Applied mathematics Books

Book SynopsisFundamentals of Matrix Computations deals with the concept of matrix computations, a technique of singular value homogenization and its application in medical therapy. It consists of modern iterative methods to generalize the issues associated with singular-value homogenization. It provides the reader with the understanding of matrix computations and preconditioning technique of singular value homogenization so as to analyze its potential applications in the field of medical therapy and the use of efficient numerical methods so as to solve the problems linked with nonlinear singular boundary value by using improved differential transform method. This book also discusses about blind distributed estimation algorithms for adaptive networks, a dft-based approximate eigenvalue and singular value decomposition of polynomial matrices, sparse signal subspace decomposition based on adaptive over-complete dictionary, lower bounds for the low-rank matrix approximation and a semi-smoothing augmented lagrange multiplier algorithm for low-rank toeplitz matrix completion.

Read more less

Book SynopsisFuzzy systems have largely replaced conventional technologies in a large number of scientific applications and engineering systems, especially in the field of control systems and pattern recognition. This book covers different topics from fuzzy systems and applications, including fuzzy sets theory, fuzzy-based expert systems, fuzzy control systems and fuzzy applications in different domains.

Read more less

Book SynopsisThe appropriate role of mathematics in economics has been controversial for two hundred years, and has been a matter of ongoing debate as economics became more mathematical after the Second World War. Controversy has been heightened after extensive criticisms of models used for analysis, prediction and risk assessment prior to the great financial crash of 2008. In this topical collection, Professor Hodgson brings together the seminal classic and recent essays published since 1945 on the role of mathematics in economics, by leading authors including six Nobel Laureates, and from a variety of perspectives. Table of ContentsContents: Acknowledgements Introduction Geoffrey M. Hodgson PART I FROM THE FORMALIST REVOLUTION TO THE AEA COMMISSION 1. Mark Blaug (2003), ‘The Formalist Revolution of the 1950s’ 2. J.M. Clark (1947), ‘Mathematical Economists and Others: A Plea for Communicability’ 3. Kenneth E. Boulding (1948), ‘Samuelson's Foundations: The Role of Mathematics in Economics’ 4. Morris A. Copeland (1951), ‘Institutional Economics and Model Analysis’ 5. David Novick (1954), ‘Mathematics: Logic, Quantity, and Method’ 6. Paul A. Samuelson (1954), ‘Some Psychological Aspects of Mathematics in Economics’ 7. Stephen Enke (1955), ‘More on the Misuse of Mathematics in Economics: A Rejoinder’ 8. Wassily Leontief (1971), ‘Theoretical Assumptions and Nonobserved Facts’ 9. Alan Coddington (1975), ‘Creaking Semaphore and Beyond: A Consideration of Shackle’s “Epistemics and Economics”’ 10. Alexander Rosenberg (1975), ‘The Nomological Character of Microeconomics’ 11. Herbert G. Grubel and Lawrence A. Boland (1986), ‘On the Efficient Use of Mathematics in Economics: Some Theory, Facts and Results of an Opinion Survey’ 12. Gerard Debreu (1986), ‘Theoretic Models: Mathematical Form and Economic Content’ 13. Herbert A. Simon (1986), ‘The Failure of Armchair Economics [Interview]’ 14. Gerard Debreu (1991), ‘The Mathematization of Economic Theory’ 15. Anne O. Krueger (1991), ‘Report of the Commission on Graduate Education in Economics’ 16. Alan S. Blinder (1990), ‘Discussion’ PART II MATHEMATICS, FIN DE SIèCLE: 1991–1999 17. Frank Hahn (1991), ‘The Next Hundred Years’ 18. Donald N. McCloskey (1991), ‘Economics Science: A Search Through the Hyperspace of Assumptions?’ 19. Philip Mirowski (1991), ‘The When, the How and the Why of Mathematical Expression in the History of Economics Analysis’ 20. E. Roy Weintraub and Philip Mirowski (1994), ‘The Pure and the Applied: Bourbakism Comes to Mathematical Economics’ 21. Munir Quddus and Salim Rashid (1994), ‘The Overuse of Mathematics in Economics: Nobel Resistance’ 22. Robert W. Clower (1995), ‘Axiomatics in Economics’ 23. Mark Blaug (1997), ‘Ugly Currents in Modern Economics’ 24. Peter J. Boettke (1997), ‘Where Did Economics Go Wrong? Modern Economics as a Flight from Reality’ 25. Paul Krugman (1998), ‘Two Cheers for Formalism’ 26. Roger E. Blackhouse (1998), ‘If Mathematics is Informal, Then Perhaps We Should Accept that Economics Must be Informal Too’ 27. Victoria Chick (1998), ‘On Knowing One’s Place: The Role of Formalism in Economics’ PART III MILLENNIAL MATHEMATICS: METHODOLOGY AND ONTOLOGY 28. Robert Sugden (2000), ‘Credible Worlds: The Status of Theoretical Models in Economics’ 29. James M. Buchanan (2001), ‘Game Theory, Mathematics, and Economics’ 30. Victoria Chick and Sheila C. Dow (2001), ‘Formalism, Logic and Reality: A Keynesian Analysis’ 31. Ken Dennis (2002), ‘Nominalising the Numeric: An Alternative to Mathematical Reduction in Economics’ 32. Tony Lawson (2004), ‘“Reorienting Economics”: On Heterodox Economics, Themata and the Use of Mathematics in Economics’ 33. Uskali Mäki (2005), ‘Models are Experiments, Experiments are Models’ 34. K. Vela Velupillai (2005), ‘The Unreasonable Ineffectiveness of Mathematics in Economics’ 35. D. Wade Hands (2007), ‘2006 HES Presidential Address: A Tale of Two Mainstreams: Economics and Philosophy of Natural Science in the Mid-Twentieth Century’ 36. Geoffrey M. Hodgson (2006), ‘The Problem of Formalism in Economics’ 37. Simon Mohun and Roberto Veneziani (2010), ‘Reorienting Economics?’ PART IV MATHEMATICAL ECONOMICS AND THE GREAT CRASH OF 2008 38. David Colander, Hans Föllmer, Armin Haas, Michael Goldberg, Katarina Juselius, Alan Kirman, Thomas Lux and Brigitte Sloth (2008), ‘The Financial Crisis and the Systematic Failure of Academic Economics’ 39. Tony Lawson (2009), ‘The Current Economic Crisis: Its Nature and the Course of Academic Economics’ 40. Timothy Besley and Peter Hennessy (2009), ‘The Global Financial Crisis – Why Didn’t Anyone Notice?’ 41. Sheila C. Dow, Peter E. Earl, John Foster, Geoffrey C. Harcourt, Geoffrey M. Hodgson, J. Stanley Metcalfe, Paul Ormerod, Bridget Rosewell, Malcolm C. Sawyer and Andrew Tylecote (2009), ‘Letter to the Queen, 10 August’ 42. Tony Lawson (2009), ‘Contemporary Economics and the Crisis’ 43. David Colander, Hans Foellmer, Armin Haas, Alan Kirman, Katarina Juselius, Brigitte Sloth and Thomas Lux (2009) ‘How Should the Collapse of the World Financial System Affect Economics?’ 44. Philip Mirowski (2010), ‘The Great Mortification: Economists’ Responses to the Crisis of 2007–(and counting)’ 45. Peter E. Earl (2010), ‘Economics Fit for the Queen: A Pessimistic Assessment of its Prospects’ 46. Geoffrey Hodgson (2011), ‘Reforming Economics after the Financial Crisis’ Index

Read more less

Book SynopsisThis book deals with corporate mergers and acquisitions by analyzing the financial and strategic aspects. It starts with a chronological justification of the evolution of external growth operations and ends with case studies in order to put into practice the theoretical contribution of the previous titles. Through this book, we wish to detail the types of mergers and acquisitions, their modes, their motivations, their consequences and their performances. First of all, we propose a panoply of scientific research, methodological explanations and logical structuring to expose a subject of experience considered for a long time as a phenomenon in finance. Then, through a sample of 90 mergers or acquisitions, we analyze the effects of these transactions on French companies. Table of ContentsIntroduction ix Part 1. Taxonomy of Mergers and Acquisitions and the Evolution of Managerial Thought 1 Chapter 1. Strategic Evolution of Mergers and Acquisitions 3 1.1. Typology of mergers and acquisitions 4 1.1.1. Horizontal mergers and acquisitions 4 1.1.2. Vertical mergers and acquisitions 9 1.1.3. Conglomerate mergers and acquisitions 10 1.2. Theory, diversification and divergence 12 1.2.1. Contributions pre-1980 12 1.2.2. Contributions during the 1980s 16 1.2.3. Management approaches and divergences 18 Chapter 2. Growth Methods and Responses 23 2.1. Merger and takeover types 23 2.1.1. Types of company mergers and acquisitions 24 2.1.2. Takeover and acquisition types 26 2.1.3. Modes of expansion and responses 29 2.2. Tender offers as a market for corporate control 32 2.2.1. Characteristics of the control market 32 2.2.2. The role of the control market 34 2.2.3. Consequences of the control market 36 Part 2. Mergers and Acquisitions Strategies:Cause and Effect 41 Chapter 3. Asset Transfers: Causes and Consequences 43 3.1. Merger/acquisition waves 44 3.1.1. Global market and merger/acquisition waves 44 3.1.2. Merger/acquisition waves in the US market 48 3.1.3. Merger/acquisition waves in the French market 51 3.2. Diversification, restructuring, divestment and respecialization 57 3.2.1. Divestment as a development strategy 57 3.2.2. Corporate restructuring 60 3.2.3. Consequences of restructuring 64 Chapter 4 Mergers/Acquisitions: Motivation and Performance 69 4.1. Motivating factors in mergers/acquisitions 69 4.1.1. The pursuit of synergy 70 4.1.2. The possibility of non-economic motivations 73 4.1.3. Causes and consequences of motivations 77 4.2. Merger/acquisition performance 81 4.2.1. The many faces of success 81 4.2.2. Performance of mergers/acquisitions 86 4.2.3. Mergers/acquisitions: causes of failure 89 Part 3. Value Creation and Measurement Methods 93 Chapter 5. Synergy in Mergers and Acquisitions 95 5.1. Synergy creation or simple wealth transfer 95 5.1.1. Financial synergy 96 5.1.2. Strategic synergies 96 5.1.3. Wealth transfer theory 97 5.2. Sources of value creation in mergers/acquisitions 98 5.2.1. Sources of strategic value creation 99 5.2.2. Operational and managerial efficiency 101 5.2.3. Sources of financial value creation 108 Chapter 6. Measurement Methods for Value Creation 113 6.1. Stock-market methods: the event method 113 6.1.1. Market efficiency and samples 114 6.1.2. Estimation and calculation of returns 115 6.1.3. Results tests 118 6.2. Statistical and accounting methods 121 6.2.1. Studies pre-1990 121 6.2.2. Studies between 1990–2000 122 6.2.3. Studies post-2000 123 6.2.4. Methods in case studies 124 Part 4. The French Market: Analyses and Case Studies 127 Chapter 7. Observations and Lessons from the French Merger/Acquisition Market 129 7.1. Sources of value creation in the French market 130 7.1.1. Variables and calculation methods 130 7.1.2. Data analysis. 135 7.1.3. Observations and findings 141 7.2. Group growth strategy: the case of Sanofi 144 7.2.1. The pharmaceutical sector and external growth 144 7.2.2. The Sanofi takeover bid: an offensive strategy 149 7.2.3. Integration and reorganization policy 153 7.2.4. Findings and observations 154 Chapter 8. Value Creation in the Sanofi-Aventis Merger 157 8.1. Did the takeover create stock market value? 158 8.1.1. Methodology and data 158 8.1.2. Results and observations 162 8.1.3. The takeover bid period 167 8.2. Accounting and financial value: in-depth study 171 8.2.1. Methodology and data 171 8.2.2. Results and remarks 175 8.2.3. Discussion and observations 184 Conclusion 187 Appendix 189 Bibliography 203 Index 241

