We introduce spin Calogero-Moser systems associated with root systems of simple Lie algebras and give the associated Lax representations (with spectral parameter) and fundamental Poisson bracket relations. Our analysis is based on a group-theoretic framework similar in spirit to the standard classical r-matrix theory for constant r-matrices. Systèmes de Calogero Moser à spins associés aux algèb...

In paper by I.T. Habibullin and our joint the algorithm for classification of integrable equations with three independent variables was proposed. This method is based on requirement existence an infinite set Darboux reductions notion characteristic Lie-Rinehart algebras. The applied cases different subclasses $u_{n,xy} = f(u_{n+1},u_n,u_{n-1}, u_{n,x},u_{n,y})$ special forms. Under this approac...

Liftings of endofunctors on sets to relations are commonly used capture bisimulation coalgebras. Lax versions have been in those cases where strict lifting fails bisimilarity, as well modeling other notions simulation. This paper provides tools for defining and manipulating lax liftings. As a central result, we define notion distributive law functor over the powerset monad, show that there is a...

Computability relative to a partial function f on the natural numbers can be formalized using notion of an oracle for this f. This generalized arbitrary combinatory algebras, yielding ‘adjoining algebra A’. A similar construction is known second-order functionals, but third-order case more difficult. In paper, we prove several results case. Given functional Φ A, show how construct A[Φ] where ‘c...

We consider some natural connections which arise between right-flat (p, q) para-conformal structures and integrable systems. We find that such systems may be formulated in Lax form, with a " Lax p-tuple " of linear differential operators, depending a spectral parameter which lives in (q − 1)-dimensional complex projective space. Generally, the differential operators contain partial derivatives ...

Four explicit finite difference schemes, including Lax-Friedrichs, Nessyahu-Tadmor, Lax-Wendroff and Lax-Wendroff with a nonlinear filter are applied to solve water hammer equations. The schemes solve the equations in a reservoir-pipe-valve with an instantaneous and gradual closure of the valve boundary. The computational results are compared with those of the method of characteristics (MOC), a...

Lie algebras a with complex underlying vector space V are
 studied that are automorphic respect to given linear
 dynamical system on , i.e., 1-parameter subgroup Gt ⊂
 Aut(a) ⊂ GL(V ). Each algebra imparts a
 algebraic structure the of trajectories of
 group Gt. The basics general automorphic
 described in terms eigenspace
 decomposition operatorM ∈ der(a) det...

we study topological von neumann regularity and principal von neumann regularity of banach algebras. our main objective is comparing these two types of banach algebras and some other known banach algebras with one another. in particular, we show that the class of topologically von neumann regular banach algebras contains all $c^*$-algebras, group algebras of compact abelian groups and cer...

since 2005 a new powerful invariant of an algebra has emerged using the earlier work of horvath, hethelyi, kulshammer and murray. the authors studied morita invariance of a sequence of ideals of the center of a nite dimensional algebra over a eld of nite characteristic. it was shown that the sequence of ideals is actually a derived invariant, and most recently a slightly modied version o...