We investigate different sets of operations on languages which results in corresponding algebraic structures, viz. in different types of full AFL’s (full Abstract Family of Languages). By iterating control on ETOL-systems we show that there exists an infinite sequence Cm (m ≥ 1) of classes of such algebraic structures (full AFL-structures): each class is a proper superset of the next class (Cm ...

Flat systems, an important subclass of nonlinear control systems introduced via differential-algebraic methods, are defined in a differential geometric framework. We utilize the infinite dimensional geometry developed by Vinogradov and coworkers: a control system is a diffiety, or more precisely, an ordinary diffiety, i.e. a smooth infinite-dimensional manifold equipped with a privileged vector...

We study a natural question in the Iwasawa theory of algebraic curves genus $$>1$$ . Fix prime number p. Let X be smooth, projective, geometrically irreducible curve defined over field K $$g>1$$ , such that Jacobian has good ordinary reduction at primes above an odd p and for any integer $$n>1$$ let $$K_n^{(p)}$$ denote degree- $$p^n$$ extension contained $$K(\mu _{p^{\infty }})$$ prove explici...

Using a known algebraic result, we obtain finite polynomial programming reformulation of semi-infinite program modeling the aircraft deconfliction problem via subliminal speed regulation. Solving yields better results than state art for most tested instances.

Abstract The method of blowing up points indeterminacy certain systems two ordinary differential equations is applied to obtain information about the singularity structure solutions corresponding non-linear equations. We first deal with so-called Painlevé example, which passes test, but have more complicated singularities. Resolving base in equivalent system we can explain singularities origina...

A short review is given of how to apply the algebraic Heisenberg quantization scheme to a system of identical particles. For two particles in one dimension the approach leads to a generalization of the Bose and Fermi description which can be expressed in the form of a 1/x statistics interaction between the particles. For an N-particle system it is shown how a particular infinite-dimensional alg...

We calculate the lower Controlled Algebraic K-theory of any finitely generated infinite subgroup of SL(3, Z), the group of 3 × 3 integral matrices of determinant 1.