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."

This book is a collection of papers devoted to the emergence and development in Bulgarian Academy of Sciences of some of the areas of informatics, including artificial intelligence. The papers are prepared by specialists from the Academy, some of whom are among the founders of these scientific and application areas in Bulgaria and in some cases - in the world. The book is interesting for specialists in informatics and computer science and researchers in history of sciences.

This book summarizes research being pursued within the Research Unit FOR 2089, funded by the German Research Foundation (DFG), the goal of which is to develop the scientific base for a paradigm shift towards dimensioning, structural realization and maintenance of pavements, and prepare road infrastructure for future requirements. It provides a coupled thermo-mechanical model for a holistic physical analysis of the pavement-tire-vehicle system: based on this model, pavement structures and materials can be optimized so that new demands become compatible with the main goal - durability of the structures and the materials. The development of these new and qualitatively improved modelling approaches requires a holistic procedure through the coupling of theoretical numerical and experimental approaches as well as an interdisciplinary and closely linked handling of the coupled pavement-tire-vehicle system. This interdisciplinary research provides a deeper understanding of the physics of the full system through complex, coupled simulation approaches and progress in terms of improved and, therefore, more durable and sustainable structures.

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.

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.

This volume explores the connections between mathematical modeling, computational methods, and high performance computing, and how recent developments in these areas can help to solve complex problems in the natural sciences and engineering. The content of the book is based on talks and papers presented at the conference Modern Mathematical Methods and High Performance Computing in Science & Technology (M3HPCST), held at Inderprastha Engineering College in Ghaziabad, India in January 2020. A wide range of both theoretical and applied topics are covered in detail, including the conceptualization of infinity, efficient domain decomposition, high capacity wireless communication, infectious disease modeling, and more. These chapters are organized around the following areas: Partial and ordinary differential equations Optimization and optimal control High performance and scientific computing Stochastic models and statistics Recent Trends in Mathematical Modeling and High Performance Computing will be of interest to researchers in both mathematics and engineering, as well as to practitioners who face complex models and extensive computations.

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.

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 is designed to serve as a textbook for courses offered to undergraduate and postgraduate students enrolled in Mathematics. Using elementary row operations and Gram-Schmidt orthogonalization as basic tools the text develops characterization of equivalence and similarity, and various factorizations such as rank factorization, OR-factorization, Schurtriangularization, Diagonalization of normal matrices, Jordan decomposition, singular value decomposition, and polar decomposition. Along with Gauss-Jordan elimination for linear systems, it also discusses best approximations and least-squares solutions. The book includes norms on matrices as a means to deal with iterative solutions of linear systems and exponential of a matrix. The topics in the book are dealt with in a lively manner. Each section of the book has exercises to reinforce the concepts, and problems have been added at the end of each chapter. Most of these problems are theoretical, and they do not fit into the running text linearly. The detailed coverage and pedagogical tools make this an ideal textbook for students and researchers enrolled in senior undergraduate and beginning postgraduate mathematics courses.

This book presents the emerging regime of zero refractive index photonics, involving metamaterials that exhibit effectively zero refractive index. Metamaterials are artificial structures whose optical properties can be tailored at will. With metamaterials, intriguing and spellbinding phenomena like negative refraction and electromagnetic cloaking could be realized, which otherwise seem unnatural or straight out of science fiction. Zero index metamaterials are also seen as a means of boosting nonlinear properties and are believed to have strong prospects for being useful in nonlinear optical applications. In summary, this book highlights almost everything currently available on zero index metamaterials and is useful for professionally interested and motivated readers.

This proceedings gather a selection of peer-reviewed papers presented at the 8th International Conference on Fracture Fatigue and Wear (FFW 2020), held as a virtual conference on 26-27 August 2020. The contributions, prepared by international scientists and engineers, cover the latest advances in and innovative applications of fracture mechanics, fatigue of materials, tribology, and wear of materials. In addition, they discuss industrial applications and cover theoretical and analytical methods, numerical simulations and experimental techniques. The book is intended for academics, including graduate students and researchers, as well as industrial practitioners working in the areas of fracture fatigue and wear.

Stokes discusses--and illustrates with output from actual problems--a number of applied econometric techniques, including OLS specification tests, recursive residual analysis, limited dependent variable models, error component models, and others. His book is clearly written and copiously illustrated with equations, with follow-up analysis to show how models are built and some of their limitations. His B34S DEGREESDTM software is available and allows readers to do further research with a large number of datasets distributed with the program. A necessary resource for applied econometrics researchers in economics, finance, and in health, energy, and labor economics.

