I have very fond memories of high school geometry. Memorizing theorems wasn't too hard, and solving proofs was like solving the logic puzzles that I did for fun anyway. But the theorems were scattered ...

Elliptic equations play a central role in the study of steady-state phenomena across physics, engineering and geometry. Their analysis not only provides insights into the qualitative behaviour of ...

The Navier-Stokes equations are fundamental in fluid dynamics, describing the motion of incompressible viscous fluids. Their analysis is critical for understanding turbulence, stability, and flow ...

Mathematics is distinguished from the sciences by the freedom it enjoys in choosing basic assumptions from which consequences can be deduced by applying the laws of logic. We call the basic ...

Mathematical Proceedings of the Royal Irish Academy, Vol. 106A, No. 1 (JUNE 2006), pp. 97-113 (17 pages) We prove that two domains of holomorphy U and V in separable Fréchet spaces with the bounded ...

For functions f ∈ L1(Rn) we consider extensions to Rn × R+ given by convolving f with an approximate identity. For a large class of approximate identities we obtain a Fatou-type theorem where the ...