Results 1 to 10 of about 50 (46)
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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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, embedding dual numbers within a formalism reminiscent of operational umbral calculus.
Nicolas Behr +3 more
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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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AIMS Mathematics, 2023 <abstract><p>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. Moreover, we presented a range of identities that provided deeper insights
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Congruences related to dual sequences and Catalan numbers [PDF]
European Journal of Combinatorics, 2022 12 ...
Michael X.X. Zhong, Rong-Hua Wang
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Dual-Numbers Reverse AD, Efficiently
, 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 backpropagator function. Its correctness and efficiency on higher-order input languages have been analysed by
Smeding, Tom, Vákár, Matthijs
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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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