Discrete Weak KAM Theory

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The aim of this book is to present a self-contained account of discrete weak KAM theory. Putting aside its intrinsic elegance, this theory also provides a toy model for classical weak KAM theory, where many technical difficulties disappear, but where the central ideas and results persist. It therefore serves as a good introduction to (continuous) weak KAM theory. The first three chapters give a general exposition of the general abstract theory, concluding with a discussion of the relations between the results proved in the discrete setting and the analogous theorems of classical weak KAM theory. Several examples are studied and some key differences between the discrete and classical theory are highlighted. The final chapter is devoted to the historical problem of conservative twist maps of the annulus.

Electronics with Discrete Components (2版)

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【簡介】 Electronics with Discrete Components delivers a comprehensive overview of electronics from the perspective of a physicist. In the first part on digital components, after an introduction to digital electronics, the text covers fundamentals of combinational logic and its implementation in combinational logic devices, followed by sequential-logic devices such as flip-flops and memory components. The second part on analog components deals with the fundamentals of signal processing, filters, components such as diodes and transistors, and a lengthy coverage of operational amplifiers. Each chapter ends with problem sets and “lab projects” that have been proven to work well for instruction. Questions on simple aspects of the lab that students should know are also included, such as regarding powering components and diagnosing signals with the oscilloscope and providing “troubleshooting tips” to help students find out why a particular circuit does not work. The new edition of this textbook adds more worked examples, exercises with answers for the self-learner, and end-of-chapter problems. It adds new electronic components, covers the latest digital technologies plus adds a new section of Fourier transforms in electronics. In addition, it features labs with Arduino or Teensy boards which have become widespread in the community as inexpensive, easy-to-use electronics platforms. 【目錄】 1 The Basics Part I Digital 2 Introduction to Digital Electronics 3 Combinational Logic 4 Advanced Combinational Devices 5 Sequential Logic Part II Analog 6 AC Signals 7 Filters and the Frequency Domain 8 Diodes 9 Transistors 10 Operational Amplifiers Appendix A Logic Board Appendix B If the Circuit Does Not Work Appendix C Curve Tracer

Modern Discrete Probability: An Essential Toolkit (Cambridge Series in Statistical and Probabilistic Mathematics) (1版)

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【簡介】 Providing a graduate-level introduction to discrete probability and its applications, this book develops a toolkit of essential techniques for analysing stochastic processes on graphs, other random discrete structures, and algorithms. Topics covered include the first and second moment methods, concentration inequalities, coupling and stochastic domination, martingales and potential theory, spectral methods, and branching processes. Each chapter expands on a fundamental technique, outlining common uses and showing them in action on simple examples and more substantial classical results. The focus is predominantly on non-asymptotic methods and results. All chapters provide a detailed background review section, plus exercises and signposts to the wider literature. Readers are assumed to have undergraduate-level linear algebra and basic real analysis, while prior exposure to graduate-level probability is recommended. This much-needed broad overview of discrete probability could serve as a textbook or as a reference for researchers in mathematics, statistics, data science, computer science and engineering. 【目錄】