Read more less

Book SynopsisThe sciences are, in essence, highly semiotized. Our ways of thinking and communicating about science are based on permanent transformations from one system of signs to another, such as scriptural, graphic, symbolic, oral and gestural signs. The semiotic focus studied in this book makes it possible to grasp part of the complexity of teaching and learning phenomena by focusing on the variety of possible interpretations of the signs that circulate within the science classroom. Semiotic Approaches in Science Didactics brings together contributions from didactic research involving various disciplines such as mathematics, chemistry, physics and geography, which mobilize different types of semiotic support. It offers the key to understanding and even reducing some of the misunderstandings that can arise between a speaker and a receiver in scientific teaching situations.Table of ContentsPart 1. A Study of the Dynamics of the Development of Scientific Knowledge: Semiotic Opportunities 1. A Walk in Semiotics and Mathematics by Catherine Houdement 2. Semiotic Systems Specific to Chemistry and Their Learning by Isabelle Kermen Part 2. The Semiotic Approach: Toward the Invention of New Forms of Didactic Intervention 3. Scientific Knowledge at the Mercy of the "BD" Comic Strip by Laurence Bordenave and Cécile de Hosson 4. The Map at the Heart of Disciplinary Learning by Sophie Gaujal and Caroline Leininger-Frézal Part 3. The Multimodal Semiotic Approach: A Look at Didactic Interactions and Cognitive Processes 5. Semiotic Modes and Models in Physics by Karine Bécu-Robinault 6. The Didactic Effects of Semiotic Microphenomena in Mathematics by Edith Petitfour and Catherine Houdement 7. Body, Matter and Signs in the Constitution of Meaning in Mathematics by Luis Radford

Read more less

Book SynopsisThis is the first English translation of Launhardt’s Mathematische Begrundung der Volkswirtschaftslehre (1885), a major contribution to neoclassical economic theory which contains many important and original analyses. This edition will provide the basis for a re-evaluation of Launhardt’s outstanding, but undervalued, contribution to economics. Taking the neoclassical emphasis on exchange as the central economic problem, Laundardt begins with a thorough treatment of the pure exchange model, then goes on to extend the treatment to the production of goods and the supply of labour, with a sophisticated general equilibrium perspective. It contains important analyses of savings and the role of capital goods, as well as an outstanding study of transport and the location of industry. Launhardt’s book can, with justice, with be described as the first comprehensive treatise on welfare economics.Mathematical Principles of Economics will prove stimulating reading for economic theorists as well as those interested in the history of economics thought.Trade Review’Launhardt stands first in the long line of economists from Dupuit in the 1830s to Abba P. Lerner in the 1930s who recognized that the pricing of public utilities presents a special problem, requiring public subventions if the welfare of consumers is to be served.’

Read more less

Book SynopsisThis must-read textbook presents an essential introduction to Kolmogorov complexity (KC), a central theory and powerful tool in information science that deals with the quantity of information in individual objects. The text covers both the fundamental concepts and the most important practical applications, supported by a wealth of didactic features.This thoroughly revised and enhanced fourth edition includes new and updated material on, amongst other topics, the Miller-Yu theorem, the Gács-Kučera theorem, the Day-Gács theorem, increasing randomness, short lists computable from an input string containing the incomputable Kolmogorov complexity of the input, the Lovász local lemma, sorting, the algorithmic full Slepian-Wolf theorem for individual strings, multiset normalized information distance and normalized web distance, and conditional universal distribution.Topics and features: describes the mathematical theory of KC, including the theories of algorithmic complexity and algorithmic probability; presents a general theory of inductive reasoning and its applications, and reviews the utility of the incompressibility method; covers the practical application of KC in great detail, including the normalized information distance (the similarity metric) and information diameter of multisets in phylogeny, language trees, music, heterogeneous files, and clustering; discusses the many applications of resource-bounded KC, and examines different physical theories from a KC point of view; includes numerous examples that elaborate the theory, and a range of exercises of varying difficulty (with solutions); offers explanatory asides on technical issues, and extensive historical sections; suggests structures for several one-semester courses in the preface.As the definitive textbook on Kolmogorov complexity, this comprehensive and self-contained work is an invaluable resource for advanced undergraduate students, graduate students, and researchers in all fields of science.Table of ContentsPreliminaries Algorithmic Complexity Algorithmic Prefix Complexity Algorithmic Probability Inductive Reasoning The Incompressibility Method Resource-Bounded Complexity Physics, Information, and Computation

Read more less

Book SynopsisThis textbook contains a rigorous exposition of the mathematical foundations of two of the most important topics in politics and economics: voting and apportionment, at the level of upper undergraduate and beginning graduate students. It stands out among comparable books by providing, in one volume, an extensive and mathematically rigorous treatment of these two topics.The text’s three chapters cover social choice, yes-no voting, and apportionment, respectively, and can be covered in any order, allowing teachers ample flexibility. Each chapter begins with an elementary introduction and several examples to motivate the concepts and to gradually lead to more advanced material. Landmark theorems are presented with detailed and streamlined proofs; those requiring more complex proofs, such as Arrow’s theorems on dictatorship, Gibbard’s theorem on oligarchy, and Gärdenfors’ theorem on manipulation, are broken down into propositions and lemmas in order to make them easier to grasp. Simple and intuitive notations are emphasized over non-standard, overly complicated symbols. Additionally, each chapter ends with exercises that vary from computational to “prove or disprove” types.The Mathematics of Voting and Apportionment will be particularly well-suited for a course in the mathematics of voting and apportionment for upper-level undergraduate and beginning graduate students in economics, political science, or philosophy, or for an elective course for math majors. In addition, this book will be a suitable read for to any curious mathematician looking for an exposition to these unpublicized mathematical applications.No political science prerequisites are needed. Mathematical prerequisites (included in the book) are minimal: elementary concepts in combinatorics, graph theory, order relations, and the harmonic and geometric means. What is needed most is the level of maturity that enables the student to think logically, derive results from axioms and hypotheses, and intuitively grasp logical notions such as “contrapositive” and “counterexample.”Trade Review“The mathematics of voting and apportionment is a well-written, thorough introduction to social choice and social welfare theory. … This book is suitable as the main text for a one-semester introduction to voting theory and apportionment. I would also recommend this book to anyone interested in independently studying these topics. It is a clearly written, entry-level text into voting theory and apportionment.” (Brittany Shelton, Mathematical Reviews, February, 2020)“As intended audience the author mentions students in economics, political science, philosophy and (applied) mathematics, but I think the book is also to be recommended to law students … . I like to suggest to include this topic in a next edition of this admirable book.” (H. C. M. de Swart, zbMATH 1426.91001, 2020)“This is a nicely written book, with clear explanations that are supported by a number of useful, fully worked out, examples. … more appropriate audience would be math majors in a proof-based course who already have some experience in reading precisely stated definitions and statements of theorems, and a willingness to track through the details of a proof.” (Mark Hunacek, MAA Reviews, August 11, 2019)“This book, is a textbook that is clearly addressing an audience of social science students, in particular in the US … . It is not only a textbook for his students, but it brings together a lot of material that is not easily found in this compact form and as such it will be of interest to any politician or anyone who is generally interested in the subject.” (Adhemar Bultheel, European Mathematical Society, euro-math-soc.eu, July 01, 2019)Table of ContentsChapter 1: Social Choice.- Introduction.- Elimination Procedures.- Condorcet Ideas and Related Procedures.- Scoring Procedures: Borda Count.- A Glimpse into Social Welfare Theory.- Social Choice Procedures: Indifference and Ties Allowed.- Manipulability of Social Choice Procedures: Indifference and Ties Allowed.- Exercises.- Chapter 2: Yes-No Voting.- Introduction.- Quantification of Power in a Yes-No Voting System.- Some Combinatorics.- Banzhaf and Shapley-Shubik Indices in One View.- Weightable Yes-No Voting Systems.- Exercises.- Chapter 3: Apportionment.- Introduction.- Axioms of Apportionment.- Quota Procedures.- Divisor Procedures.- Equity Criteria.- Apportionment Paradoxes.- Applications of Priority Formulas.- Exercises.

