multiplicative inverse

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multiplicative inverse

[‚məl·tə′plik·əd·iv ′in‚vərs]
(mathematics)
In a mathematical system with an operation of multiplication, denoted ×, the multiplicative inverse of an element e is an element ē such that e × ē = ē × e = 1, where 1 is the multiplicative identity.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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Murthy, Smarandache reciprocal function and an elementary inequality, Smarandache Notions Journal, 11(2000), No.1-2-3, 312-315.
[8] Liping Ding, On the Smarandache reciprocal function and its mean value, Scientia Magna.
In this paper, we using the elementary method to study the solvability of an equation involving the Smarandache reciprocal function [S.sub.c](n) and P(n), and give a new critical method for twin primes.
[2] A.Murthy, Smarandache reciprocal function and an elementary inequality, Smarandache Notions Journal, 11(2000), No.
After Stage 1 training, she accurately constructed 10 of 12 formulas matching the novel array of data points; however, when she was exposed to a set of curvefitting reciprocal functions during Baseline 2, she was unable to input any formulas matching these functions.
The relationships among the reciprocal functions of the estimates are
The reciprocal functions also bear the same relationships to R([beta]) as do the estimates
In considering biases for the reciprocal functions, it should be noted that ER(z) and the variance of R(z) do not exist because can be zero.
The arithmetic mean of the reciprocal functions of b estimates [z.sub.i] of z is
In table 1 we give the parametric values of [beta] and [G.sub.ST] and the corresponding reciprocal functions for SB's values of N, n, [mu], m, but for a complete census of the population (M = 128, r = 100) as well as for a sample (M = 25, r = 10).