This book contains selected chapters on recent research in topology. It bridges the gap between recent trends of topological theories and their applications in areas like social sciences, natural sciences, soft computing, economics, theoretical chemistry, cryptography, pattern recognitions and granular computing. There are 14 chapters, including two chapters on mathematical economics from the perspective of topology. The book discusses topics on function spaces, relator space, preorder, quasi-uniformities, bitopological dynamical systems, b-metric spaces and related fixed point theory. This book is useful to researchers, experts and scientists in studying the cutting-edge research in topology and related areas and helps them applying topology in solving real-life problems the society and science are facing these days.. 

The book systematically introduces smart power system design and its infrastructure, platform and operating standards. It focuses on multi-objective optimization and illustrates where the intelligence of the system lies. With abundant project data, this book is a practical guideline for engineers and researchers in electrical engineering, as well as power network designers and managers in administration.

Susanna Epp's DISCRETE MATHEMATICS WITH APPLICATIONS, 4e, International Edition provides a clear introduction to discrete mathematics. Renowned for her lucid, accessible prose, Epp explains complex, abstract concepts with clarity and precision. This book presents not only the major themes of discrete mathematics, but also the reasoning that underlies mathematical thought. Students develop the ability to think abstractly as they study the ideas of logic and proof. While learning about such concepts as logic circuits and computer addition, algorithm analysis, recursive thinking, computability, automata, cryptography, and combinatorics, students discover that the ideas of discrete mathematics underlie and are essential to the science and technology of the computer age. Overall, Epp's emphasis on reasoning provides students with a strong foundation for computer science and upper-level mathematics courses.

It is not uncommon for the Principle of Complementarity to be invoked in either Science or Philosophy, viz. the ancient oriental philosophy of Yin and Yang whose symbolic representation is portrayed on the cover of the book. Or Niels Bohr's use of it as the basis for the so-called Copenhagen interpretation of Quantum Mechanics. This book arose as an outgrowth of the author's previous book entitled 'Knots, Braids and Moebius Strips,' published by World Scientific in 2015, wherein the Principle itself was discovered to be expressible as a simple 2x2 matrix that summarizes the algebraic essence of both the well-known Microbiology of DNA and the author's version of the elementary particles of physics. At that point, the possibility of an even wider utilization of that expression of Complementarity arose.The current book, features Complementarity, in which the matrix algebra is extended to characterize not only DNA itself but the well-known process of its replication, a most gratifying outcome. The book then goes on to explore Complementarity, with and without its matrix expression, as it occurs, not only in much of physics but in its extension to cosmology as well.

In recent years, enormous progress has been made on nonlinear dynamics particularly on chaos and complex phenomena. This unique volume presents the advances made in theory, analysis, numerical simulation and experimental realization, promising novel practical applications on various topics of current interest on chaos and related fields of nonlinear dynamics.Particularly, the focus is on the following topics: synchronization vs. chaotic phenomena, chaos and its control in engineering dynamical systems, fractal-based dynamics, uncertainty and unpredictability measures vs. chaos, Hamiltonian systems and systems with time delay, local/global stability, bifurcations and their control, applications of machine learning to chaos, nonlinear vibrations of lumped mass mechanical/mechatronic systems (rigid body and coupled oscillator dynamics) governed by ODEs and continuous structural members (beams, plates, shells) vibrations governed by PDEs, patterns formation, chaos in micro- and nano-mechanical systems, chaotic reduced-order models, energy absorption/harvesting from chaotic, chaos vs. resonance phenomena, chaos exhibited by discontinuous systems, chaos in lab experiments.The present volume forms an invaluable source on recent trends in chaotic and complex dynamics for any researcher and newcomers to the field of nonlinear dynamics.

Magic squares are among the more popular mathematical recreations. Over the last 50 years, many generalizations of "magic" ideas have been applied to graphs. Recently there has been a resurgence of interest in "magic labelings" due to a number of results that have applications to the problem of decomposing graphs into trees.

Key features of this second edition include:

. a new chapter on magic labeling of directed graphs

. applications of theorems from graph theory and interesting counting arguments

. new research problems and exercises covering a range of difficulties

. a fully updated bibliography and index

This concise, self-contained exposition is unique in its focus on the theory of magic graphs/labelings. It may serve as a graduate or advanced undergraduate text for courses in mathematics or computer science, and as reference for the researcher."

