We present dichromatic and tree-expansion polynomials of integral gain graphs that underlie the problem of counting lattice points in the complement of an integral affinographic hyperplane arrangement. This is a step towards finding the universal Tutte invariant of rooted integral gain graphs. Mathematics Subject Classifications (2000): Primary 05C22; Secondary 05C15.

Let A and G be finite groups of relatively prime orders and assume that A acts on G via automorphisms. We study how certain conditions on G imply its solvability when we assume the existence of a unique A-invariant Sylow p-subgroup for p equal to 2 or 3. Mathematics Subject Classification (2010). Primary 20D20; Secondary 20D45.

In this paper we prove the existence of random attractors for the Navier–Stokes equations on 2 dimensional sphere under random forcing irregular in space and time. We also deduce the existence of an invariant measure. Mathematics Subject Classification (2010). Primary 35B41; Secondary 35Q35.

Some integral properties of zonal spherical functions, hypergeometric functions and invariant polynomials are studied for real normed division algebras.

Techniques from dynamical systems theory have been applied to the construction of transfers between unstable periodic orbits that have different energies. Invariant manifolds, trajectories that asymptotically depart or approach unstable periodic orbits, are used to connect the initial and final orbits. The transfer asymptotically departs the initial orbit on a trajectory contained within the in...