Mechanical systems (i.e., one-dimensional field theories) with constraints are the focus of this paper. In classical theory, infinite-dimensional targets considered as well (this then encompasses also higher-dimensional theories in hamiltonian formalism). The properties Hamilton–Jacobi (HJ) action described details and several examples explicitly computed (including...

We show how Andrews' generating functions for generalized Frobenius partitions can be understood within the theory of Eichler and Zagier as specific coefficients certain Jacobi forms. This reformulation leads to a recursive process which yields explicit formulas partition in terms infinite q-products. In particular, we that examples our result easily reestablish previously known formulas, descr...

Under usual assumptions on the Hamiltonian, we prove that any viscosity solution of the corresponding Hamilton-Jacobi equation on the manifold M is locally semiconcave and C loc outside the closure of its singular set (which is nowhere dense in M). Moreover, we prove that, under additional assumptions and in low dimension, any viscosity solution of that Hamilton-Jacobi equation satisfies a gene...

The simple supersymmetric approach recently used by Dutt, Gangopadhyaya, and Sukhatme for spherical harmonics is generalized to Jacobi equation, including also the intermediate Gegenbauer case. Resumen. Un procedimiento supersimétrico simple recientemente usado por Dutt, Gangopadhyaya y Sukhatme para los harmonicos esféricos, es generalizado a la ecuacion de Jacobi, incluyendo tambien el caso i...