Explore the profound connection between Euler's Identity and the Taylor series, two foundational concepts in mathematics. This overview explains how the expansion of exponential functions using the ...

For centuries, mathematicians have sought to understand and model the motion of fluids. The equations that describe how ripples crease the surface of a pond have also helped researchers to predict the ...

In this paper, we study the point vortex method for 2-D Euler equation of incompressible flow on the half plane, and the explicit Euler's scheme is considered with ...

We derive a new variational principle, leading to a new momentum map and a new multisymplectic formulation for a family of Euler–Poincaré equations defined on the Virasoro–Bott group, by using the ...