WWDC26：2026 年 6 月 8 日至 12 日 (太平洋时间)

This paper proves the existence of homeomorphic (diffeomorphic) complex 6-dimensional (7-dim) complete intersections that belong to components of the moduli space of different dimensions. These results are given as a supplement to earlier result on 5-dimensional complete intersections.

The relativistic second-order corrections at orders $mα^6$ and $mα^6(m/M)$ in hydrogen molecular ions are calculated. Convergence of numerical results is studied, which allows estimating the relative numerical uncertainty to be less then $10^{-5}$. This accuracy is sufficient to enable future improvement of theoretical predictions beyond the 1 ppt (part-per-trillion) precision level for the ro-vibrational transition frequencies.

Using simplifying assumptions that are related to the time reversal symmetry, a 1-dimensional family of 8-stage pseudo-symplectic Runge-Kutta methods of order (4, 8), i.e., methods of order 4 that preserve symplectic structure up to order 8, is derived. An example of 7-stage method of order (4, 9) is given.