# closed intervals

## closed intervals

[¦klōzd ′in·tər·vəlz]
(mathematics)
A closed interval of real numbers, denoted by [a,b ], consists of all numbers equal to or greater than a and equal to or less than b.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
If [mathematical expression not reproducible] is a sequence of nested soft closed intervals satisfying the properties [I.sub.1] [contains or equal to] [I.sub.2] [contains or equal to] ...
Kosol, "Rate of convergence of S-iteration and Ishikawa iteration for continuous functions on closed intervals," Thai Journal of Mathematics, vol.
In [35], the bounds are obtained by the maximin theorem of continuous function on closed intervals for the finite element model.
Choose the closed intervals J and I such that J [subset] I = [a, b] and that for every [t.sub.0] [member of] J, the unique solution x(-; [t.sub.0], 0) with the initial condition ([t.sub.0], 0), exists on some open interval [mathematical expression not reproducible].
However, in spherical circle planes we may have two closed intervals of such touching circles in [K.sub.x], one consisting of separating circles and the other of nonseparating ones; we do not know whether even more involved situations may occur.
Nevertheless, the abovementioned operators are straightforward extensions of their respective proposals for the case of HFEs; they only focus on the endpoints of the closed intervals of interval-valued hesitant fuzzy elements (IVHFEs) on the basis of the characteristics of interval numbers and therefore are not rich enough to capture all the information contained in IVHFEs.
Our "augmentation" terminology does not mean to suggest that the intervals themselves are larger, just that the top and bottom elements of the corresponding closed intervals are longer.
Let [bar.x] = [[x.sup.-],[x.sup.+]] and [bar.y] = [[y.sup.-],[y.sup.+]] be two closed intervals in R.
defines a binary operation on the set of closed intervals. In case of division, it is assumed that 0 [member of] B.
A bi-interval representation of a bigraph G = (U,V; E) is a pair ([I.sub.U], [I.sub.V]) of sets of closed intervals such that [I.sub.U] = {[[l.sub.u], [r.sub.u]]|u [member of] U} and [I.sub.V] = {[[l.sub.v], [r.sub.v]]|v [member of] V}, and {u, v} [member of] E (G) if and only if [[l.sub.u], [r.sub.u]] [intersection] [[l.sub.v], [r.sub.v]] = 0 for u [member of] U and v [member of] V.
Because the stress S and strength R are functions of these interval variables respectively, they will vary within some closed intervals [S.sup.I] and [R.sup.I] .

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