Randomness is an active element relevant to all scientific activities. The book explores the way in which randomness suffuses the human experience, starting with everyday chance events, followed by developments into modern probability theory, statistical mechanics, scientific data analysis, quantum mechanics, and quantum gravity. An accessible introduction to these theories is provided as a basis for going into deeper topics.Fowler unveils the influence of randomness in the two pillars of science, measurement and theory. Some emphasis is placed on the need and methods for optimal characterization of uncertainty. An example of the cost of neglecting this is the St. Petersburg Paradox, a theoretical game of chance with an infinite expected payoff value. The role of randomness in quantum mechanics reveals another particularly interesting finding: that in order for the physical universe to function as it does and permit conscious beings within it to enjoy sanity, irreducible randomness is necessary at the quantum level.The book employs a certain level of mathematics to describe physical reality in a more precise way that avoids the tendency of nonmathematical descriptions to be occasionally misleading. Thus, it is most readily digested by young students who have taken at least a class in introductory calculus, or professional scientists and engineers curious about the book's topics as a result of hearing about them in popular media. Readers not inclined to savor equations should be able to skip certain technical sections without losing the general flow of ideas. Still, it is hoped that even readers who usually avoid equations will give those within these pages a chance, as they may be surprised at how potentially foreboding concepts fall into line when one makes a legitimate attempt to follow a succession of mathematical implications.

Boltzmann and Vlasov equations played a great role in the past and still play an important role in modern natural sciences, technique and even philosophy of science. Classical Boltzmann equation derived in 1872 became a cornerstone for the molecular-kinetic theory, the second law of thermodynamics (increasing entropy) and derivation of the basic hydrodynamic equations. After modifications, the fields and numbers of its applications have increased to include diluted gas, radiation, neutral particles transportation, atmosphere optics and nuclear reactor modelling. Vlasov equation was obtained in 1938 and serves as a basis of plasma physics and describes large-scale processes and galaxies in astronomy, star wind theory. This book provides a comprehensive review of both equations and presents both classical and modern applications. In addition, it discusses several open problems of great importance.

Tensors have numerous applications in physics and engineering. There is often a fuzzy haze surrounding the concept of tensor that puzzles many students. The old-fashioned definition is difficult to understand because it is not rigorous; the modern definitions are difficult to understand because they are rigorous but at a cost of being more abstract and less intuitive.The goal of this book is to elucidate the concepts in an intuitive way but without loss of rigor, to help students gain deeper understanding. As a result, they will not need to recite those definitions in a parrot-like manner any more. This volume answers common questions and corrects many misconceptions about tensors. A large number of illuminating illustrations helps the reader to understand the concepts more easily.This unique reference text will benefit researchers, professionals, academics, graduate students and undergraduate students.

A nonsimple (complex) system indicates a mix of crucial and non-crucial events, with very different statistical properties. It is the crucial events that determine the efficiency of information exchange between complex networks. For a large class of nonsimple systems, crucial events determine catastrophic failures - from heart attacks to stock market crashes.This interesting book outlines a data processing technique that separates the effects of the crucial from those of the non-crucial events in nonsimple time series extracted from physical, social and living systems. Adopting an informal conversational style, without sacrificing the clarity necessary to explain, the contents will lead the reader through concepts such as fractals, complexity and randomness, self-organized criticality, fractional-order differential equations of motion, and crucial events, always with an eye to helping to interpret what mathematics usually does in the development of new scientific knowledge.Both researchers and novitiate will find Crucial Events useful in learning more about the science of nonsimplicity.

The book will benefit a reader with a background in physical sciences and applied mathematics interested in the mathematical models of genetic evolution. In the first chapter, we analyze several thought experiments based on a basic model of stochastic evolution of a single genomic site in the presence of the factors of random mutation, directional natural selection, and random genetic drift. In the second chapter, we present a more advanced theory for a large number of linked loci. In the third chapter, we include the effect of genetic recombination into account and find out the advantage of sexual reproduction for adaptation. These models are useful for the evolution of a broad range of asexual and sexual populations, including virus evolution in a host and a host population.

Spiritual Insights from the New Science is a guide to the deep spiritual wisdom drawn from one of the newest areas of science - the study of complex systems. The author, a former research scientist with over three decades of experience in the field of complexity science, tells her story of being attracted, as a young student, to the study of self-organizing systems where she encountered the strange and beautiful topics of chaos, fractals and other concepts that comprise complexity science. Using the events of her life, she describes lessons drawn from this science that provide insights into not only her own life, but all our lives. These insights show us how to weather the often disruptive events we all experience when growing and changing.The book goes on to explore, through the unfolding story of the author's life as a practicing scientist, other key concepts from the science of complex systems: cycles and rhythms, attractors and bifurcations, chaos, fractals, self-organization, and emergence. Examples drawn from religious rituals, dance, philosophical teachings, mysticism, native American spirituality, and other sources are used to illustrate how these scientific insights apply to all aspects of life, especially the spiritual. Spiritual Insights from the New Science shows the links between this new science and our human spirituality and presents, in engaging, accessible language, the argument that the study of nature can lead to a better understanding of the deepest meaning of our lives.

