Motivated by the Hankel determinant evaluation of moment sequences, we study a kind of Pfaffian analogue evaluation. We prove an LU -decomposition analogue for skew-symmetric matrices, called Pfaffian decomposition. We then apply this formula to evaluate Pfaffians related to some moment sequences of classical orthogonal polynomials. In particular we obtain a product formula for a kind of q-Cata...

The ‘radioactive dice’ experiment is a commonly used classroom analogue to model the decay of radioactive nuclei. However, the value of the half-life obtained from this experiment differs significantly from that calculated for real nuclei decaying exponentially with the same decay constant. This article attempts to explain the discrepancy and suggests modifications to the experiment to minimize...

In 1986, Mills and Robbins observed by computer the continued fraction expansion of certain algebraic power series over a finite field. Incidentally, they came across a particular equation of degree four in characteristic p = 13. This equation has an analogue for all primes p ≥ 5. There are two patterns for the continued fraction of the solution of this equation, according to the residue of p m...