Jacobi brackets (a generalization of standard Poisson brackets in which Leibniz's rule is replaced by a weaker condition) are extended to brackets involving an arbitrary (even) number of functions. This new structure includes, as a particular case, the recently introduced generalized Poisson structures. The linear case on simple group man-ifolds is also studied and non-trivial examples (differe...

Although the nonhomogeneous Poisson process has been intensively applied in practice, it also its own limitations. In this paper, a new counting model (called Generalized Gamma Process) is developed to overcome limitations of process. Initially, some basic stochastic properties are derived. It will be seen that includes both generalized Pólya and Lindley processes as special cases. The influenc...

In this paper we investigate Poisson-Lie transformation of dilaton and vector field J appearing in Generalized Supergravity Equations. While the formulas literature work well for isometric sigma models, present examples which Equations are not preserved. Therefore, suggest modification these formulas.