Abstract: This paper proves the existence of polynomial Lyapunov functions for rationally stable vector fields. For practical purposes the existence of polynomial Lyapunov functions plays a ...

A simple application made to visualise a polynomial function for a possibly having a maximum power of three. Any lower down to y = 0 will work as well. This is a project made for the university I am ...

Department of Mathematics and Statistics, Qinghai Minzu University, Xining, China. Since then, much attention has been paid to this topic, but they mainly focus on undirected graphs and integral trees ...

Graphs of exponential functions: examining the distinctive curve of exponential growth and decay Graphs of logarithmic functions: analysing how logarithmic functions represent the inverse of ...

This contribution is part of the special series of Inaugural Articles by members of the National Academy of Sciences elected in 2017. Edited by Kenneth A. Ribet, University of California, Berkeley, CA ...

Mathematics is the study of order, relation and pattern. From its origins in counting and measuring it has evolved in highly sophisticated and elegant ways to become the language now used to describe ...

A holy grail of theoretical computer science, with numerous fundamental implications to more applied areas of computing such as operations research and artificial intelligence, is the question of ...