This book is a tribute to Professor Ewa Orlowska, a Polish logician who was celebrating the 60th year of her scientific career in 2017. It offers a collection of contributed papers by different authors and covers the most important areas of her research. Prof. Orlowska made significant contributions to many fields of logic, such as proof theory, algebraic methods in logic and knowledge representation, and her work has been published in 3 monographs and over 100 articles in internationally acclaimed journals and conference proceedings. The book also includes Prof. Orlowska's autobiography, bibliography and a trialogue between her and the editors of the volume, as well as contributors' biographical notes, and is suitable for scholars and students of logic who are interested in understanding more about Prof. Orlowska's work.

Mathematical Physics with Partial Differential Equations, Second Edition, is designed for upper division undergraduate and beginning graduate students taking mathematical physics taught out by math departments. The new edition is based on the success of the first, with a continuing focus on clear presentation, detailed examples, mathematical rigor and a careful selection of topics. It presents the familiar classical topics and methods of mathematical physics with more extensive coverage of the three most important partial differential equations in the field of mathematical physics-the heat equation, the wave equation and Laplace's equation. The book presents the most common techniques of solving these equations, and their derivations are developed in detail for a deeper understanding of mathematical applications. Unlike many physics-leaning mathematical physics books on the market, this work is heavily rooted in math, making the book more appealing for students wanting to progress in mathematical physics, with particularly deep coverage of Green's functions, the Fourier transform, and the Laplace transform. A salient characteristic is the focus on fewer topics but at a far more rigorous level of detail than comparable undergraduate-facing textbooks. The depth of some of these topics, such as the Dirac-delta distribution, is not matched elsewhere. New features in this edition include: novel and illustrative examples from physics including the 1-dimensional quantum mechanical oscillator, the hydrogen atom and the rigid rotor model; chapter-length discussion of relevant functions, including the Hermite polynomials, Legendre polynomials, Laguerre polynomials and Bessel functions; and all-new focus on complex examples only solvable by multiple methods.

This book offers a detailed description of the histogram probabilistic multi-hypothesis tracker (H-PMHT), providing an accessible and intuitive introduction to the mathematical mechanics of H-PMHT as well as a definitive reference source for the existing literature on the method. Beginning with basic concepts, the authors then move on to address extensions of the method to a broad class of tracking problems. The latter chapters present applications using recorded data from experimental radar, sonar and video sensor systems. The book is supplemented with software that both furthers readers' understanding and acts as a toolkit for those who wish to apply the methods to their own problems.

Agenda Relevance is the first volume in the authors' omnibus investigation of
the logic of practical reasoning, under the collective title, A Practical Logic
of Cognitive Systems. In this highly original approach, practical reasoning is
identified as reasoning performed with comparatively few cognitive assets,
including resources such as information, time and computational capacity. Unlike
what is proposed in optimization models of human cognition, a practical reasoner
lacks perfect information, boundless time and unconstrained access to
computational complexity. The practical reasoner is therefore obliged to be a
cognitive economizer and to achieve his cognitive ends with considerable
efficiency. Accordingly, the practical reasoner avails himself of various
scarce-resource compensation strategies. He also possesses neurocognitive
traits that abet him in his reasoning tasks. Prominent among these is the
practical agent's striking (though not perfect) adeptness at evading irrelevant
information and staying on task. On the approach taken here, irrelevancies are
impediments to the attainment of cognitive ends. Thus, in its most basic sense,
relevant information is cognitively helpful information. Information can then be
said to be relevant for a practical reasoner to the extent that it advances or
closes some cognitive agenda of his. The book explores this idea with a
conceptual detail and nuance not seen the standard semantic, probabilistic and
pragmatic approaches to relevance; but wherever possible, the authors seek to
integrate alternative conceptions rather than reject them outright. A further
attraction of the agenda-relevance approach is the extent to which its principal
conceptual findings lend themselves to technically sophisticated re-expression
in formal models that marshal the resources of time and action logics and
label led deductive systems.

Agenda Relevance is necessary reading for researchers in logic, belief
dynamics, computer science, AI, psychology and neuroscience, linguistics,
argumentation theory, and legal reasoning and forensic science, and will repay
study by graduate students and senior undergraduates in these same fields.

