Notes on Mikania (Compositae) - II

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...

Lecture Notes on Stochastic Calculus (Part II)

2 Ito-Doeblin’s formula(s) 7 2.1 First formulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2 Generalizations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.3 Continuous semi-martingales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.4 Integration by parts formula . . . . . . . . . . . ...

Notes on the Proof of Weil Ii

1.1. Fundamental groups. Let FET/X be the category of schemes finite étale over X. Choose x̄ a geometric point of X. The fiber functor Fx̄ : FET → SET is defined as Fx̄(Y ) = HomX(x̄, Y ). Then the étale fundamental group is defined as π1(X, x̄) = AutFx̄ π1(X, x̄) is a profinite group. If f : X → Y is a morphism, then it induces f∗ : π1(X, x̄) → π1(Y, f(x̄)). In the following, we will often omit the ”ba...