Second order differential invariants of linear frames.
This paper shows that the simplicial type of a finite simplicial complex is determined by its algebra of polynomial functions on the baricentric coordinates with coefficients in any integral domain. The link between and is done through certain admissible matrix associated to in a natural way. This result was obtained for the real numbers by I. V. Savel’ev [5], using methods of real algebraic geometry. D. Kan and E. Miller had shown in [2] that determines the homotopy type of the polyhedron...
This paper describes some recent research on parametric problems in the calculus of variations. It explains the relationship between these problems and the type of problem more usual in physics, where there is a given space of independent variables, and it gives an interpretation of the first variation formula in this context in terms of cohomology.