we need to look closely at the resolution ofdescribed in [8] and [9]. Once we have this information, we apply the quadratically refined version of Bott’s residue formula, found in [19, Theorem 9.5]. This allows to proceed essentially as in [8], although one does need to extend the...
I alluded toDirty Britainsome time ago in this hither-yon postDirty Britain 1: Dog Eggs Bushwhich I hath renamed slightly to accord, and bring in line with, what is about to be a most wholesome little series. The aforementioned link concerns treading in turds, striding through stools, dodg...
The exact analytical solution for the plane S-wave, propagating along the axis of spirality in the simple 1-D anisotropic "simplified twisted crystal" model, is compared with four different approximate ray-theory solutions. The four different ray methods are (a) the coupling ray theory, (b) ...
LetK[[]]betheringofformalpowerseriesinthevariable. LetC[[]]bethesetofformalpowerserieswithcoefficientsinC,whichweview onlyasaK[[]]-module. AstarproductonC[[]]isanassociative,unital,K[[]]-bilinearmultiplication ⋆:C[[]]×C[[]]→C[[]], ...
In the sequel, we will need the approximation of 𝜁(𝑠+𝑖𝑡𝛼𝑘) by a certain absolutely convergent Dirichlet series. Let 𝜃>1/2 be a fixed number, 𝑣𝑛(𝑚)=exp{−(𝑚𝑛)𝜃},𝑚,𝑛∈ℕ, and 𝜁𝑛(𝑠)=∑𝑚=1∞𝑣𝑛(𝑚)𝑚𝑠. Since 𝑣...
The original plan was to bank at least three books in the series before dumping them in bulk, all at once, in order to manufacture momentum. But if the last few years have taught me anything, it’s that everyone and everything around me tends to drop dead, so I’m not making plans...