An invitation to the principal series

An Invitation to Polynomiography via Exponential Series

The subject of Polynomiography deals with algorithmic visualization of polynomial equations, having many applications in STEM and art, see [8]-[12]. Here we consider the polynomiography of the partial sums of the exponential series. While the exponential function is taught in standard calculus courses, it is unlikely that properties of zeros of its partial sums are considered in such courses, l...

On torsional rigidity and principal frequencies: an invitation to the Kohler-Jobin rearrangement technique

We generalize to the p−Laplacian ∆p a spectral inequality proved by M.-T. Kohler-Jobin. As a particular case of such a generalization, we obtain a sharp lower bound on the first Dirichlet eigenvalue of ∆p of a set in terms of its p−torsional rigidity. The result is valid in every space dimension, for every 1 < p < ∞ and for every open set having finite measure. Moreover, it holds by replacing t...

An Invitation to Play

Parity games and their subclasses and variants pop up in various contexts: μ-calculus, tree automata, program verification [3, 1, 8]. Such games provide only binary information indicating the winning player. However, in classical games theory [12] the emphasis is rather on how much we win or lose. Can we incorporate the information about the profits and losses into parity games?

An Invitation to Topology

An Invitation to

* The author is an Associate Professor of Accounting on the faculty of the Tepper School of Business of Carnegie Mellon University, Pittsburgh, Pennsylvania, USA. The essay is written based on a few lectures on accounting theory given at various universities. The author thanks the audience at these lectures. In preparing the written manuscript, comments by Xijia Su of City University of Hong Ko...