# harmonic mean

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## harmonic mean

[här′män·ik ′mēn]
(mathematics)
For n positive numbers x1, x2, …, xn their harmonic mean is the number n /(1/ x1+ 1/ x2+ … + 1/ xn ). Also known as harmonic average.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
Park and Park  extend the works Sun and Sun  by considering the interactions of any three aggregated arguments instead of any two to develop generalized fuzzy weighted Bonferroni harmonic mean (GFWBHM) operator and generalized fuzzy ordered weighted Bonferroni harmonic mean (GFOWBHM) operator.
In this paper, it was shown that, due to the choice of generator function, [A.sub.p], [G.sub.p], and [H.sub.p] means are reduced to ordinary arithmetic, geometric, and harmonic mean, respectively.
While the arithmetic and geometric means are ill-suited--mathematically undefined--to the kind of change in prices suggested by these scenarios, the harmonic mean converges to 2[p.sub.L] .
Name Notation Definition Arithmetic Mean A(a, b) [a + b]/2 Geometric mean G(a, b) [square root of [ab]] Harmonic Mean H(a, b) [2ab]/[a + b] Logarithmic Mean L(a, b) [[a - b]/[In a - In b]] when a [not equal to] b a when a [not equal to] b Heron Mean [H.sub.e](a, b) [a + [square root of [ab]] + b]/3 Identric Mean I(a, b) [1/e][([a.sup.a]/[b.sup.b]) .sup.[1/[a - b]]] Power Mean [M.sub.r](a, b) a when r[not equal to] 0 and a = b[[([[a.sup.r] + [b.sup.r]]/2)].sup.[1/r]] when r[not equal to] 0 [square root of [ab]] when r = 0 Now, we define the homogeneous function N [a, b; p, q; r, [alpha], [mu]] = [[{[[[a.sup.p] + [mu][M.sub.r]([a.sup.p], [b.sup.p]) + [alpha][b.sup.p]]/[[a.sup.q] + [mu][M.sub.r]([a.sup.q], [b.sup.q]) + [alpha][b.sup.p]]]}].sup.[1/[p - q]]].
The respiratory surface density was [RS.sub.d] = 122.99 [+ or -] 35.84 [mm.sup.-1] and the harmonic mean thickness of the air-hemolymph barrier was [tau]h = 0.14 [+ or -] 0.03 [micro]m (Fig.
To validate the superiority of the CSE based on the weighted harmonic mean of COPs in comparison to the IPLV index, three types of SCOPs are compared for a specified building (building A shown in Figure 1).
The asymptotic analysis of the Poisson expectation departs from the usual paradigm of analysis exemplified by [10, 14, 23] because of the coupling introduced by the harmonic mean, namely, the factor ([summation] [2.sup.-kj])-1.
We find that under remarkably weak requirements, essentially equi-proportional payout adjustment, the adjustment is uniquely given by the harmonic mean of the expected to realized survival proportions for each cohort.
The arithmetic and harmonic mean models correspond to parallel and perpendicular components and thus, as mentioned above, to upper [[lambda].sub.U] and lower [[lambda].sub.L] thermal conductivity limits of the layered media.
- Seasonal home and core ranges and maximum home ranges (Kaufman, 1962) were estimated using minimum convex polygon (home range) (Mohr, 1947) and harmonic mean (core range) (Dixon and Chapman, 1980).
Equation (1) is closely approximated by the harmonic mean (Wright 1938):

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