Let H be a Krull monoid with finite class group G such that every class contains a prime divisor. Then the global tame degree t(H) equals zero if and only if H is factorial (equivalently, |G| = 1). If |G| > 1, then D(G) ≤ t(H) ≤ 1 + D(G) (

We show that the computational power of the non-causal circuit model, i.e. the circuit model where the assumption of a global causal order is replaced by the assumption of logical consistency, is completely characterized by the complexity class UP∩coUP. An example of a problem in that class is factorization. Our result implies that classical deterministic closed timelike curves (CTCs) cannot ef...

Abstract Using a certain well-posed ODE problem introduced by Shilnikov in the sixties, Minervini proved currential “fundamental Morse equation” of Harvey–Lawson but without restrictive tameness condition for gradient flows. Here, we construct local resolutions flow section fiber bundle endowed with vertical vector field which is type every order to remove hypothesis from homotopy formula first...

The assumption that an AEC is tame is a powerful assumption permitting development of stability theory for AECs with the amalgamation property. Lately several upward categoricity theorems were discovered where tameness replaces strong set-theoretic assumptions. We present in this article two sufficient conditions for tameness, both in form of strong amalgamation properties that occur in nature....

Let G be any connected reductive group defined over a nonarchimedean local field F of residual characteristic p. Under some tameness assumptions on G, we construct families of positive-depth supercuspidal representations of G = G(F ). In particular, we classify (§2.7) the representations of G that contain any anisotropic unrefined minimal K-type (in the sense of MoyPrasad [28]) that satisfies a...

We discuss a Nash-Moser/ KAM algorithm for the construction of invariant tori for tame vector fields. Similar algorithms have been studied widely both in finite and infinite dimensional contexts: we are particularly interested in the second case where tameness properties of the vector fields become very important. We focus on the formal aspects of the algorithm and particularly on the minimal h...

The program-over-monoid model of computation originates with Barrington’s proof that it captures the complexity class NC1. Here we make progress in understanding the subtleties of the model. First, we identify a new tameness condition on a class of monoids that entails a natural characterization of the regular languages recognizable by programs over monoids from the class. Second, we prove that...