Mathematics Books

Book SynopsisProviding a unified account of nonrelativistic quantum mechanics, Fundamentals of Quantum Mechanics covers the principles and formalism of quantum mechanics and the development and application of general techniques for the solution of quantum mechanical problems. The author has done everything possible to make the math in this book accessible.The book is divided into three parts. The first part provides the historical basis and mathematical foundations on nonrelativistic quantum theory. The physical systems considered in this part are mainly in one dimension. The second part covers the fundamentals of quantum theory in three dimensions. Many-particle systems, the motion of a particle in three dimensions, angular and spin momenta, interaction of a charged particle with external fields, and matrix mechanical formulation of quantum mechanics are discussed in this part. The third part contains the approximation methods used in quantum mechanics and scattering theory. Carefully designed to cover the entire topic, the book provides sufficient breadth and depth both to familiarize readers with the basic ideas and mathematical expressions of quantum mechanics and to form the basis for deeper understanding.Table of ContentsFundamentals and One-Dimensional Systems. Three-Dimensional Systems. Approximation Methods and Scattering Theory.

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Book SynopsisExtending and generalizing the results of rational equations,Dynamics of Third Order Rational Difference Equations with Open Problems and Conjectures focuses on the boundedness nature of solutions, the global stability of equilibrium points, the periodic character of solutions, and the convergence to periodic solutions, including their periodic trichotomies. The book also provides numerous thought-provoking open problems and conjectures on the boundedness character, global stability, and periodic behavior of solutions of rational difference equations. After introducing several basic definitions and general results, the authors examine 135 special cases of rational difference equations that have only bounded solutions and the equations that have unbounded solutions in some range of their parameters. They then explore the seven known nonlinear periodic trichotomies of third order rational difference equations. The main part of the book presents the known results of each of the 225 special cases of third order rational difference equations. In addition, the appendices supply tables that feature important information on these cases as well as on the boundedness character of all fourth order rational difference equations. A Framework for Future Research The theory and techniques developed in this book to understand the dynamics of rational difference equations will be useful in analyzing the equations in any mathematical model that involves difference equations. Moreover, the stimulating conjectures will promote future investigations in this fascinating, yet surprisingly little known area of research.Table of ContentsPreface. Introduction. Preliminaries. Equations with Bounded Solutions. Existence of Unbounded Solutions. Period Trichotomies. Known Results for Each of the 225 Special Cases. Appendices. Bibliography. Index.

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Book SynopsisAlthough there are many types of ring extensions, simple extensions have yet to be thoroughly explored in one book. Covering an understudied aspect of commutative algebra, Simple Extensions with the Minimum Degree Relations of Integral Domains presents a comprehensive treatment of various simple extensions and their properties. In particular, it examines several properties of simple ring extensions of Noetherian integral domains. As experts who have been studying this field for over a decade, the authors present many arguments that they have developed themselves, mainly exploring anti-integral, super-primitive, and ultra-primitive extensions. Within this framework, they study certain properties, such as flatness, integrality, and unramifiedness. Some of the topics discussed include Sharma polynomials, vanishing points, Noetherian domains, denominator ideals, unit groups, and polynomial rings. Presenting a complete treatment of each topic, Simple Extensions with the Minimum Degree Relations of Integral Domains serves as an ideal resource for graduate students and researchers involved in the area of commutative algebra.Trade Review"All topics … are developed in a clear way and illustrated by many examples." – EMS Newsletter, September 2008Table of ContentsBirational Simple Extensions. Simple Extensions of High Degree. Subrings of Anti-Integral Extensions. Denominator Ideals and Excellent Elements. Unramified Extensions. The Unit Groups of Extensions. Exclusive Extensions of Noetherian Domains. Ultra-Primitive Extensions and Their Generators. Flatness and Contractions of Ideals. Anti-Integral Ideals and Super Primitive Polynomials. Semi Anti-Integral and Pseudo-Simple Extensions. References. Index.

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Book SynopsisExamines Critical Decisions for Transitioning Lab Science to a Clinical SettingThe development of therapeutic pharmaceutical compounds is becoming more expensive, and the success rates for getting such treatments approved for marketing and to the patients is decreasing. As a result, translational medicine (TM) is becoming increasingly important in the healthcare industry – a means of maximizing the consideration and use of information collected as compounds transition from initial lab discovery, through pre-clinical testing, early clinical trials, and late confirmatory studies that lead to regulatory approval of drug release to patients. Translational Medicine: Strategies and Statistical Methods suggests a process for transitioning from the initial lab discovery to the patient’s bedside with minimal disconnect and offers a comprehensive review of statistical design and methodology commonly employed in this bench-to-bedside research. Documents Alternative Research Approaches for Faster and More Accurate Data Judgment CallsElaborating on how to introduce TM into clinical studies, this authoritative work presents a keen approach to building, executing, and validating statistical models that consider data from various phases of development. It also delineates a truly translational example to help bolster understanding of discussed concepts. This comprehensive guide effectively demonstrates how to overcome obstacles related to successful TM practice. It contains invaluable information for pharmaceutical scientists, research executives, clinicians, and biostatisticians looking to expedite successful implementation of this important process.Trade Review"This is one of the few books published on the strategies for TM. The chapters are carefully coordinated and can be read on their own; they are independent but are still well coordinated. The book contains a good outline of the different aspects of TM and contains a series of good examples. ... this book will provide interesting reading for readers from a variety of backgrounds. Overall, this book contains a good foundation for anyone working in this area." -Richardus Vonk, Pharmaceutical Statistics "... chapters follow the natural order from discovery research to final implementation to intermediate validation." -Erik Cobo, International Society for Clinical BiostatisticsTable of ContentsTranslational Medicine: Strategies and Statistical Methods. Strategic Concepts in Translational Medicine. Design and Analysis Approaches for Discovery Translational Medicine. Biomarker Development. Targeted Clinical Trials. Statistical Methods in Translational Medicine. NonparametricMethods in Translational Research. Model Selection/Validation. Translation in Clinical Information between Populations—Bridging Studies. Translation in Clinical Technology—Traditional Chinese Medicine. Index.

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Book SynopsisProviding a basic tool for studying nonlinear problems, Spectral Theory for Random and Nonautonomous Parabolic Equations and Applications focuses on the principal spectral theory for general time-dependent and random parabolic equations and systems. The text contains many new results and considers existing results from a fresh perspective.Taking a clear, unified, and self-contained approach, the authors first develop the abstract general theory in the framework of weak solutions, before turning to cases of random and nonautonomous equations. They prove that time dependence and randomness do not reduce the principal spectrum and Lyapunov exponents of nonautonomous and random parabolic equations. The book also addresses classical Faber–Krahn inequalities for elliptic and time-periodic problems and extends the linear theory for scalar nonautonomous and random parabolic equations to cooperative systems. The final chapter presents applications to Kolmogorov systems of parabolic equations. By thoroughly explaining the spectral theory for nonautonomous and random linear parabolic equations, this resource reveals the importance of the theory in examining nonlinear problems.Trade Review... a clear and interesting account of the principal spectral theory for general time-dependent and random linear parabolic equations and systems. It contains many new results and puts some already known results in a new framework. ... -Krystyna Twardowksa, Mathematical Reviews, Issue 2010gTable of ContentsIntroduction. Fundamental Properties in the General Setting. Spectral Theory in the General Setting. Spectral Theory in Nonautonomous and Random Cases. Influence of Spatial-Temporal Variations and the Shape of Domain. Cooperative Systems of Parabolic Equations. Applications to Kolmogorov Systems of Parabolic Equations. References. Index.

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Book SynopsisBayesian Analysis with Stata is written for anyone interested in applying Bayesian methods to real data easily. The book shows how modern analyses based on Markov chain Monte Carlo (MCMC) methods are implemented in Stata both directly and by passing Stata datasets to OpenBUGS or WinBUGS for computation, allowing Stata’s data management and graphing capability to be used with OpenBUGS/WinBUGS speed and reliability.The book emphasizes practical data analysis from the Bayesian perspective, and hence covers the selection of realistic priors, computational efficiency and speed, the assessment of convergence, the evaluation of models, and the presentation of the results. Every topic is illustrated in detail using real-life examples, mostly drawn from medical research.The book takes great care in introducing concepts and coding tools incrementally so that there are no steep patches or discontinuities in the learning curve. The book's content helps the user see exactly what computations are done for simple standard models and shows the user how those computations are implemented. Understanding these concepts is important for users because Bayesian analysis lends itself to custom or very complex models, and users must be able to code these themselves.Trade Review"… the first comprehensive guide to employing Bayesian methods using Stata statistical software. … until this book, there has been no unified presentation of how to implement Bayesian methods using Stata. … A nice feature of the book is the use of real data … I recommend it for Stata users who wish to employ Bayesian modeling within the Stata environment."—International Statistical Review, 2015Table of ContentsList of figures. List of tables. Preface. Acknowledgments. The problem of priors. Evaluating the posterior. Metropolis–Hastings. Gibbs sampling. Assessing convergence. Validating the Stata code and summarizing the results. Using WinBUGS for model fitting. Model checking. Model selection. Further case studies. Writing Stata programs for specific Bayesian analysis. A Standard distributions. References . Author index . Subject index.