Key features:

relevance
action and agendas
practical reasoning
belief dynamics
non-classical logics
labelled deductive systems

"

This book contains the proceedings of the Seventh National Conference of the Italian Systems Society. The title, Systemics of Incompleteness and Quasi-Systems, aims to underline the need for Systemics and Systems Science to deal with the concepts of incompleteness and quasiness. Classical models of Systemics are intended to represent comprehensive aspects of phenomena and processes. They consider the phenomena in their temporal and spatial completeness. In these cases, possible incompleteness in the modelling is assumed to have a provisional or practical nature, which is still under study, and because there is no theoretical reason why the modelling cannot be complete. In principle, this is a matter of non-complex phenomena, to be considered using the concepts of the First Systemics. When dealing with emergence, there are phenomena which must be modelled by systems having multiple models, depending on the aspects being taken into consideration. Here, incompleteness in the modelling is intrinsic, theoretically relating changes in properties, structures, and status of system. Rather than consider the same system parametrically changing over time, we consider sequences of systems coherently. We consider contexts and processes for which modelling is incomplete, being related to only some properties, as well as those for which such modelling is theoretically incomplete-as in the case of processes of emergence and for approaches considered by the Second Systemics. In this regard, we consider here the generic concept of quasi explicating such incompleteness. The concept of quasi is used in various disciplines including quasi-crystals, quasi-particles, quasi-electric fields, and quasi-periodicity. In general, the concept of quasiness for systems concerns their continuous structural changes which are always meta-stable, waiting for events to collapse over other configurations and possible forms of stability; whose equivalence depends on the type of phenomenon under study. Interest in the concept of quasiness is not related to its meaning of rough approximation, but because it indicates an incompleteness which is structurally sufficient to accommodate processes of emergence and sustain coherence or generate new, equivalent or non-equivalent, levels. The conference was devoted to identifying, discussing and understanding possible interrelationships of theoretical disciplinary improvements, recognised as having prospective fundamental roles for a new Quasi-Systemics. The latter should be able to deal with problems related to complexity in more general and realistic ways, when a system is not always a system and not always the same system. In this context, the inter-disciplinarity should consist, for instance, of a constructionist, incomplete, non-ideological, multiple, contradiction-tolerant, Systemics, always in progress, and in its turn, emergent.

It has been known for some time that many of the familiar integrable systems of equations are symmetry reductions of self-duality equations on a metric or on a Yang-Mills connection (for example, the Korteweg-de Vries and nonlinear Schroedinger equations are reductions of the self-dual Yang-Mills equation). This book explores in detail the connections between self-duality and integrability, and also the application of twistor techniques to integrable systems. It has two central themes: first, that the symmetries of self-duality equations provide a natural classification scheme for integrable systems; and second that twistor theory provides a uniform geometric framework for the study of Backlund tranformations, the inverse scattering method, and other such general constructions of integrability theory, and that it elucidates the connections between them.

Mathematics teacher education includes the mathematics content teachers need to understand, ways that pedagogical approaches are developed, messages about the nature of mathematics teaching and learning, and interfaces between tertiary preparation and school contexts. Scholars from Sweden, France, Malawi, Singapore, New Zealand, Brazil, the USA, and Canada provide insights for the mathematics education community's understanding of how teacher educators structure, develop, and implement their respective mathematics teacher education programs. Several themes emerged across the chapters, including: varied approaches to developing culturally responsive pedagogies and/or Indigenous perspectives; issues and challenges in fostering partnerships and collaborations; strategies for developing mathematics knowledge for teaching; and preparing flexible and resourceful teachers

This book is a survey of the research work done by the author over the last 15 years, in collaboration with various eminent mathematicians and climate scientists on the subject of tropical convection and convectively coupled waves. In the areas of climate modelling and climate change science, tropical dynamics and tropical rainfall are among the biggest uncertainties of future projections. This not only puts at risk billions of human beings who populate the tropical continents but it is also of central importance for climate predictions on the global scale. This book aims to introduce the non-expert readers in mathematics and theoretical physics to this fascinating topic in order to attract interest into this difficult and exciting research area. The general thyme revolves around the use of new deterministic and stochastic multi-cloud models for tropical convection and convectively coupled waves. It draws modelling ideas from various areas of mathematics and physics and used in conjunction with state-of-the-art satellite and in-situ observations and detailed numerical simulations. After a review of preliminary material on tropical dynamics and moist thermodynamics, including recent discoveries based on satellite observations as well as Markov chains, the book immerses the reader into the area of models for convection and tropical waves. It begins with basic concepts of linear stability analysis and ends with the use of these models to improve the state-of-the-art global climate models. The book also contains a fair amount of exercises that makes it suitable as a textbook complement on the subject.

