Cybernetics and systems theory Books

Book SynopsisThis introductory course on quantum mechanics is the basic lecture that precedes and completes the author's second book Advanced Quantum Mechanics. This new edition is up-to-date and has been revised. Coverage meets the needs of students by giving all mathematical steps and worked examples with applications throughout the text as well as many problems at the end of each chapter. It contains nonrelativistic quantum mechanics and a short treatment of the quantization of the radiation field. Besides the essentials, the book also discusses topics such as the theory of measurement, the Bell inequality, and supersymmetric quantum mechanics.Trade ReviewFrom the reviews: "Any student wishing to develop mathematical skills and deepen their understanding of the technical side of quantum theory will find Schwabl's Quantum Mechanics very helpful". Contemporary Physics From the reviews of the fourth edition: "Quantum Mechanics … presents a nice balance between theory and practical applications in this work that is intended for introductory coursework. It is designed to complement the author’s Advanced Quantum Mechanics (2005). Schwabl (Technische Universität München) succinctly covers a wide range of topics in 20 chapters … . The book also includes worked examples and applications. Summing Up: Recommended. Upper-division undergraduates through researchers and faculty." (D. B. Moss, CHOICE, Vol. 45 (10), June, 2008) "It is an excellent introduction for students of physics or mathematics into the fundamentals of quantum mechanics covering the methods used in applications. … The main point is that the fundamentals and methods of quantum mechanics are mediated very well and guide the reader to apply them successfully. This book can be best recommended to students and lecturers." (K.-E. Hellwig, Zentralblatt MATH, Vol. 1166, 2009)Table of ContentsHistorical and Experimental Foundations.- The Wave Function and the Schrödinger Equation.- One-Dimensional Problems.- The Uncertainty Relation.- Angular Momentum.- The Central Potential I.- Motion in an Electromagnetic Field.- Operators, Matrices, State Vectors.- Spin.- Addition of Angular Momenta.- Approximation Methods for Stationary States.- Relativistic Corrections.- Several-Electron Atoms.- The Zeeman Effect and the Stark Effect.- Molecules.- Time Dependent Phenomena.- The Central Potential II.- Scattering Theory.- Supersymmetric Quantum Theory.- State and Measurement in Quantum Mechanics.

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Book SynopsisWhat are the relations between the shape of a system of cities and that of fish school? Which events should happen in a cell in order that it participates to one of the finger of our hands? How to interpret the shape of a sand dune? This collective book written for the non-specialist addresses these questions and more generally, the fundamental issue of the emergence of forms and patterns in physical and living systems. It is a single book gathering the different aspects of morphogenesis and approaches developed in different disciplines on shape and pattern formation. Relying on the seminal works of D’Arcy Thompson, Alan Turing and René Thom, it confronts major examples like plant growth and shape, intra-cellular organization, evolution of living forms or motifs generated by crystals. A book essential to understand universal principles at work in the shapes and patterns surrounding us but also to avoid spurious analogies.Table of ContentsIntroduction.- Self-organization at equilibrum. A model system: ferrofluids.- Hierarchical networks of fractures.- Liquid crystals and morphogenesis.- Biological self-organization by way of the dynamics of reactive processes.- Sand dunes.- Morphodynamics of secretory pathways.- From epigenomics to morphogenetic emergence.- Animal morphogenesis.- Phyllotaxy.- Logic of forms.- Forms emerging from collective motion.- Systems of cities and levels of organization.- Levels of organization and morphogenesis: the viewpoint of D'Arcy Thompson.- Morphogenetic models of René Thom.- Morphogenesis, structural stability and epigenetic landscape.- Morphological and mutational analysis: tools for morphogenesis study.- Morphogenesis in computer science.

