nonvanishing

English

Etymology

From non- +‎ vanishing.

Adjective

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 $h$, which is a solution of (2.1), we consider $\Omega$ as above and we define
     $\Omega _{i}=d\Omega (e_{i}),\;\;\;W={\frac {\Omega }{h}}$

   • 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 $\lambda =0$ is generated by
     $\sigma _{1}(\lambda )$ holomorphic and nonvanishing at 0,
     $\left(\lambda \sigma _{2}(\lambda )+(log\lambda )\sigma _{1}(\lambda )\right)$ where a $\sigma _{2}$ 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 $F(T)$ be a nonzero element of the fraction field of $\mathbb {Z} _{p}[[T]]$ for which $F(\zeta -1)$ is well defined and nonvanishing for all $\zeta \in {\mathcal {Z}}$. Then $\{|F(\zeta -1)|\mid \zeta \in {\mathcal {Z}}\}$ is bounded above and below.