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Book SynopsisOne Hundred Nineteen Stata Tips provides concise and insightful notes about commands, features, and tricks that will help you obtain a deeper understanding of Stata. The book comprises the contributions of the Stata community that have appeared in the Stata Journal since 2003.Table of ContentsIntroducing Stata tips. Stata tip 1: The eform() option of regress. Stata tip 2: Building with floors and ceilings. Stata tip 3: How to be assertive. Stata tip 4: Using display as an online calculator. Stata tip 5: Ensuring programs preserve dataset sort order. Stata tip 6: Inserting awkward characters in the plot. Stata tip 7: Copying and pasting under Windows. Stata tip 8: Splitting time-span records with categorical time-varying covariates. Stata tip 9: Following special sequences. Stata tip 10: Fine control of axis title positions. Stata tip 11: The nolog option with maximum-likelihood modeling commands. Stata tip 12: Tuning the plot region aspect ratio. Stata tip 13: generate and replace use the current sort order. Stata tip 14: Using value labels in expressions. Stata tip 15: Function graphs on the fly. Stata tip 16: Using input to generate variables. Stata tip 17: Filling in the gaps. Stata tip 18: Making keys functional. Stata tip 19: A way to leaner, faster graphs. Stata tip 20: Generating histogram bin variables. Stata tip 21: The arrows of outrageous fortune. Stata tip 22: Variable name abbreviation. Stata tip 23: Regaining control over axis ranges. Stata tip 24: Axis labels on two or more levels. Stata tip 25: Sequence index plots. Stata tip 26: Maximizing compatibility between Macintosh and Windows. Stata tip 27: Classifying data points on scatter plots. Stata tip 28: Precise control of dataset sort order. Stata tip 29: For all times and all places. Stata tip 30: May the source be with you. Stata tip 31: Scalar or variable? The problem of ambiguous names. Stata tip 32: Do not stop. Stata tip 33: Sweet sixteen: Hexadecimal formats and precision problems. Stata tip 34: Tabulation by listing. Stata tip 35: Detecting whether data have changed. Stata tip 36: Which observations? Stata tip 37: And the last shall be first. Stata tip 38: Testing for groupwise heteroskedasticity. Stata tip 39: In a list or out? In a range or out? Stata tip 40: Taking care of business. Stata tip 41: Monitoring loop iterations. Stata tip 42: The overlay problem: Offset for clarity. Stata tip 43: Remainders, selections, sequences, extractions: Uses of the modulus. Stata tip 44: Get a handle on your sample. Stata tip 45: Getting those data into shape. Stata tip 46: Step we gaily, on we go. Stata tip 47: Quantile–quantile plots without programming. Stata tip 48: Discrete uses for uniform(). Stata tip 49: Range frame plots. Stata tip 50: Efficient use of summarize. Stata tip 51: Events in intervals. Stata tip 52: Generating composite categorical variables. Stata tip 53: Where did my p-values go? Stata tip 54: Post your results. Stata tip 55: Better axis labeling for time points and time intervals. Stata tip 56: Writing parameterized text files. Stata tip 57: How to reinstall Stata. Stata tip 58: nl is not just for nonlinear models. Stata tip 59: Plotting on any transformed scale. Stata tip 60: Making fast and easy changes to files with filefilter. Stata tip 61: Decimal commas in results output and data input. Stata tip 62: Plotting on reversed scales. Stata tip 63: Modeling proportions. Stata tip 64: Cleaning up user-entered string variables. Stata tip 65: Beware the backstabbing backslash. Stata tip 66: ds—A hidden gem. Stata tip 67: J() now has greater replicating powers. Stata tip 68: Week assumptions. Stata tip 69: Producing log files based on successful interactive commands. Stata tip 70: Beware the evaluating equal sign. Stata tip 71: The problem of split identity, or how to group dyads. Stata tip 72: Using the Graph Recorder to create a pseudograph scheme. Stata tip 73: append with care! Stata tip 74: firstonly, a new option for tab2. Stata tip 75: Setting up Stata for a presentation. Stata tip 76: Separating seasonal time series. Stata tip 77: (Re)using macros in multiple do-files. Stata tip 78: Going gray gracefully: Highlighting subsets and downplaying substrates. Stata tip 79: Optional arguments to options. Stata tip 80: Constructing a group variable with specified group sizes. Stata tip 81: A table of graphs. Stata tip 82: Grounds for grids on graphs. Stata tip 83: Merging multilingual datasets. Stata tip 84: Summing missings. Stata tip 85: Looping over nonintegers. Stata tip 86: The missing() function. Stata tip 87: Interpretation of interactions in nonlinear models. Stata tip 88: Efficiently evaluating elasticities with the margins command. Stata tip 89: Estimating means and percentiles following multiple imputation. Stata tip 90: Displaying partial results. Stata tip 91: Putting unabbreviated varlists into local macros. Stata tip 92: Manual implementation of permutations and bootstraps. Stata tip 93: Handling multiple y axes on twoway graphs. Stata tip 94: Manipulation of prediction parameters for parametric survival regression. Stata tip 95: Estimation of error covariances in a linear model. Stata tip 96: Cube roots. Stata tip 97: Getting at ρ’s and σ’s. Stata tip 98: Counting substrings within strings. Stata tip 99: Taking extra care with encode. Stata tip 100: Mata and the case of the missing macros. Stata tip 101: Previous but different. Stata tip 102: Highlighting specific bars. Stata tip 103: Expressing confidence with gradations. Stata tip 104: Added text and title options. Stata tip 105: Daily dates with missing days. Stata tip 106: With or without reference. Stata tip 107: The baseline is now reported. Stata tip 108: On adding and constraining. Stata tip 109: How to combine variables with missing values. Stata tip 110: How to get the optimal k-means cluster solution. Stata tip 111: More on working with weeks. Stata tip 112: Where did my p-values go? (Part 2) Stata tip 113: Changing a variable’s format: What it does and does not mean. Stata tip 114: Expand paired dates to pairs of dates. Stata tip 115: How to properly estimate the multinomial probit model with heteroskedastic errors. Stata tip 116: Where did my p-values go? (Part 3). Stata tip 117: graph combine—Combining graphs. Stata tip 118: Orthogonalizing powered and product terms using residual centering. Stata tip 119: Expanding datasets for graphical ends.

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Book SynopsisMeta-analysis allows researchers to combine the results of several studies into a unified analysis that provides an overall estimate of the effect of interest. This collection of articles from the Stata Journal and Stata Technical Bulletin will be indispensable to researchers who wish to conduct meta-analyses using Stata and learn about the full range of user-written Stata meta-analysis commands. With these articles and the associated Stata software, you gain access to the statistical methods behind the rapid increase in the number of meta-analyses reported in the social and medical literature.Collectively, the articles provide a detailed description of a range of meta-analytic methods. They show how to conduct and interpret meta-analyses; how to produce highly flexible graphical displays; how to use meta-regression; how to examine bias; how to conduct individual participant data meta-analysis; and how to conduct multivariate meta-analysis. This edition also contains three articles on network metaanalysis, a major recent development in meta-analysis methodology.Table of ContentsMeta-analysis in Stata: metan, metaan, metacum, and metap. Meta-regression: metareg. Investigating bias in meta-analysis: metafunnel, confunnel, metabias, metatrim, and extfunnel. Multivariate meta-analysis: metandi, mvmeta. Network meta-analysis: indirect, network package, network graphs package.

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Book SynopsisThis volume is a sometimes serious and sometimes whimsical retrospective of Stata, its development, and its use over the last 30 years.The view from the inside opens with an essay by Bill Gould, Stata's president and cofounder, that discusses the challenges and concepts that guided the design and implementation of Stata. This is followed by an interview of Bill by Joe Newton that discusses Bill's early interest in computing, his early work on a program for matching prom dates in the days when you had to purchase time on computers, and further exploration of the guiding principles behind Stata. Finally, Sean Becketti, Stata's first employee, delves into the not-to-be-missed culture of Stata in its infancy.The view from the outside comprises 14 essays by prominent researchers and members of the Stata community. Most discuss Stata's use and evolution in disciplines such as behavioral sciences, business, economics, epidemiology, time series, political science, public health, public policy, veterinary epidemiology, and statistics. Some take a sweeping overview. Others are more intimate personal recollections. Mostly, we simply wanted to celebrate the relationship between Stata users and Stata software. We hope that this volume holds something interesting for everyone.Table of ContentsA VISION FROM INSIDE. Initial thoughts. A conversation with William Gould. A VISION FROM OUTSIDE. Then and now. 25 years of Statistics with Stata. Stata’s contribution to epidemiology. The evolution of veterinary epidemiology. On learning introductory biostatistics and Stata. Stata and public health in Ohio. Statistics research and Stata in my life. Public policy and Stata. Microeconometrics and Stata over the past 30 years. Stata enabling state-of-the-art research in accounting, business, and finance. Stata and political science. New tools for psychological researchers. History of Stata.

