Results 21 to 30 of about 44,238 (260)
Function Interval Arithmetic [PDF]
, 2014 We propose an arithmetic of function intervals as a basis for convenient rigorous numerical computation. Function intervals can be used as mathematical objects in their own right or as enclosures of functions over the reals. We present two areas of application of function interval arithmetic and associated software that implements the arithmetic: (1 ...
Jan Duracz +3 more
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Properties of rational arithmetic functions
International Journal of Mathematics and Mathematical Sciences, 2005 Rational arithmetic functions are arithmetic functions of the form g1∗⋯∗gr∗h1−1∗⋯∗hs−1, where gi, hj are completely multiplicative functions and ∗ denotes the Dirichlet convolution. Four aspects of these functions are studied.
Vichian Laohakosol, Nittiya Pabhapote
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Arithmetic functions associated with infinitary divisors of an integer
International Journal of Mathematics and Mathematical Sciences, 1993 The infinitary divisors of a natural number n are the products of its divisors of the form pyα2α, where py is a prime-power component of n and ∑αyα2α (where yα=0 or 1) is the binary representation of y.
Graeme L. Cohen, Peter Hagis
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Krein-space operators determined by free product algebras induced by primes and graphs
Special Matrices, 2017 In this paper, we introduce certain Krein-space operators induced by free product algebras induced by both primes and directed graphs. We study operator-theoretic properties of such operators by computing free-probabilistic data containing number ...
Cho Ilwoo, Jorgensen Palle E. T.
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On the Arithmetic of Abelina Functions [PDF]
Proceedings of the National Academy of Sciences, 1927 Systematic application of abelian functions to the theory of numbers discloses many new arithmetical phenomena of considerable interest. Particularly is this the case when the periods of the functions are connected by one or more singular relations in the usual sense.
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Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2014 Let π(x) be the number of primes not exceeding x. We prove that π(x)
Bănescu Magdalena
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A note on the approximation of divisor functions [PDF]
Notes on Number Theory and Discrete MathematicsWe offer an arithmetic proof of a result from the recent paper [1]. A more general result is provided, too.
József Sándor
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Privacy-Preserving Machine Learning With Fully Homomorphic Encryption for Deep Neural Network
IEEE Access, 2022 Fully homomorphic encryption (FHE) is a prospective tool for privacy-preserving machine learning (PPML). Several PPML models have been proposed based on various FHE schemes and approaches.
Joon-Woo Lee +10 more
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Arithmetic of the Fabius Function
Integers, 2017 I solve here a question of Vladimir Reshetnikov in Mathoverflow (question 261649) about the values of Fabius function. Namely, I prove that the numbers $R_n:=2^{-\binom{n-1}{2}}(2n)! F(2^{-n})\prod_{m=1}^{\lfloor n/2\rfloor}(2^{2m}-1)$ are integers. We show also some other arithmetical properties of the values of Fabius function at dyadic points.
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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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