# Translating “beschränkt” in a mathematical/physical context

Wolfgang Paul (not Wolfgang Pauli, another Nobel Prize winner) wrote a three-page article which got him a Nobel prize in 1989: Ein neues Massenspektrometer ohne Magnetfeld. It contains the following sentence:

Diese Gl. (3) hat nur in gewissen Bereichen der Parameter λ und q sog. „stabile" Lösungen, d. h. Lösungen, die bei beliebigen Anfangsbedingungen für alle Werte von ζ beschränkt bleiben.

I was trying to machine-translate a portion of it for quoting it in an article, but the symbols mess up. If I crudely translate it myself I arrive at:

This equation (3) has in only certain ranges of the parameter λ and q so-called stable solutions, i.e. solutions, at arbitrary beginning conditions for all values of ζ remain limited.

DeepL’s translation is:

This equation (3) only has so-called “stable” solutions in certain ranges of the parameters λ and q, i.e. solutions that remain limited for all values of ζ under any initial conditions.

I am not happy with limited as a translation for beschränkt here, as it does not make sense to me. What does it mean here and how could I translate it?

• Thanks, I got the answer for identifying relative pronouns from another book. The word order changes and the verb is at the end. May 2, 2019 at 2:27

i.e. solutions that are bounded for all values of zeta under any initial conditions.

Solutions to differential equations can be distinguished in bounded and unbounded cases.

In case like these (also in the reverse case, where you need a technical term translated from English to German), it often helps looking for the term in the localized versions of Wikipedia. This German article about 'Beschränktheit' is linked to an English article about 'Bounded set'.

• That was a good tip. Is there is way to identify when the definite article is serving as a "relative pronoun" "solutions that are..." How do we recognize that die here is a relative pronoun? May 1, 2019 at 0:24