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.
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):