This book provides a unique survey displaying the power of Riccati equations to describe reversible and irreversible processes in physics and, in particular, quantum physics. Quantum mechanics is supposedly linear, invariant under time-reversal, conserving energy and, in contrast to classical theories, essentially based on the use of complex quantities. However, on a macroscopic level, processes apparently obey nonlinear irreversible evolution equations and dissipate energy. The Riccati equation, a nonlinear equation that can be linearized, has the potential to link these two worlds when applied to complex quantities. The nonlinearity can provide information about the phase-amplitude correlations of the complex quantities that cannot be obtained from the linearized form. As revealed in this wide ranging treatment, Riccati equations can also be found in many diverse fields of physics from Bose-Einstein-condensates to cosmology. The book will appeal to graduate students and theoretical physicists interested in a consistent mathematical description of physical laws.

This book presents the state of the art in High Performance Computing on modern supercomputer architectures. It addresses trends in hardware and software development in general, as well as the future of High Performance Computing systems and heterogeneous architectures. The contributions cover a broad range of topics, from improved system management to Computational Fluid Dynamics, High Performance Data Analytics, and novel mathematical approaches for large-scale systems. In addition, they explore innovative fields like coupled multi-physics and multi-scale simulations. All contributions are based on selected papers presented at the 24th Workshop on Sustained Simulation Performance, held at the University of Stuttgart's High Performance Computing Center in Stuttgart, Germany in December 2016 and the subsequent Workshop on Sustained Simulation Performance, held at the Cyberscience Center, Tohoku University, Japan in March 2017.

"Stability of NonLinear Shells" is a compilation of the author's work on analyzing the behaviour of spherical caps and related shell structures under various (axisymmetric) load systems. Differing from other texts on shells of revolution, it is one of the first attempts to deal with effects of multi-parameter load systems. This extension leads to the discovery of some new, hitherto unknown phenomena exhibited by these structures. In addition, the book presents a novel way to characterize properties of solutions of the governing equations for spherical caps - a classification anchored in a theory called reciprocal systems. The author has introduced a deformation map, a projection of multi-dimensional solutions to two-dimensional graphs, to enable analysts to gain insight into the physical meaning of the results obtained.
Numerous examples illustrate the concepts introduced. This book also comes to grips with many misconceptions existing in engineering literature about the question of the stability of solutions.

In any linear system, the input and the output are connected by means of a linear operator. When the input can be notionally represented by a function that is null valued everywhere except at a specific location in spacetime, the corresponding output is called the Green function in field theories. Dyadic Green functions are commonplace in electromagnetics, because both the input and the output are vector functions of space and time. This book provides a survey of the state-of-the-art knowledge of infinite space dyadic Green functions.

The work presented in this book is based on the proton-proton collision data from the Large Hadron Collider at a centre-of-mass energy of 13 TeV recorded by the ATLAS detector in 2015 and 2016. The research program of the ATLAS experiment includes the precise measurement of the parameters of the Standard Model, and the search for signals of physics beyond the SM. Both these approaches are pursued in this thesis, which presents two different analyses: the measurement of the Higgs boson mass in the di-photon decay channel, and the search for production of supersymmetric particles (gluinos, squarks or winos) in a final state containing two photons and missing transverse momentum. Finally, ATLAS detector performance studies, which are key ingredients for the two analyses outlined before, are also carried out and described.

This updated edition of a classic title studies identical relations in Lie algebras and also in other classes of algebras, a theory with over 40 years of development in which new methods and connections with other areas of mathematics have arisen. New topics covered include graded identities, identities of algebras with actions and coactions of various Hopf algebras, and the representation theory of the symmetric and general linear group.

This book presents novel research ideas and offers insights into radar system design, artificial intelligence and signal processing applications. Further, it proposes a new concept of antenna spatial polarization characteristics (SPC), suggesting that the antenna polarization is a function of the spatial direction and providing new ideas for radar signal processing (RSP) and anti-jamming. It also discusses the design of an advanced signal-processing algorithm, and proposes new polarimetric and anti-jamming methods using antenna inherent properties. The book helps readers discover the potential of radar information processing and improve its anti-interference and target identification ability. It is of interest to university researchers, radar engineers and graduate students in computer science and electronics who wish to learn the core principles, methods, algorithms, and applications of RSP.

Most physical systems lose or gain stability through bifurcation behavior. This book explains a series of experimentally found bifurcation phenomena by means of the methods of static bifurcation theory.

This is the proceedings of ARK 2018, the 16th International Symposium on Advances in Robot Kinematics, that was organized by the Group of Robotics, Automation and Biomechanics (GRAB) from the University of Bologna, Italy. ARK are international symposia of the highest level organized every two years since 1988. ARK provides a forum for researchers working in robot kinematics and stimulates new directions of research by forging links between robot kinematics and other areas.The main topics of the symposium of 2018 were: kinematic analysis of robots, robot modeling and simulation, kinematic design of robots, kinematics in robot control, theories and methods in kinematics, singularity analysis, kinematic problems in parallel robots, redundant robots, cable robots, over-constrained linkages, kinematics in biological systems, humanoid robots and humanoid subsystems.

