Mittelinearne

Mittelinearne is a term that appears in a small set of European mathematical and linguistic texts but does not have a single, widely accepted definition. In general usage, it denotes a notion of linear behavior tied to a central or intermediate structure, rather than a global linearity property.

Etymology and usage

The word is formed from roots akin to “middle/mid” (mittell, mitt) and “linear,” reflecting an idea of linearity restricted to a middle region or component. Because the term is not standardized, its precise meaning can vary between authors or disciplines. Readers encountering mittelinearne are advised to consult the specific definition given in the source, as interpretations may differ.

Common interpretations

- Localized linearity: A map or relation is said to be mittelinear if it is linear when restricted to a central substructure, such as a subspace or subinterval, while allowing non-linear behavior elsewhere.

- Middle-interval linearity: A function may be piecewise defined with a central interval on which the function behaves linearly, and non-linear behavior on the outer parts.

- Context-dependent property: In some texts, mittelinearity may refer to a symmetry or linear relation that holds only under a certain set of middle parameters or conditions.

Examples

A simple illustration is a function f: R -> R that satisfies f(x) = kx for all x in the interval [-1, 1], but is defined differently outside that interval. Such a function exhibits linear behavior on a central region while permitting non-linear definitions beyond it.

See also

Linear function, piecewise linear, semi-linear, localized properties. Note that due to the term’s lack of standardization, interpretation should rely on the source’s stated definition.