Results 211 to 220 of about 76,587 (259)

Pipelining of arithmetic functions

1972 IEEE 2nd Symposium on Computer Arithmetic (ARITH), 1972
Two 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.
Thomas G. Hallin, Michael J. Flynn
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On an Arithmetical Function

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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Additive Arithmetic Functions on Arithmetic Progressions

Proceedings of the London Mathematical Society, 1987
For 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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On Arithmetical Shift for Walsh Functions

IEEE Transactions on Computers, 1972
A general expression for oo such that cal (k,θ+θ0)= sal (k,θ) is obtained and a proof is given. This new form of θ0 is more direct and thus easier to use than other existing formulas.
Chon Tam Le Dinh, Roger Y. Goulet
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Arithmetical Functions and Distributivity

Canadian Mathematical Bulletin, 1970
In 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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