Read more less

Book SynopsisClose Encounters of Art and Physics is a voyage in time through the abstract ideas harboured in the minds of humans, starting from the graffiti art of cave dwellers and extending to the street art of contemporary men and women. In seeking parallels with science, the author looks far back to the first geometric ideas of our ancestors as well as ahead to the contemporary science of present-day physicists. The parallelism and analogies between these two fields bear witness to a real entanglement in the human brain. The second part of the book contains about 25 colour images showing the author's stunning glass artwork representing ideas such as dark matter, quantum entanglement, cellular automata and many others that are almost impossible to capture in words. Furthermore, many of the physicists who have themselves made major contributions in these fields provide their comments and analysis of the works. The book provides entertaining and informative reading, not only for practicing artists and physicists, but also anyone curious about art and physics.Table of ContentsPart I Parallels Between Art and Physics.- Rock Paintings: Primordial Graffiti.- A Sense of the Beauty of Forms.- Were the Dark Ages Really Dark?.- Rebirth!.- The Age of Reason: The Enlightenment.- Impressive Impressions.- What You See Is Not What You Get.- Is Reality Really Real?.- Abstraction: Pure Thought.- Timeless Time.- Does it Belong to the Elite?.- Part II Collaborations.- What Time Is It?.- A Longer History of Time.- Just Call Me Jim.- Quintessence: The Spirit of the World.- Resolving the Unresolved.- The Brain Is an Orchestra.- Let’s Play Chess.- Are There Real Crystals in the Universe?.- Brain and Mind.- In Memory of Tom Kibble.- Conclusion.- Bibliography

Read more less

Book SynopsisThis book presents the important role of mathematics in the teaching of financial education. Through a conceptualization of financial numeracy as a social practice, it focuses on the teaching practices, resources, and needs of secondary mathematics teachers (grades 7-12) to incorporate financial concepts in their classes. The editors and authors bring forth a novel perspective regarding mathematics education in the digital era. By focusing on financial numeracy, a key component of skills required in the digital era, they discuss important issues related to the teaching and learning of mathematics and finance. In contrary to most research in the field of financial education coming from scholars in areas such as business, accounting, management and economics, this book introduces the contribution of researchers from the field of education to the debate. The book appeals to an international audience composed of researchers, stakeholders, policymakers, teachers, and teacher educators.Trade Review“This could also be used as a supplementary book for a graduate-level mathematics education student studying financial numeracy.” (Blain Patterson, MAA Reviews, December 12, 2021)Table of ContentsSection 1: Theoretical perspectives Introduction: Financial Education in the Digital Era (Annie & Alex).- Chapter 1. Financial Education and Mathematics from an epistemological point of view.- Chapter 2. Financial Education in the Mathematics curricula: Financial knowledge when teaching Mathematics.- Section 2: Research perspectives - a study on Secondary Mathematics teachers' needs.- Chapter 3. Background of the project (including how we collected the data).- Chapter 4. Building an instrument for research in Financial Education in schools (Quebec and Romania).- Chapter 5. Using tasks to elicit mathematics teachers' thinking in Financial Education.- Chapter 6. Mathematics Teachers’ representations of Financial Education.- Chapter 7. Making sense of mathematics: students questioning financial contexts when learning Mathematics.- Section 3: Financial Education and Mathematics: practice perspectives in K-12.- Chapter 8. Some situations to implement Financial Education in Mathematics classrooms.- Chapter 9. Training mathematics teachers to incorporate Financial Education.- Chapter 10. Mathematics teachers' needs in Financial Education: Implications for leadership.- Chapter 11. Ethical considerations on doing research on Financial Education in the Digital Era.- Chapter 12. Financial Education as an emerging field in Education: looking to the future.

Read more less

Book SynopsisThis book gathers papers presented at the 13th International Conference on Mesh Methods for Boundary-Value Problems and Applications, which was held in Kazan, Russia, in October 2020. The papers address the following topics: the theory of mesh methods for boundary-value problems in mathematical physics; non-linear mathematical models in mechanics and physics; algorithms for solving variational inequalities; computing science; and educational systems. Given its scope, the book is chiefly intended for students in the fields of mathematical modeling science and engineering. However, it will also benefit scientists and graduate students interested in these fields.Table of ContentsTheory of the mesh methods for the boundary-value problems in Mathematical Physics.- Non-linear mathematical models in mechanics and physics.- Algorithms for solving variational inequalities.- Computing Science and educational systems.

Read more less

Book SynopsisThis volume is a collection of essays on complex symmetries. It is curated, emphasizing the analysis of the symmetries, not the various phenomena that display those symmetries themselves. With this, the volume provides insight to nonspecialist readers into how individual simple symmetries constitute complex symmetry. The authors and the topics cover many different disciplines in various sciences and arts. Simple symmetries, such as reflection, rotation, translation, similitude, and a few other simple manifestations of the phenomenon, are all around, and we are aware of them in our everyday lives. However, there are myriads of complex symmetries (composed of a bulk of simple symmetries) as well. For example, the well-known helix represents the combination of translational and rotational symmetry. Nature produces a great variety of such complex symmetries. So do the arts. The contributions in this volume analyse selected examples (not limited to geometric symmetries). These include physical symmetries, functional (meaning not morphological) symmetries, such as symmetries in the construction of the genetic code, symmetries in human perception (e.g., in geometry education as well as in constructing physical theories), symmetries in fractal structures and structural morphology, including quasicrystal and fullerene structures in stable bindings and their applications in crystallography and architectural design, as well as color symmetries in the arts. The volume is rounded of with beautiful illustrations and presents a fascinating panorama of this interdisciplinary topic.Table of ContentsGyörgy Darvas: Complex Symmetries, Introduction.- Douglas Dunham: Complex Symmetries in Repeating Hyperbolic Patterns.- Paul Hertz: Ignotheory: A Compositional System for Intermedia Art Based on Tiling Patterns and Labelled Graphs.- Ashish Kumar Upadhyay: Symmetries of Maps on Surfaces.- Koji Miyazaki and Motonaga Ishii: Symmetry in Projection of 4-dimensional Regular Polychora.- Guy Inchbald: Morphic Polytopes and Symmetries.- Takeshi Sugimoto: Inducing the Symmetries out of the Complexity: The Kepler Triangle and its Kin as a Model Problem.- Jim Lehman: Synchronizing the Isotropic Vctor Matrix with the Stellated Vector Matrix.- András Recski: An Analogy and Several Symmetries.- Dmitriy Gurevich: Discrete Lattices on the Single Bearing Spiral: From Geometry to Botany.- Simone Brasili and Riccardo Piergallini: Symmetry and Invariance: Interdisciplinary teaching.- Eleonóra Stettner and György Emese: Dilative Rotation, Dilative Reflection in Mathematics, Nature, Art, and Education.- János Szász Saxon and Gábor Kis: Relationship of Symmetry and Combinatorics in the Poly-universe Game.- Marina Voinova: Symmetry in Arrow-like Salt Crystals.- László Szabados: Symmetries in Stellar, Galactic, and Extragalactic Astronomy.- Sergey V. Petoukhov, Elena S. Petukhova and Vladimir V. Verevkin: Symmetries and the Genetic, Code.- Kas Oosterhuis: Global Symmetry Local Asymmetry: In the Realized Buildings by the Innovation Studio ONL BV.- Katarzyna Szymańska-Stułka: Theme, Motive, Structure and Symmetry – Pentasonata by Andrzej Panufnik.- FréIlgen: Fluid Symmetry: Logical to Artists, Mesmerizing to Viewers.- Paul B. Ré: Complex Symmetries in Réograms.- Patrice Jeener: Graphic Illustrations of Complex Symmetries.

Read more less

Book SynopsisThe developments in mesh generation are usually driven by the needs of new applications and/or novel algorithms. The last decade has seen a renewed interest in mesh generation and adaptation by the computational engineering community, due to the challenges introduced by complex industrial problems.Another common challenge is the need to handle complex geometries. Nowadays, it is becoming obvious that geometry should be persistent throughout the whole simulation process. Several methodologies that can carry the geometric information throughout the simulation stage are available, but due to the novelty of these methods, the generation of suitable meshes for these techniques is still the main obstacle for the industrial uptake of this technology.This book will cover different aspects of mesh generation and adaptation, with particular emphasis on cutting-edge mesh generation techniques for advanced discretisation methods and complex geometries.Table of Contents1 Carolyn Woeber, Advances in H-P Mesh Adaptation for Finite Element Methods.- 2 Chiara Nardoni, Remeshing techniques in shape and topology optimization.- 3 Dimitrios Papadimitrakis, Building direction fields on the medial object to generate 3D domain decompositions for hexahedral meshing.- 4 Franck Ledoux, Interecode hexahedral meshing from Eulerian to Lagrangian simulations.- 5 Jean-Francois Remacle, A robust approach for mesh generation of surfaces with irregular/singular parametrizations.6 Jens Lang, Sample Adaptive Multilevel Stochastic Collocation Schemes in Uncertainty Quantification of Gas Transport in Networks.- 7 Jessica Zhang, Hexahedral dominant mesh generation and spline modeling for isogeometric analysis.- 8 Juan José Ródenas, Mesh adaptivity in the framework of the Cartesian grid finite element method, cgFEM.- 9 Mario Ricchiuto, h- and r-adaptation on simplicial meshes: implementation and applications.- 10 Onkar Sahni, Geometry and Adaptive Mesh Update Procedures for Ballistics Simulations.- 11 Per-Olof Persson, HOIST: High-Order Implicit Shock Tracking using an optimization-based discontinuous Galerkin method.- 12 Rainald Lohner, Breakthrough ‘workarounds’ in unstructured mesh generation.- 13 Simone Appella, An adaptive moving mesh method with conservative interpolation based on local projection.- 14 Suzanne Shontz, Global optimization strategies for automated edge grid generation.

Read more less

Book SynopsisThe purpose of this book is to present the current state of the art of the Virtual Element Method (VEM) by collecting contributions from many of the most active researchers in this field and covering a broad range of topics: from the mathematical foundation to real life computational applications. The book is naturally divided into three parts. The first part of the book presents recent advances in theoretical and computational aspects of VEMs, discussing the generality of the meshes suitable to the VEM, the implementation of the VEM for linear and nonlinear PDEs, and the construction of discrete hessian complexes. The second part of the volume discusses Virtual Element discretization of paradigmatic linear and non-linear partial differential problems from computational mechanics, fluid dynamics, and wave propagation phenomena. Finally, the third part contains challenging applications such as the modeling of materials with fractures, magneto-hydrodynamics phenomena and contact solid mechanics.The book is intended for graduate students and researchers in mathematics and engineering fields, interested in learning novel numerical techniques for the solution of partial differential equations. It may as well serve as useful reference material for numerical analysts practitioners of the field.Table of Contents1 Tommaso Sorgente et al., VEM and the Mesh.- 2 Dibyendu Adak et al., On the implementation of Virtual Element Method for Nonlinear problems over polygonal meshes.- 3 Long Chen and Xuehai Huang, Discrete Hessian Complexes in Three Dimensions.- 4 Edoardo Artioli et al., Some Virtual Element Methods for Infinitesimal Elasticity Problems.- 5 Lourenço Beirão da Veiga and Giuseppe Vacca, An introduction to second order divergence-free VEM for fluidodynamics.- 6 Gabriel N. Gatica et al, A virtual marriage à la mode: some recent results on the coupling of VEM and BEM.- 7 Daniele Boffi et al., Virtual element approximation of eigenvalue problems.- 8 David Mora and Alberth Silgado, Virtual element methods for a stream-function formulation of the Oseen equations.- 9 Lorenzo Mascotto et al., The nonconforming Trefftz virtual element method: general setting, applications, and dispersion analysis for the Helmholtz equation.- 10 Paola F. Antonietti et al., The conforming virtual element method for polyharmonic and elastodynamics problems: a review.- 11 Edoardo Artioli et al., The virtual element method in nonlinear and fracture solid mechanics.- 12 Sebastián Naranjo Álvarez et al., The virtual element method for the coupled system of magneto-hydrodynamics.- 13 Peter Wriggers et al., Virtual Element Methods for Engineering Applications.