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Book SynopsisThe “language-communication-society” triangle defies traditional scientific approaches. Rather, it is a phenomenon that calls for an integration of complex, transdisciplinary perspectives, if we are to make any progress in understanding how it works. The highly diverse agents in play are not merely cognitive and/or cultural, but also emotional and behavioural in their specificity. Indeed, the effort may require building a theoretical and methodological body of knowledge that can effectively convey the characteristic properties of phenomena in human terms.New complexity approaches allow us to rethink our limited and mechanistic images of human societies and create more appropriate emo-cognitive dynamic and holistic models. We have to enter into dialogue with the complexity views coming out of other more ‘material’ sciences, but we also need to take steps in the linguistic and psycho-sociological fields towards creating perspectives and concepts better fitted to human characteristics.Our understanding of complexity is different – but not opposed – to the one that is more commonly found in texts written by people working in physics or computer science, for example. The goal of this book is to extend the knowledge of these other more ‘human’ or socially oriented perspectives on complexity, taking account of the language and communication singularities of human agents in society. Our understanding of complexity is different – but not opposed – to the one that is more commonly found in texts written by people working in physics or computer science, for example. The goal of this book is to extend the knowledge of these other more ‘human’ or socially oriented perspectives on complexity, taking account of the language and communication singularities of human agents in society. Table of ContentsIntroduction .-Facing complexity: Prediction vs. adaptation .- Sociolinguistics: Towards a complex ecological view.- Language as a Complex Adaptive System: Towards an Integrative Linguistics.- An experientially-based informationless communication .- Conversation as emergent function .- Communication situations: A dialogic quiz? .-Education, emotion, complexity.-Minds and screens. Communication and socialization from a complexity perspective .-Self-organization in communicating groups: The emergence of coordination, shared references and collective intelligence .- General linguistics and communication sciences: Sociocomplexity as an integrative perspective .-The Fuzzy Complexity of Languag.- The emergence of complexity in language: An evolutionary perspective .- The ecology of pressures: Towards a tool to analyze the complex process of language shift and maintenance .- Ethics and Progress in Today’s World .Sociocomplexity as an integrative perspective .-The Fuzzy Complexity of Languag.- The emergence of complexity in language: An evolutionary perspective .- The ecology of pressures: Towards a tool to analyze the complex process of language shift and maintenance .- Ethics and Progress in Today’s World .Sociocomplexity as an integrative perspective .-The Fuzzy Complexity of Languag.- The emergence of complexity in language: An evolutionary perspective .- The ecology of pressures: Towards a tool to analyze the complex process of language shift and maintenance .- Ethics and Progress in Today’s World .Sociocomplexity as an integrative perspective .-The Fuzzy Complexity of Languag.- The emergence of complexity in language: An evolutionary perspective .- The ecology of pressures: Towards a tool to analyze the complex process of language shift and maintenance .- Ethics and Progress in Today’s World .Sociocomplexity as an integrative perspective .-The Fuzzy Complexity of Languag.- The emergence of complexity in language: An evolutionary perspective .- The ecology of pressures: Towards a tool to analyze the complex process of language shift and maintenance .- Ethics and Progress in Today’s World .Sociocomplexity as an integrative perspective .-The Fuzzy Complexity of Languag.- The emergence of complexity in language: An evolutionary perspective .- The ecology of pressures: Towards a tool to analyze the complex process of language shift and maintenance .- Ethics and Progress in Today’s World .Sociocomplexity as an integrative perspective .-The Fuzzy Complexity of Languag.- The emergence of complexity in language: An evolutionary perspective .- The ecology of pressures: Towards a tool to analyze the complex process of language shift and maintenance .- Ethics and Progress in Today’s World .Sociocomplexity as an integrative perspective .-The Fuzzy Complexity of Languag.- The emergence of complexity in language: An evolutionary perspective .- The ecology of pressures: Towards a tool to analyze the complex process of language shift and maintenance .- Ethics and Progress in Today’s World .Sociocomplexity as an integrative perspective .-The Fuzzy Complexity of Languag.- The emergence of complexity in language: An evolutionary perspective .- The ecology of pressures: Towards a tool to analyze the complex process of language shift and maintenance .- Ethics and Progress in Today’s World .