This work illustrates the use of model specification and diagnostic tests applied to a variety of econometric modeling techniques. For each technique discussed the basic mathematical models are outlined. A sample problem is discussed and estimated using the B34S DEGREESDTM Data Analysis System. The output of the program is displayed in the text and discussed. Where appropriate, output from the RATS DEGREESDTM software is displayed. Follow-up models are estimated and discussed. The examples selected are taken from a variety of sources and reflect actual applied research. Complete data are given in the text to enable the reader to use these problems with other programs and techniques. It is the author's experience that applied econometric techniques are best learned by running actual problems. Since most users experiment with a limited number of techniques, their experience is limited. This book discusses a broad range of techniques and shows how they are interrelated. DEGREESL DEGREESL The techniques discussed include the following: simple, one-equation OLS and GLS models with continuous variables on the left-hand side, which are tested with recursive residual and BLUS residual techniques. Another class of models includes restrictions on the left-hand side variables. Models studied and illustrated with data include probit, logit, multinomial logit, and ordered probit models. Other techniques discussed and illustrated include two-stage least squares, limited information maximum likelihood, three-stage least squares, iterative three-stage least squares, error component models and Markov probability models, which are illustrated with a model of OPEC production dynamics.

ARIMA and transfer function models are shown to be generalizations of the single-equation model, while VAR and VARMA models are shown to be a time series generalization of three-stage least squares and full information maximum likelihood models. VAR models are viewed in the frequency domain for added insight, and extensive nonlinearity tests are developed and applied. More specialized techniques include state space models, optimal control analysis, nonlinear analysis, and the QR approach to computation. An important feature of the book is the emphasis on nonlinear model building. The Hinich nonlinear testing approach is discussed and integrated into the OLS, times series, and nonlinear estimation procedures. The MARS and PISPLINE methods of analysis are illustrated with models that failed linearity tests when estimated with linear methods. The purpose of the monograph is to illustrate the above techniques, using actual research data. To facilitate the calculations, the B34S DEGREESDTM Data Analysis System was developed. Sample output for all procedures discussed in the text has been provided so that the availability of the B34S DEGREESDTM program is DEGREESInot DEGREESR required in order to benefit from this book. While the book is self-contained, interested readers can obtain the B34S DEGREESDTM Data Analysis program and do further research with the datasets discussed in the book which are supplied with the software.

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 book shares the latest findings on this topic, systematically introduces readers to advances made in robotic harvesting around the globe, and explores the relations between the development of robotic harvesting and the respective social/economic conditions and agricultural business patterns in various countries/regions. Due to the unstructured setting it is used in, and to the significant differences between individual fruit and vegetable targets, robotic harvesting is currently considered to be one of the most challenging robotics technologies. Accordingly, research into this area involves the integration of various aspects, including biomechanics, optimization design, advanced perception and intelligent control. In addition to rapid and damage-free robotic harvesting, which reflects the multidisciplinary nature of the topic, further aspects addressed include gripping collisions with viscoelastic objects, using lasers to cut plant material, plant-fruit response to vacuum sucking and pulling, and performance probability distribution. Highlighting outstanding innovations and reflecting the latest advances in intelligent agricultural equipment in China, the book offers a unique and valuable resource.

This book examines the problems in the field of energy and related fields (chemical, transport, aerospace, construction, metallurgy, engineering, etc.) and consists of 4 subsections: Electrical Engineering, Heat Power Engineering, Cybersecurity and Computer Science & Environmental Safety. In the first section, authors pay attention to contemporary issues related to the development of the electric power industry, electrical engineering, the physics of electrical phenomena and renewable energy sources (such as solar energy and wind energy). The second section is devoted to modern problems in heat power engineering and considers modern means and methods that increase the efficiency and reliability of the functioning of heat power facilities. The third section is devoted to issues of cybersecurity of critical facilities, in particular energy facilities, as well as the development of computer science and the introduction of modern information and measurement systems in the energy sector. The fourth subsection deals with the problems of rational use of natural resources, accounting for emissions of harmful substances, environmental issues at energy facilities, as well as the development of a methodology for environmental safety. The book includes 21 chapters. A book is for researchers, engineers, as well as lecturers and postgraduates of higher education institutions dealing with issues of control, diagnosis and monitoring of energy facilities.

The use of Bayesian statistics has grown significantly in recent years, and will undoubtedly continue to do so. Applied Bayesian Modelling is the follow-up to the author’s best selling book, Bayesian Statistical Modelling, and focuses on the potential applications of Bayesian techniques in a wide range of important topics in the social and health sciences. The applications are illustrated through many real-life examples and software implementation in WINBUGS – a popular software package that offers a simplified and flexible approach to statistical modelling. The book gives detailed explanations for each example – explaining fully the choice of model for each particular problem. The book

The book provides a good introduction to Bayesian modelling and data analysis for a wide range of people involved in applied statistical analysis, including researchers and students from statistics, and the health and social sciences. The wealth of examples makes this book an ideal reference for anyone involved in statistical modelling and analysis.

