Results 21 to 30 of about 11,114,666 (310)
Mathematics, 2021 In this paper, we find some inequalities which involve Euler’s function, extended Euler’s function, the function τ, and the generalized function τ in algebraic number fields.
Nicuşor Minculete, Diana Savin
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Objects generated by an arbitrary natural number. Part 4: New aspects [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 The set Set(n), generated by an arbitrary natural number n, was defined in [3]. There, and in [5, 6], some arithmetic functions and arithmetic operators of a modal and topological types are defined over the elements of Set(n).
Krassimir Atanassov
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The Arithmetic Optimization Algorithm
Computer Methods in Applied Mechanics and Engineering, 2021 This work proposes a new meta-heuristic method called Arithmetic Optimization Algorithm (AOA) that utilizes the distribution behavior of the main arithmetic operators in mathematics including (Multiplication ( M ), Division ( D ), Subtraction ( S ), and ...
L. Abualigah +6 more
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MEAN VALUES OF ARITHMETIC FUNCTIONS IN SHORT INTERVALS AND IN ARITHMETIC PROGRESSIONS IN THE LARGE‐DEGREE LIMIT [PDF]
Mathematika, 2018 A classical problem in number theory is showing that the mean value of an arithmetic function is asymptotic to its mean value over a short interval or over an arithmetic progression, with the interval as short as possible or the modulus as large as ...
O. Gorodetsky
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Mean values for a class of arithmetic functions in short intervals [PDF]
Mathematische Nachrichten, 2018 In this paper, we shall establish a rather general asymptotic formula in short intervals for a class of arithmetic functions and announce two applications about the distribution of divisors of square‐full numbers and integers representable as sums of two
Jie Wu, Qiang Wu
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Some new arithmetic functions [PDF]
Notes on Number Theory and Discrete MathematicsWe introduce and study some new arithmetic functions, connected with the classical functions φ (Euler's totient), ψ (Dedekind's function) and σ (sum of divisors function).
József Sándor, Krassimir Atanassov
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On certain bounds for the divisor function [PDF]
Notes on Number Theory and Discrete MathematicsWe offer various bounds for the divisor function d(n), in terms of n, or other arithmetical functions.
József Sándor
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Neural computation of arithmetic functions [PDF]
, 1990 A neuron is modeled as a linear threshold gate, and the network architecture considered is the layered feedforward network. It is shown how common arithmetic functions such as multiplication and sorting can be efficiently computed in a shallow neural ...
Bruck, Jehoshua, Siu, Kai-Yeung
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On certain arithmetical products involving the divisors of an integer [PDF]
Notes on Number Theory and Discrete MathematicsWe study the arithmetical products Π d^d, Πd^{1/d} and Πd^{log d}, where d runs through the divisors of an integer n>1.
József Sándor
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Teaching Arithmetic to Small Transformers [PDF]
arXiv.org, 2023 Large language models like GPT-4 exhibit emergent capabilities across general-purpose tasks, such as basic arithmetic, when trained on extensive text data, even though these tasks are not explicitly encoded by the unsupervised, next-token prediction ...
Nayoung Lee +4 more
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