We analyze isomonodromic deformations of rational connections on the Riemann sphere with Fuchsian and irregular singularities. The Fuchsian singularities are allowed to be of arbitrary resonant index; the irregular singularities are also allowed to be resonant in the sense that the leading coefficient matrix at each singularity may have arbitrary Jordan canonical form, with a genericity conditi...

A Las Vegas type probabilistic algorithm is presented for nding the Frobenius canonical form of an n n matrix T over any eld K. The algorithm requires O~(MM(n)) = MM(n) (logn) O(1) operations in K, where O(MM(n)) operations in K are suucient to multiply two n n matrices over K. This nearly matches the lower bound of (MM(n)) operations in K for this problem, and improves on the O(n 4) operations...

This paper is devoted to the analysis of covariant canonical formalism $F(R)$ gravity in Einstein frame. We also find transformation between formulation F(R) Jordan frame and frames we determine corresponding generating function.