On partly gentle perturbations. II

Perturbations of Operators, Ii

Turbulent Pressure and Velocity Perturbations Induced by Gentle Hills Covered with Sparse and Dense Canopies

How the spatial perturbations of the first and second moments of the velocity and pressure fields differ for flow over a train of gentle hills covered by either sparse or dense vegetation is explored using large-eddy simulation (LES). Two simulations are investigated where the canopy is composed of uniformly arrayed rods each with a height that is comparable to the hill height. In the first sim...

A Gentle Introduction to Multi-stage Programming, Part II

As domain-specific languages (DSLs) permeate into mainstream software engineering, there is a need for economic methods for implementing languages. Following up on a paper with a similar title, this paper focuses on dynamically typed languages, covering issues ranging from parsing to defining and staging an interpreter for an interesting subset of Dr. Scheme. Preliminary experimental results in...

On Partly Ordered Fields

On perturbations of matrix pencils with real spectra. II

A well-known result on spectral variation of a Hermitian matrix due to Mirsky is the following: Let A and à be two n×n Hermitian matrices, and let λ1, . . . , λn and λ̃1, . . . , λ̃n be their eigenvalues arranged in ascending order. Then ∣∣∣∣∣∣diag (λ1 − λ̃1, . . . , λn − λ̃n)∣∣∣∣∣∣ ≤ ∣∣∣∣∣∣A− Ã∣∣∣∣∣∣ for any unitarily invariant norm ||| · |||. In this paper, we generalize this to the perturbation ...