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.

This book pedagogically describes recent developments in gauge theory, in particular four-dimensional N = 2 supersymmetric gauge theory, in relation to various fields in mathematics, including algebraic geometry, geometric representation theory, vertex operator algebras. The key concept is the instanton, which is a solution to the anti-self-dual Yang-Mills equation in four dimensions. In the first part of the book, starting with the systematic description of the instanton, how to integrate out the instanton moduli space is explained together with the equivariant localization formula. It is then illustrated that this formalism is generalized to various situations, including quiver and fractional quiver gauge theory, supergroup gauge theory. The second part of the book is devoted to the algebraic geometric description of supersymmetric gauge theory, known as the Seiberg-Witten theory, together with string/M-theory point of view. Based on its relation to integrable systems, how to quantize such a geometric structure via the -deformation of gauge theory is addressed. The third part of the book focuses on the quantum algebraic structure of supersymmetric gauge theory. After introducing the free field realization of gauge theory, the underlying infinite dimensional algebraic structure is discussed with emphasis on the connection with representation theory of quiver, which leads to the notion of quiver W-algebra. It is then clarified that such a gauge theory construction of the algebra naturally gives rise to further affinization and elliptic deformation of W-algebra.

This book aims to gather the insight of leading experts on corruption and anti-corruption studies working at the scientific frontier of this phenomenon using the multidisciplinary tools of data and network science, in order to present current theoretical, empirical, and operational efforts being performed in order to curb this problem. The research results strengthen the importance of evidence-based approaches in the fight against corruption in all its forms, and foster the discussion about the best ways to convert the obtained knowledge into public policy. The contributed chapters provide comprehensive and multidisciplinary approaches to handle the non-trivial structural and dynamical aspects that characterize the modern social, economic, political and technological systems where corruption takes place. This book will serve a broad multi-disciplinary audience from natural to social scientists, applied mathematicians, including law and policymakers.

Financial market modeling is a prime example of a real-life application of probability theory and stochastics. This authoritative book discusses the discrete-time approximation and other qualitative properties of models of financial markets, like the Black-Scholes model and its generalizations, offering in this way rigorous insights on one of the most interesting applications of mathematics nowadays.

This monograph develops an innovative approach that utilizes the Birman-Schwinger principle from quantum mechanics to investigate stability properties of steady state solutions in galactic dynamics. The opening chapters lay the framework for the main result through detailed treatments of nonrelativistic galactic dynamics and the Vlasov-Poisson system, the Antonov stability estimate, and the period function $T_1$. Then, as the main application, the Birman-Schwinger type principle is used to characterize in which cases the "best constant" in the Antonov stability estimate is attained. The final two chapters consider the relation to the Guo-Lin operator and invariance properties for the Vlasov-Poisson system, respectively. Several appendices are also included that cover necessary background material, such as spherically symmetric models, action-angle variables, relevant function spaces and operators, and some aspects of Kato-Rellich perturbation theory. A Birman-Schwinger Principle in Galactic Dynamics will be of interest to researchers in galactic dynamics, kinetic theory, and various aspects of quantum mechanics, as well as those in related areas of mathematical physics and applied mathematics.

This monograph explores classical electrodynamics from a geometrical perspective with a clear visual presentation throughout. Featuring over 200 figures, readers will delve into the definitions, properties, and uses of directed quantities in classical field theory. With an emphasis on both mathematical and electrodynamic concepts, the author's illustrative approach will help readers understand the critical role directed quantities play in physics and mathematics. Chapters are organized so that they gradually scale in complexity, and carefully guide readers through important topics. The first three chapters introduce directed quantities in three dimensions with and without the metric, as well as the development of the algebra and analysis of directed quantities. Chapters four through seven then focus on electrodynamics without the metric, such as the premetric case, waves, and fully covariant four-dimensional electrodynamics. Complementing the book's careful structure, exercises are included throughout for readers seeking further opportunities to practice the material. Directed Quantities in Electrodynamics will appeal to students, lecturers, and researchers of electromagnetism. It is particularly suitable as a supplement to standard textbooks on electrodynamics.