This edited volume presents state-of-the-art developments in various areas in which Harmonic Analysis is applied. Contributions cover a variety of different topics and problems treated such as structure and optimization in computational harmonic analysis, sampling and approximation in shift invariant subspaces of L2( ), optimal rank one matrix decomposition, the Riemann Hypothesis, large sets avoiding rough patterns, Hardy Littlewood series, Navier-Stokes equations, sleep dynamics exploration and automatic annotation by combining modern harmonic analysis tools, harmonic functions in slabs and half-spaces, Andoni -Krauthgamer -Razenshteyn characterization of sketchable norms fails for sketchable metrics, random matrix theory, multiplicative completion of redundant systems in Hilbert and Banach function spaces. Efforts have been made to ensure that the content of the book constitutes a valuable resource for graduate students as well as senior researchers working on Harmonic Analysis and its various interconnections with related areas.

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.

This book highlights a comprehensive introduction to the fundamental statistical mechanics underneath the inner workings of neural networks. The book discusses in details important concepts and techniques including the cavity method, the mean-field theory, replica techniques, the Nishimori condition, variational methods, the dynamical mean-field theory, unsupervised learning, associative memory models, perceptron models, the chaos theory of recurrent neural networks, and eigen-spectrums of neural networks, walking new learners through the theories and must-have skillsets to understand and use neural networks. The book focuses on quantitative frameworks of neural network models where the underlying mechanisms can be precisely isolated by physics of mathematical beauty and theoretical predictions. It is a good reference for students, researchers, and practitioners in the area of neural networks.

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.

This book is about algebraic and differential methods, as well as fractional calculus, applied to diagnose and reject faults in nonlinear systems, which are of integer or fractional order. This represents an extension of a very important and widely studied problem in control theory, namely fault diagnosis and rejection (using differential algebraic approaches), to systems presenting fractional dynamics, i.e. systems whose dynamics are represented by derivatives and integrals of non-integer order. The authors offer a thorough overview devoted to fault diagnosis and fault-tolerant control applied to fractional-order and integer-order dynamical systems, and they introduce new methodologies for control and observation described by fractional and integer models, together with successful simulations and real-time applications. The basic concepts and tools of mathematics required to understand the methodologies proposed are all clearly introduced and explained. Consequently, the book is useful as supplementary reading in courses of applied mathematics and nonlinear control theory. This book is meant for engineers, mathematicians, physicists and, in general, to researchers and postgraduate students in diverse areas who have a minimum knowledge of calculus. It also contains advanced topics for researchers and professionals interested in the area of states and faults estimation.

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 book presents a theoretical study of the generation and conversion of phonon angular momentum in crystals. Recently, rotational motions of lattice vibrations, i.e., phonons, in crystals attract considerable attentions. As such, the book theoretically demonstrate generations of phonons with rotational motions, based on model calculations and first-principle calculations. In systems without inversion symmetry, the phonon angular momentum is shown to be caused by the temperature gradient, which is demonstrated in crystals such as wurtzite gallium nitride, tellurium, and selenium using the first-principle calculations. In systems with neither time-reversal nor inversion symmetries, the phonon angular momentum is shown to be generated by an electric field. Secondly, the book presents the microscopic mechanisms developed by the author and his collaborator on how these microscopic rotations of nuclei are coupled with electron spins. These predictions serve as building blocks for spintronics with phonons or mechanical motions.

This volume gathers papers presented at the Workshop on Computational Diffusion MRI (CDMRI 2019), held under the auspices of the International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), which took place in Shenzhen, China on October 17, 2019. This book presents the latest advances in the rapidly expanding field of diffusion MRI. It shares new perspectives on the latest research challenges for those currently working in the field, but also offers a valuable starting point for anyone interested in learning about computational techniques in diffusion MRI. The book includes rigorous mathematical derivations, a wealth of rich, full-colour visualisations and extensive clinically relevant results. As such, it will be of interest to researchers and practitioners in the fields of computer science, MRI physics and applied mathematics. Readers will find contributions covering a broad range of topics, from the mathematical foundations of the diffusion process and signal generation, to new computational methods and estimation techniques for the in vivo recovery of microstructural and connectivity features, as well as diffusion-relaxometry and frontline applications in research and clinical practice. This edition includes invited works from high-profile researchers with a specific focus on three new and important topics that are gaining momentum within the diffusion MRI community, including diffusion MRI signal acquisition and processing strategies, machine learning for diffusion MRI, and diffusion MRI outside the brain and clinical applications.