The aim of this book is to present recent results in both theoretical and applied knot theory-which are at the same time stimulating for leading researchers in the field as well as accessible to non-experts. The book comprises recent research results while covering a wide range of different sub-disciplines, such as the young field of geometric knot theory, combinatorial knot theory, as well as applications in microbiology and theoretical physics.

The development of man's understanding of planetary motions is the crown jewel of Newtonian mechanics. This book offers a concise but self-contained handbook-length treatment of this historically important topic for students at about the third-year-level of an undergraduate physics curriculum. After opening with a review of Kepler's three laws of planetary motion, it proceeds to analyze the general dynamics of "central force" orbits in spherical coordinates, how elliptical orbits satisfy Newton's gravitational law and how the geometry of ellipses relates to physical quantities such as energy and momentum. Exercises are provided and derivations are set up in such a way that readers can gain analytic practice by filling in missing steps. A brief bibliography lists sources for readers who wish to pursue further study on their own.

Electroencephalography and magnetoencephalography are the two most efficient techniques to study the functional brain. This book completely aswers the fundamental mathematical question of uniqueness of the representations obtained using these techniques, and also covers many other concrete results for special geometric models of the brain, presenting the research of the authors and their groups in the last two decades.

This book introduces the fundamental concepts, methods, and applications of Hausdorff calculus, with a focus on its applications in fractal systems. Topics such as the Hausdorff diffusion equation, Hausdorff radial basis function, Hausdorff derivative nonlinear systems, PDE modeling, statistics on fractals, etc. are discussed in detail. It is an essential reference for researchers in mathematics, physics, geomechanics, and mechanics.

This book demonstrates some of the ways in which Microsoft Excel (R) may be used to solve numerical problems in the field of physics.

This book addresses the mechanism of enrichment of heavy elements in galaxies, a long standing problem in astronomy. It mainly focuses on explaining the origin of heavy elements by performing state-of-the-art, high-resolution hydrodynamic simulations of dwarf galaxies. In this book, the author successfully develops a model of galactic chemodynamical evolution by means of which the neutron star mergers can be used to explain the observed abundance pattern of the heavy elements synthesized by the rapid neutron capture process, such as europium, gold, and uranium in the Local Group dwarf galaxies. The book argues that heavy elements are significant indicators of the evolutionary history of the early galaxies, and presents theoretical findings that open new avenues to understanding the formation and evolution of galaxies based on the abundance of heavy elements in metal-poor stars.

This book provides a concise introduction to the special theory of relativity and the general theory of relativity. The format has been chosen to provide the basis for a single semester course that can take the students all the way from the foundations of special relativity to the core results of general relativity: the Einstein equation, and the equations of motion for particles and light in curved spacetime. To facilitate access to the topics of special and general relativity for science and engineering students, without prior training in relativity or geometry, the relevant geometric notions are also introduced.

The revised edition gives a comprehensive mathematical and physical presentation of fluid flows in non-classical models of convection - relevant in nature as well as in industry. After the concise coverage of fluid dynamics and heat transfer theory it discusses recent research. This monograph provides the theoretical foundation on a topic relevant to metallurgy, ecology, meteorology, geo-and astrophysics, aerospace industry, chemistry, crystal physics, and many other fields.

Blockchain Technology: Platforms, Tools and Use Cases, Volume 111, the latest release in the Advances in Computers series published since 1960, presents detailed coverage of innovations in computer hardware, software, theory, design and applications. In addition, it provides contributors with a medium in which they can explore their subjects in greater depth and breadth than journal articles usually allow. This volume has 8 Chapters that discuss the various aspects of Blockchain technology.

Reliability is one of the fundamental criteria in engineering systems. Design and maintenance serve to support it throughout the systems life. As such, maintenance acts in parallel to production and can have a great impact on the availability and capacity of production and the quality of the products. The authors describe current and innovative methods useful to industry and society.

This book discusses in detail the special theory of relativity without including all the instruments of theoretical physics, enabling readers who are not budding theoretical physicists to develop competence in the field. An arbitrary but fixed inertial system is chosen, where the known velocity of light is measured. With respect to this system a moving clock loses time and a moving length contracts. The book then presents a definition of simultaneity for the other inertial frames without using the velocity of light. To do so it employs the known reciprocity principle, which in this context serves to provide a definition of simultaneity in the other inertial frames. As a consequence, the Lorentz transformation is deduced and the universal constancy of light is established. With the help of a lattice model of the special theory of relativity the book provides a deeper understanding of the relativistic effects. Further, it discusses the key STR experiments and formulates and solves 54 problems in detail.

This book aims to bring together researchers and practitioners working across domains and research disciplines to measure, model, and visualize complex networks. It collects the works presented at the 9th International Conference on Complex Networks (CompleNet) in Boston, MA, March, 2018. With roots in physical, information and social science, the study of complex networks provides a formal set of mathematical methods, computational tools and theories to describe, prescribe and predict dynamics and behaviors of complex systems. Despite their diversity, whether the systems are made up of physical, technological, informational, or social networks, they share many common organizing principles and thus can be studied with similar approaches. This book provides a view of the state-of-the-art in this dynamic field and covers topics such as group decision-making, brain and cellular connectivity, network controllability and resiliency, online activism, recommendation systems, and cyber security.

This is the third volume in a three-part series that uses art photography as a point of departure for learning about physics, while also using physics to ask fundamental questions about the nature of photography as an art.

