We show that Carathéodory's conjecture on umbilical points of closed convex surfaces may be reformulated in terms of the existence of at least one umbilical point in the graphs of functions f: R 2 → R ...

Left graph follows the conventional approach of plotting the energy spectrum, E(k), where energy is a is distributed across ...

SIAM Journal on Applied Mathematics contains research articles on mathematical methods and their applications in the physical, engineering, financial, and life sciences. Publisher Information "The ...