This book presents quantum theory as a theory based on new relationships among matter, thought, and experimental technology, as against those previously found in physics, relationships that also redefine those between mathematics and physics in quantum theory. The argument of the book is based on its title concept, reality without realism (RWR), and in the corresponding view, the RWR view, of quantum theory. The book considers, from this perspective, the thinking of Bohr, Heisenberg, Schroedinger, and Dirac, with the aim of bringing together the philosophy and history of quantum theory. With quantum theory, the book argues, the architecture of thought in theoretical physics was radically changed by the irreducible role of experimental technology in the constitution of physical phenomena, accordingly, no longer defined independently by matter alone, as they were in classical physics or relativity. Or so it appeared. For, quantum theory, the book further argues, made us realize that experimental technology, beginning with that of our bodies, irreducibly shapes all physical phenomena, and thus makes us rethink the relationships among matter, thought, and technology in all of physics.

This book provides awareness of methods used for functional encryption in the academic and professional communities. The book covers functional encryption algorithms and its modern applications in developing secure systems via entity authentication, message authentication, software security, cyber security, hardware security, Internet of Thing (IoT), cloud security, smart card technology, CAPTCHA, digital signature, and digital watermarking. This book is organized into fifteen chapters; topics include foundations of functional encryption, impact of group theory in cryptosystems, elliptic curve cryptography, XTR algorithm, pairing based cryptography, NTRU algorithms, ring units, cocks IBE schemes, Boneh-Franklin IBE, Sakai-Kasahara IBE, hierarchical identity based encryption, attribute based Encryption, extensions of IBE and related primitives, and digital signatures. Explains the latest functional encryption algorithms in a simple way with examples; Includes applications of functional encryption in information security, application security, and network security; Relevant to academics, research scholars, software developers, etc.

Chapters collected from "The Virtual Conference on Chemistry and its Applications (VCCA-2021) - Research and Innovations in Chemical Sciences: Paving the Way Forward". This conference was held in August 2021 and organized by the Computational Chemistry Group of the University of Mauritius. These peer-reviewed chapters offer insights into research on fundamental and applied chemistry with interdisciplinary subject matter.

For various scientific and engineering problems, how to deal with variables and parameters of uncertain value is an important issue. Full analysis of the specific errors in measurement, observations, experiments, and applications are vital in dealing with the parameters taken to simplify the problem. Mathematics of Uncertainty Modeling in the Analysis of Engineering and Science Problems aims to provide the reader with basic concepts for soft computing and other methods for various means of uncertainty in handling solutions, analysis, and applications. This book is an essential reference work for students, scholars, practitioners and researchers in the assorted fields of engineering and applied mathematics interested in a model for uncertain physical problems.

This book provides a comprehensive examination of preconditioners for boundary element discretisations of first-kind integral equations. Focusing on domain-decomposition-type and multilevel methods, it allows readers to gain a good understanding of the mechanisms and necessary techniques in the analysis of the preconditioners. These techniques are unique for the discretisation of first-kind integral equations since the resulting systems of linear equations are not only large and ill-conditioned, but also dense. The book showcases state-of-the-art preconditioning techniques for boundary integral equations, presenting up-to-date research. It also includes a detailed discussion of Sobolev spaces of fractional orders to familiarise readers with important mathematical tools for the analysis. Furthermore, the concise overview of adaptive BEM, hp-version BEM, and coupling of FEM-BEM provides efficient computational tools for solving practical problems with applications in science and engineering.