Read more less

Book SynopsisThis volume is addressed to people who are interested in modern mathematical solutions for real life applications. In particular, mathematical modeling, simulation and optimization is nowadays successfully used in various fields of application, like the energy- or health-sector. Here, mathematics is often the driving force for new innovations and most relevant for the success of many interdisciplinary projects. The presented chapters demonstrate the power of this emerging research field and show how society can benefit from applied mathematics.Table of ContentsPart I Prognostic MR Thermometry for Thermal Ablation of Liver Tumours.- 1 Sebastian Blauth et al., Mathematical Modeling and Simulation of Laser-Induced Thermotherapy for the Treatment of Liver Tumors.- 2 Matthias Andres and René Pinnau, The Cattaneo Model for Laser-Induced Thermotherapy: Identification of the Blood-Perfusion Rate.- 3 Kevin Tolle and Nicole Marheineke, On Online Parameter Identification in Laser-Induced Thermotherapy.- Part II Energy-efficient High Temperature Processes via Shape Optimisation.- 4 Robert Feßler at al., Feasibility Study on Simulating a 3D Furnace Including the Effects of Reactions and Vaporization.- 5 Thomas Marx et al., Shape Optimization for the SP1–Model for Convective Radiative Heat Transfer- 6 Nicolas Dietrich et al., Diffusive Radiation Models for Optimal Shape Design in Phosphate Production.- 7 Ruben Sanchez at al., Adjoint-based sensitivity analysis in high-temperature fluid flows with participating media.

Read more less

Book SynopsisCognitive mathematics provides insights into how mathematics works inside the brain and how it is interconnected with other faculties through so-called blending and other associative processes. This handbook is the first large collection of various aspects of cognitive mathematics to be amassed into a single title, covering decades of connection between mathematics and other figurative processes as they manifest themselves in language, art, and even algorithms. It will be of use to anyone working in math cognition and education, with each section of the handbook edited by an international leader in that field. Table of ContentsIntroduction: Marcel Danesi: What Is Cognitive Mathematics?.- BASIC NOTIONS: Rafael Núnez.- Embodied Cognition and Mathematics.- Numeracy.- Numerosity.- Spatial Reasoning in a Cognitive Mathematical Framework.- Mathematics, Culture, and History.- CONCEPTUAL BLENDING IN MATHEMATICS: Mark Turner.- Conceptual Metaphor Theory.- Conceptual Blending.- Conceptual Integration.- Compression.- Mathematical Modeling.- NEURIOSCIENTIFIC ASPECTS OF MATHEMATICS: Brian Butterworth.- Computational Neuroscience.- Creativity in Mathematics.- Modularity Theory.- Parallel Processing.- Species-Specificities.- MATHEMATICS AND LANGUAGE: Keith Devlin.- Metaphor in Language and Mathematics.- Metonymy in Language and Mathematics.- Overlapping Sign Systems.- Theories of Syntax and the Nature of Equations.- Semantics in Language and Mathematics.- V. MATHEMATICS AND THE ARTS: Gizem Karaali.- Drawing.- Music.- Poetry.- Dance.- Literature.- VI. LEARNING MATHEMATICS: Dragana Martinovic.- Learning Arithmetic.- Learning Geometry.- Learning Set Theory.- Learning Advanced Mathematics.- Role of Symbolism in Learning.- VII. APPLICATIONS: Robert Logan.- Problem-Solving.- Proofs.- Fractal Geometry.- Probability Theory.- Mathematics and Science.- VIII. INTERFACES: Gila Hanna.- Knowledge Representation.- Development of Algorithms.- Natural Language Processing and Mathematics.- Automated Proofs and Cognitive Theory.- Technology and Mathematics

Read more less

Book SynopsisThis book presents fixed point theory, one of the crucial tools in applied mathematics, functional analysis, and topology, which has been used to solve distinct real-world problems in computer science, engineering, and physics. The authors begin with an overview of the extension of metric spaces. Readers are introduced to general fixed-point theorems while comparing and contrasting important and insignificant metric spaces. The book is intended to be self-contained and serves as a unique resource for researchers in various disciplines.Table of ContentsMetric Spaces.- Extension of Metric Spaces.- Fixed Point Theorems on Extended Metric Spaces.

Read more less

Book SynopsisThis textbook provides an introduction to methods for solving nonlinear partial differential equations (NLPDEs). After the introduction of several PDEs drawn from science and engineering, readers are introduced to techniques to obtain exact solutions of NLPDEs. The chapters include the following topics: Nonlinear PDEs are Everywhere; Differential Substitutions; Point and Contact Transformations; First Integrals; and Functional Separability. Readers are guided through these chapters and are provided with several detailed examples. Each chapter ends with a series of exercises illustrating the material presented in each chapter. This Second Edition includes a new method of generating contact transformations and focuses on a solution method (parametric Legendre transformations) to solve a particular class of two nonlinear PDEs.Table of ContentsNonlinear PDEs are Everywhere.- Differential Substitutions.- Point and Contact Transformations.- First Integrals.- Functional Separability.

Read more less

Book Synopsis< div="">This book introduces undergraduate students of engineering and science to applied mathematics essential to the study of many problems. Topics are differential equations, power series, Laplace transforms, matrices and determinants, vector analysis, partial differential equations, complex variables, and numerical methods. Approximately, 160 examples and 1000 homework problems aid students in their study. This book presents mathematical topics using derivations rather than theorems and proofs. This textbook is uniquely qualified to apply mathematics to physical applications (spring-mass systems, electrical circuits, conduction, diffusion, etc.), in a manner that is efficient and understandable. This book is written to support a mathematics course after differential equations, to permit several topics to be covered in one semester, and to make the material comprehensible to undergraduates. An Instructor Solutions Manual, and also a Student Solutions Manual that provides solutions to select problems, is available.^Table of ContentsDocument Attached

Read more less

Book SynopsisThis two-volume set, LNCS 13826 and LNCS 13827, constitutes the proceedings of the 14th International Conference on Parallel Processing and Applied Mathematics, PPAM 2022, held in Gdansk, Poland, in September 2022.The 77 regular papers presented in these volumes were selected from 132 submissions. For regular tracks of the conference, 33 papers were selected from 62 submissions.The papers were organized in topical sections named as follows:Part I: numerical algorithms and parallel scientific computing; parallel non-numerical algorithms; GPU computing; performance analysis and prediction in HPC systems; scheduling for parallel computing; environments and frameworks for parallel/cloud computing; applications of parallel and distributed computing; soft computing with applications and special session on parallel EVD/SVD and its application in matrix computations.Part II: 9th Workshop on Language-Based Parallel Programming (WLPP 2022); 6th Workshop on Models, Algorithms and Methodologies for Hybrid Parallelism in New HPC Systems (MAMHYP 2022); first workshop on quantum computing and communication; First Workshop on Applications of Machine Learning and Artificial Intelligence in High Performance Computing (WAML 2022); 4th workshop on applied high performance numerical algorithms for PDEs; 5th minisymposium on HPC applications in physical sciences; 8th minisymposium on high performance computing interval methods; 7th workshop on complex collective systems.Table of Contents​Numerical Algorithms and Parallel Scientific Computing.- How accurate does Newton have to be?.- General framework for deriving reproducible Krylov subspace algorithms: BiCGStab case.- A generalized parallel prefix sums algorithm for arbitrary size array.- Infinite-Precision Inner Product and Sparse Matrix-Vector Multiplication Using Ozaki Scheme with Dot2 on Manycore Processors.- Advanced Stochastic Approaches for Applied Computing in Environmental Modeling.- Parallel Non-numerical Algorithms.- Parallel Suffix Sorting for Large String Analytics.- Parallel Extremely Randomized Decision Forests on Graphics Processors for Text Classification.- RDBMS speculative support improvement by the use of the query hypergraph representation.- GPU Computing.- Mixed Precision Algebraic Multigrid on GPUs.- Compact in-memory representation of decision trees in GPU-accelerated evolutionary induction.- Neural Nets with a Newton Conjugate Gradient Method on Multiple GPUs.- Performance Analysis and Prediction in HPC Systems.- Exploring Techniques for the Analysis of Spontaneous Asynchronicity in MPI-Parallel Applications.- Cost and Performance Analysis of MPI-based SaaS on the Private Cloud Infrastructure.- Building a Fine-Grained Analytical Performance Model for Complex Scientific Simulations.- Evaluation of machine learning techniques for predicting run times of scientific workflow jobs.- Smart clustering of HPC applications using similar job detection methods.- Scheduling for Parallel Computing.- Distributed Work Stealing in a Task-Based Dataflow Runtime.- Task Scheduler for Heterogeneous Data Centres based on Deep Reinforcement Learning.- Shisha: Online scheduling of CNN pipelines on heterogeneous architectures.- Proactive Task Offloading for Load Balancing in Iterative Applications.- Environments and Frameworks for Parallel/Cloud Computing.- Language Agnostic Approach for Unification of Implementation Variants for Different Computing Devices.- High Performance Dataframes from Parallel Processing Patterns.- Global Access to Legacy Data-Sets in Multi-Cloud Applications with Onedata.- Applications of Parallel and Distributed Computing.- MD-Bench: A generic proxy-app toolbox for state-of-the-art molecular dynamics algorithms.- Breaking Down the Parallel Performance of GROMACS, a High-Performance Molecular Dynamics Software.- GPU-based Molecular Dynamics of Turbulent Liquid Flows with OpenMM.- A novel parallel approach for modeling the dynamics of aerodynamically interacting particles in turbulent flows.- Reliable energy measurement on heterogeneous Systems–on–Chip based environments.- Distributed Objective Function Evaluation for Optimization of Radiation Therapy Treatment Plans.- Soft Computing with Applications.- GPU4SNN: GPU-based Acceleration for Spiking Neural Network Simulations.- Ant System Inspired Heuristic Optimization of UAVs Deployment for k-Coverage Problem.- Dataset related experimental investigation of chess position evaluation using a deep neural network.- Using AI-based edge processing in monitoring the pedestrian crossing.- Special Session on Parallel EVD/SVD and its Application in Matrix Computations.- Automatic code selection for the dense symmetric generalized eigenvalue problem using ATMathCoreLib.- On Relative Accuracy of the One-Sided Block-Jacobi SVD Algorithm.

