Restoration of controls under conditions of incomplete information on the dynamics of the system

The inverse dynamical problem of the restoration of the controls or parameters of a dynamical system which are unknown in advance is considered, using results from the observation of the motion of the system under conditions when there is incomplete information on the phase states of the system. It is assumed that, at appropriate actual instants of time, the observer only obtains certain information sets containing the actual phase states of the system. It is well known that this problem is ill posed. Constructive dynamic regularizing algorithms for solving the problem are constructed which posses the property of physical feasibility and are capable of working under real-time conditions while processing incoming information during the motion of the system and producing a result in dynamics as the motion develops.     

New families of flag-transitive linear spaces

In this paper, we construct new families of flag-transitive linear spaces with $q^{2n}$ points and $q^2$ points on each line that admit a one-dimensional affine automorphism group. We achieve this by building a natural connection with permutation polynomials of ${\mathbb{F}}_{q^2}$ of a particular form and following the scheme of Pauley and Bamberg in (2008) [14].     

Induction and Skolemization in saturation theorem proving

We consider a typical integration of induction in saturation-based theorem provers and investigate the effects of Skolem symbols occurring in the induction formulas. In a practically relevant setting we establish a Skolem-free characterization of refutation in saturation-based proof systems with induction. Finally, we use this characterization to obtain unprovability results for a concrete saturation-based induction prover.     

Threshold functions for incidence properties in finite vector spaces

The main purpose of this paper is to provide threshold functions for the events that a random subset of the points of a finite vector space has certain properties related to point-flat incidences. Specifically, we consider the events that there is an ℓ-rich m-flat with regard to a random set of points in ${\mathbb{F}}_q^n$, the event that a random set of points is an m-blocking set, and the event that there is an incidence between a random set of points and a random set of m-flats. One of our key ingredients is a stronger version of a recent result obtained by Chen and Greenhill (2021).     

Construction of extremal Type II Z2k-codes

We give methods for constructing many self-dual ${\mathbb{Z}}_m$-codes and Type II ${\mathbb{Z}}_{2k}$-codes of length 2n starting from a given self-dual ${\mathbb{Z}}_m$-code and Type II ${\mathbb{Z}}_{2k}$-code of length 2n, respectively. As an application, we construct extremal Type II ${\mathbb{Z}}_{2k}$-codes of length 24 for $k=4,5,\dots ,20$ and extremal Type II ${\mathbb{Z}}_{2k}$-codes of length 32 for $k=4,5,\dots ,10$. We also construct new extremal Type II ${\mathbb{Z}}_4$-codes of lengths 56 and 64.