In this paper, we introduce and study fractional versions of the Bell–Touchard process, Poisson-logarithmic process generalized Pólya–Aeppli process. The state probabilities these compound Poisson processes solve a system differential equations that involves Caputo derivative order 0<β<1. It is shown are limiting cases recently introduced namely, counting We obtain mean, variance, covaria...

The Schouten-Nijenhuis bracket on the module of K\"ahler differentials is introduced. We recover Lichnerowicz's notion Poisson manifold by using universal property derivations. prove that a nondegenerate structure corresponds exactly to symplectic structure. Finally, we explore Hamiltonian vector fields in terms

In this paper we employ the construction of Dirac bracket for the remaining current of sl(2)q deformed Kac-Moody algebra when constraints similar to those connecting the sl(2)-WZW model and the Liouville theory are imposed and show that it satisfy the q-Virasoro algebra proposed by Frenkel and Reshetikhin. The crucial assumption considered in our calculation is the existence of a classical Pois...

We consider the double field formulation of closed bosonic string theory, and calculate Poisson bracket algebra symmetry generators governing both general coordinate local gauge transformations. Parameters these symmetries depend on a coordinate, defined as direct sum initial T-dual coordinate. When no antisymmetric is present, $C$-bracket appears Lie generalization in theory. With introduction...

We define a graded twisted-coassociative coproduct on the tensor algebra TW of any Zn-graded vector space W . If W is the desuspension space ↓V of a graded vector space V , the coderivations (resp. quadratic “degree 1” codifferentials, arbitrary odd codifferentials) of this coalgebra are 1to-1 with sequences πs, s ≥ 1, of s-linear maps on V (resp. Zn-graded Loday structures on V , sequences tha...

We develop a Hamiltonian discontinuous finite element discretization of a generalized Hamiltonian system for linear hyperbolic systems, which includes the rotating shallow water equations, the acoustic and Maxwell equations. These equations have a Hamiltonian structure with a bilinear Poisson bracket, and as a consequence the phase-space structure, mass and energy are preserved. We discretize t...