Notes on Japanese Ferns 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...

Stasis and convergence characterize morphological evolution in eupolypod II ferns.

BACKGROUND AND AIMS Patterns of morphological evolution at levels above family rank remain underexplored in the ferns. The present study seeks to address this gap through analysis of 79 morphological characters for 81 taxa, including representatives of all ten families of eupolypod II ferns. Recent molecular phylogenetic studies demonstrate that the evolution of the large eupolypod II clade (wh...

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 . . . . . . . . . . . ...