We characterize Poisson and Jacobi structures by means of complete lifts of the corresponding tensors: the lifts have to be related to canonical structures by morphisms of corresponding vector bundles. Similar results hold for generalized Poisson and Jacobi structures (canonical structures) associated with Lie algebroids and Jacobi algebroids. MSC 2000: 17B62 17B66 53D10 53D17

The characterization of the Nambu-Poisson n-tensors as a subfamily of the generalized Poisson ones recently introduced (and here extended to the odd order case) is discussed. The homology and cohomology complexes of both structures are compared, and some physical considerations are made.

Now a days, an important and interesting alternative in the control of tick-infestation in cattle is to select resistant animals, and identify the respective quantitative trait loci (QTLs) and DNA markers, for posterior use in breeding programs. The number of ticks/animal is characterized as a discrete-counting trait, which could potentially follow Poisson distribution. However, in the case of ...

Statistical distributions of geometrical characteristics concerning the Poisson Voronoi cells, namely, Voronoi cells for the homogeneous Poisson point processes, are numerically obtained in twoand three-dimensional spaces based on the computer experiments. In this paper, ten million and five million independent samples of Voronoi cells in twoand three-dimensional spaces, respectively, are gener...

A class of n-ary Poisson structures of constant rank is indicated. Then, one proves that the ternary Poisson brackets are exactly those which are defined by a decomposable 3-vector field. The key point is the proof of a lemma which tells that an n-vector (n ≥ 3) is decomposable iff all its contractions with up to n− 2 covectors are decomposable. In the last years, several authors have studied g...

We present the third in the series of papers describing Poisson properties of planar directed networks in the disk or in the annulus. In this paper we concentrate on special networks Nu,v in the disk that correspond to the choice of a pair (u, v) of Coxeter elements in the symmetric group S n and the corresponding networks N u,v in the annulus. Boundary measurements for Nu,v represent elements ...

A class of n-ary Poisson structures of constant rank is indicated. Then, one proves that the ternary Poisson brackets are exactly those which are defined by a decomposable 3-vector field. The key point is the proof of a lemma which tells that an n-vector (n ≥ 3) is decomposable iff all its contractions with up to n − 2 covectors are decomposable. In the last years, several authors have studied ...

An introduction to inhomogeneous Poisson groups is given. Poisson inhomogeneous O(p, q) are shown to be coboundary, the generalized classical Yang-Baxter equation having only one-dimensional right hand side. Normal forms of the classical r-matrices for the Poincaré group (inhomogeneous O(1, 3)) are calculated.

Virginia Kiryakova Dedicated to the 75th anniversary of Professor Gary Roach Abstract A generalization of the Poisson-type integral transformation proposed by Dimovski is applied to hyper-Bessel differential equations of arbitrary order, as a transmutation operator. By this method, their solutions are written in an explicit form, by evaluating operators of the generalized fractional calculus of...

A Z-graded Lie bracket { , }P on the exterior algebra Ω(M) of differential forms, which is an extension of the Poisson bracket of functions on a Poisson manifold (M,P ), is found. This bracket is simultaneously graded skew-symmetric and satisfies the graded Jacobi identity. It is a kind of an ‘integral’ of the Koszul-Schouten bracket [ , ]P of differential forms in the sense that the exterior d...