In Pi ( ) in Nature, Art, and Culture Marcel Danesi revisits the importance of as a pattern in the structure of reality, fitting in with the Pythagorean view of Order. Pi has cropped up in formulas that describe natural and physical structures which, on the surface, seem to have nothing to do with a circle, but might harbor the archetype of circularity as a principle. Through , this book thus revisits the implicit ancient Greek view that geometry was a 'hermeneutic science,' a discipline aiming to investigate the connectivity among numbers, shapes, and natural phenomena. It also examines its manifestations in aesthetic, symbolic and cultural structures, which point to an abiding fascination with the circle as an unconscious archetype. Hermeneutic geometry is ultimately about the exploration of the meanings of geometric-mathematical notions to science and human life.

This book provides a comprehensive and systematic approach to the study of the qualitative theory of boundedness, periodicity, and stability of Volterra difference equations. The book bridges together the theoretical aspects of Volterra difference equations with its applications to population dynamics. Applications to real-world problems and open-ended problems are included throughout. This book will be of use as a primary reference to researchers and graduate students who are interested in the study of boundedness of solutions, the stability of the zero solution, or in the existence of periodic solutions using Lyapunov functionals and the notion of fixed point theory.

This book is a self-contained account of the method based on Carleman estimates for inverse problems of determining spatially varying functions of differential equations of the hyperbolic type by non-overdetermining data of solutions. The formulation is different from that of Dirichlet-to-Neumann maps and can often prove the global uniqueness and Lipschitz stability even with a single measurement. These types of inverse problems include coefficient inverse problems of determining physical parameters in inhomogeneous media that appear in many applications related to electromagnetism, elasticity, and related phenomena. Although the methodology was created in 1981 by Bukhgeim and Klibanov, its comprehensive development has been accomplished only recently. In spite of the wide applicability of the method, there are few monographs focusing on combined accounts of Carleman estimates and applications to inverse problems. The aim in this book is to fill that gap. The basic tool is Carleman estimates, the theory of which has been established within a very general framework, so that the method using Carleman estimates for inverse problems is misunderstood as being very difficult. The main purpose of the book is to provide an accessible approach to the methodology. To accomplish that goal, the authors include a direct derivation of Carleman estimates, the derivation being based essentially on elementary calculus working flexibly for various equations. Because the inverse problem depends heavily on respective equations, too general and abstract an approach may not be balanced. Thus a direct and concrete means was chosen not only because it is friendly to readers but also is much more relevant. By practical necessity, there is surely a wide range of inverse problems and the method delineated here can solve them. The intention is for readers to learn that method and then apply it to solving new inverse problems.

This book provides a comprehensive review of complex networks from three different domains, presents novel methods for analyzing them, and highlights applications with accompanying case studies. Special emphasis is placed on three specific kinds of complex networks of high technological and scientific importance: software networks extracted from the source code of computer programs, ontology networks describing semantic web ontologies, and co-authorship networks reflecting collaboration in science. The book is primarily intended for researchers, teachers and students interested in complex networks and network data analysis. However, it will also be valuable for researchers dealing with software engineering, ontology engineering and scientometrics, as it demonstrates how complex network analysis can be used to address important research issues in these three disciplines.

Vortices comprising swirling motion of matter are observable in classical systems at all scales ranging from atomic size to the scale of galaxies. In quantum mechanical systems, such vortices are robust entities whose behaviours are governed by the strict rules of topology. The physics of quantum vortices is pivotal to basic science of quantum turbulence and high temperature superconductors, and underpins emerging quantum technologies including topological quantum computation. This handbook is aimed at providing a dictionary style portal to the fascinating quantum world of vortices.

A Deep Dive into NoSQL Databases: The Use Cases and Applications, Volume 109, the latest release in the Advances in Computers series first published in 1960, presents detailed coverage of innovations in computer hardware, software, theory, design and applications. In addition, it provides contributors with a medium in which they can explore their subjects in greater depth and breadth. This update includes sections on NoSQL and NewSQL databases for big data analytics and distributed computing, NewSQL databases and scalable in-memory analytics, NoSQL web crawler application, NoSQL Security, a Comparative Study of different In-Memory (No/New)SQL Databases, NoSQL Hands On-4 NoSQLs, the Hadoop Ecosystem, and more.

Numerical and computational methods play a major role in modelling compressible flow and are important tools in solving fluid dynamical problems faced in many areas of science and technology. This book thoroughly surveys and analyzes up-to-date methods, while reviewing the basic theoretical mathematical analysis.

Domain theory is a subject that emerged as a response to natural concerns in the semantics of computation, and it involves the study of ordered sets that possess an unusual amount of mathematical structure. Disorder in Domain Theory explores the connection between domain theory and quantum information science and the concept that relates them: disorder.

This book investigates a wide range of phase equilibrium modelling and calculation problems for compositional thermal simulation. Further, it provides an effective solution for multiphase isenthalpic flash under the classical framework, and it also presents a new flash calculation framework for multiphase systems, which can handle phase equilibrium and chemical reaction equilibrium simultaneously. The framework is particularly suitable for systems with many phases and reactions. In this book, the author shows how the new framework can be generalised for different flash specifications and different independent variables. Since the flash calculation is at the heart of various types of compositional simulation, the findings presented here will promote the combination of phase equilibrium and chemical equilibrium calculations in future simulators, aiming at improving their robustness and efficiency.

"Difference Equations, Second Edition," presents a practical introduction to this important field of solutions for engineering and the physical sciences. Topic coverage includes numerical analysis, numerical methods, differential equations, combinatorics and discrete modeling. A hallmark of this revision is the diverse application to many subfields of mathematics.

* Phase plane analysis for systems of two linear equations
* Use of equations of variation to approximate solutions
* Fundamental matrices and Floquet theory for periodic systems
* LaSalle invariance theorem
* Additional applications: secant line method, Bison problem, juvenile-adult population model, probability theory
* Appendix on the use of "Mathematica" for analyzing difference equaitons
* Exponential generating functions
* Many new examples and exercises