Search

By making use of the Cauchy double alternant and the Laplace expansion formula, we establish two closed formulae for the determinants of factorial fractions that are then utilised to evaluate several determinants of binomial coefficients and Catalan numbers, including those obtained recently by Chammam [‘Generalized harmonic numbers, Jacobi numbers and a Hankel determinant evaluation’, Integral Transforms Spec. Funct. 30(7) (2019), 581–593].

New directions in Markov processes and research on master equations are showcased by example. The utility of Magnus expansions for handling time-varying rates is demonstrated. The useful notion in applied mathematics often turns out to be the pseudospectra and not simply the eigenvalues. We highlight that general principle with our own examples of Markov processes where exact eigenvalues are found and contrasted with the large errors produced by standard numerical methods. As a motivating application, isomerisation provides a running example and an illustration of our approaches to chemical kinetics. We also present a brief example of a totally asymmetric exclusion process.

Search Results

Refine search

Refine search

Actions for selected content:

2 results

HANKEL DETERMINANTS OF FACTORIAL FRACTIONS

Applications of Magnus expansions and pseudospectra to Markov processes

Search Results

Refine search

Refine search

Actions for selected content:

Save Search

2 results

HANKEL DETERMINANTS OF FACTORIAL FRACTIONS

Applications of Magnus expansions and pseudospectra to Markov processes