nichtverschwindende

Nichtverschwindende is a German term meaning non-vanishing or persistent. In German-language texts it is used to describe quantities, functions, or objects that do not disappear or reduce to zero under specified conditions. The expression can serve as an adjective, as in nichtverschwindende Funktionen, or as a nominalized form like die Nichtverschwindenden, depending on context and grammar.

In mathematics the closest standardized notion is nowehre vanishing. A function f on a domain is nowhere vanishing if f(x) ≠ 0 for every x in the domain. This idea also appears for sections of a fiber bundle that are nowhere zero, or for matrices with nonzero determinant, which are invertible and do not vanish in solution sets. Nowhere-vanishing objects are important in analysis and geometry because their nonzero character cannot be eliminated by restricting the domain, and they often allow for division by the function or the definition of logarithms locally.

In physics and engineering, a related usage describes quantities that persist without decay under the dynamics considered, such as non-dissipative signals or conserved currents. In philosophy or linguistics, the term may be used metaphorically to denote ideas, memories, or meanings that endure across contexts.

Usage notes: Nichtverschwindende is primarily a German-language term and is not a universally standardized technical term across disciplines. Readers may translate the concept as “non-vanishing,” “nowhere vanishing,” or “persistent,” depending on context. Related expressions include beständig, dauerhaft, or unverändert when referring to persistence rather than mathematical non-zeroness.