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Book SynopsisHealth Econometrics Using Stata by Partha Deb, Edward C. Norton, and Willard G. Manning provides an excellent overview of the methods used to analyze data on healthcare expenditure and use. Aimed at researchers, graduate students, and practitioners, this book introduces readers to widely used methods, shows them how to perform these methods in Stata, and illustrates how to interpret the results. Each method is discussed in the context of an example using an extract from the Medical Expenditure Panel Survey.After the overview chapters, the book provides excellent introductions to a series of topics aimed specifically at those analyzing healthcare expenditure and use data. The basic topics of linear regression, the generalized linear model, and log and Box-Cox models are covered with a tight focus on the problems presented by these data. Using this foundation, the authors cover the more advanced topics of models for continuous outcome with mass points, count models, and models for heterogeneous effects. Finally, they discuss endogeneity and how to address inference questions using data from complex surveys.The authors use their formidable experience to guide readers toward useful methods and away from less recommended ones. Their discussion of "health econometric myths" and the chapter presenting a framework for approaching health econometric estimation problems are especially useful for this aspect.Table of ContentsIntroduction Framework MEPS data The linear regression model: Specification and checks Generalized linear models Log and Box–Cox models Models for continuous outcomes with mass at zero Count models Models for heterogeneous effects Endogeneity Design effects

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Book SynopsisThe Mata Book: A Book for Serious Programmers and Those Who Want to Be is the book that Stata programmers have been waiting for. Mata is a serious programming language for developing small- and large-scale projects and for adding features to Stata. What makes Mata serious is that it provides structures, classes, and pointers along with matrix capabilities. The book is serious in that it covers those advanced features, and teaches them. The reader is assumed to have programming experience, but only some programming experience. That experience could be with Stata's ado language, or with Python, Java, C++, Fortran, or other languages like them. As the book says, "being serious is a matter of attitude, not current skill level or knowledge".The author of the book is William Gould, who is also the designer and original programmer of Mata, of Stata, and who also happens to be the president of StataCorp. Table of ContentsThe mechanics of using Mata. A programmer’s tour of Mata. Mata’s programming statements. Mata’s expressions. Mata’s variable types. Mata’s strict option and Mata’s pragmas. Mata’s function arguments. Programming example: n_choose_k() three ways. Mata’s structures. Programming example: Linear regression. Mata’s classes. Programming example: Linear regression 2. Better variable types. Programming constants. Mata’s associative arrays. Programming example: Sparse matrices. Programming example: Sparse matrices, continued. The Mata Reference Manual. Writing Mata code to add new commands to Stata. Mata’s storage type for complex numbers. How Mata differs from C and C++. Three-dimensional arrays (advanced use of pointers).

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Book SynopsisStata Tips provides concise and insightful notes about commands, features, and tricks that will help you obtain a deeper understanding of Stata.The book comprises the contributions of the Stata community that have appeared in the Stata Journal since 2003. Each tip is a brief article that provides practical advice on using Stata. With tips covering a breadth of topics in statistics, graphics, data management, and programming, both new and experienced Stata users are sure to find tips that will be useful in their research.Table of ContentsIntroducing Stata tips Stata tip 120: Certifying subroutines, M. L. Buis Stata tip 121: Box plots side by side, N. J. Cox Stata tip 122: Variable bar widths in two-way graphs, B. Jann Stata tip 123: Spell boundaries, N. J. Cox Stata tip 124: Passing temporary variables to subprograms, M. L. Buis Stata tip 125: Binned residual plots for assessing the fit of regression models for binary outcomes, J. Kasza Stata tip 126: Handling irregularly spaced high-frequency transactions data, C. F. Baum and S. Bibo Stata tip 127: Use capture noisily groups, R. B. Newson Stata tip 128: Marginal effects in log-transformed models: A trade application, L. J. Uberti Stata tip 129: Efficiently processing textual data with Stata’s new Unicode features, A. Koplenig Stata tip 130: 106610 and all that: Date variables that need to be fixed., N. J. Cox Stata tip 131: Custom legends for graphs that use translucency, T. P. Morris Stata tip 132: Tiny tricks and tips on ticks, N. J. Cox and V. Wiggins Stata tip 133: Box plots that show median and quartiles only, N. J. Cox Stata tip 134: Multiplicative and marginal interaction effects in nonlinear models, W. H. Dow, E. C. Norton, and J. T. Donahoe Stata tip 135: Leaps and bounds, M. L. Buis Stata tip 136: Between-group comparisons in a scatterplot with weighted markers, A. Musau Stata tip 137: Interpreting constraints on slopes of rank-deficient design matrices, D. Christodoulou Stata tip 138: Local macros have local scope, N. J. Cox Stata tip 139: The by() option of graph can work better than graph combine, N. J. Cox Stata tip 140: Shorter or fewer category labels with graph bar, N. J. Cox Stata tip 141: Adding marginal spike histograms to quantile and cumulative distribution plots, N. J. Cox Stata tip 142: joinby is the real merge m:m, D. Mazrekaj and J. Wursten Stata tip 143: Creating donut charts in Stata, A. Musau Stata tip 144: Adding variable text to graphs that use a by() option, N. J. Cox Stata tip 145: Numbering weeks within months, N. J. Cox Stata tip 146: Using margins after a Poisson regression model to estimate the number of events prevented by an intervention, M. Falcaro, R. B. Newson, and P. Sasieni Erratum: Stata tip 145: Numbering weeks within months, N. J. Cox Stata tip 147: Porting downloaded packages between machines, R. B. Newson Stata tip 148: Searching for words within strings, N. J. Cox Stata tip 149: Weighted estimation of fixed-effects and first-differences models, J. Gardner Stata tip 150: When is it appropriate to xtset a panel dataset with panelvar only? C. Lazzaro Stata tip 151: Puzzling out some logical operators, N. J. Cox Stata tip 152: if and if: When to use the if qualifier and when to use the if command, N. J. Cox and C. B. Schechter

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Book SynopsisFranz Buscha's book, Graphs Everyone Should Know and How to Create Them in Stata, is written for anyone who uses Stata to make graphs. Beginners will find a complete collection of tools for effectively visualizing their data and results. Experienced Stata users are certain to learn some new tricks as well.The chapters of the book are organized into four main sections: graphs for univariate data, graphs for bivariate data, graphs for multivariate data, and special graphs. Each chapter introduces a type of graph, explains when and why it is useful for visualizing a particular kind of data, demonstrates how to create that graph using Stata, and shows a few variations. The special graph section covers topics such as how to create maps, plot equations, create animated graphs, and create other specialty graphs.Readers will find it easy to learn to make graphs by example. Buscha demonstrates most graphs using datasets that are installed with your copy of Stata, so it is straightforward to follow along. He also clearly pairs each graph with the command used to create it in a box just above the graph. If you find a graph that you wish to create with your own data, you can take the command from the box and replace the variable names in the example with your own variable names.Buscha's book has two unique features that distinguish it from other books about Stata graphs. First, the book's goal is to clearly demonstrate how to effectively visualize different kinds of data and results from models using only necessary features. It focuses on important options but does not discuss all the options available for customizing each graph. Second, the book introduces many community-contributed graph commands that are freely available and can be downloaded from the internet. Readers may be unaware of these commands before finding them in this book, and they can learn how to use them quickly rather than spend time trying to write custom code for themselves.Graphs Everyone Should Know and How to Create Them in Stata is a reference you will use again and again as you visualize different types of data. You will quickly find the graphs that are applicable to your data and the Stata commands necessary to create them.

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Book SynopsisTwo veteran math educators demonstrate how some "magnificent mistakes" had profound consequences for our understanding of mathematics' key concepts. In the nineteenth century, English mathematician William Shanks spent fifteen years calculating the value of pi, setting a record for the number of decimal places. Later, his calculation was reproduced using large wooden numerals to decorate the cupola of a hall in the Palais de la Decouverte in Paris. However, in 1946, with the aid of a mechanical desk calculator that ran for seventy hours, it was discovered that there was a mistake in the 528th decimal place. Today, supercomputers have determined the value of pi to trillions of decimal places. This is just one of the amusing and intriguing stories about mistakes in mathematics in this layperson's guide to mathematical principles. In another example, the authors show that when we "prove" that every triangle is isosceles, we are violating a concept not even known to Euclid - that of "betweenness." And if we disregard the time-honored Pythagorean theorem, this is a misuse of the concept of infinity. Even using correct procedures can sometimes lead to absurd - but enlightening - results. Requiring no more than high-school-level math competency, this playful excursion through the nuances of math will give you a better grasp of this fundamental, all-important science.