The scale transitions are essential to physical knowledge. The book describes the history of essential moments of physics, viewed as necessary consequences of the unavoidable process of scale transition, and provides the mathematical techniques for the construction of a theoretical physics founded on scale transition. The indispensable mathematical technique is analyticity, helping in the construction of space coordinate systems. The indispensable theoretical technique from physical point of view is the affine theory of surfaces. The connection between the two techniques is provided by a duality in defining the physical properties.

This book reports on the latest knowledge concerning critical phenomena arising in fluid-structure interaction due to movement and/or deformation of bodies. The focus of the book is on reporting progress in understanding turbulence and flow control to improve aerodynamic / hydrodynamic performance by reducing drag, increasing lift or thrust and reducing noise under critical conditions that may result in massive separation, strong vortex dynamics, amplification of harmful instabilities (flutter, buffet), and flow -induced vibrations. Theory together with large-scale simulations and experiments have revealed new features of turbulent flow in the boundary layer over bodies and in thin shear layers immediately downstream of separation. New insights into turbulent flow interacting with actively deformable structures, leading to new ways of adapting and controlling the body shape and vibrations to respond to these critical conditions, are investigated. The book covers new features of turbulent flows in boundary layers over wings and in shear layers immediately downstream: studies of natural and artificially generated fluctuations; reduction of noise and drag; and electromechanical conversion topics. Smart actuators as well as how smart designs lead to considerable benefits compared with conventional methods are also extensively discussed. Based on contributions presented at the IUTAM Symposium "Critical Flow Dynamics involving Moving/Deformable Structures with Design applications", held in June 18-22, 2018, in Santorini, Greece, the book provides readers with extensive information about current theories, methods and challenges in flow and turbulence control, and practical knowledge about how to use this information together with smart and bio-inspired design tools to improve aerodynamic and hydrodynamic design and safety.

A variety of quantitative concepts and models essential to understanding financial markets are introduced and explained in this broad overview of financial analytical tools designed for financial practitioners, advanced students, and researchers lacking a strong mathematical background. Coverage ranges from matrix mathematics and elementary calculus with their applications to portfolio and fixed income analysis to probability and stochastic processes with their applications to option pricing. The book is sequenced by mathematics topics, most of which are followed by relevant usage to areas such as valuation, risk management, derivatives, back-testing of financial models, and market efficiency.

The book begins by motivating the need for understanding quantitative technique with a brief discussion of financial mathematics and financial literature review. Preliminary concepts including geometric expansion, elementary statistics, and basic portfolio techniques are introduced in chapters 2 and 3. Chapters 4 and 5 present matrix mathematics and differential calculus applied to yield curves, APT, state preference theory, binomal option pricing, mean-variance analysis, and other applications. Integral calculus and differential equations follow in chapter 6. The rest of the book covers applications of probability, statistics and stochastic processes as well as a sampling of topics from numerical methods used in financial analysis.

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.

This book gives a complete spectral analysis of the non-self-adjoint Schroedinger operator with a periodic complex-valued potential. Building from the investigation of the spectrum and spectral singularities and construction of the spectral expansion for the non-self-adjoint Schroedinger operator, the book features a complete spectral analysis of the Mathieu-Schroedinger operator and the Schroedinger operator with a parity-time (PT)-symmetric periodic optical potential. There currently exists no general spectral theorem for non-self-adjoint operators; the approaches in this book thus open up new possibilities for spectral analysis of some of the most important operators used in non-Hermitian quantum mechanics and optics. Featuring detailed proofs and a comprehensive treatment of the subject matter, the book is ideally suited for graduate students at the intersection of physics and mathematics.

