We study the (non-uniform) quantified constraint satisfaction problem QCSP(H) as H ranges over semicomplete digraphs. We obtain a complexity-theoretic trichotomy: QCSP(H) is either in P, is NP-hard or is Pspace-complete. The largest part of our work is the algebraic classification of precisely which semicompletes enjoy only essentially unary polymorphisms, which is combinatorially interesting i...

We give a construction of nonsmooth self-dual projective algebraic varieties. They appear as certain projectivized orbit closures for some linear actions of reductive algebraic groups. Applying this construction to adjoint representations, we obtain geometric characterization of distinguished nilpotent elements of semisimple Lie algebras [BC1], [BC2] (i.e., nilpotent elements whose centralizer ...

It is well known that a convolutional code is essentially a linear system defined over a finite field. In this paper we elaborate on this connection. We define a convolutional code as the dual of a complete linear behavior in the sense of Willems (1979). Using ideas from systems theory, we describe a set of generalized first-order descriptions for convolutional codes. As an application of these...

An analogue of the genuinely nonlinear character of an one-dimensional simple waves solution is identified and essentially used in the construction of some multidimensional extensions (simple waves solutions, regular interactions of simple waves solutions). A class of exact multidimensional gasdynamic solutions is constructed whose interactive elements are regular. Some specific aspects of Burn...