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Scheduling and Congestion Control for Wireless and Processing Networks
In this book, we consider the problem of achieving the maximum throughput and utility in a class of networks with resource-sharing constraints. This is a classical problem of great importance. In the context of wireless networks, we first propose a fully distributed scheduling algorithm that achieves the maximum throughput. Inspired by CSMA (Carrier Sense Multiple Access), which is widely deployed in today's wireless networks, our algorithm is simple, asynchronous, and easy to implement. Second, using a novel maximal-entropy technique, we combine the CSMA scheduling algorithm with congestion control to approach the maximum utility. Also, we further show that CSMA scheduling is a modular MAC-...
Differential Equations
This book presents, in a unitary frame and from a new perspective, the main concepts and results of one of the most fascinating branches of modern mathematics, namely differential equations, and offers the reader another point of view concerning a possible way to approach the problems of existence, uniqueness, approximation, and continuation of the solutions to a Cauchy problem. In addition, it contains simple introductions to some topics which are not usually included in classical textbooks: the exponential formula, conservation laws, generalized solutions, Caratheodory solutions, differential inclusions, variational inequalities, viability, invariance, gradient systems. In this new edition we have corrected several small errors and added the following new topics: Volterra Integral Equations and Elements of Calculus of Variations. Some problems and exercises, referring to these two new topics are also included. The bibliography has been updated and expanded.
Ordinary Differential Equations
Ordinary Differential Equations: 1971 NRL–MRC Conference provides information pertinent to the fundamental aspects of ordinary differential equations. This book covers a variety of topics, including geometric and qualitative theory, analytic theory, functional differential equation, dynamical systems, and algebraic theory. Organized into two parts encompassing 51 chapters, this book begins with an overview of the results on the existence of periodic solutions of a differential equation. This text then describes an index for the isolated invariant sets of a flow on a compact metric space, which contains exactly the information of the Morse index. Other chapters consider the studies of certain classes of equations that can be interpreted as models of biological or economic processes. This book discusses as well the absolute stability of some classes of integro-differential systems. The final chapter deals with first-order differential equations. This book is a valuable resource for mathematicians, graduate students, and research workers.
Adaptive Systems
Loosely speaking, adaptive systems are designed to deal with, to adapt to, chang ing environmental conditions whilst maintaining performance objectives. Over the years, the theory of adaptive systems evolved from relatively simple and intuitive concepts to a complex multifaceted theory dealing with stochastic, nonlinear and infinite dimensional systems. This book provides a first introduction to the theory of adaptive systems. The book grew out of a graduate course that the authors taught several times in Australia, Belgium, and The Netherlands for students with an engineering and/or mathemat ics background. When we taught the course for the first time, we felt that there was a need for a textbook that would introduce the reader to the main aspects of adaptation with emphasis on clarity of presentation and precision rather than on comprehensiveness. The present book tries to serve this need. We expect that the reader will have taken a basic course in linear algebra and mul tivariable calculus. Apart from the basic concepts borrowed from these areas of mathematics, the book is intended to be self contained.
A Modern Theory of Integration
The theory of integration is one of the twin pillars on which analysis is built. The first version of integration that students see is the Riemann integral. Later, graduate students learn that the Lebesgue integral is ?better? because it removes some restrictions on the integrands and the domains over which we integrate. However, there are still drawbacks to Lebesgue integration, for instance, dealing with the Fundamental Theorem of Calculus, or with ?improper? integrals. This book is an introduction to a relatively new theory of the integral (called the ?generalized Riemann integral? or the ?Henstock-Kurzweil integral?) that corrects the defects in the classical Riemann theory and both simp...
Stochastic Processes
Based on a highly popular, well-established course taught by the authors, Stochastic Processes: An Introduction, Second Edition discusses the modeling and analysis of random experiments using the theory of probability. It focuses on the way in which the results or outcomes of experiments vary and evolve over time. The text begins with a review of relevant fundamental probability. It then covers several basic gambling problems, random walks, and Markov chains. The authors go on to develop random processes continuous in time, including Poisson, birth and death processes, and general population models. While focusing on queues, they present an extended discussion on the analysis of associated s...
Integral and Functional Analysis
This book is based on two closely-related courses. The first of these courses is Integration and Metric Spaces, and the second being Functional Analysis. Though the contents of Functional Analysis have been used for both an undergraduate course and an introductory graduate course, this text is designed primarily for undergraduate students. The prerequisites of this book are deliberately modest, and it is assumed that the students have some familiarity with Introductory Calculus and Linear Algebra plus the basic (direct, indirect) proof methods.
Mathematical Analysis of Continuum Mechanics and Industrial Applications III
This book focuses on mathematical theory and numerical simulation related to various areas of continuum mechanics, such as fracture mechanics, (visco)elasticity, optimal shape design, modelling of earthquakes and Tsunami waves, material structure, interface dynamics and complex systems. Written by leading researchers from the fields of applied mathematics, physics, seismology, engineering, and industry with an extensive knowledge of mathematical analysis, it helps readers understand how mathematical theory can be applied to various phenomena, and conversely, how to formulate actual phenomena as mathematical problems. This book is the sequel to the proceedings of the International Conference of Continuum Mechanics Focusing on Singularities (CoMFoS) 15 and CoMFoS16.
Higher Order Derivatives
The concept of higher order derivatives is useful in many branches of mathematics and its applications. As they are useful in many places, nth order derivatives are often defined directly. Higher Order Derivatives discusses these derivatives, their uses, and the relations among them. It covers higher order generalized derivatives, including the Pea