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Book SynopsisAn Introduction to Numerical Methods using MATLAB is designed to be used in any introductory level numerical methods course. It provides excellent coverage of numerical methods while simultaneously demonstrating the general applicability of MATLAB to problem solving. This textbook also provides a reliable source of reference material to practicing engineers, scientists, and students in other junior and senior-level courses where MATLAB can be effectively utilized as a software tool in problem solving.The principal goal of this book is to furnish the background needed to generate numerical solutions to a variety of problems. Specific applications involving root-finding, interpolation, curve-fitting, matrices, derivatives, integrals and differential equations are discussed and the broad applicability of MATLAB demonstrated.This book employs MATLAB as the software and programming environment and provides the user with powerful tools in the solution of numerical problems.

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Book SynopsisThis book focuses mainly on the recent developments of all types of theoretical, mathematical, and computational conceptions, as well as modelling and simulation of specific research themes covering all scientific and technical disciplines from chemistry, physics, and engineering to biology and medicine. The book contains timely reviews and research covering fundamental and applied research aspects in all disciplines of natural sciences, including their historical representations and philosophical perspectives. The book discusses the fact that the largest and smallest values of the fukui function and local softness do not necessarily correspond to the softness and hardness regions of the molecules such as porphyrins. The authors have adopted two popular calculation procedures for this venture. One is the very old Hückel molecular orbital calculation, and the other is one of best semi-empirical AM-1 procedures for such systems. Our finding is that neither the fukui functions nor the local softnesses can predict the preferred donor sites of porphyrins toward metal ions. Table of ContentsPreface. The Time Evolution of the Hard and Soft Acids and Bases (HSAB) Theory. Magneto Hydrodynamic Effects on an Atherosclerotic Artery: A Theoretical Study. A Fast Solver for the Backward Heat Conduction Problem in Unbounded Domains. Steganographic Method for Color Images Using Variance Field Estimation and Scaling Factor for Energy Conservation. Breviary of Quantum Computation. Classical Charged Particles in Arbitrary Motion. Second Order Linear Differential Equation in Its Exact Form. On the Operator Exp( 2 Λ (P + Q)). Quantum Computational Studies on Porphycene. The Evaluation of Protonation Energy of Molecules in Terms of Quantum Theoretical Descriptors. Analysis of Casson Fluid Model for Blood Flow in Externally Applied Magnetic Field. Index.

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Book SynopsisEdited by professionals with years of experience, this book provides an introduction to the theory of evolutionary algorithms and single- and multi-objective optimization, and then goes on to discuss to explore applications of evolutionary algorithms for many uses with real-world applications. Covering both the theory and applications of evolutionary computation, the book offers exhaustive coverage of several topics on nontraditional evolutionary techniques, details working principles of new and popular evolutionary algorithms, and discusses case studies on both scientific and real-world applications of optimizationTable of ContentsTheory and Applications in Engineering Systems. Introduction. Bio-Mimetic Adaptations of Genetic Algorithm and Their Applications to Chemical Engineering. Surrogate-Assisted Evolutionary Computing Methods. Evolutionary Algorithms in Ironmaking Applications. Harmony Search Optimization for Multilevel Thresholding in Digital Images. Swarm Intelligence in Software Engineering Design Problems. Gene Expression Programming in Nanotechnology Applications. Theory and Applications of Single Objective Optimization Studies. An Alternate Hybrid Evolutionary Method for Solving MINLP Problems. Differential Evolution for Optimal Design of Shell-and-Tube Heat Exchangers. Evolutionary Computation Based QoS-Aware Multicast Routing. Performance Assessment of the Canonical Genetic. An Efficient Approach for Populating Deep Web Repositories Using SFLA. Closed Loop Simulation of Quadraple Tank Process Using Adaptive Multi-Loop Fractional. Theory and Applications of Single and Multi-Objective Optimization Studies. A Practical Approach towards Multi Objective Shape Optimization. Nature-Inspired Computing Techniques for Integer Factorization. Genetic Algorithm Based Real-Time Parameter Identifier for an Adaptive Power System Stabilizer. Applied Evolutionary Computation in Fire Safety Upgrading. Elitist Multi-Objective Evolutionary Algorithms for Voltage and Reactive Power Optimization in Power Systems. Evaluation of Simulated Annealing, Differential Evolution and Particle Swarm Optimization for Solving Pooling Problems. Performance Improvement of NSGA-II Algorithm by Modifying Crossover Probability Distribution. Evolutionary Algorithms for Malware Detection and Classification. Index.

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Book SynopsisThis new book focuses on nanomaterial development as well as investigations of combustion and explosion processes. It presents valuable information on the modeling of processes and on quantum chemical calculations and leading-edge research from around the world in this dynamic field, focusing on concepts above formal experimental techniques and theoretical methods of chemical physics for micro- and nanotechnologies. Also presented are non-linear kinetic appearances and their possible applications.Table of ContentsNanotechnology. Self-Organization of Nanoscale Structures by Epitaxial Deposition. Theoretical Bases of Non-Contact Measurements of Electromagnetic Parameters of Nanomaterials. Structure, Physical, Chemical, and Biological Properties of Magnerot Nanoscale Drug. X-Ray Photoelectron Study of the Mechanism of the Functionalization of the Carbon Copper-Containing Nanostructure Surface with sp-Elements. Comparative Analysis of Elemental and Structural Composition of Nanocrystalline Tantalum Powders. Phase Transformations in Nanostructed Steel 08H15N5D2T at Heat. Formation of the Material Structure from the Nano-Sized TiO2 Powder during Sintering Process. The Development of a New Nanoscale Kit on Alumina Nanopowder-Based for Generator of Technetium-99M and the Study on Its Functional Suitability for Diagnosis in Oncology. Nano Structures by Severe Plastic Deformation (SPD) Processes. Controlling Electrospun Polymer Nanofibers Structure Using Microscopic Model for Ideal Tissue Engineering Scaffolds. Polymers. Assessment of Structural Condition of Amorphous Alloys Thin Surface Layers. Synthesis of Ultrafine Metal Oxide Particles in the Polymer Matrix of Ultra High Molecular Weight Polyethylene. Polyanilines: Two Cases Studies and Updates. Study of Heat Protection Polymer Materials Containing Silicon Carbide and Perlite. Method of the Increase of Thermostability of Filled Polymers. Insights in Modeling and Chemical Physics. The Particles’ Dynamic Motion Modeling on a Centrifugal Shock Mill Blades. Condensation-Lingual Captivity Associated Oil Gas in Thin-Walled Pipes on Multiple Speeds. Study of Laminar Diffusion Combustion Models. Mathematical Modeling of Flow with Homogeneous Condensation. Simulation of Phase Transformations in the Fe-Cr Alloys at High Temperatures. The Mobility of Technogenic Arsenic in the Soils of Udmurtia under the Influence of Atmospheric Precipitation. Synthesis of Diamond Precursor MW CVD Method for Forming Diamond Films on Tungsten Carbide Material. The Influence of Non-Specific Binding of Antibodies on Forming of Analytical Response of Amperometric Immunosensor. Molecular Modeling of the 2-(Pyridin-2-yl)-1H-Benzimidazole Intramolecular Dynamics. NMR 13C Spectra of the 1,1,3-Trimethyl-3-(4-Methylphenyl) Butyl Hydroperoxide in Various Solvents: Molecular Modeling.

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Book SynopsisThis new book brings together innovative research, new concepts, and novel developments in the application of informatics tools for applied chemistry and computer science. It presents a modern approach to modeling and calculation and also looks at experimental design in applied chemistry and chemical engineering. The volume discusses the developments of advanced chemical products and respective tools to characterize and predict the chemical material properties and behavior.Providing numerous comparisons of different methods with one another and with different experiments, not only does this book summarize the classical theories, but it also exhibits their engineering applications in response to the current key issues. Recent trends in several areas of chemistry and chemical engineering science, which have important application to practice, are discussed.Applied Chemistry and Chemical Engineering: Volume 1: Mathematical and Analytical Techniques provides valuable information for chemical engineers and researchers as well as for graduate students. It demonstrates the progress and promise for developing chemical materials that seem capable of moving this field from laboratory-scale prototypes to actual industrial applications. Volume 2 will focus principles and methodologies in applied chemistry and chemical engineering.Table of ContentsDigraphs, Graphs and Thermodynamic Equations. Usefulness and Limits of Predictive Relationships. Computational Model for By-Product of Wastewater Treatment. Complex Calculation of a Critical Path of Motion of a Corpuscle Taking into Account a Regime and Design of the Apparatus. The Modern Approach to Modelling and Calculation of Efficiency of Process of a Gas Cleaning. Numerical Modelling and Visualization of Traffic of Dispersion Particles in the Apparatus. Computing the Augmented Eccentric Connectivity Indices of Nanostar Dendrimer D3[N]. Hydraulic Model Calibration Process. Quantum-Chemical Calculations of the Molecules 1- Methylbicycleo[4,1,0] Heptane 2,4-Spiroheptane by PM3 Method. District Meter Area (DMA) of Water Distribution System. Metal Control on Structure and Function of Ni(Fe) Dioxygenases Included in methionine Salvage Oathway. Role of Tyr-fragment and Macrostructures in Mechanism of Catalysis on Model Systems. The Silica-Polymer Composites of the System of HEMA-TEOS: The Synthesis, Thermo Mechanical Properties and the Features of the Kinetic of the Process. Photo Responsive Materials Containing Azomoieties: A Facile Approach in Molecular Imprinting. Green Nanotechnology: An Approach towards Environment Safety. A Note on Preparation of Nanofilter from carbon Nanotubes. Control of Fluidic Jet Repulsion in Electro Spinning Process. Modification of Urea-Formaldehyde Resin with Collagen Biopolymers. A Research Note on Polymerization of 2-Hydroxyethyl Methacrylate Initiated with Vanadyl Ionic Complex.

