Specifically, we consider upper bound
constraints dk given as dk =[mathematical expression not reproducible]; see (11).
The following theorem shows an exact expression for the upper bound
[[bar.[rho]].sub.R] in a closed form.
In this section, we evaluate the partition function in the presence of the upper bound
In the above formula, the nonlinear shear strength index [[phi].sub.t] can be optimized by the least energy principle when the upper bound
Thus, the deviation as the percent absolute error with respect to solar PV system performance is calculated in both the lower bound and upper bound
sections from the result of the crisp value of solar PV system performance.
Take an arbitrary total ordered subset N [subset] [OMEGA]/ ~, next, to show that the set N has an upper bound
in [OMEGA]/ ~.
The effectiveness of this test depends on the current value of the upper bound
; that is, tighter upper bound
values lead to more effectiveness in the test.
The lower and upper bounds
of sin([[THETA].sup.I.sub.n]) and cos([[THETA].sup.I.sub.n]) are given by
In Figure 5(d), the control measure [w.sub.4] is at upper bound
at the beginning and after 140 days it rapidly drops to the lower bound at the final time.
The upper bound
of p(q) is [mathematical expression not reproducible] for 0 < r < 0.5, w = ([D.sub.1]/2)/[square root of ([[sigma].sup.2.sub.1]/[n.sub.1] + [[sigma].sup.2.sub.2]/[n.sup.2])], where [mathematical expression not reproducible] is the t-distribution function with [n.sub.1] + [n.sub.2] - 2 degrees of freedom and [mathematical expression not reproducible] is the inverse function of [mathematical expression not reproducible].
. We now obtain an upper bound
of R([t.sub.0], [A.sub.i,j] + [d.sub.i]) of the total amount of processor time demand.
To use a lower-dimensional transformation F for SSDD, we need to find an upper bound
function upper([mathematical expression not reproducible]) that satisfies (1), where [??] and [??] are f-dimensional feature vectors transformed from n-dimensional vectors, [??] and [??], respectively, by the transformation F.