Read more less

Book SynopsisThis two-volume set, LNCS 13826 and LNCS 13827, constitutes the proceedings of the 14th International Conference on Parallel Processing and Applied Mathematics, PPAM 2022, held in Gdansk, Poland, in September 2022.The 77 regular papers presented in these volumes were selected from 132 submissions. For regular tracks of the conference, 33 papers were selected from 62 submissions.The papers were organized in topical sections named as follows:Part I: numerical algorithms and parallel scientific computing; parallel non-numerical algorithms; GPU computing; performance analysis and prediction in HPC systems; scheduling for parallel computing; environments and frameworks for parallel/cloud computing; applications of parallel and distributed computing; soft computing with applications and special session on parallel EVD/SVD and its application in matrix computations.Part II: 9th Workshop on Language-Based Parallel Programming (WLPP 2022); 6th Workshop on Models, Algorithms and Methodologies for Hybrid Parallelism in New HPC Systems (MAMHYP 2022); first workshop on quantum computing and communication; First Workshop on Applications of Machine Learning and Artificial Intelligence in High Performance Computing (WAML 2022); 4th workshop on applied high performance numerical algorithms for PDEs; 5th minisymposium on HPC applications in physical sciences; 8th minisymposium on high performance computing interval methods; 7th workshop on complex collective systems.Table of Contents​9th Workshop on Language-Based Parallel Programming (WLPP 2022).- Kokkos-Based Implementation of MPCD on Heterogeneous Nodes.- Comparison of Load Balancing Schemes for Asynchronous Many-Task Runtimes.- New Insights on the Revised Definition of the Performance Portability Metric.- Inferential statistical analysis of performance portability.- NPDP Benchmark Suite for Loop Tiling Effectiveness Evaluation.- Parallel Vectorized Implementations of Compensated Summation Algorithms.- 6th Workshop on Models, Algorithms and Methodologies for Hybrid Parallelism in New HPC Systems (MAMHYP 2022).- Malleability Techniques for HPC Systems.- Algorithm and software overhead: a theoretical approach to performance portability.- Benchmarking A High Performance Computing Heterogeneous Cluster.- A Generative Adversarial Network approach for noise and artifacts reduction in MRI head and neck imaging.- A GPU accelerated Hyperspectral 3D Convolutional Neural Network Classification at the Edge with Principal Component Analysis preprocessing.- Parallel gEUD models for accelerated IMRT planning on modern HPC platforms.- First Workshop on Quantum Computing and Communication.- On Quantum-Assisted LDPC Decoding Augmented with Classical Post-Processing.- Quantum annealing to solve the unrelated parallel machine scheduling problem.- Early experiences with a photonic quantum simulator for solving Job Shop Scheduling Problem.- Some remarks on super-gram operators for general bipartite quantum states.- Solving the Traveling Salesman Problem with a Hybrid Quantum-Classical Feedforward Neural Network.- Software aided analysis of EWL based quantum games.- First Workshop on Applications of Machine Learning and Artificial Intelligence in High Performance Computing (WAML 2022).- Adaptation of AI-accelerated CFD simulations to the IPU platform.- Performance Analysis of Convolution Algorithms for Deep Learning on Edge Processors.- Machine Learning-based Online Scheduling in Distributed Computing.- High Performance Computing Queue Time Prediction using Clustering and Regression.- Acceptance Rates of Invertible Neural Networks on Electron Spectra from Near-Critical Laser-Plasmas: A Comparison.- 4th Workshop on Applied High Performance Numerical Algorithms for PDEs.- MATLAB implementation of hp finite elements on rectangles using hierarchical basis functions.- Adaptive Parallel Average Schwarz Preconditioner for Crouzeix-Raviart Finite Volume Method.- Parareal method for anisotropic diffusion denoising.- Comparison of block preconditioners for the Stokes problem with discontinuous viscosity and friction.- On minimization of nonlinear energies using FEM in MATLAB.- A model for crowd evacuation dynamics: 2D numerical simulations.- 5th Minisymposium on HPC Applications in Physical Sciences.- Parallel Identification of Unique Sequences in Nuclear Structure Calculations.- Experimental and computer study of molecular dynamics of a new pyridazine derivative.- Description of magnetic nanomolecules by the extended multi-orbital Hubbard model: perturbative vs numerical approach.- Structural and electronic properties of small-diameter Carbon NanoTubes: a DFT study.- 8th Minisymposium on High Performance Computing Interval Methods.- Need for Techniques Intermediate Between Interval and Probabilistic Ones.- A Cross-Platform Benchmark for Interval Computation Libraries.- Testing interval arithmetic libraries, including their IEEE-1788 compliance.- A survey of interval algorithms for solving multicriteria analysis problems.- 7th Workshop on Complex Collective Systems.- Social Fragmentation Transitions in Large-Scale Parameter Sweep Simulations of Adaptive Social Networks.- Parking search in urban street networks: Taming down the complexity of the search-time problem via a coarse-graining approach.- A multi-agent cellular automata model of lane changing behaviour considering the aggressiveness and the autonomy.- Comparison of the use of UWB and BLE as positioning methods in data-driven modeling of pedestrian dynamics.- An Insight into the State-of-the-Art Vehicular Fog Computing with an Opportunistic Flavour.

Read more less

Book SynopsisThis book presents a new search paradigm for solving the Traveling Salesman Problem (TSP). The intrinsic difficulty of the TSP is associated with the combinatorial explosion of potential solutions in the solution space. The author introduces the idea of using the attractor concept in dynamical systems theory to reduce the search space for exhaustive search for the TSP. Numerous examples are used to describe how to use this new search algorithm to solve the TSP and its variants including: multi-objective TSP, dynamic TSP, and probabilistic TSP. This book is intended for readers in the field of optimization research and application.Table of ContentsIntroduction.- The Traveling Salesman Problem (TSP).- The Nature of Heuristic Local Search.- he Attractor-Based Search System.- Solving Multi-objective TSP.- Solving Dynamic TSP.- Solving Probabilistic TSP.- Conclusion.

Read more less

Book SynopsisThis book explores the profound and ancient relationship between music and astronomy. Throughout history, Music has occupied a significant place among the disciplines of the Quadrivium, which also include Geometry, Arithmetic, and Astronomy. The captivating bond between these two realms has not only inspired eminent scientists like Kepler, Newton, and Einstein, but has also captured the imagination of NASA and astronauts in modern times. The author delves into various aspects of the intersection between music and astronomy, encompassing everything from ancient cosmological beliefs to groundbreaking discoveries such as the cosmic background radiation and gravitational waves. This enthralling theme has not only stimulated renowned artists like David Bowie and Elton John, but has also served as a muse for movies like Close Encounters of the Third Kind. Within the book, readers will find an extensive photo gallery and a specially curated soundtrack that enhances the reading experience. It caters to a broad audience, appealing to those with a general interest in both music and astronomy, as well as to specialized individuals in either field of study.Table of ContentsForeword.- Preface.- ToC.- Introduction.- The Universe Born of Sound.- Everything Is Number. Pythagoras and the Pythagoreans.- The Music of the Spheres in Kepler’s Cosmos.- Musicians and Scientists.- From Newton to Einstein.- The Music of the Cosmos.- The Universe Is Teeming with Music.- Songs of the Space Race.- Space, the Music of the Spheres, and Movies.- Close Encounters of the Third Kind.- Conclusion.- Appendix.- Index of names.

Read more less

Book SynopsisCollaborative Workshop for Women in Mathematical Biology: Mathematical Modeling for Women's Health.- Extended-Release Pre-Exposure Prophylaxis and Drug-Resistant HIV.- A Survey of Mathematical Modeling of Hormonal Contraception and the Menstrual Cycle.- Studying the Effects of Oral Contraceptives on Coagulation Using a Mathematical Modeling Approach.- Deconstructing the Contributions of Heterogeneity to Combination Treatment of Hormone Sensitive Breast Cancer.- Towards a Mathematical Understanding of Ventilator-Induced Lung Injury in Preterm Rat Pups.- Estimation of Time-Dependent Transmission Rate for COVID-19 SVIRD Model Using Predictor-Corrector Algorithm.- Index.

Read more less

Book SynopsisIntroduction.- Classical Random Number Generators for Computer Simulation.- Searching for Large Order MRG's.- Methods to Improve Basic Generators and Statistical Justifications.- Family of Efficient MRGs.- Quality Assessment for Random Number Generators.- Spectral Test for Judging MRG Quality.- Parallel RNG Methods.- MRGs with Many Non-zero Terms and its Efficient Implementation.- Empirical Tests on RNG.- Review of Secure Random Number Generators.- Secure RNG for Security Applications.- Review of Classical Ciphers.- Modern Software and Hardware Stream Ciphers.- Design of Secure Random Number Generators.- General Design Principle of New Class of Secure RNGs.- Specific Classes of Secure and Efficient RNGs.- Design and Implementation of R packages.

Read more less

Book SynopsisMotivation and outline.- Fibonacci numbers, the golden ratio, and co-prime integers.- Co-primality, continued fractions, and Möbius maps.- The geometry of cylindrical lattices.- Classifying cylindrical lattices.- Transformed Lattices.- Developmental biology of the plant.- Statisical phyllotaxis.- Placement models.- Stacked-disk models.- Some future directions.

Read more less

Book SynopsisThe starting point for this monograph is the previously unknown connection between the Continuum Hypothesis and the saturation of the non-stationary ideal on ω1; and the principle result of this monograph is the identification of a canonical model in which the Continuum Hypothesis is false. This is the first example of such a model and moreover the model can be characterized in terms of maximality principles concerning the universal-existential theory of all sets of countable ordinals. This model is arguably the long sought goal of the study of forcing axioms and iterated forcing but is obtained by completely different methods, for example no theory of iterated forcing whatsoever is required. The construction of the model reveals a powerful technique for obtaining independence results regarding the combinatorics of the continuum, yielding a number of results which have yet to be obtained by any other method. This monograph is directed to researchers and advanced graduate students in Set Theory. The second edition is updated to take into account some of the developments in the decade since the first edition appeared, this includes a revised discussion of Ω-logic and related matters.

Read more less

Book Synopsis

Read more less

Book SynopsisThis book presents a comprehensive overview of the mathematics and physics behind the simulation of turbulent flows and discusses in detail (i) the phenomenology of turbulence in fluid dynamics, (ii) the role of direct and large-eddy simulation in predicting these dynamics, (iii) the multiple considerations underpinning subgrid modelling, and, (iv) the issue of validation and reliability resulting from interacting modelling and numerical errors.

Read more less

Book SynopsisThis specialized and authoritative book contains an overview of modern approaches to constructing approximations to solutions of ill-posed operator equations, both linear and nonlinear. These approximation schemes form a basis for implementable numerical algorithms for the stable solution of operator equations arising in contemporary mathematical modeling, and in particular when solving inverse problems of mathematical physics. The book presents in detail stable solution methods for ill-posed problems using the methodology of iterative regularization of classical iterative schemes and the techniques of finite dimensional and finite difference approximations of the problems under study. Special attention is paid to ill-posed Cauchy problems for linear operator differential equations and to ill-posed variational inequalities and optimization problems. The readers are expected to have basic knowledge in functional analysis and differential equations. The book will be of interest to applied mathematicians and specialists in mathematical modeling and inverse problems, and also to advanced students in these fields. ContentsIntroductionRegularization Methods For Linear EquationsFinite Difference MethodsIterative Regularization MethodsFinite-Dimensional Iterative ProcessesVariational Inequalities and Optimization Problems

Read more less

Book SynopsisThis two-volume work focuses on the mathematical aspects of Darwinian evolution starting from the basic model of stochastic evolution of a single isolated locus in the presence of mutation to the multi–locus models of sexual and asexual populations. Volume 2 discusses the inference of fi tness landscape from DNA sequence data, discovery of the evolutionary roles of enygmatic traits, co-evolution of adversarial species, and various applications to virus evolution.

