Results 11 to 20 of about 3,505,093 (295)

On tertions and dual numbers [PDF]

Notes on Number Theory and Discrete Mathematics
In 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
doaj   +3 more sources

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, Giuseppe Dattoli, Ambra Lattanzi, Silvia Licciardi   +3 more
doaj   +5 more sources

Parallel dual-numbers reverse AD

Journal of Functional Programming, 2022
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 ...
Tom J. Smeding, Matthijs V'ak'ar
semanticscholar   +8 more sources

On the Dual Symbolic 2-Plithogenic Numbers [PDF]

Neutrosophic Sets and Systems, 2023
The objective of this paper is to combine dual numbers with symbolic 2-plithogenic numbers in one algebraic structure called dual symbolic 2-plithogenic real numbers.
Khadija Ben Othman, Maretta Sarkis, Murat Ozcek   +2 more
doaj   +3 more sources

Application of Generalized (Hyper-) Dual Numbers in Equation of State Modeling

Frontiers in Chemical Engineering, 2021
The calculation of derivatives is ubiquitous in science and engineering. In thermodynamics, in particular, state properties can be expressed as derivatives of thermodynamic potentials. The manual differentiation of complex models can be tedious and error-
Philipp Rehner, Gernot Bauer
doaj   +2 more sources

De-Moivre and Euler Formulae for Dual-Complex Numbers

Universal Journal of Mathematics and Applications, 2019
In this study, we generalize the well-known formulae of De-Moivre and Euler of complex numbers to dual-complex numbers. Furthermore, we investigate the roots and powers of a dual-complex number by using these formulae. Consequently, we give some examples
Mehmet Ali Güngör, Ömer Tetik
doaj   +9 more sources

Automatic differential kinematics of serial manipulator robots through dual numbers

TESEA, Transactions on Energy Systems and Engineering Applications
Dual Numbers are an extension of real numbers known for its capability of performing exact automatic differentiation of one-valued functions theoretically without error approximation.
Luis Antonio Orbegoso Moreno, Edgar David Valverde Ramírez   +1 more
doaj   +2 more sources

Dual Numbers Approach in Multiaxis Machines Error Modeling

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
doaj   +2 more sources

Dual number automatic differentiation as applied to two-group cross-section uncertainty propagation [PDF]

Nuclear Technology and Radiation Protection, 2021
This work addresses the problem of propagating uncertainty from group-wise neutron cross-sections to the results of neutronics diffusion calculations.
Bokov Pavel M., Botes Danniell, Groenewald Suzanne A.   +2 more
doaj   +1 more source

Dual-Numbers Reverse AD, Efficiently [PDF]

arXiv.org, 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 ...
Tom J. Smeding, Matthijs V'ak'ar
semanticscholar   +1 more source