# 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.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

## 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 ?
Typically, regression discontinuity uses a continuous variable as the outcome.
The audiological outcomes of patients with ossicular discontinuity were found to be very similar to fixation cases (Table 1); there was no statistical difference between the gap change (15.2 dB vs.
A single-beam RF MEMS switch with microstrip discontinuity t-line can be considered as a series switch.
Figure 2A depicts the discontinuity at age 62 for log suicide rates among all residents, while Figures 2B and 2C do the same for each gender.
In this context, discontinuity in infrastructures and services becomes a constraint [14, 15].
The discontinuity path of the proposed numerical model is compared with the experimental cracking pattern and with the discontinuity path computed by other authors [43-47].
Possible slope face orientations: The pole concentrations of the discontinuities data showed that the quarry sites had three major discontinuity planes (J1 J2 and J3); two of them were steeper while the other one was relatively flat (Table 2).
In order for the velocity field (4) to be compatible with the motion of rigid zones 1 and 2 (Figure 1), it is necessary to introduce velocity discontinuity lines through points A and B.
1 where [S.sub.i] represents the aperture of the ith discontinuity. [[epsilon].sub.r] and [[mu].sub.r] denote the relative permittivity and the relative permeability of the medium, respectively.
For delta shock wave, by a definition of measure solutions to (7), we derive the generalized Rankine-Hugoniot relation which describes the relation among the limit states on both sides of the discontinuity, location, propagation speed, weight, and the assignment of the component u on its discontinuity relative to the delta shock wave.

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