Read more less

Book SynopsisThis book covers all aspects of inertial navigation systems (INS), including the sensor technology and the estimation of instrument errors, as well as their integration with Global Navigation Satellite Systems, specifically the Global Positioning System (GPS) for geodetic applications. The text is of interest to geodesists, including surveyors, mappers, and photogrammetrists; to engineers in aviation, navigation, guidance, transportation, and robotics; and to scientists involved in aerogeophysics and remote sensing. The most recent developments are covered with this second edition that also features an updated treatment of the classical material. Detailed mathematical derivations of the principles of measurement and data processing of inertial measurement units for both stabilized and strapdown systems. Complete treatment of the error dynamics from a statistical viewpoint, including the Kalman filter. A self-contained description of GPS with emphasis on kinematic applications. Key concepts supported by illustrations and numerical examples.

Read more less

Book Synopsis This volume deals with two complementary topics. On one hand the book deals with the problem of determining the the probability distribution of a positive compound random variable, a problem which appears in the banking and insurance industries, in many areas of operational research and in reliability problems in the engineering sciences. On the other hand, the methodology proposed to solve such problems, which is based on an application of the maximum entropy method to invert the Laplace transform of the distributions, can be applied to many other problems. The book contains applications to a large variety of problems, including the problem of dependence of the sample data used to estimate empirically the Laplace transform of the random variable. ContentsIntroductionFrequency modelsIndividual severity modelsSome detailed examplesSome traditional approaches to the aggregation problemLaplace transforms and fractional moment problemsThe standard maximum entropy methodExtensions of the method of maximum entropySuperresolution in maxentropic Laplace transform inversionSample data dependenceDisentangling frequencies and decompounding lossesComputations using the maxentropic densityReview of statistical procedures

Read more less

Book Synopsis

Read more less

Book Synopsis

Read more less

Book Synopsis

Read more less

Book SynopsisThe two main themes of this book, logic and complexity, are both essential for understanding the main problems about the foundations of mathematics. Logical Foundations of Mathematics and Computational Complexity covers a broad spectrum of results in logic and set theory that are relevant to the foundations, as well as the results in computational complexity and the interdisciplinary area of proof complexity. The author presents his ideas on how these areas are connected, what are the most fundamental problems and how they should be approached. In particular, he argues that complexity is as important for foundations as are the more traditional concepts of computability and provability.Emphasis is on explaining the essence of concepts and the ideas of proofs, rather than presenting precise formal statements and full proofs. Each section starts with concepts and results easily explained, and gradually proceeds to more difficult ones. The notes after each section present some formal definitions, theorems and proofs.Logical Foundations of Mathematics and Computational Complexity is aimed at graduate students of all fields of mathematics who are interested in logic, complexity and foundations. It will also be of interest for both physicists and philosophers who are curious to learn the basics of logic and complexity theory.Trade Review“This monograph by the outstanding Czech logician Pavel Pudlák provides a broad but also deep survey of work in logic and computer science relevant to foundational issues, interpreted in a wide sense. … This is a fine overview of logic and complexity theory that can be confidently recommended to anybody who would like to orient themselves in an increasingly intricate and difficult field.” (Alasdair Urquhart, Philosophia Mathematica, Vol. 23 (3), October, 2015)“For the non-expert it offers indeed a ‘gentle introduction’ to logic that is well selected and excellently explained. And for the logician it certainly offers some of the best introductions to those topics outside their area of direct expertise. … it contains plenty of informal explanations, intuition and motivation. … It is truly a gift to the logic and wider communities … . This book is very enjoyable to read and I wish it all success.” (Olaf Beyersdorff, Mathematical Reviews, August, 2014)“It spans the historical, logical, and at times philosophical underpinnings of the theory of computational complexity. Students of mathematics seeking a transition to higher mathematics will find it helpful, as will mathematicians with expertise in other areas. … an excellent choice for a first text in studying complexity, or as a clarifying adjunct to any assigned text in this area. … a compact guide for graduate students with a need for or interest in computational complexity and its foundations.” (Tom Schulte, MAA Reviews, July, 2014)“This book, exactly as indicated by its title, deals with the main philosophical, historical, logical and mathematical aspects … in a quite approachable and attractive way. … the prospective readers of this book are mathematicians with an interest in the foundations, philosophers with a good background in mathematics, and also philosophically minded scientists. Due to the author’s nice style, the book will be a very good choice for the first text in studying this subject.” (Branislav Boričić, zbMATH, Vol. 1270, 2013)Table of Contents​​​​​​​​​​Mathematician’s world.- Language, logic and computations.- Set theory.- Proofs of impossibility.- The complexity of computations.- Proof complexity.- Consistency, Truth and Existence.- References.

Read more less

Book SynopsisThis volume is a user-friendly presentation of the main theoretical properties of the Fourier-Malliavin volatility estimation, allowing the readers to experience the potential of the approach and its application in various financial settings. Readers are given examples and instruments to implement this methodology in various financial settings and applications of real-life data. A detailed bibliographic reference is included to permit an in-depth study. Trade Review“This is a very interesting book on Fourier-Malliavin volatility estimation. … this is a easy-to-read and self-contained book for everyone interested in Fourier methods in volatility estimation.” (Elisa Alòs, zbMath 1416.91005, 2019)Table of ContentsIntroduction.- A First Glance at Fourier Method.- Estimation of Integrated Volatility.- Estimation of Instantaneous Volatility.- High Frequency Analysis: Market Microstructure Noise Issues.- Getting Inside the Latent Volatility.- Mathematical Essentials.- Codes for the Fourier Estimator.

Read more less

Book SynopsisThis book analyses investment management policies for institutional investors. It is composed of four parts. The first one analyses the various types of institutional investors, institutions which, with different objectives, professionally manage portfolios of financial and real assets on behalf of a wide variety of individuals. This part goes on with an in-depth analysis of the economic, technical and regulatory characteristics of the different types of investment funds and of other types of asset management products, which have a high rate of substitutability with investment funds and represent their natural competitors. The second part of the book identifies and investigates the stages of the investment portfolio management. Given the importance of strategic asset allocation in explaining the ex post performance of any type of investment portfolio, this part provides an in-depth analysis of asset allocation methods, illustrating the different theoretical and operational solutions available to institutional investors. The third part describes performance assessment, its breakdown and risk control, with an in-depth examination of performance evaluation techniques, returns-based style analysis approaches, and performance attribution models. Finally, the fourth part deals with the subject of diversification into alternative asset classes, identifying the common characteristics and their possible role within the framework of investment management policies. This part analyses hedge funds, private equity, real estate, commodities, and currency overlay techniques. Table of Contents

Read more less

Book SynopsisBiometrische Erkennung statt PINs und Passwort als einfache und sichere Alternative? Mit dem vorliegenden Buch werden erstmals im deutschsprachigen Raum Grundlagen, Verfahren und Perspektiven biometrischer Identifikation zusammenhängend dargelegt. Die Beiträge von Ingenieuren, Juristen, Mathematikern, Medizinern, Philosophen und Sozialwissenschaftlern zeigen die Vielschichtigkeit der Thematik, sinnvolle Einsatzmöglichkeiten und Business-Perspektiven einer faszinierenden Technologie.Trade Review"Ein empfehlenswertes Buch zu der Thematik ist "Biometrische Identifikation" von Michael Behrens und Richard Roth. [...] Dieses Buch ist besonders interessant, weil es einen interdisziplinären Ansatz verfolgt: Das Thema wird nicht nur aus technischer Sicht beleuchtet, sondern in diesem Werk sind auch rechtliche, biologische und ethische Hintergründe und Überlegungen ausgeführt." (factum, Heft 7-8/02) "Wer sich in dieser Situation intensiver mit den wissenschaftlichen Grundlagen der biometrischen Identifikation von Menschen auseinander setzen möchte, dem bietet dieses Buch einen guten Überblick." (DIE WELT vom 13.03.02.) "Mit dem vorliegenden Buch werden erstmals im deutschsprachigen Raum Grundlagen, Verfahren und Perspektiven biometrischer Identifikation zusammenhängend dargelegt." (Netzguide E-Security, 5/02)Table of ContentsTheoretische Grundlagen biometrischer Identifikation - politische und rechtliche Rahmenbedingungen - biometrische Identifikation und Ethik - biometrische Identifikationsverfahren - Nutzer- und Marktperspektiven

Read more less

Book SynopsisDie Simulation technischer Prozesse erfordert in der Regel die Lösung von linearen Gleichungssystemen großer Dimension. Hierfür werden moderne vorkonditionierte Iterationsverfahren (z.B. CG, GMRES, BiCGStab) hergeleitet und die zur Realisierung notwendigen Algorithmen beschrieben. Für Systeme mit strukturierten Matrizen werden effiziente direkte Lösungsverfahren angegeben. Numerische Beispiele für praktische Problemstellungen illustrieren die Effizienz der vorgestellten Verfahren.Table of Contents1 Grundlagen.- 1.1 Normen von Vektoren und Matrizen.- 1.2 Eigenwerte und Singulärwerte.- 1.3 Orthogonalisierung von Vektorsystemen.- 1.4 Tschebyscheff-Polynome.- 2 Lineare Gleichungssysteme.- 2.1 Interpolation.- 2.2 Projektionsmethoden.- 2.3 Finite Element Methoden.- 2.4 Randelementmethoden.- 3 Strukturierte Matrizen.- 3.1 Schnelle Fouriertransformation.- 3.2 Zirkulante Matrizen.- 3.3 Toeplitz Matrizen.- 3.4 Niedrig-Rang-Störung regulärer Matrizen.- 4 Klassische Iterationsverfahren.- 4.1 Stationäre Iterationsverfahren.- 4.2 Gradientenverfahren.- 5 Verfahren orthogonaler Richtungen.- 5.1 Verfahren konjugierter Gradienten.- 5.2 Verfahren des minimalen Residuums.- 5.3 Verfahren biorthogonaler Richtungen.- 6 Gleichungssysteme mit Blockstruktur.- 6.1 Symmetrische Gleichungssysteme.- 6.2 Blockschiefsymmetrische Systeme.- 6.3 Zweifache Sattelpunktprobleme.- 7 Hierarchische Matrizen.- 7.1 Partitionierte Matrizen.- 7.2 Approximation mit Niedrigrang-Matrizen.- 7.2.1 Approximation symmetrischer Matrizen.- 7.2.2 Approximation allgemeiner Matrizen.- 7.3 Arithmetik von Hierarchischen Matrizen.- 7.3.1 Matrix-Vektor-Multiplikation.- 7.3.2 Addition.- 7.3.3 Matrix-Matrix-Multiplikation.- 7.3.4 Invertierung.- 7.4 Geometrische Partitionierungen.- 7.4.1 Box-Clustering.- 7.4.2 Bisektionsverfahren.- 7.5 Niedrigrang-Approximation von Funktionen.- 7.5.1 Darstellung mit Taylor-Reihen.- 7.5.2 Explizite Reihendarstellung.- 7.5.3 Adaptive Cross-Approximation.- 7.6 Anwendungen in der FEM.- 7.6.1 L2-Projektion.- 7.6.2 Randwertprobleme zweiter Ordnung.- Literatur.

