论文标题
序列通过数字分析延续：生物膜的坎汉姆模型的独特性
Sequence Positivity Through Numeric Analytic Continuation: Uniqueness of the Canham Model for Biomembranes
论文作者
论文摘要
我们证明了在生物膜的形状预测中产生的canham变异问题的属唯一性。证明是基于Yu和Chen的结果，该结果将变异问题降低到证明由线性复发与多项式系数定义的序列的非阴性。我们将D-FILITE函数的严格数字分析延续与从奇异性分析的经典边界相结合，以得出一个有效的指标，其中序列的渐近行为（正为正）主导了序列行为。然后，按计算检查剩余项的有限数量的积极性。
We prove solution uniqueness for the genus one Canham variational problem arising in the shape prediction of biomembranes. The proof builds on a result of Yu and Chen that reduces the variational problem to proving non-negativity of a sequence defined by a linear recurrence relation with polynomial coefficients. We combine rigorous numeric analytic continuation of D-finite functions with classic bounds from singularity analysis to derive an effective index where the asymptotic behaviour of the sequence, which is positive, dominates the sequence behaviour. Positivity of the finite number of remaining terms is then checked computationally.
