Results 11 to 20 of about 4,452,319 (321)
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
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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. Also, many elementary properties of the suggested system such as inverses and idempotents will be handled by many related theorems and examples.
Khadija Ben Othman +2 more
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A Study on Dual Hyperbolic Fibonacci and Lucas Numbers
Analele Universitatii "Ovidius" Constanta - Seria Matematica, 2019 Abstract In this study, the dual-hyperbolic Fibonacci and dual-hyperbolic Lucas numbers are introduced. Then, the fundamental identities are proven for these numbers. Additionally, we give the identities regarding negadual-hyperbolic Fibonacci and negadual-hyperbolic Lucas numbers.
Arzu Cihan +3 more
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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
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Calculus on Dual Real Numbers [PDF]
arXiv, 2018 We present the basic theory of calculus on dual real numbers, and prove the counterpart of the ordinary fundamental theorem of calculus in the context of dual real numbers.
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Representations of quivers over the algebra of dual numbers [PDF]
Journal of Algebra, 2017 This is a slightly revised version. The paper now includes a proof that H yields a chomological functor from the stable category of \Cal L to mod kQ, see section 2 ...
Ringel, Claus Michael, Zhang, Pu
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Radix form in hyperbolic and dual numbers [PDF]
arXiv, 2022 We investigate number systems for the ring of integers of hyperbolic and dual numbers. We characterize all canonical number systems providing radix form for hyperbolic and dual numbers. Our approach allows us to get suitable bases by means of Banach lattice algebra structure.
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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. +2 more
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Generalization of Neural Networks on Second-Order Hypercomplex Numbers
Mathematics, 2023 The vast majority of existing neural networks operate by rules set within the algebra of real numbers. However, as theoretical understanding of the fundamentals of neural networks and their practical applications grow stronger, new problems arise, which ...
Stanislav Pavlov +5 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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