# jump discontinuity

## jump discontinuity

[′jəmp dis‚känt·ən′ü·əd·ē]
(mathematics)
A point a where for a real-valued function ƒ(x) the limit on the left of ƒ(x) as x approaches a and the limit on the right both exist but are distinct.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
In , an algorithm (EDAS-3) to approximate the jump discontinuity set of functions defined on subsets of R based in these methods was proposed.
The present paper shows an accurate algorithm (DA3DED) that can obtain a point based representation of the jump discontinuity set of a 3D image.
EDAS-1 is an algorithm to approximate the jump discontinuity set of functions of one variable.
In this last case, it is possible that the discontinuity surface is nonsmooth and this makes it necessary to consider small discrete rectangles to obtain a detailed description of the jump discontinuity set.
In fact, many procedures to detect 3D edges assume that the jump discontinuity set is smooth.
Keywords: Jump discontinuity point, [F.sub.[sigma]]-set, monotone operator, duality mapping.
Then, the set of all jump discontinuity points of f is at most a countable set in R.
Since monotone functions from R to R admit only jump discontinuity points, Froda's result has the following classical corollary:
As noted previously, the Gibbs phenomenon results from crossing over a jump discontinuity in the domain.
Note that these points do not correspond to the same point values in [S.sub.[[theta], but rather they are the points that surround the particular value [theta] for which we want to determine whether or not a jump discontinuity exists.
Specifically ms m increases, oscillations that occur in the neighborhood of a jump discontinuity can be misidentified as true edges, as is evident in Figure 3.2(d).
Specifically, we assume that only one jump discontinuity can exist between two neighboring points.

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