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Book SynopsisThe application of statistical methods to physics is essential. This unique book on statistical physics offers an advanced approach with numerous applications to the modern problems students are confronted with. Therefore the text contains more concepts and methods in statistics than the student would need for statistical mechanics alone. Methods from mathematical statistics and stochastics for the analysis of data are discussed as well. The book is divided into two parts, focusing first on the modeling of statistical systems and then on the analysis of these systems. Problems with hints for solution help the students to deepen their knowledge. The third edition has been updated and enlarged with new sections deepening the knowledge about data analysis. Moreover, a customized set of problems with solutions is accessible on the Web at extras.springer.com.Trade ReviewFrom the book reviews:“The book is carefully divided into two parts. The first part deals with modeling of statistical systems. The second part is devoted to the analysis of the respective systems. … followed by a section that offers helpful hints and solutions to problems throughout the text, making it easier for students to deepen their understanding and confidence in their newfound knowledge. … topics in each chapter are carefully selected and are well presented, making it a reliable reference for ‘statistical physics.’” (Technometrics, Vol. 55 (2), May, 2013)Table of ContentsStatistical Physics is more than Statistical Mechanics.- Part I: Modeling of Statistical Systems.- Random Variables: Fundamentals of Probability Theory and Statistics.- Random Variables in State Space: Classical Statistical Mechanics of Fluids.- Random Fields: Textures and Classical Statistical Mechanics of Spin Systems.- Time-Dependent Random Variables: Classical Stochastic Processes.- Quantum Random Systems.- Changes of External Conditions.- Part II: Analysis of Statistical Systems.- Estimation of Parameters.- Signal Analysis: Estimation of Spectra.- Estimators Based on a Probability Distribution for the Parameters.- Identification of Stochastic Models from Observations.- Estimating the Parameters of a Hidden Stochastic Model.- Statistical Tests and Classification Methods.- Appendix: Random Number Generation for Simulating Realizations of Random Variables.- Problems.- Hints and Solutions.

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Book SynopsisOne of the driving forces behind much of modern science and technology is the desire to foresee and thereby control the future. In recent years, however, it has become clear that, even in a deterministic world, there is alimit to the accuracy with which we can predict the future. This book details, in a largely nontechnical style, the extent to which we can predict the future development of various physical, biological and socio-economic processes.Table of Contents1. Introduction.- References.- 2. Forecasting Weather and Climate.- 2.1 Weather and Climate.- 2.2 Dynamical Systems and Their Properties.- 2.3 Weather Predictability.- 2.4 Elements of Stationary Random Process Prediction Theory.- 2.5 Predictability of Climatic Processes.- 2.6 Ways to Improve Statistical Forecasting.- 2.7 Utilization of Forecasting Results.- 2.8 Conclusion.- References.- 3. How an Active Autowave Medium Can Be Used to Predict the Future.- 3.1 Prediction.- 3.2 Active Autowave Media.- 3.3 Autowave Propagation in Energy-Restoring Active Media.- 3.4 Dynamics of Autowave Interaction.- 3.5 The External Medium Model and Its Fourier Image.- 3.6 Non-isochronism of Cyclic Processes.- 3.7 Harmonious Modulation and Modulation of Harmonics.- 3.8 The Fourier Image Cleared by the Active Autowave Medium.- References.- 4. Synergetics, Predictability and Deterministic Chaos.- 4.1 Dynamical Chaos.- 4.2 Nonlinearity and Open Systems Behavior.- 4.3 Synergetics and Order Parameters.- 4.4 Strangeness of the Strange Attractors.- 4.5 Dynamical Chaos and Reality.- 4.6 Dynamical Chaos. Gates of Fairyland.- References.- 5. The Information-Theoretic Approach to Assessing Reliability of Forecasts.- 5.1 Assessing Forecasts.- 5.2 Forecasting as the Subject Matter of Information Theory.- 5.3 An Example.- 5.4 Optimization of Forecasting Methods.- 5.5 Properties Shared by Prediction Methods.- 5.6 The Connection Between Discounting and Non-stationarity.- 5.7 Conclusion.- References.- 6. Prediction of Time Series.- 6.1 The Problem.- 6.2 Genesis of Random Phenomena.- 6.3 Time Series Prediction Based on Dynamical Chaos Theory.- 6.4 Prediction of Point Processes.- 6.5 The Nature of Errors Hindering Prediction.- 6.6 Prediction of Strong Earthquakes.- References.- 7. Fundamental and Practical Limits of Predictability.- 7.1 Predictability.- 7.2 Real, Observed, and Model Processes.- 7.3 Degree of Predictability. The Predictability Horizon.- 7.4 Searching for Prediction Models.- 7.5 Limits to Predictability.- 7.6 Dynamical Analogs to Social and Economic Phenomena.- 7.7 Conclusion.- References.- 8. The Future is Foreseeable but not Predictable: The ‘Oedipus Effect’ in Social Forecasting.- 8.1 Historical Background.- 8.2 The ‘Oedipus Effect’ in Social Forecasting.- 8.3 The Problem of Foresight and Prediction in Globalistics.- 8.4 The Problem of Foreseeing and Predicting the Development of the Former Soviet Society.- References.- Appendix A: Looking Back on the August 1991 Coup.- Appendix B: Looking Ahead.- 9. The Self-Organization of American Society in Presidential and Senatorial Elections.- 9.1 Historical Background.- 9.2 The American Presidential Election: Formal Analysis.- 9.3 Midterm Senatorial Elections: Formal Analysis.- 9.4 Discussion.- References.- 10. Problems of Predictability in Ethnogenic Studies.- References.

