斜导数边值问题中Bessel向量积的零点
Zeros of Bessel cross-products coming from oblique derivative boundary value problems
摘要：
本文致力于（组合）贝塞尔向量积所产生的斜导数边值问题的拉普拉斯算子在一个圆环。我们表明，像他们的Neumann-Laplacian对应（而不像Dirichlet-Laplacian），他们拥有两种零点：那些可以由McMahon级数导出，并发散到无限的极限，和例外的，仍然有限。对于这两种情况下，我们找到一个固定的倾斜角和消失的厚度的环的渐近表达式。我们进一步提出了数字计算的零图，并讨论了它们的行为时，倾斜角的变化和厚度保持不变。
英文摘要：
The paper is devoted to (combinations of) Bessel cross-products that arise from oblique derivative boundary value problems for the Laplacian in a circular annulus. We show that like their Neumann-Laplacian counterpart (and unlike the Dirichlet-Laplacian), they possess two kinds of zeros: those that can be derived by McMahon series and diverge to infinity in the limit, and exceptional ones that remain finite. For both cases we find asymptotic expressions for a fixed oblique angle and vanishing thickness of the annulus. We further present plots of numerically computed zeros and discuss their behaviour when the oblique angle changes and the thickness remains fixed.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