Read more less

Book SynopsisDieses Buch behandelt die Kernfragen und grundlegenden Verfahren der Kryptographie. Diese werden aus Sicht der modernen Kryptographie studiert, die durch eine präzise mathematische und informatische Herangehensweise geprägt ist. Die Inhalte dieser Einführung sind dabei aus der Praxis motiviert und es werden wichtige, in der Praxis eingesetzte kryptographische Verfahren, vorgestellt und diskutiert.Table of ContentsSymmetrische Verschlüsselung - Blockkryptosysteme, AES - Verschlüssungsmodi, CTR, CBC - Asymmetrische Verschlüsselung, RSA, ElGamal - Hybride Verschlüsselung - Kryptographische Hashfunktionen, die SHA-Familie, Merkle-Damgård-Konstruktion - Nachrichtenauthentifizierung, CBC-MAC, HMAC - Digitale Signaturen, FDH-RSA, Random-Oracle-Modell, PKCS#1, DSA - Ansätze der Kryptanalyse - Informationstheoretische bzw. beweisbare Sicherheit der betrachteten Verfahren - Public-Key-Infrastrukturen und Web of Trust

Read more less

Book SynopsisIm landläufigen Mathematikunterricht an Schulen und Hochschulen wird die Mathematik überwiegend als eine geistige Disziplin vermittelt, in der es um die Klarheit und Stringenz des Denkens geht. Systematik und formale Eleganz der Darstellung stehen im Vorder­ grund. Dabei wird aber ignoriert, daß die Mathematik nicht allein aus sich heraus lebt, sondern in andere Bereiche unserer Kultur eingebunden ist. Ohne allzusehr zu übertreiben, kann man sogar behaupten, daß sie ein integrativer Bestandteil unserer technologischen Welt ist und damit einen Einfluß ausübt, der weit über ihr Selbstverständnis hinausgeht. Mit der Sprache der Mathematik lassen sich auch nicht-mathematische Inhalte, zu­ mindest bis zu einem gewissen Grade ausdrücken. Man gelangt auf diese Weise oft zu Einsichten, die man ohne die Sprache der Mathematik nicht so klar und präzise aus­ drücken könnte. Man muß dabei allerdings auch beachten, daß mit der Umsetzung nicht­ mathematischer Sachverhalte in Mathematik eine starke Vereinfachung einhergeht als Preis für die mathematische Abstraktion. Diese Vereinfachung muß bei der Interpretation der durch Mathematik gewonnenen Einsichten berücksichtigt werden. Der Zweck dieses Buches besteht darin, die soeben skizzierte Rolle der Mathematik ins Bewußtsein der Mathematiker zu bringen. Danken möchte ich Frau A. Garhammer für das Schreiben dieses Buchtextes auf dem Computer und Herrn S. Bott für die Herstellung der Graphiken.Table of ContentsProblemstellung - Ein mathematisches Modell des Informationsbegriffes Modell des Informationsbegriffes - Entscheidungs- und Spielmodelle - Wachstumsmodelle - Zwei mathematische Modelle in der Medizin - Konkurrenzmodelle - Ein mathematisches Modell der Hämodialyse - Ein mathematisches Modell für Rüstung

Read more less

Book Synopsis1 Optimierungsaufgaben und Optimalitätskriterien.- 1.1 Globale und lokale Optima, Konvexität.- 1.2 Optimalitätsbedingungen.- 1.3 Semiinfinite Probleme.- 1.4 Ganzzahlige Probleme.- 1.5 Optimierung über Graphen.- 2 Dualität.- 2.1 Duale Probleme.- 2.2 Gestörte Optimierungsprobleme.- 2.3 Anwendungen der Dualität.- 3 Minimierung ohne Restriktionen.- 3.1 Gradientenverfahren.- 3.2 Das Newton-Verfahren.- 3.3 Quasi-Newton-Verfahren.- 3.4 CG-Verfahren.- 3.5 Minimierung nichtglatter Funktionen.- 4 Linear restringierte Probleme.- 4.1 Polyedrische Mengen.- 4.2 Lineare Optimierung.- 4.3 Minimierung über Mannigfaltigkeiten.- 4.4 Probleme mit Ungleichungsrestriktionen.- 5 Strafmethoden.- 5.1 Das Grundprinzip von Strafmethoden.- 5.2 Konvergenzabschätzungen.- 5.3 Modifizierte Lagrange-Funktionen.- 5.4 Strafmethoden und elliptische Randwertprobleme.- 6 Approximationsverfahren.- 6.1 Verfahren der zulässigen Richtungen.- 6.2 Überlinear konvergente Verfahren.- 7 Komplexität.- 7.1 Definitionen, Polynomialität.- 7.2 Nichtdeterministisch polynomiale Algorithmen.- 7.3 Optimierungsprobleme und die Klasse NP-hart.- 7.4 Komplexität in der linearen Optimierung.- 8 Innere-Punkt-Methoden.- 8.1 Innerer-Pfad-Methode für lineare Probleme.- 8.2 Parameterfreies Potential.- 8.3 Der Algorithmus von Karmarkar.- 8.4 Komplementaritätsprobleme.- 8.5 Komplexität der linearen Optimierung.- 9 Aufgaben über Graphen.- 9.1 Definitionen.- 9.2 Graphen und lineare Optimierung.- 9.3 Aufdatierungen in Graphen.- 9.4 Probleme aus der Klasse NP-vollständig.- 10 Die Methode branch and bound.- 10.1 Relaxation, Separation, Strategien.- 10.2 Branch and bound für GLO.- 10.3 Das Rundreiseproblem.- 11 Dekomposition.- 11.1 Dekompositionsprinzipien.- 11.2 Dynamische Optimierung.- 11.3 Ausgewählte Anwendungen.- 12Strukturuntersuchungen.- 12.1 Ganzzahlige Polyeder.- 12.2 Gültige Ungleichungen.- 12.3 Matroide, Greedy-Algorithmus.Table of ContentsAufgabenstellung und Optimalitätskriterien - Dualität, Minimierung ohne Restriktionen - Optimierungsverfahren für linear restringierte Probleme - Penalty-Verfahren und modifizierte Lagrange-Methoden - Verfahren auf der Basis lokaler Approximationen - Komplexität - Innere-Punkt-Methoden - Graphentheoretische Modelle und Verfahren - Die Methode branch and bound - Dekompositionstechniken für strukturierte Optimierungsprobleme - Strukturuntersuchungen in ganzzahligen Optimierungsproblemen

