# Discontinuity

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Related to Discontinuity: MohoroviCiC discontinuity, discontinuity theory

## 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 ?
Three different slope faces (called SN-1, SN-2 and SN-3) were defined for the study based on their discontinuity properties (Figs 4b, c, d).
And for many, perhaps even all, of the most important themes, I believe it will not be difficult to find both continuity and discontinuity on different levels and from different perspectives.
Ideal opening size with respect to discontinuity geometry and frequency;
Some mature organizations have embraced this discontinuity by encouraging customers to make on-line purchases, but also come into the stores.
Specifically, we assume that only one jump discontinuity can exist between two neighboring points.
The fundamental source of the discontinuity is that the border is being interpolated twice according to two different covariance matrices.
The larger the discontinuity, the more high-frequency components that reflect to the source and the fewer that get launched into the transmission line.
The Climetrix discontinuity detection service relies on continuous statistical analysis and improved metadata to monitor daily temperature data for the most commonly traded weather stations.
Basically, any discontinuity that appreciably alters the normal flow of eddy currents can be detected by eddy current inspection.
In fact, in a patient with a missing incus and ossicular discontinuity, the tympanogram should have revealed an axis-deviation curve.
A detailed stress analysis by finite element can determine discontinuity stresses.

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