbers reverse-mode AD attempts to achieve reverse AD using a similarly simple idea: by pairing each scalar value with a backpropagator function.
TOM J. SMEDING, MATTHIJS I. L. VÁKÁR
semanticscholar +9 more sources
AIMS Mathematics, 2023 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.
Adnan Karataş
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Polynomial functions on rings of dual numbers over residue class rings of the integers [PDF]
Mathematica Slovaca, 2021 The ring of dual numbers over a ring R is R[α] = R[x]/(x2), where α denotes x + (x2). For any finite commutative ring R, we characterize null polynomials and permutation polynomials on R[α] in terms of the functions induced by their coordinate ...
Hasan Al-Ezeh +2 more
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On Simple Transitive 2-representations of Bimodules over the Dual Numbers [PDF]
Algebras and Representation Theory, 2020 We study the problem of classification of simple transitive 2-representations for the (non-finitary) 2-category of bimodules over the dual numbers. We show that simple transitive 2-representations with finitary apex are necessarily of rank 1 or 2, and ...
Helena Jonsson
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Dual-Gaussian Pell and Pell-Lucas numbers
Cumhuriyet Science Journal, 2022 In this study, we define a new type of Pell and Pell-Lucas numbers which are called dual-Gaussian Pell and dual-Gaussian Pell-Lucas numbers. We also give the relationship between negadual-Gaussian Pell and Pell-Lucas numbers and dual-complex Pell
Hasan Gökbaş
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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
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Kinematic Applications of Hyper-Dual Numbers
International Electronic Journal of Geometry, 2021 Hyper-dual numbers are a new number system that is an extension of dual numbers. A hyper-dual number can be written uniquely as an ordered pair of dual numbers. In this paper, some basic algebraic properties of hyper-dual numbers are given using their ordered pair representaions of dual numbers.
Selahattin Aslan
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