Kategoria BISAC: Mathematics >> Discrete Mathematics

This book provides a comprehensive algebraic treatment of hypergroups, as defined by F. Marty in 1934. It starts with structural results, which are developed along the lines of the structure theory of groups. The focus then turns to a number of concrete classes of hypergroups with small parameters, and continues with a closer look at the role of involutions (modeled after the definition of group-theoretic involutions) within the theory of hypergroups. Hypergroups generated by involutions lead to the exchange condition (a genuine generalization of the group-theoretic exchange condition),...

This book concisely presents the optimization process and optimal control process with examples and simulations to help self-learning and better comprehension. It starts with function optimization and constraint inclusion and then extends to functional optimization using the calculus of variations. The development of optimal controls for continuous-time, linear, open-loop systems is presented using Lagrangian and Pontryagin-Hamiltonian methods, showing how to introduce the end-point conditions in time and state. The closed-loop optimal control for linear systems with a quadratic cost...

The focus of this monograph is converting-reshaping-one 3D convex polyhedron to another via an operation the authors call "tailoring." A convex polyhedron is a gem-like shape composed of flat facets, the focus of study since Plato and Euclid. The tailoring operation snips off a corner (a "vertex") of a polyhedron and sutures closed the hole. This is akin to Johannes Kepler's "vertex truncation," but differs in that the hole left by a truncated vertex is filled with new surface, whereas tailoring zips the hole closed. A powerful "gluing" theorem of A.D. Alexandrov from 1950...