Results 41 to 50 of about 381,379 (275)
Some Properties of Extended Euler’s Function and Extended Dedekind’s Function
Mathematics, 2020 In this paper, we find some properties of Euler’s function and Dedekind’s function. We also generalize these results, from an algebraic point of view, for extended Euler’s function and extended Dedekind’s function, in algebraic number fields ...
Nicuşor Minculete, Diana Savin
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Arithmetic Levi-Civita connection
, 2019 This paper is part of a series of papers where an arithmetic analogue of classical differential geometry is being developed. In this arithmetic differential geometry functions are replaced by integer numbers, derivations are replaced by Fermat quotient ...
Buium, Alexandru
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Advanced Engineering Materials, EarlyView.This study presents an infrared monitoring approach for direct laser interference patterning (DLIP) combined with a convolutional neural network (CNN). Thermal emission data captured during structuring are used to predict surface topography parameters.
Lukas Olawsky +5 more
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Inequalities with Some Arithmetic Functions
MathematicsIn the paper, some new inequalities are formulated and proved with the classical arithmetic functions φ (of Euler) and ψ (of Dedekind).
József Sándor, Krassimir Atanassov
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A new class of infinite products, and Euler's totient
International Journal of Mathematics and Mathematical Sciences, 1994 We introduce some new infinite products, the simplest being(1−y)∏k=2∞∏j∈ϕk(1−ykqj)1/k=(1−y1−qy)1/(1−q),where ϕk is the set of positive integers less than and relatively prime to k, valid for |y|∧|qy| both less than unity, with q≠1.
Geoffrey B. Campbell
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A note on $(a,b)$-Fibonacci sequences and specially multiplicative arithmetic functions [PDF]
Mathematica BohemicaA specially multiplicative arithmetic function is the Dirichlet convolution of two completely multiplicative arithmetic functions. The aim of this paper is to prove explicitly that two mathematical objects, namely $(a,b)$-Fibonacci sequences and ...
Emil Daniel Schwab, Gabriela Schwab
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Effect of Oxygen Content on Surface and Subsurface Integrity During Turning of Ti–6Al–4V
Advanced Engineering Materials, EarlyView.This study examines how oxygen content in the ambient atmosphere affects the surface and subsurface properties of Ti–6Al–4V during turning. Results show that oxygen does not influence surface roughness. However, machining in an extremely high vacuum‐adequate atmosphere increases surface hardness by up to 7.8% and induces compressive residual stresses ...
Benjamin Bergmann +3 more
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Matrices induced by arithmetic functions acting on certain Krein spaces
Special Matrices, 2017 In this paper, we study matrices induced by arithmetic functions under certain Krein-space representations induced by (multi-)primes less than or equal to fixed positive real numbers.
Cho Ilwoo
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Arithmetic Means for a Class of Functions and the Modified Bessel Functions of the First Kind
Mathematics, 2019 In the paper, by virtue of the residue theorem in the theory of complex functions, the authors establish several identities between arithmetic means for a class of functions and the modified Bessel functions of the first kind, present several identities ...
Feng Qi, Shao-Wen Yao, Bai-Ni Guo
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On the Growth of Some Functions Related to z(n)
Mathematics, 2020 The order of appearance z : Z > 0 → Z > 0 is an arithmetic function related to the Fibonacci sequence ( F n ) n . This function is defined as the smallest positive integer solution of the congruence F k ≡ 0 ( mod n )
Pavel Trojovský
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