The inverse tempered stable subordinator is a stochastic process that models power law waiting times between particle movements, with an exponential tempering that allows all moments to exist. This paper shows that the probability density function of an inverse tempered stable subordinator solves a tempered time-fractional diffusion equation, and its ‘‘folded’’ density solves a tempered time-fr...

We consider Nambu-Poisson 3-algebras on three dimensional manifolds M3, such as the Euclidean 3-space R, the 3-sphere S as well as the 3-torus T . We demonstrate that in the Clebsch-Monge gauge, the Lie algebra of volume preserving diffeomorphisms SDiff(M3) is identical to the Nambu-Poisson algebra on M3. Moreover the fundamental identity for the Nambu 3-bracket is just the commutation relation...

This lecture is a short review on the role entropy plays in those classical dissipative systems whose equations of motion may be expressed via a Leibniz Bracket Algebra (LBA). This means that the time derivative of any physical observable f of the system is calculated by putting this f in a “bracket” together with a “special observable” F, referred to as a Leibniz generator of the dynamics. Whi...

Double (quasi-)Poisson algebras were introduced by Van den Bergh as non-commutative analogues of endowed with a bracket. In this work, we provide study morphisms double algebras, which relate to the $H_0$-Poisson structures Crawley-Boevey. We prove in particular that algebra structure defined for an arbitrary quiver only depends upon seen undirected graph, up isomorphism. derive from our result...

In this paper the well-known Dubrovin–Novikov problem posed as long ago as 1984 in connection with the Hamiltonian theory of systems of hydrodynamic type, namely, the classification problem for multidimensional Poisson brackets of hydrodynamic type, is solved. In contrast to the one-dimensional case, in the general case, a nondegenerate multidimensional Poisson bracket of hydrodynamic type cann...

We consider coefficient bodies Mn for univalent functions. Based on the Löwner-Kufarev parametric representation we get a partially integrable Hamiltonian system in which the first integrals are Kirillov’s operators for a representation of the Virasoro algebra. Then Mn are defined as sub-Riemannian manifolds. Given a Lie-Poisson bracket they form a grading of subspaces with the first subspace a...

We suggest kinetic models of dissipation for an ensemble of interacting oriented particles, for example, moving magnetized particles. This is achieved by introducing a double bracket dissipation in kinetic equations using an oriented Poisson bracket, and employing the moment method to derive continuum equations for magnetization and density evolution. We show how our continuum equations general...