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Book SynopsisThis book reviews the basic ideas of the Law of Large Numbers with its consequences to the deterministic world and the issue of ergodicity. Applications of Large Deviations and their outcomes to Physics are surveyed. The book covers topics encompassing ergodicity and its breaking and the modern applications of Large deviations to equilibrium and non-equilibrium statistical physics, disordered and chaotic systems, and turbulence.Table of ContentsErgodicity – A Basic Concept.- Large Deviations in Statistical Mechanics: Rigorous and Non-Rigorous.- Large Deviation Techniques for Long-Range Interactions.- Fluctuation-Dissipation and Fluctuation Relations: From Equilibrium to Nonequilibrium Phenomena and Back.- Stochastic Fluctuations in Deterministic Systems.- Large Deviation and Disordered Systems.- Large Deviations in Turbulence.- Ergodicity Breaking Challenges Monte Carlo Methods.- Anomalous Diffusion: Deterministic and Stochastic Perspectives.- The Use of Fluctuation Relations for the Analysis of Free-Energy Landscapes.

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Book SynopsisSince the publication of the first edition of our book, geometric algorithms and combinatorial optimization have kept growing at the same fast pace as before. Nevertheless, we do not feel that the ongoing research has made this book outdated. Rather, it seems that many of the new results build on the models, algorithms, and theorems presented here. For instance, the celebrated Dyer-Frieze-Kannan algorithm for approximating the volume of a convex body is based on the oracle model of convex bodies and uses the ellipsoid method as a preprocessing technique. The polynomial time equivalence of optimization, separation, and membership has become a commonly employed tool in the study of the complexity of combinatorial optimization problems and in the newly developing field of computational convexity. Implementations of the basis reduction algorithm can be found in various computer algebra software systems. On the other hand, several of the open problems discussed in the first edition are still unsolved. For example, there are still no combinatorial polynomial time algorithms known for minimizing a submodular function or finding a maximum clique in a perfect graph. Moreover, despite the success of the interior point methods for the solution of explicitly given linear programs there is still no method known that solves implicitly given linear programs, such as those described in this book, and that is both practically and theoretically efficient. In particular, it is not known how to adapt interior point methods to such linear programs.Table of Contents0. Mathematical Preliminaries.- 0.1 Linear Algebra and Linear Programming.- Basic Notation.- Hulls, Independence, Dimension.- Eigenvalues, Positive Definite Matrices.- Vector Norms, Balls.- Matrix Norms.- Some Inequalities.- Polyhedra, Inequality Systems.- Linear (Diophantine) Equations and Inequalities.- Linear Programming and Duality.- 0.2 Graph Theory.- Graphs.- Digraphs.- Walks, Paths, Circuits, Trees.- 1. Complexity, Oracles, and Numerical Computation.- 1.1 Complexity Theory: P and NP.- Problems.- Algorithms and Turing Machines.- Encoding.- Time and Space Complexity.- Decision Problems: The Classes P and NP.- 1.2 Oracles.- The Running Time of Oracle Algorithms.- Transformation and Reduction.- NP-Completeness and Related Notion.- 1.3 Approximation and Computation of Numbers.- Encoding Length of Numbers.- Polynomial and Strongly Polynomial Computations.- Polynomial Time Approximation of Real Numbers.- 1.4 Pivoting and Related Procedures.- Gaussian Elimination.- Gram-Schmidt Orthogonalization.- The Simplex Method.- Computation of the Hermite Normal Form.- 2. Algorithmic Aspects of Convex Sets: Formulation of the Problems.- 2.1 Basic Algorithmic Problems for Convex Sets.- 2.2 Nondeterministic Decision Problems for Convex Sets.- 3. The Ellipsoid Method.- 3.1 Geometric Background and an Informal Description.- Properties of Ellipsoids.- Description of the Basic Ellipsoid Method.- Proofs of Some Lemmas.- Implementation Problems and Polynomiality.- Some Examples.- 3.2 The Central-Cut Ellipsoid Method.- 3.3 The Shallow-Cut Ellipsoid Method.- 4. Algorithms for Convex Bodies.- 4.1 Summary of Results.- 4.2 Optimization from Separation.- 4.3 Optimization from Membership.- 4.4 Equivalence of the Basic Problems.- 4.5 Some Negative Results.- 4.6 Further Algorithmic Problems for Convex Bodies.- 4.7 Operations on Convex Bodies.- The Sum.- The Convex Hull of the Union.- The Intersection.- Polars, Blockers, Antiblockers.