This book is based on lectures from a one-year course at the Far Eastern Federal University (Vladivostok, Russia) as well as on workshops on optimal control offered to students at various mathematical departments at the university level. The main themes of the theory of linear and nonlinear systems are considered, including the basic problem of establishing the necessary and sufficient conditions of optimal processes. In the first part of the course, the theory of linear control systems is constructed on the basis of the separation theorem and the concept of a reachability set. The authors prove the closure of a reachability set in the class of piecewise continuous controls, and the problems of controllability, observability, identification, performance and terminal control are also considered. The second part of the course is devoted to nonlinear control systems. Using the method of variations and the Lagrange multipliers rule of nonlinear problems, the authors prove the Pontryagin maximum principle for problems with mobile ends of trajectories. Further exercises and a large number of additional tasks are provided for use as practical training in order for the reader to consolidate the theoretical material.

With a novel quality theory of consumption which treats opulence and self-restraint in consumption styles symmetrically, Ernst Mohr shows how social distance and proximity are communicated by consumption and produced by communication. He positions fringe styles with those of the mainstream in an overall stylistic system of society and analyses their encounters. Rigorously derived, the approach casts fresh light on the cultural and social evolution as well as the business models of the consumer industry. It provides a coherent interdisciplinary access to the aesthetic turn of society that has so far been treated with contradictory paradigms.

This textbook, now in its second edition, results from lectures, practical problems, and workshops on Optimal Control, given by the authors at Irkutsk State University, Far Eastern Federal University (both in Vladivostok, Russia), and Kwangwoon University (Seoul, South Korea). In this work, the authors cover the theory of linear and nonlinear systems, touching on the basic problem of establishing the necessary and sufficient conditions of optimal processes. Readers will find two new chapters, with results of potential interest to researchers with a focus on the theory of optimal control, as well as to those interested in applications in Engineering and related sciences. In addition, several improvements have been made through the text. This book is structured in three parts. Part I starts with a gentle introduction to the basic concepts in Optimal Control. In Part II, the theory of linear control systems is constructed on the basis of the separation theorem and the concept of a reachability set. The authors prove the closure of reachability set in the class of piecewise continuous controls and touch on the problems of controllability, observability, identification, performance, and terminal control. Part III, in its turn, is devoted to nonlinear control systems. Using the method of variations and the Lagrange multipliers rule of nonlinear problems, the authors prove the Pontryagin maximum principle for problems with mobile ends of trajectories. Problem sets at the end of chapters and a list of additional tasks, provided in the appendix, are offered for students seeking to master the subject. The exercises have been chosen not only as a way to assimilate the theory but also as to induct the application of such knowledge in more advanced problems.

Everyone wants to live an amazing life. But in reality, most Christians are disappointed by their lack of authentic, life-changing encounters with God. However, here's the deal: "You don't have to settle for spiritual mediocrity!" All In is designed to help readers overcome what may be the greatest problem facing so many of us today-the lack of a genuine experience with God. Tapping into the widely felt need of spiritual dissatisfaction, gifted author and speaker Mike Guzzardo guides you along the path of total surrender to Jesus Christ. He deals with topics like self-deception, God's rightful place, biblical joy, temptation, and character development. He tells great stories that will lead you to experience your own story, for better or worse, and he helps to open your eyes to how a genuine encounter with God will irrevocably change your whole life.

The Common Extremalities in Biology and Physics is the first unified systemic description of dissipative phenomena, taking place in biology, and non-dissipative (conservative) phenomena, which is more relevant to physics. Fully updated and revised, this new edition extends our understanding of nonlinear phenomena in biology and physics from the extreme / optimal perspective. - The first book to provide understanding of physical phenomena from a biological perspective and biological phenomena from a physical perspective - Discusses emerging fields and analysis - Provides examples

"This book introduces Gottfried Wilhelm Leibniz's Principle of Optimality and argues that it plays a central role his physics and philosophy, with profound implications for both. Each chapter begins with an introduction to one of Leibniz's ground-breaking studies in natural philosophy, paying special attention to the role of optimal form in those investigations. Each chapter then goes on to explore the philosophical implications of optimal form for Leibniz's broader philosophical system. Individual chapters include discussions of Leibniz's understanding of teleology, the nature of bodies, laws of nature, and free will. The final chapter explores the legacy of Leibniz's physics in light of his work on optimal form"--

Have you ever faced a mathematical problem and had no idea how to approach it? Or perhaps you had an idea but got stuck halfway through? This book guides you in developing your creativity, as it takes you on a voyage of discovery into mathematics. Readers will not only learn strategies for solving problems and logical reasoning, but they will also learn about the importance of proofs and various proof techniques. Other topics covered include recursion, mathematical induction, graphs, counting, elementary number theory, and the pigeonhole, extremal and invariance principles. Designed to help students make the transition from secondary school to university level, this book provides readers with a refreshing look at mathematics and deep insights into universal principles that are valuable far beyond the scope of this book. Aimed especially at undergraduate and secondary school students as well as teachers, this book will appeal to anyone interested in mathematics. Only basic secondary school mathematics is required, including an understanding of numbers and elementary geometry, but no calculus. Including numerous exercises, with hints provided, this textbook is suitable for self-study and use alongside lecture courses.

Many mathematicians have been drawn to mathematics through their experience with math circles. The Berkeley Math Circle (BMC) started in 1998 as one of the very first math circles in the U.S. Over the last decade and a half, 100 instructors--university professors, business tycoons, high school teachers, and more--have shared their passion for mathematics by delivering over 800 BMC sessions on the UC Berkeley campus every week during the school year. This second volume of the book series is based on a dozen of these sessions, encompassing a variety of enticing and stimulating mathematical topics, some new and some continuing from Volume I: from dismantling Rubik's Cube and randomly putting it back together to solving it with the power of group theory;from raising knot-eating machines and letting Alexander the Great cut the Gordian Knot to breaking through knot theory via the Jones polynomial;from entering a seemingly hopeless infinite raffle to becoming friendly with multiplicative functions in the land of Dirichlet, Möbius, and Euler;from leading an army of jumping fleas in an old problem from the International Mathematical Olympiads to improving our own essay-writing strategies;from searching for optimal paths on a hot summer day to questioning whether Archimedes was on his way to discovering trigonometry 2000 years ago Do some of these scenarios sound bizarre, having never before been associated with mathematics? Mathematicians love having fun while doing serious mathematics and that love is what this book intends to share with the reader. Whether at a beginner, an intermediate, or an advanced level, anyone can find a place here to be provoked to think deeply and to be inspired to create. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession. Titles in this series are co-published with the Mathematical Sciences Research Institute (MSRI).