Mathematical Aspects of Pattern Formation in Biological Systems will be of interest to graduate students and researchers who are active in reaction-diffusion systems, pattern formation and mathematical biology.

These lecture notes on selected topics in numerical methods for hyperbolic equations are from renowned academics in both theoretical and applied fields, and include contributions on:

• Nonlinear hyperbolic conservation laws
• First order schemes for the Euler equations
• High-order accuracy: monotonicity and non-linear methods
• High-order schemes for multidimensional hyperbolic problems
• A numerical method for the simulation of turbulent mixing and its basis in mathematical theory

Lectures Notes on Numerical Methods for Hyperbolic Equations is intended primarily for research students and post-doctoral research fellows. Some background knowledge on the basics of the theoretical aspects of the partial differential equations, their physical meaning and discretization methods is assumed.

The author surveys the known results in these fields and indicates directions for further research and wider application of the methods of Lie sphere geometry. Further key features of Lie Sphere Geometry 2/ Provides the reader with all the necessary background to reach the frontiers of research in this area; Fills a gap in the literature; no other thorough examination of Lie sphere geometry and its applications to submanifold theory; Complete treatment of the cyclides of Dupin, including 11 computer-generated illustrations; Rigorous exposition driven by motivation and ample examples.

As there is currently no efficient systematic analytical or numerical approach for solving them, the biggest bottle-neck to the practical application of the nonlinear equivalent of the H∞-control theory has been the difficulty in solving the Hamilton-Jacobi-Isaacs partial differential-equations (or inequalities). In light of this challenge, the author hopes to inspire continuing research and discussion on this topic via examples and simulations, as well as helpful notes and a rich bibliography.

Nonlinear H∞-Control, Hamiltonian Systems and Hamilton-Jacobi Equations was written for practicing professionals, educators, researchers and graduate students in electrical, computer, mechanical, aeronautical, chemical, instrumentation, industrial and systems engineering, as well as applied mathematics, economics and management.

This monograph should be of value and interest to specialists in the fields of applied and computational mathematics, geophysics and differential equations.

The book presents a large variety of resource allocation models with special mathematical structures and provides elegant, efficient algorithms that compute optimal solutions to these models.

Authored by one of the leading researchers in the field, Equitable Resource Allocation:

• Is the only book that provides a comprehensive exposition of equitable resource allocation problems
• Presents a collection of resource allocation models with applications in communication networks, transportation, content distribution, manufacturing, emergency services, and more
• Exhibits practical algorithms for solving a variety of resource allocation models
• Uses real-world applications and examples to explain important concepts
• Includes end-of-chapter exercises

Bringing together much of the equitable resource allocation research from the past thirty years, this book is a valuable reference for anyone interested in solving diverse optimization problems.