Abstract: In this paper, we consider a dynamical system whose trajectory is a result of minimizing a multiphase cost function. The multiphase cost function is assumed to be a weighted sum of specified ...

Functions are one of the most fundamental concepts in mathematics, forming the foundation for topics in algebra, calculus and many other areas. A solid understanding of the basics of functions, ...

We present a systematic derivation of three mathematical models of increasing complexity for optical design, based on Hamilton’s characteristic functions and conservation of luminous flux, and briefly ...

To set prices that produce sales, small business owners need to understand the demand curves and inverse demand curves for their products and services. Knowing how each curve works will help owners ...

Quadratic functions are essential in the world of mathematics and have a wide range of applications in various fields, such as physics, engineering, and finance. An inverse function can be thought of ...

Mathematics is a fascinating world, especially when it comes to finding the inverse of a function. An inverse function is a function that undoes the action of another function – meaning, if you input ...