This volume contains a re-edition of Max Koecher's famous Minnesota Notes. The main objects are homogeneous, but not necessarily convex, cones. They are described in terms of Jordan algebras. The central point is a correspondence between semisimple real Jordan algebras and so-called omega-domains. This leads to a construction of half-spaces which give an essential part of all bounded symmetric domains. The theory is presented in a concise manner, with only elementary prerequisites. The editors have added notes on each chapter containing an account of the relevant developments of the theory since these notes were first written.
The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.
This book provides an approach to the study of perturbation and discretization effects on the long-time behavior of dynamical and control systems. It analyzes the impact of time and space discretizations on asymptotically stable attracting sets, attractors, asumptotically controllable sets and their respective domains of attractions and reachable sets. Combining robust stability concepts from nonlinear control theory, techniques from optimal control and differential games and methods from nonsmooth analysis, both qualitative and quantitative results are obtained and new algorithms are developed, analyzed and illustrated by examples.
This text provides an approach to the study of perturbation and discretization effects on the long-time behaviour of dynamical and control systems. It analyzes the impact of time and space discretizations on asymptotically stable attracting sets, attractors and asumptotically controllable sets.
Detailed review of optimization from first principles, supported by rigorous math and computer science explanations and various learning aids Supported by rigorous math and computer science foundations, Combinatorial and Algorithmic Mathematics: From Foundation to Optimization provides a from-scratch understanding to the field of optimization, discussing 70 algorithms with roughly 220 illustrative examples, 160 nontrivial end-of-chapter exercises with complete solutions to ensure readers can apply appropriate theories, principles, and concepts when required, and Matlab codes that solve some specific problems. This book helps readers to develop mathematical maturity, including skills such as handling increasingly abstract ideas, recognizing mathematical patterns, and generalizing from specific examples to broad concepts. Starting from first principles of mathematical logic, set-theoretic structures, and analytic and algebraic structures, this book covers both combinatorics and algorithms in separate sections, then brings the material together in a final section on optimization. This book focuses on topics essential for anyone wanting to develop and apply their understanding of optimization to areas such as data structures, algorithms, artificial intelligence, machine learning, data science, computer systems, networks, and computer security. Combinatorial and Algorithmic Mathematics includes discussion on: Propositional logic and predicate logic, set-theoretic structures such as sets, relations, and functions, and basic analytic and algebraic structures such as sequences, series, subspaces, convex structures, and polyhedra Recurrence-solving techniques, counting methods, permutations, combinations, arrangements of objects and sets, and graph basics and properties Asymptotic notations, techniques for analyzing algorithms, and computational complexity of various algorithms Linear optimization and its geometry and duality, simplex and non-simplex algorithms for linear optimization, second-order cone programming, and semidefinite programming Combinatorial and Algorithmic Mathematics is an ideal textbook resource on the subject for students studying discrete structures, combinatorics, algorithms, and optimization. It also caters to scientists across diverse disciplines that incorporate algorithms and academics and researchers who wish to better understand some modern optimization methodologies.
The monograph gives a theoretical explanation of observed cooperative behavior in common pool situations. The incentives for cooperative decision making are investigated by means of a cooperative game theoretical framework. In a first step core existence results are worked out. Whereas general core existence results provide us with an answer for mutual cooperation, nothing can be said how strong these incentives and how stable these cooperative agreements are. To clarify these questions the convexity property for common pool TU-games in scrutinized in a second step. It is proved that the convexity property holds for a large subclass of symmetrical as well as asymmetrical cooperative common pool games. Core existence and the convexity results provide us with a theoretical explanation to bridge the gap between the observation in field studies for cooperation and the noncooperative prediction that the common pool resource will be overused and perhaps endangered.
Quilts are 2-complexes used to analyze actions and subgroups of the 3-string braid group and similar groups. This monograph establishes the fundamentals of quilts and discusses connections with central extensions, braid actions, and finite groups. Most results have not previously appeared in a widely available form, and many results appear in print for the first time. This monograph is accessible to graduate students, as a substantial amount of background material is included. The methods and results may be relevant to researchers interested in infinite groups, moonshine, central extensions, triangle groups, dessins d'enfants, and monodromy actions of braid groups.
This book presents endeavors to join synergies in order to create added value for society, using the latest scientific knowledge to boost technology transfer from academia to industry. It potentiates the foundations for the creation of knowledge- and entrepreneurial cooperation networks involving engineering, innovation, and entrepreneurship stakeholders. The Regional HELIX 2018 conference was organized at the University of Minho’s School of Engineering by the MEtRICs and Algoritmi Research Centers, and took place in Guimarães, Portugal, from June 27th to 29th, 2018. After a rigorous peer-review process, 160 were accepted for publication, covering a wide range of topics, including Control, Automation and Robotics; Mechatronics Design, Medical Devices and Wellbeing; Cyber-Physical Systems, IoT and Industry 4.0; Innovations in Industrial Context and Advanced Manufacturing; New Trends in Mechanical Systems Development; Advanced Materials and Innovative Applications; Waste to Energy and Sustainable Environment; Operational Research and Industrial Mathematics; Innovation and Collaborative Arrangements; Entrepreneurship and Internationalization; and Oriented Education for Innovation, Engineering and/or Entrepreneurship.
