Results 11 to 20 of about 4,249,593 (344)

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

Some applications in classical mechanics of the double and the dual numbers

Revista mexicana de física E, 2019
We give some examples of the application in classical mechanics of the double and the dual numbers, which are analogous to the complex numbers.
G. F. Torres del Castillo
openalex   +2 more sources

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, Azak Ayşe Zeynep, Güngör Mehmet Ali, Tosun Murat   +3 more
doaj   +2 more sources

The Groups of Two by Two Matrices in Double and Dual Numbers, and Associated Möbius Transformations [PDF]

Advances in Applied Clifford Algebras, 2018
Möbius transformations have been studied over the field of complex numbers. In this paper, we investigate Möbius transformations over two rings which are not fields: the ring of double numbers and the ring of dual numbers. We give types of continuous one-
Khawlah A. Mustafa
openalex   +2 more sources

Three-axes error modeling based on second order dual numbers [PDF]

, 2015
The aim of the paper is to employ the dual numbers in the multi axes machine error modelling in order to apply the algebraic methods in computations.
Michal Holub, Jaroslav Hrdina, Petr Vašík, Jan Vetiška   +3 more
openalex   +2 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

On Dual Hyperbolic Guglielmo Numbers

Journal of Advances in Mathematics and Computer Science
In this research, the generalized dual hyperbolic Guglielmo numbers are introduced. Various special cases are explored (including dual hyperbolic triangular numbers, dual hyperbolic triangular-Lucas numbers, dual hyperbolic oblong numbers, and dual hyperbolic pentagonal numbers).
Bahadır Yılmaz, Yüksel Soykan
openalex   +4 more sources

Dual Hyperbolic Generalized Adrien Numbers

Asian Research Journal of Mathematics
This study introduces the generalized dual hyperbolic Adrien numbers, a novel extension of the classic Adrien framework, enriched by dual and hyperbolic algebraic structures. These sequences are constructed within a fourth-order linear recurrence system, offering intricate mathematical behavior and promising structural versatility. Special attention is
Feyza Demirci, Yüksel Soykan
openalex   +3 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