# upper bound

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Related to upper bound: Upper Bound and Lower Bound

## upper bound

[¦əp·ər ′bau̇nd]
(mathematics)
If S is a subset of an ordered set A, an upper bound b for S in A is an element b of A such that xb for all x belonging to A.
An upper bound on a function ƒ with values in a partially ordered set A is an element of A which is larger than every element in the range of ƒ.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

## upper bound

An upper bound of two elements x and y under some relation <= is an element z such that x <= z and y <= z.

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References in periodicals archive ?
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 is calculated.
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].
Upper Bound. 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.

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