nonvanishing

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English

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Etymology

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From non- +‎ vanishing.

Adjective

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nonvanishing (not comparable)

  1. (mathematics) Of an expression, especially a function, being nonzero at a value, everywhere on a specified set, or on the entire domain.
    • 2001 January 1, A. A. Coley, Bäcklund and Darboux Transformations: The Geometry of Solitons : AARMS-CRM Workshop, June 4-9, 1999, Halifax, N.S., Canada (CRM proceedings & lecture notes)‎[1], American Mathematical Soc., →ISBN, page 153:
      For each nonvanishing function , which is a solution of (2.1), we consider as above and we define
    • 2013 November 11, C. Herbert Clemens, A Scrapbook of Complex Curve Theory (University Series in Mathematics)‎[2], Springer Science & Business Media, →ISBN, →OCLC, page 61:
      This means that the vector space of solutions of (2.25) near is generated by
      holomorphic and nonvanishing at 0,
      where a is holomorphic and nonvanishing at 0.
    • 2017 October 19, Jim Cogdell, Ju-Lee Kim, Chen-Bo Zhu, Representation Theory, Number Theory, and Invariant Theory: In Honor of Roger Howe on the Occasion of His 70th Birthday (Progress in Mathematics)‎[3], Birkhäuser, →ISBN, →OCLC, page 205:
      Lemma 2 Let be a nonzero element of the fraction field of for which is well defined and nonvanishing for all . Then is bounded above and below.