We propose an approach to obtaining explicit estimates on the resolvent of hypocoercive operators by using Schur complements, rather than from exponential decay evolution semigroup combined with a time integral. present applications Langevin-like dynamics and Fokker–Planck equations, as well linear Boltzmann equation (which is also generator randomized Hybrid Monte Carlo in molecular dynamics)....

An eye tracking experiment was conducted in order to investigate the role of verb information in resolving structural ambiguity during sentence comprehension. Reading time was measured on sentences containing temporarily ambiguous noun phrases (e.g. "The athlete revealed the problem") that were continued as tensed sentence (S) complements or noun phrase (NP) complements. Ambiguous noun phrases ...

Diagrams often complement sentential proofs in mathematics. However, diagrams are rarely used as standalone reasoning tools. Thus we propose to integrate diagrammatic reasoning with an existing sentential theorem prover, thus enabling so-called heterogeneous reasoning, particularly in real arithmetic. We will study a set of diagrammatic proof examples from which we will construct a diagrammatic...

2. Problem 3.1.20. Let S be a subspace of Rn. Explain what (S⊥)⊥ = S means and why it is true. Answer: First, (S⊥)⊥ is the orthogonal complement of S⊥, which is itself the orthogonal complement of S, so (S⊥)⊥ = S means that S is the orthogonal complement of its orthogonal complement. To show that it is true, we want to show that S is contained in (S⊥)⊥ and, conversely, that (S⊥)⊥ is contained i...

We show that all two-bridge knot and link complements are virtually fibered. We also show that spherical Montesinos knot and link complements are virtually fibered. This is accomplished by showing that such knot complements are finitely covered by great circle link complements.