- 5. Diophantine Approximation and Basis Reduction.- 5.1 Continued Fractions.- 5.2 Simultaneous Diophantine Approximation: Formulation of the Problems.- 5.3 Basis Reduction in Lattices.- 5.4 More on Lattice Algorithms.- 6. Rational Polyhedra.- 6.1 Optimization over Polyhedra: A Preview.- 6.2 Complexity of Rational Polyhedra.- 6.3 Weak and Strong Problems.- 6.4 Equivalence of Strong Optimization and Separation.- 6.5 Further Problems for Polyhedra.- 6.6 Strongly Polynomial Algorithms.- 6.7 Integer Programming in Bounded Dimension.- 7. Combinatorial Optimization: Some Basic Examples.- 7.1 Flows and Cuts.- 7.2 Arborescences.- 7.3 Matching.- 7.4 Edge Coloring.- 7.5 Matroids.- 7.6 Subset Sums.- 7.7 Concluding Remarks.- 8. Combinatorial Optimization: A Tour d’Horizon.- 8.1 Blocking Hypergraphs and Polyhedra.- 8.2 Problems on Bipartite Graphs.- 8.3 Flows, Paths, Chains, and Cuts.- 8.4 Trees, Branchings, and Rooted and Directed Cuts.- Arborescences and Rooted Cuts.- Trees and Cuts in Undirected Graphs.- Dicuts and Dijoins.- 8.5 Matchings, Odd Cuts, and Generalizations.- Matching.- b-Matching.- T-Joins and T-Cuts.- Chinese Postmen and Traveling Salesmen.- 8.6 Multicommodity Flows.- 9. Stable Sets in Graphs.- 9.1 Odd Circuit Constraints and t-Perfect Graphs.- 9.2 Clique Constraints and Perfect Graphs.- Antiblockers of Hypergraphs.- 9.3 Orthonormal Representations.- 9.4 Coloring Perfect Graphs.- 9.5 More Algorithmic Results on Stable Sets.- 10. Submodular Functions.- 10.1 Submodular Functions and Polymatroids.- 10.2 Algorithms for Polymatroids and Submodular Functions.- Packing Bases of a Matroid.- 10.3 Submodular Functions on Lattice, Intersecting, and Crossing Families.- 10.4 Odd Submodular Function Minimization and Extensions.- References.- Notation Index.- Author Index.

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Book SynopsisThis book is conceived as a comprehensive and detailed text-book on non-linear dynamical systems with particular emphasis on the exploration of chaotic phenomena. The self-contained introductory presentation is addressed both to those who wish to study the physics of chaotic systems and non-linear dynamics intensively as well as those who are curious to learn more about the fascinating world of chaotic phenomena. Basic concepts like Poincaré section, iterated mappings, Hamiltonian chaos and KAM theory, strange attractors, fractal dimensions, Lyapunov exponents, bifurcation theory, self-similarity and renormalisation and transitions to chaos are thoroughly explained. To facilitate comprehension, mathematical concepts and tools are introduced in short sub-sections. The text is supported by numerous computer experiments and a multitude of graphical illustrations and colour plates emphasising the geometrical and topological characteristics of the underlying dynamics.This volume is a completely revised and enlarged second edition which comprises recently obtained research results of topical interest, and has been extended to include a new section on the basic concepts of probability theory. A completely new chapter on fully developed turbulence presents the successes of chaos theory, its limitations as well as future trends in the development of complex spatio-temporal structures."This book will be of valuable help for my lectures" Hermann Haken, Stuttgart"This text-book should not be missing in any introductory lecture on non-linear systems and deterministic chaos" Wolfgang Kinzel, Würzburg“This well written book represents a comprehensive treatise on dynamical systems. It may serve as reference book for the whole field of nonlinear and chaotic systems and reports in a unique way on scientific developments of recent decades as well as important applications.” Joachim Peinke, Institute of Physics, Carl-von-Ossietzky University Oldenburg, GermanyTrade Review“Familiarity with ideas and tools presented here is of doubtless use for all those who apply methods of the theory of dynamical systems to various problems in science and technology. I expect the book to find its readership basically as an introduction to nonlinear dynamics for undergraduate students of natural sciences, but also as a general reference work for researchers confronted with the need to understand dynamical mechanisms behind the phenomena which they encounter in their experiments and numerical simulations.” (Mikhail Zaks, Mathematical Reviews, May, 2016)Table of ContentsDescriptive synopsis of the text.- Mathematical introduction to dynamical systems.- Dynamical systems without dissipation.- Dynamical systems with dissipation.- Local bifurcation theory.- Convective flow: Benard problem.- Routes to chaos.- Turbulence.- Computer experiments.

