Abstract: We introduce an algorithm for synthesizing and verifying piecewise linear Lyapunov functions to prove global exponential stability of piecewise linear dynamical systems. The Lyapunov ...

Abstract: A classical difficult isomorphism testing problem is to test isomorphism of p-groups of class 2 and exponent p in time polynomial in the group order. It is known that this problem can be ...

Understanding a linear function graph is fundamental to grasping core mathematical concepts and their real-world applications. By analyzing the visual representation of a linear equation, we can ...

Linear functions are used to model a broad range of real-world problems. The ability to solve linear equations and inequalities is an essential skill for analysing these models. This section covers ...

Linear graphs are straight-line graphs that visually represent a constant rate of change in the relationship between two variables, showing how one changes in response to the other. They are expressed ...

A linear demand curve is a line representing the relationship between the demand for a product or service and its price. Everyone knows that sales are proportional to price: The more you charge for an ...

A function is a rule that is applied to one set of values to give another set of values. A function can be illustrated on a graph – points are plotted as coordinates and joined by either a straight ...

Department of Systems Biology, Harvard Medical School, Boston, MA, United States The linear framework uses finite, directed graphs with labelled edges to model biomolecular systems. Graph vertices ...