Wave-averaged balance: a simple example

Birkhoff's Theorem from a geometric perspective: A simple example

‎From Hilbert's theorem of zeroes‎, ‎and from Noether's ideal theory‎, ‎Birkhoff derived certain algebraic concepts (as explained by Tholen) that have a dual significance in general toposes‎, ‎similar to their role in the original examples of algebraic geometry‎. ‎I will describe a simple example that illustrates some of the aspects of this relationship‎. The dualization from algebra to geometr...

birkhoff's theorem from a geometric perspective: a simple example

‎from hilbert's theorem of zeroes‎, ‎and from noether's ideal theory‎, ‎birkhoff derived certain algebraic concepts (as explained by tholen) that have a dual significance in general toposes‎, ‎similar to their role in the original examples of algebraic geometry‎. ‎i will describe a simple example that illustrates some of the aspects of this relationship‎. the dualization from algebra to geometr...

A Singular Example for the Averaged Mean Curvature Flow

An embedded curve is presented which under numerical simulation of the averaged mean curvature flow develops first a loss of embeddedness and then a singularity where the curvature becomes infinite, all in finite time. This leads to the conjecture that not all smooth embedded curves persist for all times under the averaged mean curvature flow.

A Simple Example of Localized Parametric Resonance for the Wave Equation

Constructions on unbounded domains are more difficult as energy tends to radiate to infinity. It tends to leave the domain where the periodic variations can be amplifying. The examples we know use a ray, trapped by reflection or refraction ([C1], [C3], [CR], [PR]). The paper [PR] gives a definitive analysis for rays trapped by reflection using fine tools from microlocal analysis. [CR] has no bo...

Example Segmentations : Simple Scenes