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Book SynopsisThis book covers many important aspects of applied chemistry and chemical engineering, focusing on three main aspects: principles, methodology and evaluation methods. It presents a selection of chapters on recent developments of theoretical, mathematical, and computational conceptions, as well as chapters on modeling and simulation of specific research themes covering applied chemistry and chemical engineering. This book attempts to bridge the gap between classical analysis and modern applications.Covering a selection of topics within the field of applied chemistry and chemical engineering, the book is divided into several parts: polymer chemistry and technology bioorganic and biological chemistry nanoscale technology selected topics This book is the second of the two-volume series Applied Chemistry and Chemical Engineering. The first volume is Volume 1: Mathematical and Analytical Techniques.Table of ContentsPolymer-Graphene Nanocomposites: A Smart Material for Next Generation Applications. Modification of Waste Polystyrene Food Containers and Study on Its Efficiency as Oil Spill Cleanup. Technical Note on Surface Modification of Silica by Epoxy Resin. Photosensitive Copolymers of Para-(2-Carboxy) Cyclopropyl Styrene with 2,3-Dimethylbutadiene-1,3. Polymeric Materials and Their Use in Agriculture. Electro-Conductive Polymer Materials on the Basis of Oligo-4-Aminophenol. Modification and Application Possibilities of Bio-Composites Based on Thermoplastic Collagen. Synthesis of Syndiotactic 1,2-Polybutadiene with Cobalt Alkylxhanthogenate + Trialkylaluminum Catalytic Dithiosystems. Vinylcyclopropanes in the Addition and Polymerization Reactions: A Detailed Review. Hyaluronan: Biological Function and Medical Applications. Protective Effects of Catalase Indicate Hydrogen Peroxide Involvement in Hyaluronan Degradation Initiated by Cu (II) Ions Plus Ascorbate in situ. Protein Structure Prediction. The Condensation Reactions of 1-Chloro-2, 3, 4, 6-Tetra-O-Acetyl-ɑ-D-Gluco (Galacto) Pyranose with Heterocyclic Amines. 3d Simulation of Electrospun Nanofiber Jet. Some Aspects of Cubic B-Spline Approximation Method for 3d Simulation of Electrospun Nanofiber Jet. Synthesis of 1.4-Cis Polybutadiene by the Heterogenized Dithiosystem on Base of Nanosize Montmorillonite. Research of Hydrodynamic Characteristics and Sampling of an Optimum Design of the Bubble-Vortex Apparatus. Emission of Clusters During N+, O+, N2+, O2+, Ar+ Ions Bombardment of C, Nacl, Mg, Al, Si, S, Ti, GaAs Surfaces. Advanced Oxidation Processes, Membrane Separation Processes and Environmental Engineering Techniques: A Vision for the Future and a Critical Overview. Fructose and Its Impact on the Diffusion of Electrolytes in Aqueous Systems. Cheminformatics: The Promising Future: Managing Change of Approach Through ICT Emerging Technology. Application of Evolutionary Multi-Objective Optimization in Designing Chemical Engineering and Petroleum Engineering Systems and Its Wide Technological Vision: A Critical Overview and A Broad Scientific Perspective. Intensification of Efficiency of Process of a Gas Cleaning in Apparatuses "Rotoklon".

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Book SynopsisUnderstanding mathematical modeling is fundamental in chemical engineering. This book reviews, introduces, and develops the mathematical models that are most frequently encountered in sophisticated chemical engineering domains. The volume provides a collection of models illustrating the power and richness of the mathematical sciences in supplying insight into the operation of important real-world systems. It fills a gap within modeling texts, focusing on applications across a broad range of disciplines. The first part of the book discusses the general components of the modeling process and highlights the potential of modeling in the production of nanofibers. These chapters discuss the general components of the modeling process and the evolutionary nature of successful model building in the electrospinning process. Electrospinning is the most versatile technique for the preparation of continuous nanofibers obtained from numerous materials. This section of book summarizes the state-of-the art in electrospinning as well as updates on theoretical aspects and applications.Part 2 of the book presents a selection of special topics on issues in applied chemistry and chemical engineering, including nanocomposite coating processes by electrocodeposition method, entropic factors conformational interactions, and the application of artificial neural network and meta-heuristic algorithms.This volume covers a wide range of topics in mathematical modeling, computational science, and applied mathematics. It presents a wealth of new results in the development of modeling theories and methods, advancing diverse areas of applications and promoting interdisciplinary interactions between mathematicians, scientists, engineers and representatives from other disciplines.Table of ContentsAn Overview on Electrospun Nanofibers: Influences of Various Parameters and Applications. Updates on Electrospinning Process Models (Part I). Updates on Electrospinning Process Models (Part II). Conductive Viscous Jet and Electrohydrodynamics: Update on Models. Macroscopic Models for Electrospinning. Update on One-Dimensional Models of Steady, Inviscid, Annular Liquid Jets. The Electrically Forced Jet and Instabilities. Update on Deformation of Newtonian and Non-Newtonian Conducting Drops in the Electric Field. Update on Behaviour of Electrospun Fluid Jet Simulation Using Microscopic Model. Update on Controlling Instability of Electrospun Nanofibers (Part I). Update on Controlling Instability of Electrospun Nanofibers (Part II). Update on Thermo-Electro-Hydrodynamic Model for Electrospinning Process. Update on Numerical Analysis and Numerical Methods for Solving Equations. The Multilevel Modeling of the Nanocomposite Coating Processes by Electrocodeposition Method. Local Anaesthetics Classification: Artificial Intelligence Information Entropy. Entropic Factors Conformational Interactions. Application of Artificial Neural Network and Meta-Heuristic Algorithm in Applied Chemistry and Chemical Engineering.

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Book SynopsisThis volume provides a good understanding of the binary fluid system, highlighting new dimensions of the existing Kalina cycle system, a thermodynamic process for converting thermal energy into usable mechanical power. The book illustrates that providing new flexibility leads to new research outcomes and possible new projects in this field.The information provided in the book simplifies the application of the Kalina cycle system with an easy-to-understand and thorough explanation of properties development, processes solutions, sub-system work, and total system work. There are currently no books available in the area of binary fluid system in the field of KCS with added fallibility in the operation and process design. Currently decentralized power systems are gaining more attention due to shortages in power, and cooling demands are competing with other electrical loads. This book fills a valuable information gap, providing insight into a new dimension for designers, practicing engineers, and academicians in this area.Table of ContentsHistory of Developments. Basic Thermodynamics. Thermodynamic Properties of Ammonia-Water Mixture. Binary Mixture Thermodynamic Processes. Kalina Cycle System with Low Temperature Heat Recovery. Kalina Cycle System with Intermediate Temperature Heat Recovery. Kalina Cycle System with High Temperature Heat Recovery. Cooling Cogeneration.

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Book SynopsisBeginning with a review of formal languages and their syntax and semantics, Logic, Proof and Computation conducts a computer assisted course in formal reasoning and the relevance of logic to mathematical proof, information processing and philosophy. Topics covered include formal grammars, semantics of formal languages, sequent systems, truth-tables, propositional and first order logic, identity, proof heuristics, regimentation, set theory, databases, automated deduction, proof by induction, Turing machines, undecidability and a computer illustration of the reasoning underpinning Gödel's incompleteness proof. LPC is designed as a multidisciplinary reader for students in computing, philosophy and mathematics.

