Thom's theory of differential forms on simplical sets

Differential forms in the model theory of differential fields

Fields of characteristic zero with several commuting derivations can be treated as fields equipped with a space of derivations that is closed under the Lie bracket. The existentially closed instances of such structures can then be given a coordinate-free characterization in terms of differential forms. The main tool for doing this is a generalization of the Frobenius Theorem of differential geo...

Theory of hybrid differential equations on time scales

‎In this paper‎, ‎we develop the theory of hybrid differential‎ ‎equations on time scales‎. ‎An existence theorem for hybrid‎ ‎differential equations on time scales is given under Lipschitz ‎conditions‎. ‎Some fundamental fractional differential inequalities‎ ‎are also established which are utilized to prove the existence of‎ ‎extremal solutions‎. ‎Necessary tools are considered and the‎ ‎compa...

Herbert King Thoms

Herbert Thoms

The eventful chapters of contemporaneous medical history in Connecticut have not yet received the historian's scrutiny and are still only records scattered here and there in organization archives and miscellaneous correspondence. Many of us have been a part of these events and as participants are poorly qualified to place values on them. As in all history, one must await the developing vista of...

Complexes of Discrete Distributional Differential Forms and Their Homology Theory

Complexes of discrete distributional differential forms are introduced into finite element exterior calculus. Thus we generalize a notion of Braess and Schöberl, originally studied for a posteriori error estimation. We construct isomorphisms between the simplicial homology groups of the triangulation, the discrete harmonic forms of the finite element complex, and the harmonic forms of the distr...