Diskontinuierlichem

Diskontinuierlichem is a declined form of the German adjective diskontinuierlich, meaning not continuous or intermittent. It is used in technical and scientific writing to describe something that exhibits discontinuity, such as a break, gap, or abrupt change. The form diskontinuierlichem occurs in contexts requiring the dative singular masculine or neuter form, for example in a phrase like mit diskontinuierlichem Verhalten.

In mathematics and related fields, diskontinuierlich characterizes functions or sets with discontinuities. A function is diskontinuierlich at a point if it is not continuous there. Discontinuities can be classified as removable, jump, or infinite, depending on how the function behaves near the problematic point. The concept helps in analysis, modeling, and numerical computation where abrupt changes occur.

In physics, engineering and signal processing, discontinuities describe interfaces, phase boundaries, or abrupt changes in material properties, amplitude, or other observables. For instance, a piecewise constant signal has diskontinuierliche jumps at transition points, which influence how the signal is sampled or filtered.

In linguistics, diskontinuierliche Strukturen (discontinuous structures) refer to phenomena where related elements are separated by other material in the surface structure, such as non-adjacent dependencies in syntax. The term highlights how meaningful units can be related despite intervening elements.

Etymologically, diskontinuierlich derives from dis- (not) and continuus (continuous), with the German suffixes adapted into Diskontinuität and related adjectives. The concept appears across disciplines to denote a break from smooth, uninterrupted variation.