# Discontinuity

(redirected from discontinuities)
Also found in: Dictionary, Thesaurus, Medical, Legal, Wikipedia.
Related to discontinuities: Jump discontinuity

## 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 ?
Analysts Examine Disruptive Discontinuities During Gartner Symposium/ITxpo 2007, October 7-12, in Orlando
Identify potential discontinuities through an analysis of system-related functions and customer-related functions
It is to be expected that such predictor will often fit well to the local signal properties and make it possible for the wavelets to contract in the neighbourhood of signal discontinuities.
The working groups wanted a smooth curve for the benefit buildup pattern, avoiding discontinuities that distort termination and retirement patterns.
Darrell Brooks, partner at The Buncke Clinic and Principal Investigator of the study, declared, "The data from the study will help change the treatment paradigm for surgeons with patients that have peripheral nerve discontinuities.
Using the best of series and parallel termination in a new analog technology, series termination is best for reflections from impedance discontinuities and parallel termination is best for loads distributed along the cable.
The wet method of inspection is more sensitive than the dry method and can detect smaller or finer discontinuities due to the smaller size of the iron particles.
But disruptions or discontinuities can force strategic change.
Such sharp discontinuities in grain direction look like defects in a partially ordered liquid-crystal system, Kramer says.
Such debate, I think, is what the editors of Discontinuities aspired both to document and to promote, and their collection goes some way toward realizing those aspirations.

Site: Follow: Share:
Open / Close