In this paper we show that the moduli space of twisted polygons in G/P , where G is semisimple and P parabolic, and where g has two coordinated gradations, has a natural Poisson bracket that is directly linked to G-invariant evolutions of polygons. This structure is obtained by reducing the quotient twisted bracket on GN defined in [23] to the moduli space GN/PN . We prove that any Hamiltonian ...

We discuss the notion of Volterra, l-Volterra and separable quadratic stochastic operators defined on (m− 1)-dimensional simplex, where l ∈ {0, 1, ...,m}. The l-Volterra operator is a Volterra operator if and only if l = m. We study the structure of the set of all Volterra and l-Volterra operators and describe their several fixed and periodic points. For m = 2 and m = 3 we describe behavior of ...

Starting with a Lie algebroid A over a space M we lift its action to the canonical transformations on the affine bundle R over the cotangent bundle T * M. Such lifts are classified by the first cohomology H 1 (A). The resulting object is a Hamiltonian algebroid A H over R with the anchor map from Γ(A H) to Hamiltonians of canonical transformations. Hamiltonian algebroids generalize Lie algebras...

The present paper describes a novel method of implementation of a stochastic optimization technique for the face recognition problem. The method proposed divides the original images into patches in space, and seeks a non-linear functional mapping using second-order Volterra kernels. The artificial bee colony optimization technique, a modern stochastic optimization algorithm, is used to derive o...

We consider nonlinear, probability measure{valued dynamical systems that generalise those classical Lotka{Volterra equations in which, to use ecological terminology, the total size of a nite number of populations of interacting species is conserved. In our generalisation there is a \di erent species" at each point of an arbitrary measurable space. Such in nitely{many{species analogues of the cl...

In this work, the existence and uniqueness solution of fractional nonlinear mixed integro-differential equation (FrNMIoDE) is guaranteed with a general discontinuous kernel based on position time-space L2Ω×C0,T, T<1. The FrNMIoDE conformed to Volterra-Hammerstein integral (V-HIE) second kind, after applying characteristics integral, in for Hammerstein term continuous time Volterra (VI) term....