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Book SynopsisThe world can be an amazing place if you know the right questions to ask: How much does a ghost reduce a house's value? How are winemakers responding to climate change? How much should you tip your Uber driver? Should your dog fear Easter more than fireworks? The keen minds of The Economist love to look beyond everyday appearances to find out what really makes things tick. In this latest collection of The Economist Explains, they have gathered the weirdest and most counter-intuitive answers they've found in their endless quest to explain our bizarre world. Take a peek at some Unconventional Wisdom - and pass it on! The world only gets more amazing when discoveries are shared.Trade ReviewThe Father Christmas of knowledge -- Giles CorenPraise for Go Figure: Books like this make you wary of ever guessing the answer to anything -- Mark Mason * Daily Mail *

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Book SynopsisMild Cognitive Impairment (MCI) has been identified as an important clinical transition between normal aging and the early stages of Alzheimer's disease (AD). Since treatments for AD are most likely to be most effective early in the course of the disease, MCI has become a topic of great importance and has been investigated in different populations of interest in many countries. This book brings together these differing perspectives on MCI for the first time. This volume provides a comprehensive resource for clinicians, researchers, and students involved in the study, diagnosis, treatment, and rehabilitation of people with MCI. Clinical investigators initially defined mild cognitive impairment (MCI) as a transitional condition between normal aging and the early stages of Alzheimer’s disease (AD). Because the prevalence of AD increases with age and very large numbers of older adults are affected worldwide, these clinicians saw a pressing need to identify AD as early as possible. It is at this very early stage in the disease course that treatments to slow the progress and control symptoms are likely to be most effective.Since the first introduction of MCI, research interest has grown exponentially, and the utility of the concept has been investigated from a variety of perspectives in different populations of interest (e.g., clinical samples, volunteers, population-based screening) in many different countries. Much variability in findings has resulted. Although it has been acknowledged that the differences observed between samples may be ‘legitimate variations’, there has been no attempt to understand what it is we have learned about MCI (i.e., common features and differences) from each of these perspectives.This book brings together information about MCI in different populations from around the world. Mild Cognitive Impairment will be an important resource for any clinician, researcher, or student involved in the study, detection, treatment, and rehabilitation of people with MCI.Trade Review"This valuable volume brings the kind of broad perspective to mild cognitive impairment that has long been needed. Rather than basing conclusions on a single sample or framework, the editors have pulled together articles from leading research groups around the world. This is the kind of comprehensive approach that is needed for developing systematic and valid definitions of MCI and identifying better tools that make it possible to differentiate between benign memory changes in later life and the early signs of pathological processes." - Steven H. Zarit, Department of Human Development and Family Studies, The Pennsylvania State University"This volume provides the most comprehensive overview of mild cognitive impairment currently available. The conceptual and methodological challenges for studying MCI are tackled with rigor, and the complexities of defining the syndrome are not underestimated. This book is certain to become a classic text for those studying or researching cognitive agin, MCI and dementia, and for clinicians seeking an authoritative reference on the clinical manifestations of MCI." - Kaarin J. Anstey, Centre for Mental Health Research, Australian National University"The editors of this book have done a great job. The description of the issues is laid out in a well-written introduction, making the descriptions of the research papers very accessible, even to the less well-informed reader. The conclusion likewise pulled together the various strands, including defining what still needs to be done to further refine the concept of MCI." - Graham A. Jackson, Laverndale Hospital, Scotland. In Dementia, August, 2008"This valuable volume brings the kind of broad perspective to mild cognitive impairment that has long been needed. Rather than basing conclusions on a single sample or framework, the editors have pulled together articles from leading research groups around the world. This is the kind of comprehensive approach that is needed for developing systematic and valid definitions of MCI and identifying better tools that make it possible to differentiate between benign memory changes in later life and the early signs of pathological processes." - Steven H. Zarit, Department of Human Development and Family Studies, The Pennsylvania State University"This volume provides the most comprehensive overview of mild cognitive impairment currently available. The conceptual and methodological challenges for studying MCI are tackled with rigor, and the complexities of defining the syndrome are not underestimated. This book is certain to become a classic text for those studying or researching cognitive agin, MCI and dementia, and for clinicians seeking an authoritative reference on the clinical manifestations of MCI." - Kaarin J. Anstey, Centre for Mental Health Research, Australian National University"The editors of this book have done a great job. The description of the issues is laid out in a well-written introduction, making the descriptions of the research papers very accessible, even to the less well-informed reader. The conclusion likewise pulled together the various strands, including defining what still needs to be done to further refine the concept of MCI." - Graham A. Jackson, Laverndale Hospital, Scotland. In Dementia, August, 2008Table of ContentsPart 1. Introduction. H. Tuokko, I. McDowell, An Overview of Mild Cognitive Impairment. Part 2. General Population Research on MCI. C. Fabrigoule, P. Barberger-Gateau, J.-F. Dartigues, The PAQUID Study. K. Palmer, L. Bäckman, B.J. Small, L. Fratiglioni, Cognitive Impairment in Elderly Persons without Dementia: Findings from the Kungsholmen Project. J. Fleming, F.E. Matthews, M. Chatfield, C. Brayne, Population Levels of Mild Cognitive Impairment in England and Wales. A. Collie, P. Maruff, D.G. Darby, C. Masters, J. Currie, The Melbourne Aging Study. Part 3. Specific Samples. R. Wilson, N.T. Aggarwal, D.A. Bennett, Mild Cognitive Impairment in the Religious Orders Study. G. Smith, M. Machulda, K. Kantarci, A Perspective from the Mayo Clinic. M.C. Tierney, Prediction of Probable Alzheimer's Disease: The Sunnybrook Memory Study. H. Wolf, H.-J. Gertz, Studies in the Leipzig Memory Clinic: Contribution to the Concept of Mild Cognitive Impairment. Part 4. Interventions. H. Chertkow, Emerging Pharmacological Therapies for Mild Cognitive Impairment. B. Woods, L. Clare, Cognition-based Therapies and Mild Cognitive Impairment. K. Peters, G. Winocur, Combined Therapies in Mild Cognitive Impairment. Part 5. Summary and Future Directions. H. Tuokko, D.F. Hultsch, The Future of Mild Cognitive Impairment.

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Book SynopsisRecent years have seen a significant rise of interest in max-linear theory and techniques. Specialised international conferences and seminars or special sessions devoted to max-algebra have been organised. This book aims to provide a first detailed and self-contained account of linear-algebraic aspects of max-algebra for general (that is both irreducible and reducible) matrices. Among the main features of the book is the presentation of the fundamental max-algebraic theory (Chapters 1-4), often scattered in research articles, reports and theses, in one place in a comprehensive and unified form. This presentation is made with all proofs and in full generality (that is for both irreducible and reducible matrices). Another feature is the presence of advanced material (Chapters 5-10), most of which has not appeared in a book before and in many cases has not been published at all. Intended for a wide-ranging readership, this book will be useful for anyone with basic mathematical knowledge (including undergraduate students) who wish to learn fundamental max-algebraic ideas and techniques. It will also be useful for researchers working in tropical geometry or idempotent analysis.Table of ContentsMax-algebra: Two Special Features.- One-sided Max-linear Systems and Max-algebraic Subspaces.- Eigenvalues and Eigenvectors.- Maxpolynomials. The Characteristic Maxpolynomial.- Linear Independence and Rank. The Simple Image Set.- Two-sided Max-linear Systems.- Reachability of Eigenspaces.- Generalized Eigenproblem.- Max-linear Programs.- Conclusions and Open Problems.

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Book SynopsisWhy can't we tickle ourselves? Which properties give you the best chance of winning Monopoly? What would happen if you fell into a black hole? Is it possible to hurt your brain if you think too much? In this entertaining and enlightening tour of day-to-day life, award-winning writer and scientist Robert Matthews tackles everything from the puzzling maths of odd socks to the real 'string theory' mystery: how does string acquire all those unwanted knots?Trade Review"simply fabulous." Jon

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Book SynopsisAn examination of Neolithic timber circles in the east of England with reference to Alexander Thom's work on the geometrical setting out and astronomical alignments of stone circles in the west of Britain

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Book SynopsisThis book will help your students develop a thorough understanding of the essential mathematical skills required in A Level Biology. / Supports the core mathematical skills that have an increased relevance and importance in A Level Biology specifications. / Reassuring support for students who do not have a strong maths background. / Clearly explains how numerical, geometrical and statistical concepts are used in A Level Biology and post-16 biology courses and how students should approach these concepts when taking these courses and sitting their exams. / Explains each mathematical concept using plenty of relevant worked examples, with advice on how to avoid common misunderstandings when making calculations. / Helps students decode examination questions to find the biological question being asked and put the problem into a mathematical form to find an answer. / The material has been mapped against the new mathematical requirements for the A Level Biology courses from AQA, Pearson, OCR, WJEC, CCEA, the International Baccalaureate and the Cambridge Pre-U.Table of Contents1. Numbers (new section on using logarithms); 2. Processed numbers (new sections on per cent increase and decrease; percentage error; Heterozygosity index; joints as levers and unfamiliar mathematical expressions). 3. Graphs (extra sections on substrate concentration and rate of reaction and compensation point); 4. Scale; 5. Ratios and their use in genetics; 6. The Hardy-Weinberg equilibrium; 7. Statistics (new section on percentiles and quartiles); Quickfire answers; Test yourself answers; Glossary; Specification Map; Index.

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Book Synopsis"Tell the administration what they want to hear, then do what is best for your students." That's Barry Garelick's philosophy in a nutshell. As the Mark Twain of education writing, this collection of essays chronicles Garelick's experiences at two schools, teaching math. With essays such as, Not Making Sense, and a Conversation I Never Had; "Math Talk", Stalin's Hemorrhoids, and Murder of Crows; and The Parole Officer's Check List, the Dialectic of Competition, and Gnarly Problems, Garelick gives the reader a glimpse into the daily routines of math taught in a verite style and exposes a lot of the edu-crap that teachers hear they are supposed to do, and feel guilty about when they teach in the way they see fit.

