non-vanishingとは 意味・読み方・使い方

形容詞

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

   • 2013 November 11, C. Herbert Clemens, A Scrapbook of Complex Curve Theory (University Series in Mathematics)‎^[2], Springer Science & Business Media, →ISBN, OCLC 1001480441, page 61:

     This means that the vector space of solutions of (2.25) near ${\displaystyle \lambda =0}$ is generated by
     ${\displaystyle \sigma _{1}(\lambda )}$ holomorphic and nonvanishing at 0,
     ${\displaystyle \left(\lambda \sigma _{2}(\lambda )+(log\lambda )\sigma _{1}(\lambda )\right)}$ where a ${\displaystyle \sigma _{2}}$ 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 1007699203, page 205:

     Lemma 2 Let ${\displaystyle F(T)}$ be a nonzero element of the fraction field of ${\displaystyle \mathbb {Z} _{p}[[T]]}$ for which ${\displaystyle F(\zeta -1)}$ is well defined and nonvanishing for all ${\displaystyle \zeta \in {\mathcal {Z}}}$. Then ${\displaystyle \{|F(\zeta -1)|\mid \zeta \in {\mathcal {Z}}\}}$ is bounded above and below.