Water waves, mathematics & computation

Fourier Multipliers as Operators Fourier analysis is especially useful for linear, translation-invariant operators. In physical space, such an operator may involve derivatives…

Index Notation and Embedded Surfaces Index notation and differential geometry provide compact ways to describe vectors, tensors, and curved surfaces. This short note collects a…

In a Green's function \(G(x,x')\), the primed variable \(x'\) marks the source point — the location of a unit impulse — while \(x\) is the field point where the response is…

浓雾氤氲的森林，分不清是清晨还是黄昏，天边应该是有丝丝破碎的晨曦亦或是夕阳，还未走进你眼眸，便融化进了昏霭，染成一片模糊的光晕。你的思绪也仿若虚无之地，白茫茫一片，犹豫，抬起脚，犹豫，犹豫，犹豫，向前？向后？是追忆还是邂逅迷茫？

We show how the spectral relation ∑ Formula implies the physical-space operator identity ∑ Formula, by inverse Fourier transform and the commutation of \(\partial_z\) with the hori…