Arnold introduced invariants $J^+$, $J^-$ and $St$ for generic planar curves. It is known that both $J^+ /2 + St$ and $J^- /2 + St$ are invariants forgeneric spherical curves. Applying these invariants to underlying curves of knot diagrams, we canobtain lower bounds for the number of Reidemeister moves for uknotting. $J^- /2 + St$ works well for unmatched RII moves. However, it works only by halves for RI moves. Let $w$ denote the writhe for a knot diagram. We show that $J^- /2 + St \pm w/2$ works well also for RI moves, anddemonstrate that it gives a precise estimation for a certain knot diagram ofthe unknot with the underlying curve $r = 2 + \cos (n \theta/(n+1)),\ (0 \le\theta \le 2(n+1)\pi$).
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机译：Arnold为通用平面曲线引入了不变量$ J ^ + $，$ J ^-$和$ St $。已知$ J ^ + / 2 + St $和$ J ^-/ 2 + St $都是一般球形曲线的不变量。将这些不变量应用到结图的基础曲线上，我们可以得出用于Renotmeister移动的数量的下限。 $ J ^-/ 2 + St $非常适合无与伦比的RII动作。但是，对于RI动作，它只起作用一半。令$ w $表示结图的旋转。我们证明$ J ^-/ 2 + St \ pm w / 2 $对于RI的移动也很好地工作，并证明它对带有基础曲线$ r = 2 + \ cos（ n \ theta /（n + 1）），\（0 \ le \ theta \ le 2（n + 1）\ pi $）。
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