Results 271 to 280 of about 484,117 (322)
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The Ramanujan Journal, 2004
For the positive integer \(n\) one denotes by \(d(n)\) the number of its positive divisors, and by \(\sigma(n)\) their sum. \(\delta(n)\) denotes the difference between the number of those positive divisors of \(n\) which are congruent to \(1\pmod 3\) and the number of those positive divisors of \(n\) which are congruent to \(-1\pmod 3\); \(\delta\) is
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For the positive integer \(n\) one denotes by \(d(n)\) the number of its positive divisors, and by \(\sigma(n)\) their sum. \(\delta(n)\) denotes the difference between the number of those positive divisors of \(n\) which are congruent to \(1\pmod 3\) and the number of those positive divisors of \(n\) which are congruent to \(-1\pmod 3\); \(\delta\) is
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Pipelining of arithmetic functions
1972 IEEE 2nd Symposium on Computer Arithmetic (ARITH), 1972Two addition and three multiplication algorithms were studied to see the effect of pipelining on system efficiency. A definition of efficiency was derived to compare the relative merits of various algorithms and implementations for addition and multiplication. This definition is basically defined as bandwidth cost.
Hallin, Thomas G., Flynn, Michael J.
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Additive Arithmetic Functions on Arithmetic Progressions
Proceedings of the London Mathematical Society, 1987For an additive arithmetic function f, and positive integer D, let E(x,D) be \[ \max_{y\leq x}\max_{(r,D)=1}| \sum_{n\leq y,\quad n\equiv r (mod D)}f(n)-(1/\phi (D))\sum_{n\leq y,\quad (n,D)=1}f(n)|. \] Strengthening results from Chapter 7 of his monograph ''Arithmetic functions and integer products'' (1985; Zbl 0559.10032), the author proves that for ...
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Arithmetical Functions and Distributivity
Canadian Mathematical Bulletin, 1970In this note we shall present a result about incidence functions on a locally finite partially ordered set, a result which is related to theorems of Lambek [2] and Subbarao [6]. Our terminology and notation will be that of Smith [4, 5] and Rota [7].Let (L, ≤) be a partially ordered set which is locally finite in the sense that for all x, y ∊ L the ...
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1994
The aim of this book is to characterize certain multiplicative and additive arithmetical functions by combining methods from number theory with some simple ideas from functional and harmonic analysis. The authors achieve this goal by considering convolutions of arithmetical functions, elementary mean-value theorems, and properties of related ...
Wolfgang Schwarz, Jürgen Spilker
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The aim of this book is to characterize certain multiplicative and additive arithmetical functions by combining methods from number theory with some simple ideas from functional and harmonic analysis. The authors achieve this goal by considering convolutions of arithmetical functions, elementary mean-value theorems, and properties of related ...
Wolfgang Schwarz, Jürgen Spilker
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The Arithmetic Optimization Algorithm
Computer Methods in Applied Mechanics and Engineering, 2021Laith Mohammad Abualigah +2 more
exaly