Systems of orthogonal polynomials arising from the modular j-function

Appendix: Polynomials Arising from the Tautological Ring

Weber's law orthogonal to the psychometric function

Psychometric function plots the percentage of the correct responses among an entire pool of responses (cumulative probability) in a psychophysical task versus the amount of change in an independent variable. These changes in the independent variable are made with reference to a constant initial value. If this initial value is altered, the psychometric function will change according to Weber’s l...

Weber's law orthogonal to the psychometric function

Psychometric function plots the percentage of the correct responses among an entire pool of responses (cumulative probability) in a psychophysical task versus the amount of change in an independent variable. These changes in the independent variable are made with reference to a constant initial value. If this initial value is altered, the psychometric function will change according to Weber’s l...

Quasi-Exactly Solvable Systems and Orthogonal Polynomials

This paper shows that there is a correspondence between quasi-exactly solvable models in quantum mechanics and sets of orthogonal polynomials {Pn}. The quantum-mechanical wave function is the generating function for the Pn(E), which are polynomials in the energy E. The condition of quasi-exact solvability is reflected in the vanishing of the norm of all polynomials whose index n exceeds a criti...

Roots of Ehrhart Polynomials Arising from Graphs

Several polytopes arise from finite graphs. For edge and symmetric edge polytopes, in particular, exhaustive computation of the Ehrhart polynomials not merely supports the conjecture of Beck et al. that all roots α of Ehrhart polynomials of polytopes of dimension D satisfy −D ≤ Re(α) ≤ D − 1, but also reveals some interesting phenomena for each type of polytope. Here we present two new conjectu...