Results 21 to 30 of about 3,505,093 (295)
Dual-Gaussian Pell and Pell-Lucas numbers
Cumhuriyet Science Journal, 2022 In this study, we define a new type of Pell and Pell-Lucas numbers which are called dual-Gaussian Pell and dual-Gaussian Pell-Lucas numbers. We also give the relationship between negadual-Gaussian Pell and Pell-Lucas numbers and dual-complex Pell
Hasan Gökbaş
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Efficient Dual-Numbers Reverse AD via Well-Known Program Transformations
Proc. ACM Program. Lang., 2023 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 Vákár
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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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Applications of the complex, double and dual numbers in Lagrangian mechanics
Revista mexicana de física, 2023 It is shown that in some examples of classical mechanics, the complex, double and dual numbers are useful in the search of symmetries of the equations of motion. As a byproduct, we obtain non-standard Lagrangians for the systems under consideration.
G. F. Torres del Castillo +1 more
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The inequalities on dual numbers and their topological structures
Turkish Journal of Mathematics, 2023 : Inequalities are frequently used in various fields of mathematics to prove theorems. The existence of inequalities contributes significantly to the foundations of such branches. In this paper, we study the properties of order relations in the system of
Buşra Aktaş +2 more
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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 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 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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Investigating generalized quaternions with dual-generalized complex numbers [PDF]
Mathematica Bohemica, 2023 We aim to introduce generalized quaternions with dual-generalized complex number coefficients for all real values $\alpha$, $\beta$ and $\mathfrak{p}$.
Nurten Gürses +2 more
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Congruences related to dual sequences and Catalan numbers [PDF]
European Journal of Combinatorics, 2022 12 ...
Rong-Hua Wang, Michael X. X. Zhong
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