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Collects the theoretical developments of optimal partitions. This book provides a general framework to unify these results and present them in an organized fashion. It deals with practical problems of optimal partitions and shows show how they can be solved using the theory - or why they cannot be.

The need for optimal partition arises from many real-world problems involving the distribution of limited resources to many users. The "clustering" problem, which has received a lot of attention, is a special case of optimal partitioning. This book attempts to collect the theoretical developments of optimal partitions.

Pooling designs have been widely used in various aspects of DNA sequencing. This book collects research on pooling designs in one convenient place. It covers real biological applications such as clone library screening, contig sequencing, exon boundary finding and protein-protein interaction detecting and introduces the mathematics behind it.

Written in a straightforward and easily accessible style, this volume is suitable as a textbook for advanced undergraduate or first-year graduate students in mathematics, physical sciences, and engineering. The aim is to provide students with a strong background in the theories of Ordinary Differential Equations, Dynamical Systems and Boundary Value Problems, including regular and singular perturbations. It is also a valuable resource for researchers.This volume presents an abundance of examples in physical and biological sciences, and engineering to illustrate the applications of the theorems in the text. Readers are introduced to some important theorems in Nonlinear Analysis, for example, Brouwer fixed point theorem and fundamental theorem of algebras. A chapter on Monotone Dynamical Systems takes care of the new developments in Ordinary Differential Equations and Dynamical Systems.In this third edition, an introduction to Hamiltonian Systems is included to enhance and complete its coverage on Ordinary Differential Equations with applications in Mathematical Biology and Classical Mechanics.