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Book SynopsisThis textbook is the result of many years of teaching quantum and statistical mechanics, drawing on exercises and exam papers used on courses taught by the authors. The subjects of the exercises have been carefully selected to cover all the material which is most needed by students. Each exercise is carefully solved in full details, explaining the theory behind the solution with particular care for those issues that students often find difficult, or which are often neglected in other books on the subject. The exercises in this book never require extensive calculations but tend to be somewhat unusual and force the solver to think about the problem starting from first principles, rather than by analogy with some previously solved exercise.Table of ContentsIntroduction to Quantum Mechanics.- Problems on Quantum Mechanics.- Problems on Statistical Mechanics.

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Book SynopsisThe aim of this work is to bridge the gap between the well-known Newtonian mechanics and the studies on chaos, ordinarily reserved to experts. Several topics are treated: Lagrangian, Hamiltonian and Jacobi formalisms, studies of integrable and quasi-integrable systems. The chapter devoted to chaos also enables a simple presentation of the KAM theorem. All the important notions are recalled in summaries of the lectures. They are illustrated by many original problems, stemming from real-life situations, the solutions of which are worked out in great detail for the benefit of the reader. This book will be of interest to undergraduate students as well as others whose work involves mechanics, physics and engineering in general.Trade ReviewFrom the reviews:“The present book fills an important gap in the scientific literature since most books on analytical mechanics concentrate on the theoretical aspects. A great number of exercises and problems are divided into eight chapters … . In conclusion, this is an excellent source of concrete examples for students and mathematicians from several fields.” (Mircea Crâşmăreanu, Zentralblatt MATH, Vol. 1172, 2009)Table of ContentsForeword Synoptic Tables. Chapter 1 : The Lagrangian formulation (1 1 problems) Chapter 2 : Lagrangian systems (14 problems) Chapter 3 : The Hamilton's principle (15 problems) Chapter 4 : The Hamiltonian formalism (17 problems) Chapter 5 : The Hamilton-Jacobi formalism (1 1 problems) Chapter 6 : Integrable systems (18 problems) Chapter 7 : Quasi-integrable systems (9 problems) Chapter 8 : From order to chaos (12 problems). Bibliography.

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Book SynopsisOur book introduces a method to evaluate the accuracy of trend estimation algorithms under conditions similar to those encountered in real time series processing. This method is based on Monte Carlo experiments with artificial time series numerically generated by an original algorithm. The second part of the book contains several automatic algorithms for trend estimation and time series partitioning. The source codes of the computer programs implementing these original automatic algorithms are given in the appendix and will be freely available on the web. The book contains clear statement of the conditions and the approximations under which the algorithms work, as well as the proper interpretation of their results. We illustrate the functioning of the analyzed algorithms by processing time series from astrophysics, finance, biophysics, and paleoclimatology. The numerical experiment method extensively used in our book is already in common use in computational and statistical physics.Table of ContentsDiscrete stochastic processes and time series.- Trend definition.- Finite AR(1) stochastic process.- Monte Carlo experiments. - Monte Carlo statistical ensembles.- Numerical generation of trends.- Numerical generation of noisy time series.- Statistical hypothesis testing.- Testing the i.i.d. property.- Polynomial fitting.- Linear regression.- Polynomial fitting.- Polynomial fitting of artificial time series.- An astrophysical example.- Noise smoothing.- Moving average.- Repeated moving average (RMA).- Smoothing of artificial time series.- A financial example.- Automatic estimation of monotonic trends.- Average conditional displacement (ACD) algorithm.- Artificial time series with monotonic trends.- Automatic ACD algorithm.- Evaluation of the ACD algorithm.- A paleoclimatological example.- Statistical significance of the ACD trend.- Time series partitioning.- Partitioning of trends into monotonic segments.- Partitioning of noisy signals into monotonic segments.- Partitioning of a real time series.- Estimation of the ratio between the trend and noise.- Automatic estimation of arbitrary trends.- Automatic RMA (AutRMA).- Monotonic segments of the AutRMA trend.- Partitioning of a financial time series.

