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 deened by a decomposable 3-vector eld. The key point is the proof of a lemma which tells that an n-vector (n 3) is decomposable ii all its contractions with up to n ? 2 covectors are decomposable. In the last years, several authors have studied genera...

It is shown that the elliptic algebra Aq,p(sl(2)c) at the critical level c = −2 has a multidimensional center containing some trace-like operators t(z). A family of Poisson structures indexed by a non-negative integer and containing the q-deformed Virasoro algebra is constructed on this center. We show also that t(z) close an exchange algebra when p m = q c+2 for m ∈ Z, they commute when in add...

We consider design of linear projection measurements for a vector Poisson signal model. The projections are performed on the vector Poisson rate,X ∈ R+, and the observed data are a vector of counts, Y ∈ Z+ . The projection matrix is designed by maximizing mutual information between Y and X , I(Y ;X). When there is a latent class label C ∈ {1, . . . , L} associated with X , we consider the mutua...

Basic properties of probability with Poisson distribution is used in obtaining the coefficient bound by subordination principle which fundamental purpose this work. A class analytic function $f:\xi \rightarrow \mathbb{C}$ unit disc $\xi :\{z\in\mathbb{C}:|z|<1\}$ established. Likewise known results Fekete-Szegö inequalities type and second Toeplitz determinant are obtained.