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Automatic differential kinematics of serial manipulator robots through dual numbers
TESEA, Transactions on Energy Systems and Engineering ApplicationsDual 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 +1 more
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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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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
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On a generalization of dual-generalized complex Fibonacci quaternions [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 In this study, we introduce a new class of generalized quaternions whose components are dual-generalized complex Horadam numbers. We investigate some algebraic properties of them.
Elif Tan, Umut Öcal
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On hyper-dual generalized Fibonacci numbers [PDF]
Notes on Number Theory and Discrete Mathematics, 2020 In this paper, we define hyper-dual generalized Fibonacci numbers. We give the Binet formulae, the generating functions and some basic identities for these numbers.
KOPARAL, SİBEL, ÖMÜR, NEŞE
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Jacobsthal Representation Hybrinomials
Annales Mathematicae Silesianae, 2022 Jacobsthal numbers are a special case of numbers defined recursively by the second order linear relation and for these reasons they are also named as numbers of the Fibonacci type.
Liana Mirosław +2 more
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On invariants dual to the Bass numbers [PDF]
Proceedings of the American Mathematical Society, 1997 Let R R be a commutative Noetherian ring, and let M M be an R R -module. In earlier papers by Bass (1963) and Roberts (1980) the Bass numbers μ i ( p , M ) \mu _i(p,M) were defined for all primes p p
Jinzhong Xu, Edgar E. Enochs
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Dual of bass numbers and dualizing modules [PDF]
Communications in Algebra, 2016 Let $R$ be a Noetherian ring and let $C$ be a semidualizing $R$-module. In this paper, by using relative homological dimensions with respect to $C$, we impose various conditions on $C$ to be dualizing. First, we show that $C$ is dualizing if and only if there exists a Cohen-Macaulay $R$-module of type 1 and of finite G$ _C $-dimension.
Mohammad Rahmani, Abdoljavad Taherizadeh
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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,
Lingguang Li, Lingguang Li
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