supremum


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supremum

[su′prē·məm]
(mathematics)

supremum

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The average and exponential tests have higher power than the supremum.
However, it is worth mentioning that the hybrid numerical scheme proposed by Cen in [1], is an well-known fitted mesh method for solving singularly perturbed BVPs of the form (1.1)-(1.2) with discontinuous convection coefficient and the method is almost second-order accurate throughout the domain [0, 1] provided the perturbation parameter [epsilon] satisfies [epsilon] [much less than] [N.sup.-1], otherwise the method is at worst first-order uniformly convergent with respect to [epsilon] in the discrete supremum norm (see the detailed discussion in Section 6).
Using the standard argument of the Bertrand-Edgeworth model, we obtain the supremum and infimum of the price distributions as follows:
Since [mathematical expression not reproducible] and [mathematical expression not reproducible] for all [lambda] [member of] A, by the property of supremum for any [lambda] [member of] A, there exists a [mathematical expression not reproducible] such that [mathematical expression not reproducible]; that is, [mathematical expression not reproducible], which implies [mathematical expression not reproducible].
All definitions (supremum, infimum, and magnitude) and operations in IR* are defined the same as IR but computation over IR* is more complicated than IR.
The corresponding physical quantity would be the Yang-Mills action functional, but we get here an average value instead of a supremum. This questions the choice of the supremum in the formula
Let [mathematical expression not reproducible], Banach space of real bounded sequences x = {[x.sub.n]} with [mathematical expression not reproducible] and supremum norm
where [x.sub.1] and [x.sub.s] are called infimum and supremum, respectively.
where inf{[A.sup.[alpha].sub.1]} and inf{[A.sup.[alpha].sub.2]} are infimum of [A.sub.1] and [A.sub.2], and sup{[A.sup.[alpha].sub.1]} and sup{[A.sup.[alpha].sub.2]} are supremum of [A.sub.1] and [A.sub.2] (Figure 1).
Therefore g(*) attains its supremum over [R.sup.d] at some [eta] [member of] [R.sup.d], for which
According to Proposition 4.1 of [6], in the case of the -[DELTA] operator, the supremum of [mathematical expression not reproducible] is equal to L.