Detectability of nontrivial topologies

Every Nontrivial Knot in S Has Nontrivial A-polynomial

We show that every nontrivial knot in the 3-sphere has a nontrivial A-polynomial. In Theorem 1 of [3], Kronheimer and Mrowka give a proof of the following remarkable theorem, thereby establishing the truth of the Property P conjecture. Theorem 0.1 (Kronheimer-Mrowka). Let K be any nontrivial knot in S and let M(r) be the manifold obtained by Dehn surgery on K with slope r with respect to the st...

On Nontrivial Approximation of CSPs

Nontrivial spontaneous synchronization.

The collective behavior of an ensemble of multimode stochastic oscillators is investigated. The oscillators are pulse coupled; they are able to emit pulses and to detect the pulses emitted by the others. As a function of the output intensity in the system they can operate in different modes having different pulsing periods. The system is designed to optimize the output intensity around a fixed ...

Detectability of Nonlinear Systems

We propose a definition of detectability for nonlinear systems. This definition generalizes naturally the standard property in the linear case, and is consistent with the “input to state stability” approach to controlled stability. We provide a characterization in terms of a dissipation inequality involving storage (Lyapunov) functions.

Nontrivial Galois Module Structure of . . .

We say a tame Galois field extension L/K with Galois group G has trivial Galois module structure if the rings of integers have the property that OL is a free OK [G]-module. The work of Greither, Replogle, Rubin, and Srivastav shows that for each algebraic number field other than the rational numbers there will exist infinitely many primes l so that for each there is a tame Galois field extensio...