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Book SynopsisIn this book on mathematical programming, the postulate spacial-time certainty of economic process at uncertainty conditions in finite-dimensional vector space and the principle piecewise-linear homogeneity of economic process at uncertainty conditions in finite-dimensional vector space are first suggested. A special theory on constructing piecewise-linear economic-mathematical models was developed, and a criterion of multivariate prediction of economic process and their control at uncertainty conditions in a finite-dimensional vector space was suggested. A packet of numerical programs for computer simulation in constructing and multivariate prediction of economic state with the help of n-element piecewise-linear economic-mathematical models with regard to the uncertainty factors effect in m-dimensional vector space is also suggested.This book is intended for students of economic and administrative specialties as well as for research associates in the sphere of economic-mathematical methods, management, and banking.Table of ContentsBrief Information on Finite-Dimensional Vector Space and its Application in Economics. Bases of Piecewise-Linear Economic-Mathematical Models with Regard to Influence of Unaccounted Factors in Finite-Dimensional Vector Space. Piecewise Linear Economic-Mathematical Models with Regard to Unaccounted Factors Influence in Three-Dimensional Vector Space. Piecewise-Linear Economic-Mathematical Models with Regard to Unaccounted Factors Influence on a Plane. Bases of Software for Computer Simulation and Multivariant Prediction of Economic Even at Uncertainty Conditions on the Base of N-Component Piecewise-Linear Economic-Mathematical Models in M-Dimensional Vector Space. Index.

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Book SynopsisThere is a wonderfully weird but real world out there, and we are a part of it. It is time for physics to take life seriously.Can we ever truly comprehend the universe before we fully understand consciousness and the wonders, and limits, of the mind? Ulf Danielsson, an acclaimed theoretical physicist who has dedicated his career to probing the deepest mysteries of nature, thinks not. As he dismantles the arguments of esteemed mathematicians and scientists, who would substitute their mathematical models for reality and equate the mind to a computer, he makes a lucid and passionate case that it is nature, full of beauty and meaning, which must compel us. In challenging established worldviews, he also takes a fresh look at major philosophical debates, including the notion of free will.Fearless, provocative, and witty, The World Itself is essential reading for anyone curious about the profound questions surrounding life, the universe, and everything.Trade Review“[A] thought-provoking treatment of an array of issues at the frontier of science and philosophy. . . . Well worth our attention.” —PopMatters“Engaging and varied. . . . Books like this invite us to direct our curiosities—both as groups and individuals—in useful ways.” —North of Oxford“Engrossing. . . . Danielsson’s clarity of thought and expression and his use of illuminating literary and historical references are equal to the quality of his writing. Science ‘popularizing’ doesn’t get much more comprehensible, or provocative, than this.” —Kirkus Reviews (starred review)“Danielsson takes readers on an odyssey through the width and depth of his field, and it is truly a fascinating journey. Touching on subjects as diverse as evolutionary biology, philosophy, and even popular culture, Danielsson makes his topics both appreciably substantial and approachable.” —Library Journal (starred review)“There are some mind-bending ideas and the philosophical reflections on math and physics are stimulating. . . . This pensive take on physics has much to offer.” —Publishers Weekly“The World Itself offers a bold perspective on mathematics, physics, and the nature of reality. There’s much I agree with and less that I don’t, but Ulf Danielsson, a leading theoretical physicist, proves himself an insightful and patient guide through some of the universe’s deepest mysteries.” —Brian Greene, author of The Fabric of the Cosmos and Until the End of Time“Danielsson is Sweden’s most important public writer on the implications of natural science. His lucid, powerful, passionate, and engaging work advances original arguments of great importance. The World Itself is destined to become a modern classic as it upends many of the received wisdoms about the scientific worldview.” —Martin Hägglund, author of This Life: Secular Faith and Spiritual Freedom“Danielsson displays a remarkably broad understanding of science and philosophy, and dispenses with false notions about the world in this brief, yet provocative book. I hope it stimulates lots of discussion and debate, as it should. For those who have thought about these issues, there is much of interest here. For those who haven’t, this is a great place to start.” —Lawrence M. Krauss, author of A Universe from Nothing and The Known Unknowns“In this accessible and beautifully written book, Danielsson argues for views diametrically opposite to mine on the nature of intelligence, consciousness, and physical reality—I highly recommend it!” —Max Tegmark, author of Our Mathematical Universe and Life 3.0: Being Human In the Age of Artificial Intelligence

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Book SynopsisWhile the architecture of present-day parallel supercomputers is largely based on the concept of a shared memory, with its attendant limitations of common access, advances in semicoductor technology have led to the development of highly parellel computer architectures with decentralized storage and limited connections in which each processor possesses high bandwidth local memory connected to a small number of such architectures, enabling cost-effective high-speed parallel processing for large volumes of data, with ultra-high throughput rates. Algorithms suitable for implementation on systolic arrays find applications in areas such as signal and image processing, pattern matching, linear algebra, recurrence algorithms and graph problems. This book provides an insight into the implementation of systolic arrays and gives a comprehensive overview of the techniques and theories contributing to the design of systolic algorithms.Table of ContentsPREFACE 1. INTRODUCTION Systolic Algorithms 2. POLYNOMIAL AND ROOT FINDING METHODS 3. SYSTOLIC MATRIX OPERATIONS 4. QUADRATURE AND DIFFERENTIAL EQUATIONS 5 . SOLUTION OF LINEAR SYSTEMS 6. EIGENV ALOE-EIGENVECTOR COMPUTATIONS 7. LINEAR AND DYNAMIC PROGRAMMING

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Book SynopsisPart II of the Selected Works of Ivan Georgievich Petrowsky, contains his major papers on second order Partial differential equations, systems of ordinary. Differential equations, the theory, of Probability, the theory of functions, and the calculus of variations. Many of the articles contained in this book have Profoundly, influenced the development of modern mathematics. Of exceptional value is the article on the equation of diffusion with growing quantity of the substance. This work has found extensive application in biology, genetics, economics and other branches of natural science. Also of great importance is Petrowsky's work on a Problem which still remains unsolved - that of the number of limit cycles for ordinary differential equations with rational right-hand sides.Table of ContentsForeword, Editor’s Preface, Ivan Georgievich Petrowsky, PETROWSKY’S ARTICLES ON PARTIAL DIFFERENTIAL EQUATIONS, PETROWSKY’S ARTICLES ON ORDINARY DIFFERENTIAL EQUATIONS, PETROWSKY’S ARTICLES ON THE THEORY OF PROBABILITY AND OTHER PROBLEMS OF ANALYSIS, APPENDIX: COMMENTARIES, Index

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Book SynopsisThis book presents articles of L.V. Kantorovich on the descriptive theory of sets and function and on functional analysis in semi-ordered spaces, to demonstrate the unity of L.V. Kantorovich's creative research. It also includes two papers on the extension of Hilbert space.

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Book SynopsisThis open access book chronicles the rise of a new scientific paradigm offering novel insights into the age-old enigmas of existence. Over 300 years ago, the human mind discovered the machine code of reality: mathematics. By utilizing abstract thought systems, humans began to decode the workings of the cosmos. From this understanding, the current scientific paradigm emerged, ultimately discovering the gift of technology. Today, however, our island of knowledge is surrounded by ever longer shores of ignorance. Science appears to have hit a dead end when confronted with the nature of reality and consciousness. In this fascinating and accessible volume, James Glattfelder explores a radical paradigm shift uncovering the ontology of reality. It is found to be information-theoretic and participatory, yielding a computational and programmable universe.Table of ContentsPart I Climbing to the Summit.- Deciphering the Rules of Nature.- The Simplicity of Complexity.- Crafting Technology.- Part II The Downfall.- The Truth about Reality.- The Missing Foundations of Science.- Problems with Consciousness.- Part III A New Horizon.- So, How Can You Be Sure?.- A Universe Built of Information.- Fabricating Reality.

