Graph theory is very much tied to the geometric properties of optimization and combinatorial optimization. Moreover, graph theory's geometric properties are at the core of many research interests in operations research and applied mathematics. Its techniques have been used in solving many classical problems including maximum flow problems, independent set problems, and the traveling salesman problem.

Reactive ?uids are present in many situations of great importance, such as in combustion chambers or around spacecraft re-entering the atmosphere. - alyzing the ?ow properties of such ?uids represents one of the most di?cult challenges to current technology. Indeed, all of the most di?cult aspects of ?uid mechanics appear to be grouped together in this research ?eld! Such ?uids are complex mixtures with compositions that vary rapidly in time and space. They are not usually at thermodynamic equilibrium, since the reaction times of the chemical reactions involved may not be negligible in comparison with the transit time of the ?uid. However, the author of this book limits its scope to typical phenomena that are not very far from local equilibrium but can nevertheless exhibit the most important types of irreversible processes. The production of entropy is highly dependent on the chemical reactionpa- way, which is di?cult to simplify. Also, most of the classical problems that characterize?uid mechanics—such as turbulence, the presence of thin bou- ary layers or shear layers, and the propagation of acoustic waves and shock waves—are also present, and are much more di?cult to analyze and describe than they are for homogeneous?uids, because reactive mixtures interact with these phenomena. For example, density is highly dependent on the chemical pathway since it is determined by the local and instantaneous production of chemical species, and so its value a?ects many other quantities through the equation of state and the balances of mass, momentum, and energy.

This book contains a collection of papers that were presented at the IUTAM Symposium
on “Computer Models in Biomechanics: From Nano to Macro” held at Stanford University, California, USA, from August 29 to September 2, 2011.

This book covers the most important issues in the theory of functional differential equations and their applications for both deterministic and stochastic cases. Among the subjects treated are qualitative theory, stability, periodic solutions, optimal control and estimation, the theory of linear equations, and basic principles of mathematical modelling. The work, which treats many concrete problems in detail, gives a good overview of the entire field and will serve as a stimulating guide to further research.

Because of its versatility in analyzing a broad range of applications, multibody dynamics has grown in the past two decades to be an important tool for designing, prototyping, and simulating complex articulated mechanical systems. This textbook brings together diverse concepts and bridges the gap between dynamics and engineering applications such as microrobotics, virtual reality simulation of interactive mechanical systems, nanomechanics, flexible biosystems, crash simulation, and biomechanics.

Unsichtbar und zugleich omnipräsent, erobern sich Computermodelle ständig neue Anwendungsfelder. Ihre Macht verdanken sie den immensen Kapazitäten moderner Rechnersysteme, und sie wird zusätzlich befeuert durch das maschinelle Lernen aus riesigen Datenbergen.

The origins of Graph Theory date back to Euler (1736) with the solution of the celebrated 'Koenigsberg Bridges Problem'; and to Hamilton with the famous 'Trip around the World' game (1859), stating for the first time a problem which, in its most recent version – the 'Traveling Salesman Problem' -, is still the subject of active research. Yet, it has been during the last fifty years or so—with the rise of the electronic computers—that Graph theory has become an indispensable discipline in terms of the number and importance of its applications across the Applied Sciences. Graph theory has been especially central to Theoretical and Algorithmic Computer Science, and Automatic Control, Systems Optimization, Economy and Operations Research, Data Analysis in the Engineering Sciences. Close connections between graphs and algebraic structures have been widely used in the analysis and implementation of efficient algorithms for many problems, for example: transportation network optimization, telecommunication network optimization and planning, optimization in scheduling and production systems, etc.

This book presents a computer-aided approach to the design of mechatronic systems. Its subject is an integrated modeling and simulation in a visual computer environment. Since the first edition, the simulation software changed enormously, became more user-friendly and easier to use. Therefore, a second edition became necessary taking these improvements into account.

An Introduction to Nonlinear Analysis: Theory is an overview of some basic, important aspects of Nonlinear Analysis, with an emphasis on those not included in the classical treatment of the field. Today Nonlinear Analysis is a very prolific part of modern mathematical analysis, with fascinating theory and many different applications ranging from mathematical physics and engineering to social sciences and economics. Topics covered in this book include the necessary background material from topology, measure theory and functional analysis (Banach space theory). The text also deals with multivalued analysis and basic features of nonsmooth analysis, providing a solid background for the more applications-oriented material of the book An Introduction to Nonlinear Analysis: Applications by the same authors.

This Green Book is an essential resource for power system engineers seeking comprehensive information on contemporary power system dynamic modelling and analysis. With today's rapid adoption of inverter-based resources and the resulting changes in power system dynamics, this book compares conventional power systems with evolving power systems characterized by high shares of grid-connected and distributed inverter-based resources. It covers dynamic phenomena, analysis methods, simulation tools and enablers required for secure and reliable system planning and operation.

The 2007 Abel Symposium took place at the University of Oslo in August 2007. The goal of the symposium was to bring together mathematicians whose research efforts have led to recent advances in algebraic geometry, algebraic K-theory, algebraic topology, and mathematical physics. A common theme of this symposium was the development of new perspectives and new constructions with a categorical flavor. As the lectures at the symposium and the papers of this volume demonstrate, these perspectives and constructions have enabled a broadening of vistas, a synergy between once-differentiated subjects, and solutions to mathematical problems both old and new.

Computer algebra systems are revolutionizing the teaching, the learning, and the exploration of science. Not only can students and researchers work through mathematical models more efficiently and with fewer errors than with pencil and paper, they can also easily explore, both analytically and numerically, more complex and computationally intensive models.

This book covers the basics of numerical methods. Avoiding the definition-theorem-proof style, it instead focuses on numerical examples and simple pseudo-codes.

This Green Book is an essential resource for power system engineers seeking comprehensive information on contemporary power system dynamic modelling and analysis. With today's rapid adoption of inverter-based resources and the resulting changes in power system dynamics, this book compares conventional power systems with evolving power systems characterized by high shares of grid-connected and distributed inverter-based resources. It covers dynamic phenomena, analysis methods, simulation tools and enablers required for secure and reliable system planning and operation.

This book studies the theoretical aspects for a variety of coupled fractional differential systems involving Riemann-Liouville, Caputo, ψ-Riemann–Liouville, Hilfer, ψ–Hilfer, Hadamard, Hilfer–Hadamard, Erdelyi–Kober, (k, ψ)-Hilfer, generalized, Proportional, ψ-Proportional, Hilfer–proportional, ψ-Hilfer–proportional type fractional derivative operators, subject to different types of nonlocal boundary conditions. The topic of fractional differential systems is one of the hot and important topics of research as such systems appear in the mathematical modeling of physical and technical phenomena. As the book contains some recent new work on the existence theory for nonlocal boundary value problems of fractional differential systems, it is expected that it will attract the attention of researchers, modelers and graduate students who are interested in doing their research on fractional differential systems.