Micha Wasem

Micha Wasem Mathematical Modelling, Econometrics, Differential Geometry

Counting the Solutions of an Equation without Solving it

winding-number

A basic task in mathematics or mathematical modelling consists in solving equations. Since it is often times impossible to solve equations analytically, one is interested in understanding properties of the solution space of the equation, e.g. its cardinality. In this work we construct a method that allows to count the number of solutions of a real equation in one real variable without solving the equation. Based on geometric ideas, we construct an integral that counts the number of solutions to an equation under mild regularity assumptions.

N. Hungerbühler, M. Wasem, An integral that counts the zeros of a function, Open Math, 2018

Absolute vs Relative Key Performance Indicator

key performance indicator

Absolute and relative change might be insufficient to meaningfully compare and interpret the sales volume of different sales channels. The goal of this project was to single out a meaningful indicator which is determined by some economically natural axioms and which allows to compare sales channels of different scales. The indicator proves to be interesting in its own right since it uncovers a relationship between marginal functions and economic elasticity and might be interpreted as a special kind of Cobb-Douglas-Function.