This book describes computational problems related to kernel density estimation (KDE) - one of the most important and widely used data smoothing techniques. A very detailed description of novel FFT-based algorithms for both KDE computations and bandwidth selection are presented. The theory of KDE appears to have matured and is now well developed and understood. However, there is not much progress observed in terms of performance improvements. This book is an attempt to remedy this. The book primarily addresses researchers and advanced graduate or postgraduate students who are interested in KDE and its computational aspects. The book contains both some background and much more sophisticated material, hence also more experienced researchers in the KDE area may find it interesting. The presented material is richly illustrated with many numerical examples using both artificial and real datasets. Also, a number of practical applications related to KDE are presented.

Quadratic equations, Pythagoras' theorem, imaginary numbers, and pi - you may remember studying these at school, but did anyone ever explain why? Never fear - bestselling science writer, and your new favourite maths teacher, Michael Brooks, is here to help. In The Maths That Made Us, Brooks reminds us of the wonders of numbers: how they enabled explorers to travel far across the seas and astronomers to map the heavens; how they won wars and halted the HIV epidemic; how they are responsible for the design of your home and almost everything in it, down to the smartphone in your pocket. His clear explanations of the maths that built our world, along with stories about where it came from and how it shaped human history, will engage and delight. From ancient Egyptian priests to the Apollo astronauts, and Babylonian tax collectors to juggling robots, join Brooks and his extraordinarily eccentric cast of characters in discovering how maths made us who we are today.

The relationship between research and practice has long been an area of interest for researchers, policy makers, and practitioners alike. One obvious arena where mathematics education research can contribute to practice is the design and implementation of school mathematics curricula. This observation holds whether we are talking about curriculum as a set of broad, measurable competencies (i.e., standards) or as a comprehensive set of resources for teaching and learning mathematics. Impacting practice in this way requires fine-grained research that is focused on individual student learning trajectories and intimate analyses of classroom pedagogical practices as well as large-scale research that explores how student populations typically engage with the big ideas of mathematics over time. Both types of research provide an empirical basis for identifying what aspects of mathematics are important and how they develop over time. This book has its origins in independent but parallel work in Australia and the United States over the last 10 to 15 years. It was prompted by a research seminar at the 2017 PME Conference in Singapore that brought the contributors to this volume together to consider the development and use of evidence-based learning progressions/trajectories in mathematics education, their basis in theory, their focus and scale, and the methods used to identify and validate them. In this volume they elaborate on their work to consider what is meant by learning progressions/trajectories and explore a range of issues associated with their development, implementation, evaluation, and on-going review. Implications for curriculum design and future research in this field are also considered. Contributors are: Michael Askew, Tasos Barkatsas, Michael Belcher, Rosemary Callingham, Doug Clements, Jere Confrey, Lorraine Day, Margaret Hennessey, Marj Horne, Alan Maloney, William McGowan, Greg Oates, Claudia Orellana, Julie Sarama, Rebecca Seah, Meetal Shah, Dianne Siemon, Max Stephens, Ron Tzur, and Jane Watson.

This work introduces heavy ion beam probe diagnostics and presents an overview of its applications. The heavy ion beam probe is a unique tool for the measurement of potential in the plasma core in order to understand the role of the electric field in plasma confinement, including the mechanism of transition from low to high confinement regimes (L-H transition). This allows measurement of the steady-state profile of the plasma potential, and its use has been extended to include the measurement of quasi-monochromatic and broadband oscillating components, the turbulent-particle flux and oscillations of the electron density and poloidal magnetic field. Special emphasis is placed on the study of Geodesic Acoustic Modes and Alfven Eigenmodes excited by energetic particles with experimental data sets. These experimental studies help to understand the link between broadband turbulent physics and quasi-coherent oscillations in devices with a rather different magnetic configuration. The book also compares spontaneous and biased transitions from low to high confinement regimes on both classes of closed magnetic traps (tokamak and stellarator) and highlights the common features in the behavior of electric potential and turbulence of magnetized plasmas. A valuable resource for physicists, postgraduates and students specializing in plasma physics and controlled fusion.

Algebraic combinatorics is the study of combinatorial objects as an extension of the study of finite permutation groups, or, in other words, group theory without groups. In the spirit of Delsarte's theory, this book studies combinatorial objects such as graphs, codes, designs, etc. in the general framework of association schemes, providing a comprehensive overview of the theory as well as pointing out to extensions.