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Book SynopsisThis book provides a concise introduction to the mathematical foundations of time series analysis, with an emphasis on mathematical clarity. The text is reduced to the essential logical core, mostly using the symbolic language of mathematics, thus enabling readers to very quickly grasp the essential reasoning behind time series analysis. It appeals to anybody wanting to understand time series in a precise, mathematical manner. It is suitable for graduate courses in time series analysis but is equally useful as a reference work for students and researchers alike.Trade Review“‘This book provides a concise introduction to the mathematical foundations of time series analysis, with an emphasis on mathematical clarity. … It appeals to anybody wanting to understand time series in a precise, mathematical manner. It is suitable for graduate courses in time series analysis but is equally useful as a reference work for students and researchers alike.’ … The book can be recommended to all readers, who are interested in this field.” (Ludwig Paditz, zbMath 1414.62001, 2019)“This book is a rigorous, mathematically clear and self-contained and quite complete text on time series analysis, suitable both for graduate courses and as a reference book for researchers and users of stochastic temporal models.” (Nazaré Mendes Lopes, Mathematical Reviews, December, 2018)“Beran (Univ. of Konstanz, Germany) presents the mathematical foundations of time series analysis at a level suitable for advanced graduate students and researchers in statistics. The presentation is extremely concise … . the book gives definitions, theorems, and proofs, along with a few exercises and solutions. … it may be useful to graduate students and researchers as a reference.” (B. Borchers, Choice, Vol. 56 (03), November, 2018)​Table of Contents1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 What is a time series? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Time series versus iid data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 Typical assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.1 Fundamental properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.1.1 Ergodic property with a constant limit . . . . . . . . . . . . . . . . . . . 52.1.2 Strict Stationarity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.1.3 Weak Stationarity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.1.4 Weak stationarity and Hilbert spaces . . . . . . . . . . . . . . . . . . . . 92.1.5 Ergodic processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252.1.6 Sufficient conditions for the a.s. ergodic property with a constant limit. . . . . . . . . . . 262.1.7 Sufficient conditions for the L2-ergodic property with a constant limit . .. . . . .. . . 272.2 Specific assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302.2.1 Gaussian processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302.2.2 Linear processes in L2(Ω) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312.2.3 Linear processes with E(X2t ) = ∞ . . . . . . . . . . . . . . . . . . . . . . 342.2.4 Multivariate linear processes . . . . . . . . . . . . . . . . . . . . . . . . . . . 372.2.5 Invertibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382.2.6 Restrictions on the dependence structure . . . . . . . . . . . . . . . . . 493 Defining probability measures for time series . . . . . . . . . . . . . . . . . . . . . . 553.1 Finite dimensional distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 553.2 Transformations and equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 563.3 Conditions on the expected value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 573.4 Conditions on the autocovariance function . . . . . . . . . . . . . . . . . . . . . . 583.4.1 Positive semidefinite functions . . . . . . . . . . . . . . . . . . . . . . . . . 593.4.2 Spectral distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 613.4.3 Calculation and properties of F and f . . . . . . . . . . . . . . . . .4 Spectral representation of univariate time series . . . . . . . . . . . . . . . . . . . 814.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 814.2 Harmonic processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 814.3 Extension to general processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 844.3.1 Stochastic integrals with respect to Z . . . . . . . . . . . . . . . . . . . . 844.3.2 Existence and definition of Z . . . . . . . . . . . . . . . . . . . . . . . . . . 894.3.3 Interpretation of the spectral representation . . . . . . . . . . . . . . 974.4 Further properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 984.4.1 Relationship between ReZ and ImZ . . . . . . . . . . . . . . . . . . . . 984.4.2 Frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 994.4.3 Overtones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 994.4.4 Why are frequencies restricted to the range [-π,π]? . . . . . . . 1004.5 Linear filters and the spectral representation . . . . . . . . . . . . . . . . . . . . 1034.5.1 Effect on the spectral representation . . . . . . . . . . . . . . . . . . . . . 1034.5.2 Elimination of Frequency Bands . . . . . . . . . . . . . . . . . . . . . . . 1075 Spectral representation of real valued vector time series . . . . . . . . . . . . 1095.1 Cross-spectrum and spectral representation . . . . . . . . . . . . . . . . . . . . . 1095.2 Coherence and phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1166 Univariate ARMA processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1276.1 Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1276.2 Stationary solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1276.3 Causal stationary solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1316.4 Causal invertible stationary solution . . . . . . . . . . . . . . . . . . . . . . . . . . . 1336.5 Autocovariances of ARMA processes . . . . . . . . . . . . . . . . . . . . . . . . . . 1346.5.1 Calculation by integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1346.5.2 Calculation using the autocovariance generating function . . . 1356.5.3 Calculation using the Wold representation . . . . . . . . . . . . . . . 1386.5.4 Recursive calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1396.5.5 Asymptotic decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1406.6 Integrated, seasonal and fractional ARMA and ARIMA processes . . 1476.6.1 Integrated processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1476.6.2 Seasonal ARMA processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1476.6.3 Fractional ARIMA processes . . . . . . . . . . . . . . . . . . . . . . . . . . 1486.7 Unit roots, spurious correlation, cointegration . . . . . . . . . . . . . . . . . . . 1597 Generalized autoregressive processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1637.1 Definition of generalized autoregressive processes . . . . . . . . . . . . . . . 1637.2 Stationary solution of generalized autoregressive equations . . . . . . . . 1647.3 Definition of VARMA processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1687.4 Stationary solution of VARMA equations . . . . . . . . . . . . . . . . . . . . . . 1697.5 Definition of GARCH processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1717.6 Stationary solution of GARCH equations . . . . . . . . . . . . . . . . . . . . . . . 1727.7 Definition of ARCH(∞) processes . . . . . . . . . . . . . . . . . . . . .7.8 Stationary solution of ARCH(∞) equations . . . . . . . . . . . . . . . . . . . . . 1778 Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1818.1 Best linear prediction given an infinite past . . . . . . . . . . . . . . . . . . . . . 1818.2 Predictability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1828.3 Construction of the Wold decomposition from f . . . . . . . . . . . . . . . . . 1878.4 Best linear prediction given a finite past . . . . . . . . . . . . . . . . . . . . . . . . 1909 Inference for µ, γ and F . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1959.1 Location estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1959.2 Linear regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1979.3 Nonparametric estimation of γ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2059.4 Nonparametric estimation of f . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21110 Parametric estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22710.1 Gaussian and quasi maximum likelihood estimation . . . . . . . . . . . . . . 22710.2 Whittle approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22910.3 Autoregressive approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23210.4 Model choice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243 Subject Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245

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Book SynopsisDesigned for the 21st century classroom, this textbook poses, refines, and analyzes questions of sustainability in a quantitative environment. Building mathematical knowledge in the context of issues relevant to every global citizen today, this text takes an approach that empowers students of all disciplines to understand and reason with quantitative information. Whatever conclusions may be reached on a given topic, this book will prepare the reader to think critically about their own and other people’s arguments and to support them with careful, mathematical reasoning. Topics are grouped in themes of measurement, flow, connectivity, change, risk, and decision-making. Mathematical thinking is at the fore throughout, as students learn to model sustainability on local, regional, and global scales. Exercises emphasize concepts, while projects build and challenge communication skills. With no prerequisites beyond high school algebra, instructors will find this book a rich resource for engaging all majors in the mathematics classroom. From the Foreword No longer will you be just a spectator when people give you quantitative information—you will become an active participant who can engage and contribute new insights to any discussion.[…] There are many math books that will feed you knowledge, but it is rare to see a book like this one that will help you cultivate wisdom.[…] As the authors illustrate, mathematics that pays attention to human considerations can help you look at the world with a new lens, help you frame important questions, and help you make wise decisions. Francis Edward Su, Harvey Mudd CollegeTrade Review“This is a most revolutionary book, and I would love to teach a course using it! There is much interest in what is variously termed quantitative literacy (QL), quantitative reasoning (QR), and critical thinking (CT). This book is the first in a series of Texts for Quantitative Critical Thinking … . I do not want to fail to mention that the book’s layout is simply beautiful.” (Paul J. Campbell, Mathematics Magazine, Vol. 92 (1), November, 2018)Table of Contents1. Measuring.- 2. Flowing.- 3. Networking.- 4. Changing.- 5. Risking.- 6. Deciding.- 7. Case Studies.- 8. Resources.- List of Figures.- List of Tables.- Bibliography.- Index.

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Book SynopsisDie Theorie gewöhnlicher Differentialgleichungen und dynamischer Systeme spielt eine zentrale Rolle in der Modellierung realer zeitabhängiger Prozesse. Damit gehört sie zur universitären Grundausbildung von Mathematikern, Physikern, Informatikern und Ingenieuren. Der Band liefert eine zeitgemäße Darstellung der Theorie, wobei der Schwerpunkt auf Dynamik liegt. Um die Leistungsfähigkeit der Theorie zu belegen, nehmen Beispiele viel Raum ein. Neue Anwendungen in Biologie, Chemie und Physik werden in Modellierung und Analysis detailliert behandelt.Table of ContentsProlog.- Notationen.- I Gewöhnliche Differentialgleichungen.- 1. Einführung.- 2 Existenz und Eindeutigkeit.- 3 Lineare Systeme.- 4 Stetige und differenzierbare Abhängigkeit.- 5 Elementare Stabilitätstheorie.- II Dynamische Systeme.- 6 Existenz und Eindeutigkeit II.- 7 Invarianz.- 8 Ljapunov-Funktionen und Stabilität.- 9 Ebene autonome Systeme.- 10 Linearisierung und invariante Mannigfaltigkeiten.- 11 Periodische Lösungen.- 12 Verzweigungstheorie.- 13 Differentialgleichungen auf Mannigfaltigkeiten.- Epilog.- Abbildungsverzeichnis.- Literaturverzeichnis.- Lehrbücher und Monographien.- Originalliteratur.- Index.

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