Founders, Feminists, and a Fascist -- Some Notable Women in the Missouri Section of the MAA

In the history of the Missouri Section of the MAA, some of the more interesting people who influenced the growth and development of the section through the years were and are women. In this chapter, we discuss the contributions of a few (certainly not all) of these women to the Missouri Section and mathematics as a whole, including Emily Kathryn Wyant (founder of KME), Margaret F. Willerding (who dealt with sexism in the 1940s), Maria Castellani (an official in Mussolini’s Italy before coming to America), and T. Christine Stevens (co-founder of Project NExT). Without them, and others like them, both mathematics and the Missouri Section of the MAA would be poorer

Representations for Laguerre temperatures

AbstractThe Laguerre difference heat equation ∇nu(n,t)=∂∂u(n,t),where∇nƒ(n)=(n+1)−(2n+a+1)ƒ(n)+(n+a)ƒ(n−1)a⩾0, provides an important discrete analogue of the classical heat equation ∂2u⧸∂x2=∂t. Conditions are established for solutions of this equation to be represented by integral and series transforms

Inversion of integral transforms associated with a class of perturbed heat equations

AbstractLet Lx be the Sturm-Liouville differential operator Lx = −d2dx2 + q(x); x ϵ (0, ∞). We assume that Lx has either a purely discrete spectrum that is bounded from below by zero or a continuous spectrum that fills up the interval (0, ∞) with, possibly, a finite number of negative eigenvalues. The W-transform ψ of ψ(y) ϵ L2(0, ∞) is defined by ϵ(x) = ∫0∞ ϵ(y) g(x,y;1)dy, where g(x, y; t) is a function associated with the fundamental solution of the perturbed equation −Lxu(x, t) = ∂u(x, t)∂t. The main purpose of this paper is to derive an inversion formula for the W-transform. This inversion formula generalizes the known inversion formulae for the Weierstrass, Weierstrass-Hankel convolution, and Weierstrass-Laguerre transforms. The results of this paper are easily extended to the case where Lx is considered over the entire line (−∞, ∞)