We consider families of symmetric linear programs (LPs) that decide a property graphs (or other relational structures) in the sense that, for each size graph, there is an LP defining polyhedral lift separates integer points corresponding to with from those without property. show this equivalent, at most polynomial blow-up size, Boolean circuits threshold gates. In particular, when we polynomial...

We consider the Schrödinger partial differential equation of a rotating symmetric rigid molecule (symmetric rotor) driven by z-linearly polarized electric field, as prototype degenerate infinite-dimensional bilinear control system. By introducing an abstract perturbative criterium, we classify its simultaneous approximate controllability; based on this insight, numerically perform orientational...

Using semi-tensor product of matrices, the structures of several kinds of symmetric games are investigated via the linear representation of symmetric group in the structure vector of games as its representation space. First of all, the symmetry, described as the action of symmetric group on payoff functions, is converted into the product of permutation matrices with structure vectors of payoff ...

In this note, we discuss symmetric brackets on skew-symmetric algebroids associated with metric or symplectic structures. Given a pseudo-Riemannian structure, describe the induced by connections totally torsion in language of Lie derivatives and differentials functions. We formulate generalization fundamental theorem Riemannian geometry. particular, obtain an explicit formula Levi-Civita connec...