Read more less

Book Synopsis1: Grundbegriffe.- 1.1 Die reellen Zahlen.- 1.2 Beträge und Ungleichungen.- 1.3 Grundbegriffe aus der Mengenlehre.- 1.4 Mathematische Beweismethoden.- 1.5 Elementare Kombinatorik.- 2: Polynome.- 2.1 Definition und Homer-Schema.- 2.2 Division von Polynomen.- 2.3 Nullstellen von Polynomen.- 3: Analytische Geometrie in Ebene und Raum.- 3.1 Koordinaten und Winkelfunktionen.- 3.2 Geraden in der Ebene.- 3.3 Vektoren im ?2.- 3.4 Vektoren im ?3.- 3.5 Ebenen und Geraden im ?3.- 4: Komplexe Zahlen.- 4.1 Definitionen und Rechenregeln.- 4.2 Wurzeln.- 4.3 Polynome.- 5: Konvergenz und Stetigkeit.- 5.1 Zahlenmengen und Häufungspunkte.- 5.2 Grenzwerte von Zahlenfolgen.- 5.3 Stetigkeit von Funktionen.- 5.4 Eigenschaften stetiger Funktionen.- 6: Differentiation von Funktionen.- 6.1 Begriff der Ableitung und Differentiationsregeln.- 6.2 Umkehrfunktionen.- 6.3 Der Mittelwertsatz der Differentialrechnung.- 6.4 Anwendungen des Mittelwertsatzes.- 7: Reihen.- 7.1 Unendliche Reihen.- 7.2 Potenzreihen.- 7.3 Das Rechnen mit Potenzreihen.- 7.4 Exponentialfunktion und Logarithmus.- 8: Taylor'sche Formel und Potenzreihenentwicklungen.- 8.1 Taylor-Polynome und Taylor-Reihen.- 8.2 Die binomische Reihe.- 8.3 Potenzreihen für Logarithmusfunktionen.- 8.4 Potenzreihen der Kreis- und Hyperbelfunktionen.- 8.5 Weitere Beispiele.- 9: Integration von Funktionen.- 9.1 Grundlegende Definitionen.- 9.2 Sätze über Integrale.- 9.3 Integrationsregeln.- 9.4 Die Integration der rationalen Funktionen.- 9.5 Uneigentliche Integrale.- 9.6 Numerische Integration.- 10: Lineare Algebra.- 10.1 Lineare Vektorräume.- 10.2 Lineare Abbildungen.- 10.3 Matrizen.- 10.4 Determinanten.- 10.5 Lineare Gleichungssysteme.- 10.6 Eigenwert-Theorie und quadratische Formen.- 10.7 Koordinatensysteme und der Tensorbegriff.- 11:Differentialgeometrie auf Kurven.- 11.1 Grundlegende Definitionen; Bogenlänge.- 11.2 Krümmung und Flächeninhalt.- 11.3 Bewegung im Zentralkraftfeld.- 12: Differentiation von Funktionen mehrerer Variabler.- 12.1 Stetigkeit und Differenzierbarkeit.- 12.2 Die Kettenregel, Differentiation höherer Ordnung.- 12.3 Mittelwertsatz und Taylor'sche Formel.- 12.4 Anwendungen.- 13: Integration von Funktionen mehrerer Variabler.- 13.1 Gebietsintegrale.- 13.2 Substitutionsregel für mehrfache Integrale.- 13.3 Beispiele.- 13.4 Kurvenintegrale.- 13.5 Oberflächenintegrale.- 14: Vektoranalysis und Integralsätze.- 14.1 Differentiation von Vektorfeldern.- 14.2 Beispiele.- 14.3 Die Integralsätze von Gauß, Stokes und Green.- 14.4 Physikalische Deutung und Anwendungen.- 15: Gewöhnliche Differentialgleichungen erster Ordnung.- 15.1 Einteilung der Dgln und Beispiele.- 15.2 Geometrische Betrachtungen.- 15.3 Spezielle Dgln erster Ordnung.- 15.4 Existenz- und Eindeutigkeitsfragen.- 15.5 Approximative Lösungsverfahren.- 16: Gewöhnliche Differentialgleichungen höherer Ordnung und Systeme.- 16.1 Umformung von Dgln höherer Ordnung in Systeme erster Ordnung.- 16.2 Spezielle Dgln zweiter Ordnung.- 16.3 Lineare Differentialgleichungen.- 16.4 Lineare Dgln mit konstanten Koeffizienten.- 16.5 Lineare Systeme von Dgln.- 16.6 Approximative Lösungsverfahren.- 17: Rand- und Eigenwertprobleme gewöhnlicher Differentialgleichungen.- 17.1 Beispiele von Randwertaufgaben.- 17.2 Lineare Randwertprobleme.- 17.3 Eigenwertprobleme.- 17.4 Numerische Lösungsverfahren.- 18: Fourier-Reihen.- 18.1 Approximation von Funktionen durch trigonometrische Polynome.- 18.2 Beispiele.- 18.3 Darstellung von Funktionen durch Fourier-Reihen.- 19: Partielle Differentialgleichungen.- 19.1 Klassifizierung und Beispielepartieller Dgln 2. Ordnung.- 19.2 Die Poisson-Gleichung.- 19.3 Die Wellengleichung.- 19.4 Die Wärmeleitungsgleichung.- 19.5 Partielle Dgln erster Ordnung.- 19.6 Die Gleichungen der Hydrodynamik.- 20: Funktionen einer komplexen Veränderlichen.- 20.1 Differentiation, holomorphe Funktionen.- 20.2 Integration der holomorphen Funktionen.- 20.3 Der Residuensatz mit Anwendungen.- 20.4 Potenzreihen und Laurent-Reihen.- 20.5 Die Integralformeln von Cauchy.- 20.6 Konforme Abbildungen.- 21: Grundbegriffe der Variationsrechnung.- 21.1 Beispiele von Variationsaufgaben.- 21.2 Erste Variation und Euler'sche Gleichung.- 21.3 Lösung von Variationsaufgaben.- Anhang über numerische Methoden.- A 1 Interpolatorische Quadratur.- A 2 Iterative Lösung linearer Gleichungssysteme.- A 3 Iterative Berechnung von Eigenwerten und Eigenvektoren.- A 4 Verfahren vom Runge-Kutta-Typ zur numerischen Lösung gewöhnlicher Differentialgleichungen.- Symbolverzeichnis.Table of Contents1: Grundbegriffe.- 1.1 Die reellen Zahlen.- 1.2 Beträge und Ungleichungen.- 1.3 Grundbegriffe aus der Mengenlehre.- 1.4 Mathematische Beweismethoden.- 1.5 Elementare Kombinatorik.- 2: Polynome.- 2.1 Definition und Homer-Schema.- 2.2 Division von Polynomen.- 2.3 Nullstellen von Polynomen.- 3: Analytische Geometrie in Ebene und Raum.- 3.1 Koordinaten und Winkelfunktionen.- 3.2 Geraden in der Ebene.- 3.3 Vektoren im ?2.- 3.4 Vektoren im ?3.- 3.5 Ebenen und Geraden im ?3.- 4: Komplexe Zahlen.- 4.1 Definitionen und Rechenregeln.- 4.2 Wurzeln.- 4.3 Polynome.- 5: Konvergenz und Stetigkeit.- 5.1 Zahlenmengen und Häufungspunkte.- 5.2 Grenzwerte von Zahlenfolgen.- 5.3 Stetigkeit von Funktionen.- 5.4 Eigenschaften stetiger Funktionen.- 6: Differentiation von Funktionen.- 6.1 Begriff der Ableitung und Differentiationsregeln.- 6.2 Umkehrfunktionen.- 6.3 Der Mittelwertsatz der Differentialrechnung.- 6.4 Anwendungen des Mittelwertsatzes.- 7: Reihen.- 7.1 Unendliche Reihen.- 7.2 Potenzreihen.- 7.3 Das Rechnen mit Potenzreihen.- 7.4 Exponentialfunktion und Logarithmus.- 8: Taylor’sche Formel und Potenzreihenentwicklungen.- 8.1 Taylor-Polynome und Taylor-Reihen.- 8.2 Die binomische Reihe.- 8.3 Potenzreihen für Logarithmusfunktionen.- 8.4 Potenzreihen der Kreis- und Hyperbelfunktionen.- 8.5 Weitere Beispiele.- 9: Integration von Funktionen.- 9.1 Grundlegende Definitionen.- 9.2 Sätze über Integrale.- 9.3 Integrationsregeln.- 9.4 Die Integration der rationalen Funktionen.- 9.5 Uneigentliche Integrale.- 9.6 Numerische Integration.- 10: Lineare Algebra.- 10.1 Lineare Vektorräume.- 10.2 Lineare Abbildungen.- 10.3 Matrizen.- 10.4 Determinanten.- 10.5 Lineare Gleichungssysteme.- 10.6 Eigenwert-Theorie und quadratische Formen.- 10.7 Koordinatensysteme und der Tensorbegriff.- 11: Differentialgeometrie auf Kurven.- 11.1 Grundlegende Definitionen; Bogenlänge.- 11.2 Krümmung und Flächeninhalt.- 11.3 Bewegung im Zentralkraftfeld.- 12: Differentiation von Funktionen mehrerer Variabler.- 12.1 Stetigkeit und Differenzierbarkeit.- 12.2 Die Kettenregel, Differentiation höherer Ordnung.- 12.3 Mittelwertsatz und Taylor’sche Formel.- 12.4 Anwendungen.- 13: Integration von Funktionen mehrerer Variabler.- 13.1 Gebietsintegrale.- 13.2 Substitutionsregel für mehrfache Integrale.- 13.3 Beispiele.- 13.4 Kurvenintegrale.- 13.5 Oberflächenintegrale.- 14: Vektoranalysis und Integralsätze.- 14.1 Differentiation von Vektorfeldern.- 14.2 Beispiele.- 14.3 Die Integralsätze von Gauß, Stokes und Green.- 14.4 Physikalische Deutung und Anwendungen.- 15: Gewöhnliche Differentialgleichungen erster Ordnung.- 15.1 Einteilung der Dgln und Beispiele.- 15.2 Geometrische Betrachtungen.- 15.3 Spezielle Dgln erster Ordnung.- 15.4 Existenz- und Eindeutigkeitsfragen.- 15.5 Approximative Lösungsverfahren.- 16: Gewöhnliche Differentialgleichungen höherer Ordnung und Systeme.- 16.1 Umformung von Dgln höherer Ordnung in Systeme erster Ordnung.- 16.2 Spezielle Dgln zweiter Ordnung.- 16.3 Lineare Differentialgleichungen.- 16.4 Lineare Dgln mit konstanten Koeffizienten.- 16.5 Lineare Systeme von Dgln.- 16.6 Approximative Lösungsverfahren.- 17: Rand- und Eigenwertprobleme gewöhnlicher Differentialgleichungen.- 17.1 Beispiele von Randwertaufgaben.- 17.2 Lineare Randwertprobleme.- 17.3 Eigenwertprobleme.- 17.4 Numerische Lösungsverfahren.- 18: Fourier-Reihen.- 18.1 Approximation von Funktionen durch trigonometrische Polynome.- 18.2 Beispiele.- 18.3 Darstellung von Funktionen durch Fourier-Reihen.- 19: Partielle Differentialgleichungen.- 19.1 Klassifizierung und Beispiele partieller Dgln 2. Ordnung.- 19.2 Die Poisson-Gleichung.- 19.3 Die Wellengleichung.- 19.4 Die Wärmeleitungsgleichung.- 19.5 Partielle Dgln erster Ordnung.- 19.6 Die Gleichungen der Hydrodynamik.- 20: Funktionen einer komplexen Veränderlichen.- 20.1 Differentiation, holomorphe Funktionen.- 20.2 Integration der holomorphen Funktionen.- 20.3 Der Residuensatz mit Anwendungen.- 20.4 Potenzreihen und Laurent-Reihen.- 20.5 Die Integralformeln von Cauchy.- 20.6 Konforme Abbildungen.- 21: Grundbegriffe der Variationsrechnung.- 21.1 Beispiele von Variationsaufgaben.- 21.2 Erste Variation und Euler’sche Gleichung.- 21.3 Lösung von Variationsaufgaben.- Anhang über numerische Methoden.- A 1 Interpolatorische Quadratur.- A 2 Iterative Lösung linearer Gleichungssysteme.- A 3 Iterative Berechnung von Eigenwerten und Eigenvektoren.- A 4 Verfahren vom Runge-Kutta-Typ zur numerischen Lösung gewöhnlicher Differentialgleichungen.- Symbolverzeichnis.

Read more less

Book SynopsisMit zahlreichen Aufgaben und technischen Zeichnungen vermittelt das Buch praxisnah und nach bewährtem Prinzip die mathematischen Grundlagen für alle Bauberufe. Table of ContentsGrundrechenarten - Längen und Flächen - Körper - Physikalische Größen - Baustoffbedarf

Read more less

Book SynopsisDer Prozess der Vernetzung von Computern, vom firmeninternen Intranet bis zum weltweiten Internet, hat gerade erst richtig begonnen. Dieses Buch bietet auf dem Gebiet der Netzwerk- und Übertragungstechnologien in der sich schnell verändernden Welt zwischen Mainframe, Desktopcomputer, Laptop und Internet Hilfe und Orientierung. Es wendet sich vor allem an Praktiker und Systemverantwortliche, die oft nach nur kurzer Einweisung die Verantwortung für das neu installierte System übernehmen müssen. Die vierte überarbeitete und erweiterte Ausgabe beschreibt neueste Netzformen und Sicherheitskonzepte, berücksichtigt aktuelle Fassungen geltender Normen und behandelt Trends bei der Verkabelung und im Netzdesign.Trade Review"Das Buch zeichnet sich -trotz der in diesem Bereich rasanten Entwicklung- durch eine hohe Aktualität und Professionalität aus. Durch die hohe Kompetenz der beiden Autoren wird -auch dem weniger erfahrenem Anwender- ein schneller und unkomplizierter Einstieg in ein recht komplexes Gebiet ermöglicht." www.chemieonline.de, 02.12.2002Table of ContentsGrundlagen - Das physikalische Netz: Verkabelung und Anschlusstechnik - Netzarten, Topologien und Zugriffsverfahren - Aktive Netzwerkkomponenten, Koppelelemente und Internetworking - Protokolle - Verteilte Systeme - Betriebssysteme - Internet: Netz der Netze - Sicherheit - Management, Konzeption und Trends

Read more less