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Book SynopsisThe aim of this work is to bridge the gap between the well-known Newtonian mechanics and the studies on chaos, ordinarily reserved to experts. Several topics are treated: Lagrangian, Hamiltonian and Jacobi formalisms, studies of integrable and quasi-integrable systems. The chapter devoted to chaos also enables a simple presentation of the KAM theorem. All the important notions are recalled in summaries of the lectures. They are illustrated by many original problems, stemming from real-life situations, the solutions of which are worked out in great detail for the benefit of the reader. This book will be of interest to undergraduate students as well as others whose work involves mechanics, physics and engineering in general.Trade ReviewFrom the reviews:“The present book fills an important gap in the scientific literature since most books on analytical mechanics concentrate on the theoretical aspects. A great number of exercises and problems are divided into eight chapters … . In conclusion, this is an excellent source of concrete examples for students and mathematicians from several fields.” (Mircea Crâşmăreanu, Zentralblatt MATH, Vol. 1172, 2009)Table of ContentsForeword Synoptic Tables. Chapter 1 : The Lagrangian formulation (1 1 problems) Chapter 2 : Lagrangian systems (14 problems) Chapter 3 : The Hamilton's principle (15 problems) Chapter 4 : The Hamiltonian formalism (17 problems) Chapter 5 : The Hamilton-Jacobi formalism (1 1 problems) Chapter 6 : Integrable systems (18 problems) Chapter 7 : Quasi-integrable systems (9 problems) Chapter 8 : From order to chaos (12 problems). Bibliography.

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Book SynopsisNow in its fully updated fourth edition, this leading text in its field is an exhaustive monograph on turbulence in fluids in its theoretical and applied aspects. The authors examine a number of advanced developments using mathematical spectral methods, direct-numerical simulations, and large-eddy simulations. The book remains a hugely important contribution to the literature on a topic of great importance for engineering and environmental applications, and presents a very detailed presentation of the field.Trade ReviewFrom the reviews of the fourth edition: "Turbulence in Fluids contains a wealth of information, and its author is a top-tier scientist. … The book is logically ordered and contains a comprehensive list of 738 references. … Lesieur’s monograph is recommended for those who already know quite a bit about turbulence, for the theoretically inclined, and in particular for those interested in homogeneous turbulence and geophysical flows and their numerical simulation." (Mohamed Gad-El-Hak, Siam Review, Vol. 51 (1), 2009)Table of Contentsto Turbulence in Fluid Mechanics.- Basic Fluid Dynamics.- Transition to Turbulence.- Shear Flow Turbulence.- Fourier Analysis of Homogeneous Turbulence.- Isotropic Turbulence: Phenomenology and Simulations.- Analytical Theories and Stochastic Models.- Two-Dimensional Turbulence.- Beyond Two-Dimensional Turbulence in GFD.- Statistical Thermodynamics of Turbulence.- Statistical Predictability Theory.- Large-Eddy Simulations.- Towards “Real World Turbulence”.

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Book SynopsisConstant and Self variable Polynomial Systems.- Constant and Crossing variable Polynomial Systems.- Single univariate Polynomial Systems.- Higher order Infinite equilibrium Bifurcations.

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Book SynopsisChapter 1 Fractional Differential Equations in Engineering Sciences.- Chapter 2 A New Operator Approach for Solving Time-Fractional Nonlinear Burgess Equation.- Chapter 3 Explicit Formulas for the Solutions of a Solvable.- Chapter 4 Stochastic Equations with Deviating Argument Driven by Poisson Jumps.- Chapter 5 A Review on Fractional Calculus in Modelling of Cancer.

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