TWO NOTES ON ISAIAH xli 5–7: II

Two Notes on Subshifts

We prove two unrelated results about subshifts. First, we give a condition on the lengths of forbidden words that is sufficient to guarantee that the corresponding subshift is nonempty. The condition implies that, for example, any sequence of binary words of lengths 5, 6, 7, . . . is avoidable. As another application, we derive a result of Durand, Levin and Shen [2, 3] that there are infinite s...

Notes on Sandflies. Part II

Lecture Notes on Acoustics II

Cumulative spectral decay of a loudspeaker showing the transient behavior.

Notes on Galois Theory II

Lemma 2.1. Let F be a field, let E = F (α) be a simple extension of F , where α is algebraic over F and f = irr(α, F, x), let ψ : F → K be a homomorphism from F to a field K, and let L be an extension of K. If β ∈ L is a root of ψ(f), then there is a unique extension of ψ to a homomorphism φ : E → L such that φ(α) = β. Hence there is a bijection from the set of homomorphisms φ : E → L such that...

Two notes on the Hippiatrica.

P ELAGONIUS' BOOK on horse medicine,l a main source of Vegetius' Mulomedicina, was composed around the middle of the fourth century. It was later incorporated in the Greek collection of hippiatric texts known as the Hippiatrica. 2 When a Latin manuscript of Pelagonius (originally copied in 1485 on behalf of Politian and bearing his subscriptio 3) was discovered and edited in the early nineteent...