The paper investigates the realization problem for a class of analytic nonlinear hybrid systems without autonomous switching. Similarly to the classical nonlinear realization theory the realization problem for hybrid systems is translated to a formal realization problem of a class of abstract systems defined on rings of formal power series. Necessary conditions are presented for existence of a ...

In this paper, we study the generalized derivation of a Lie sub-algebra algebra polynomial vector fields on $\mathbb{R}^n$ where $n\geq1$, containing all constant and Euler field, under some conditions sub-algebra.

Previous work (Pradines, 1966, Aof and Brown, 1992) has given a setting for a holon-omy Lie groupoid of a locally Lie groupoid. Here we develop analogous 2-dimensional notions starting from a locally Lie crossed module of groupoids. This involves replacing the Ehresmann notion of a local smooth coadmissible section of a groupoid by a local smooth coadmissible homotopy (or free derivation) for t...

A bi-Hamiltonian hierarchy of complex vector soliton equations is derived from geometric flows of non-stretching curves in the Lie groups G = SO(N + 1), SU(N) ⊂ U(N), generalizing previous work on integrable curve flows in Riemannian symmetric spaces G/SO(N). The derivation uses a parallel frame and connection along the curves, involving the Klein geometry of the group G. This is shown to yield...

Let R be a prime ring, H a generalized derivation of R and L a noncommutative Lie ideal of R. Suppose that usH(u)ut = 0 for all u ∈ L, where s ≥ 0, t ≥ 0 are fixed integers. Then H(x) = 0 for all x ∈ R unless char R = 2 and R satisfies S4, the standard identity in four variables. Let R be an associative ring with center Z(R). For x, y ∈ R, the commutator xy− yx will be denoted by [x, y]. An add...

A bi-Hamiltonian hierarchy of complex vector soliton equations is derived from geometric flows of non-stretching curves in the Lie groups G = SO(N + 1), SU(N) ⊂ U(N), generalizing previous work on integrable curve flows in Riemannian symmetric spaces G/SO(N). The derivation uses a parallel frame and connection along the curves, involving the Klein geometry of the group G. This is shown to yield...

An efficient and accurate computational approach is proposed for a nonconvex optimal attitude control for a rigid body. The problem is formulated directly as a discrete time optimization problem using a Lie group variational integrator. Discrete time necessary conditions for optimality are derived, and an efficient computational approach is proposed to solve the resulting two-point boundary-val...

some preliminaries about the integrable families of riccati equations and solutions structure of these equations in several cases are presented in this paper, then by using of definitions for fractional derivative we apply the new extended of tanh method to the perturbed nonlinear fractional schrodinger equation with the kerr law nonlinearity. finally by using of this method and solutions of ri...