We describe the reduction procedure for a symplectic Lie algebroid by a Lie subalgebroid and a symmetry Lie group. Moreover, given an invariant Hamiltonian function we obtain the corresponding reduced Hamiltonian dynamics. Several examples illustrate the generality of the theory.

A new procedure named direct Hamiltonization gives another foundations to Hamiltonian Analytical Mechanics, since in this formalism the Hamiltonian function can be obtained for any mechanical system. The main change proposed in this procedure is that the conjugate momenta cannot be defined a priori, but instead of this, they are determinate as a consequence of a canonical description of the mec...

We have given some arguments that a two-dimensional Lorentz-invariant Hamiltonian may be relevant to the Riemann hypothesis concerning zero points of the Riemann zeta function. Some eigenfunction of the Hamiltonian corresponding to infinite-dimensional representation of the Lorentz group have many interesting properties. Especially, a relationship exists between the zero zeta function condition...

This paper investigates the asymptotical stabilization of the time-invariant and the time-varying Port-Hamiltonian (PH) systems via a new kinetic energy-shaping (KES) method. Firstly, a desired kinetic energy function is designed for the non-trivial points. Secondly, applying the KES method to the Hamiltonian function with the desired kinetic energy function builds some matching equations. Thir...

Hamiltonian cycles on planar random lattices are considered. The generating function for the number of Hamiltonian cycles is obtained and its singularity is studied. Hamiltonian cycles have often been used to model collapsed polymer globules[1]. A Hamiltonian cycle of a graph is a closed path which visits each of the vertices once and only once. The number of Hamiltonian cycles on a lattice cor...

Manoussakis, Y. and D. Amar, Hamiltonian paths and cycles, number of arcs and independence number in digraphs, Discrete Mathematics 105 (1992) 157-172. We let D denote a digraph with n vertices, independence number at least (Y and half-degrees at least k. We give (i) a function f(n, a) (respectively f (n, k, a)) such that any digraph with at least f(n, a) (respectively f(n, k, a)) arcs is Hamil...

Adaptive beamforming with Hamiltonian algorithm is proposed for ESPAR antenna. Hamilton’s equations describing the motion of particles are used to solve optimization problems. In an application of Hamiltonian algorithm to ESPAR antenna, the cost function for beamforming is considered as the potential energy. Although the kinetic energy, acted by momentums, does not appear in the issue of the be...

Karshon constructed the first counterexample to the log-concavity conjecture for the Duistermaat-Heckman measure: a Hamiltonian six manifold whose fixed points set is the disjoint union of two copies of T. In this article, for any closed symplectic four manifold N with b > 1, we show that there is a Hamiltonian circle manifold M fibred over N such that its DuistermaatHeckman function is not log...

In this paper we provide explicit formulas for the number of elements/subgroups/cyclic subgroups of a given order and for the total number of subgroups/cyclic subgroups in a finite Hamiltonian group. The coverings with three proper subgroups and the principal series of such a group are also counted. Finally, we give a complete description of the lattice of characteristic subgroups of a finite H...

Almost all d-regular graphs are Hamiltonian, for d ≥ 3 [8]. In this note we conjecture that in a similar, yet somewhat different, sense almost all cubic non-Hamiltonian graphs are bridge graphs, and present supporting empirical results for this prevalence of the latter among all connected cubic non-Hamiltonian graphs.