Kybernetik og systemteori

This book introduces some basic mathematical tools in reaction-diffusion models, with applications to spatial ecology and evolutionary biology. It is divided into four parts.The first part is an introduction to the maximum principle, the theory of principal eigenvalues for elliptic and periodic-parabolic equations and systems, and the theory of principal Floquet bundles.The second part concerns the applications in spatial ecology. We discuss the dynamics of a single species and two competing species, as well as some recent progress on N competing species in bounded domains. Some related results on stream populations and phytoplankton populations are also included. We also discuss the spreading properties of a single species in an unbounded spatial domain, as modeled by the Fisher-KPP equation.The third part concerns the applications in evolutionary biology. We describe the basic notions of adaptive dynamics, such as evolutionarily stable strategies and evolutionary branching points, in the context of a competition model of stream populations. We also discuss a class of selection-mutation models describing a population structured along a continuous phenotypical trait.The fourth part consists of several appendices, which present a self-contained treatment of some basic abstract theories in functional analysis and dynamical systems. Topics include the Krein-Rutman theorem for linear and nonlinear operators, as well as some elements of monotone dynamical systems and abstract competition systems.Most of the book is self-contained and it is aimed at graduate students and researchers who are interested in the theory and applications of reaction-diffusion equations.        

This book explores interesting possibilities of extracting information about quantum states from data readily obtained from experiments, such as tomograms and expectation values of appropriate observables. The procedures suggested for identifying nonclassical ei ects such as wave packet revivals, squeezing and entanglement solely from tomograms circumvent detailed state reconstruction. Several bipartite entanglement indicators are defined based on tomograms, and their ei cacy assessed in models of atom-field interactions and qubit systems. Tools of classical ergodic theory such as time series and network analysis are applied to quantum observables treated as dynamical variables. This brings out novel aspects involving dii erent time scales. The book is aimed at researchers in the areas of quantum optics and quantum dynamics.

Available for the first time in English, this two-volume course on theoretical and applied mechanics has been honed over decades by leading scientists and teachers, and is a primary teaching resource for engineering and maths students at St. Petersburg University.The course addresses classical branches of theoretical mechanics (Vol. 1), along with a wide range of advanced topics, special problems and applications (Vol. 2). Among the special applications addressed in this second volume are: stability of motion, nonlinear oscillations, dynamics and statics of the Stewart platform, mechanics under random forces, elements of control theory, relations between nonholonomic mechanics and the control theory, vibration and autobalancing of rotor systems, physical theory of impact, statics and dynamics of a thin rod.This textbook is aimed at students in mathematics and mechanics and at post-graduates and researchers in analytical mechanics.

5G, the emerging technology in mobile communication, is expected to deliver an important and decisive impact on several of the UN's Sustainable Development Goals where universal accessibility to ICTs remains a serious concern. However, cyber security has emerged as a serious challenge, not least because of the increased accessibility and broader usage with associated vulnerability. Developing countries have additional challenges associated with both the expected faster build-up of accessibility and lack of qualified competencies within cyber security. Discussion of these challenges is the overall theme and motivation for this book.Technical topics discussed in the book include:5G in rural networksCritical infrastructuresOpen RANProtection of privacyCybersecurity and machine learningCybersecurity and disaster monitoring

This book gives an introduction to discrete-time Markov chains which evolve on a separable metric space. The focus is on the ergodic properties of such chains, i.e., on their long-term statistical behaviour. Among the main topics are existence and uniqueness of invariant probability measures, irreducibility, recurrence, regularizing properties for Markov kernels, and convergence to equilibrium. These concepts are investigated with tools such as Lyapunov functions, petite and small sets, Doeblin and accessible points, coupling, as well as key notions from classical ergodic theory. The theory is illustrated through several recurring classes of examples, e.g., random contractions, randomly switched vector fields, and stochastic differential equations, the latter providing a bridge to continuous-time Markov processes.  The book can serve as the core for a semester- or year-long graduate course in probability theory with an emphasis on Markov chains or random dynamics. Some of the material is also well suited for an ergodic theory course. Readers should have taken an introductory course on probability theory, based on measure theory. While there is a chapter devoted to chains on a countable state space, a certain familiarity with Markov chains on a finite state space is also recommended.

This updated book, reconfigured as a textbook, covers the key technologies associated with the physical transmission of data on 5G mobile systems. Following an updated overview of these technologies, the author provides a high-level description of 3GPP's mobile communications standard (5G NR) and shows how the key technologies presented earlier facilitate the transmission of very high-speed user data and control data and can provide very low latency for use cases where this is important. In the final chapter, an overview and the physical layer aspects of 5G NR enabled Fixed Wireless Access (FWA) networks is presented. Material in the first edition addressed mainly the key physical layer technologies and features associated with 3GPP release 15, the first release to support 5G. This edition adds descriptions of some of the technological advancements supported in release 16, including integrated access and backhaul (IAB), sidelink communication, NR positioning, operation in unlicensed bands, and multiple transmission points transmission. This textbook is intended for graduate and upper undergraduate engineering students and practicing engineers who have an interest in 3GPP's 5G enabled mobile and or FWA networks and want to acquire, where missing, the necessary technology background in order to understand 3GPP's physical layer specifications and operation. The author provides working problems and helpful examples throughout the text.