This volume provides a detailed description of some of the most active areas in astrophysics from the largest scales probed by the Planck satellite to massive black holes that lie at the heart of galaxies and up to the much awaited but stunning discovery of thousands of exoplanets. It contains the following chapters: * Jean-Philippe UZAN, The Big-Bang Theory: Construction, Evolution and Status * Jean-Loup PUGET, The Planck Mission and the Cosmic Microwave Background * Reinhard GENZEL, Massive Black Holes: Evidence, Demographics and Cosmic Evolution * Arnaud CASSAN, New Worlds Ahead: The Discovery of Exoplanets Reinhard Genzel and Andrea Ghez shared the 2020 Nobel Prize in Physics "for the discovery of a supermassive compact object at the centre of our galaxy'", alongside Roger Penrose "for the discovery that black hole formation is a robust prediction of the general theory of relativity". The book corresponds to the twentieth Poincare Seminar, held on November 21, 2015, at Institut Henri Poincare in Paris. Originally written as lectures to a broad scientific audience, these four chapters are of high value and will be of general interest to astrophysicists, physicists, mathematicians and historians.

This book includes discussions related to solutions of such tasks as: probabilistic description of the investment function; recovering the income function from GDP estimates; development of models for the economic cycles; selecting the time interval of pseudo-stationarity of cycles; estimating characteristics/parameters of cycle models; analysis of accuracy of model factors. All of the above constitute the general principles of a theory explaining the phenomenon of economic cycles and provide mathematical tools for their quantitative description. The introduced theory is applicable to macroeconomic analyses as well as econometric estimations of economic cycles.

This book is the second edition of the first complete study and monograph dedicated to singular traces. The text offers, due to the contributions of Albrecht Pietsch and Nigel Kalton, a complete theory of traces and their spectral properties on ideals of compact operators on a separable Hilbert space. The second edition has been updated on the fundamental approach provided by Albrecht Pietsch. For mathematical physicists and other users of Connes' noncommutative geometry the text offers a complete reference to traces on weak trace class operators, including Dixmier traces and associated formulas involving residues of spectral zeta functions and asymptotics of partition functions.

Hulchul: The Common Ingredient of MotionMotionMotionMotion and Time Author, Sohan Jain, proposes the following in the book: Instants of Motion, Instants of Time and Time Outage: Just as time has instants of time, motion has instants of motion, too. Instants of time and motion can be divided into three classes: pure instants of time, pure instants of motion, and composite instants of time and motion. The sequences of the three types of instants are interspersed into a single sequence of their occurrences. A body does not experience time during pure instants of motion, a phenomenon we will call time outage -the cause of time dilation. Time outage is not continuous; it is intermittent. Internal and external motion of a body and their inheritance: Each body has, generally, two kinds of motions: internal motion and external motion. A body goes, wherever its outer bodies go. An inner body inherits external motion of its outer bodies. An outer body inherits internal motion of its inner bodies. Photons and light do not inherit motion; may be, this is why their motions are independent of their sources. Prime ticks, the building blocks of time and any motion: Motion of a common body is not continuous; it is intermittent. Any kind of motion is perceived to be made of discrete, indivisible tiny movements, called prime ticks (p-ticks). P-ticks are to motion what elementary particles are to matter or what photons are to light. There is time only because there is motion. Prime ticks are events and imply motion. Events have concurrency, which implies time. Total concurrency hulchul, a universal constant: Concurrency events of external and internal p-ticks of a body are precisely the instants of motion and time. The sum of the two is called the total concurrency hulchul (c-hulchul). Total c-hulchul is the same for all bodies. The proposed theory possibly explains: Why a particle accelerator works. Why atoms have compartmentalized internal structure. Why lighter bodies, such as elementary particles and photons, have wavy straight motion rather than straight motion. The theory predicts: The sharing of an electron by two atoms is not continuous; it alternates between the two atoms.

This eighteenth volume in the Poincare Seminar Series provides a thorough description of Information Theory and some of its most active areas, in particular, its relation to thermodynamics at the nanoscale and the Maxwell Demon, and the emergence of quantum computation and of its counterpart, quantum verification. It also includes two introductory tutorials, one on the fundamental relation between thermodynamics and information theory, and a primer on Shannon's entropy and information theory. The book offers a unique and manifold perspective on recent mathematical and physical developments in this field.