Spiritual Insights from the New Science is a guide to the deep spiritual wisdom drawn from one of the newest areas of science - the study of complex systems. The author, a former research scientist with over three decades of experience in the field of complexity science, tells her story of being attracted, as a young student, to the study of self-organizing systems where she encountered the strange and beautiful topics of chaos, fractals and other concepts that comprise complexity science. Using the events of her life, she describes lessons drawn from this science that provide insights into not only her own life, but all our lives. These insights show us how to weather the often disruptive events we all experience when growing and changing.The book goes on to explore, through the unfolding story of the author's life as a practicing scientist, other key concepts from the science of complex systems: cycles and rhythms, attractors and bifurcations, chaos, fractals, self-organization, and emergence. Examples drawn from religious rituals, dance, philosophical teachings, mysticism, native American spirituality, and other sources are used to illustrate how these scientific insights apply to all aspects of life, especially the spiritual. Spiritual Insights from the New Science shows the links between this new science and our human spirituality and presents, in engaging, accessible language, the argument that the study of nature can lead to a better understanding of the deepest meaning of our lives.

An essential contribution to the study of the history of computers, this work identifies the computer's impact on the physical, biological, cognitive, and medical sciences. References fundamental to the understudied area of the history of scientific computing also document the significant role of the sciences in helping to shape the development of computer technology. More broadly, the many resources on scientific computing help demonstrate how the computer was the most significant scientific instrument of the 20th century.

The only guide of its kind covering the use and impact of computers on the the physical, biological, medical, and cognitive sciences, it contains more than 1,000 annotated citations to carefully selected secondary and primary resources. Historians of technology and science will find this a very useful resource. Computer scientists, physicians, biologists, chemists, and geologists will also benefit from this extensive bibliography on the history of computer applications and the sciences.

Calculations for Molecular Biology and Biotechnology: A Guide to Mathematics in the Laboratory, Second Edition, provides an introduction to the myriad of laboratory calculations used in molecular biology and biotechnology. The book begins by discussing the use of scientific notation and metric prefixes, which require the use of exponents and an understanding of significant digits. It explains the mathematics involved in making solutions; the characteristics of cell growth; the multiplicity of infection; and the quantification of nucleic acids. It includes chapters that deal with the mathematics involved in the use of radioisotopes in nucleic acid research; the synthesis of oligonucleotides; the polymerase chain reaction (PCR) method; and the development of recombinant DNA technology. Protein quantification and the assessment of protein activity are also discussed, along with the centrifugation method and applications of PCR in forensics and paternity testing.

This book is a description of why and how to do Scientific Computing for fundamental models of fluid flow. It contains introduction, motivation, analysis, and algorithms and is closely tied to freely available MATLAB codes that implement the methods described. The focus is on finite element approximation methods and fast iterative solution methods for the consequent linear(ized) systems arising in important problems that model incompressible fluid flow. The problems addressed are the Poisson equation, Convection-Diffusion problem, Stokes problem and Navier-Stokes problem, including new material on time-dependent problems and models of multi-physics. The corresponding iterative algebra based on preconditioned Krylov subspace and multigrid techniques is for symmetric and positive definite, nonsymmetric positive definite, symmetric indefinite and nonsymmetric indefinite matrix systems respectively. For each problem and associated solvers there is a description of how to compute together with theoretical analysis that guides the choice of approaches and describes what happens in practice in the many illustrative numerical results throughout the book (computed with the freely downloadable IFISS software). All of the numerical results should be reproducible by readers who have access to MATLAB and there is considerable scope for experimentation in the "computational laboratory " provided by the software. Developments in the field since the first edition was published have been represented in three new chapters covering optimization with PDE constraints (Chapter 5); solution of unsteady Navier-Stokes equations (Chapter 10); solution of models of buoyancy-driven flow (Chapter 11). Each chapter has many theoretical problems and practical computer exercises that involve the use of the IFISS software. This book is suitable as an introduction to iterative linear solvers or more generally as a model of Scientific Computing at an advanced undergraduate or beginning graduate level.

This is the second volume in a four-part series on fluid dynamics: Part 1. Classical Fluid Dynamics Part 2. Asymptotic Problems of Fluid Dynamics Part 3. Boundary Layers Part 4. Hydrodynamic Stability Theory The series is designed to give a comprehensive and coherent description of fluid dynamics, starting with chapters on classical theory suitable for an introductory undergraduate lecture course, and then progressing through more advanced material up to the level of modern research in the field. In Part 2 the reader is introduced to asymptotic methods, and their applications to fluid dynamics. Firstly, it discusses the mathematical aspects of the asymptotic theory. This is followed by an exposition of the results of inviscid flow theory, starting with subsonic flows past thin aerofoils. This includes unsteady flow theory and the analysis of separated flows. The authors then consider supersonic flow past a thin aerofoil, where the linear approximation leads to the Ackeret formula for the pressure. They also discuss the second order Buzemann approximation, and the flow behaviour at large distances from the aerofoil. Then the properties of transonic and hypersonic flows are examined in detail. Part 2 concludes with a discussion of viscous low-Reynolds-number flows. Two classical problems of the low-Reynolds-number flow theory are considered, the flow past a sphere and the flow past a circular cylinder. In both cases the flow analysis leads to a difficulty, known as Stokes paradox. The authors show that this paradox can be resolved using the formalism of matched asymptotic expansions.