We provide some details about the recently discovered integrable systems implied by commutativity of $W$ operators along rays on plane roots $w_\infty$-algebra. The simplest system this type is rational Calogero model, other escaped attention in past. Existence these intimately tied to very interesting WLZZ matrix models, which are now under intensive study.

This article shows how the external gravity force on core of planet leads to appearance magnetic field (MF) planet. How this provides acceptable conditions for existence life. Natural phenomena, which can easily be explained using proposed mechanism interaction planets, such as earthquakes, mountain formation, ocean currents, tides, time jumps, changes in duration day, periodic Solar activity a...