# Discontinuity

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## discontinuity

[dis‚känt·ən′ü·əd·ē]
(electromagnetism)
An abrupt change in the shape of a waveguide. Also known as waveguide discontinuity.
(geology)
An interruption in sedimentation.
A surface that separates unrelated groups of rocks.
(geophysics)
A boundary at which the velocity of seismic waves changes abruptly.
(mathematics)
A point at which a function is not continuous.
(metallurgy)
The place where the structural nature of a weldment is interfered with because of the materials involved or where the mechanical, physical, or metallurgical aspects are not homogeneous.
(physics)
A break in the continuity of a medium or material at which a reflection of wave energy can occur.

## Discontinuity

(or point of discontinuity), a value of the argument at which the continuity of a function is violated. In the simplest case, continuity is violated at some point a in the sense that the right and left limits

exist, but at least one of them differs from f(a). When this occurs, a is called a jump discontinuity of f, or the discontinuity of the first kind.

If f(a + 0) = f(a – 0), the discontinuity is said to be removable, since f(x) becomes continuous at a if we set f(a) = f(a + 0) = f(a – 0). For example, the point a = 0 is a removable discontinuity of the function

since f is continuous at 0, if we set f(0) = 1. If, however, the jump δ = f(a + 0) – f(a – 0) of the function f(x) at the point is nonzero, then a is a discontinuity for any definition of the value of f(a). An example of such a discontinuity is the point a = 0 for the function f(x)= arc tan 1/x. In this case, the function may not be defined at the point a. The jump discontinuity is called regular if the condition f(a) = ½[f(a – 0) + f(a + 0)] is satisfied. If either of the one-side limits does not exist, then the point a is called the discontinuity point of the second kind. Examples are the point a = 2 for the function f(x) = 1/(x – 2) and the point a = 0 for f(x) = sin 1/x.

References in periodicals archive ?
CASE : Considering slope face orientation of 69/318 and stereographic projection of mean discontinuity planes drawn through DIPS showed a phenomena of kinematic instability (Figure-4).
The internal friction angles of the discontinuity planes vary from 24" to 33", which were obtained from the laboratory tests for each slope, and these angles were used for the kinematic analyses (Table 3).
Once the GSM of each abrupt discontinuity has been calculated, we have to determine the total GSM of a cascaded set of abrupt discontinuities.
Some mature organizations have embraced this discontinuity by encouraging customers to make on-line purchases, but also come into the stores.
The larger the discontinuity, the more high-frequency components that reflect to the source and the fewer that get launched into the transmission line.
GAMMA]1 = coefficient of reflection due to a discontinuity at the interface
He is concerned mostly about the direction of contemporary New Testament scholarship which he feels waters down the discontinuity of Jesus from his Jewish roots.
have made two additions to the Climetrix weather derivative trading and risk management system: a discontinuity detection service for a number of the most frequently traded stations and enhanced historical Canadian temperature data.
When a discontinuity gap between what we expect and what happens becomes wide enough to cause us concern, we come to believe that we have a problem.
When a physical discontinuity (cracks, voids, seams) is present, it alters the interaction between the two magnetic fields.

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