— We construct explicitly some analytic families of étale (φ, Γ)-modules, which give rise to analytic families of 2-dimensional crystalline representations. As an application of our constructions, we… (More)

We give a generator-free formulation of sofic measure entropy using finite partitions and establish a Kolmogorov-Sinai theorem. We also show how to compute the values for general Bernoulli actions in… (More)

Doust and Weston [8] have introduced a new method called enhanced negative type for calculating a non-trivial lower bound ℘T on the supremal strict p-negative type of any given finite metric tree (T,… (More)

For discrete measured groupoids preserving a probability measure we introduce a notion of sofic dimension that measures the asymptotic growth of the number of sofic approximations on larger and… (More)

In this paper we prove that there exists a Zariski dense open subset U defined over Q in the parameter space of one-variable rational functions with prescribed ℓ poles with fixed orders, such that… (More)

We show that for any amenable group Γ and any ZΓ-module M of type FL with vanishing Euler characteristic, the entropy of the natural Γ-action on the Pontryagin dual of M is equal to the L-torsion of… (More)

An algebraic action of a discrete group Γ is a homomorphism from Γ to the group of continuous automorphisms of a compact abelian group X. By duality, such an action of Γ is determined by a module M =… (More)

Let (A,LA) be a quantum metric space. Then clearly S(A) with the metric ρLA is a compact balanced convex metric space, i.e. the metric ρLA is convex and balanced. Another important property of S(A)… (More)

This paper is concerned with the adaptive backstepping quantized control problem for a class of output-constrained nonlinear systems. Based on a new transformation of the control signal, the system… (More)