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The last fifteen years have seen a flurry of exciting developments in Fourier restriction theory, leading to significant new applications in diverse fields. This timely text brings the reader from the classical results to state-of-the-art advances in multilinear restriction theory, the Bourgain-Guth induction on scales and the polynomial method. Also discussed in the second part are decoupling for curved manifolds and a wide variety of applications in geometric analysis, PDEs (Strichartz estimates on tori, local smoothing for the wave equation) and number theory (exponential sum estimates and the proof of the Main Conjecture for Vinogradov's Mean Value Theorem). More than 100 exercises in the text help reinforce these important but often difficult ideas, making it suitable for graduate students as well as specialists. Written by an author at the forefront of the modern theory, this book will be of interest to everybody working in harmonic analysis.

Fourier analysis. --- Decoupling (Mathematics)

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Decoupling theory provides a general framework for analyzing problems involving dependent random variables as if they were independent. It was born in the early eighties as a natural continuation of martingale theory and has acquired a life of its own due to vigorous development and wide applicability. The authors provide a friendly and systematic introduction to the theory and applications of decoupling. The book begins with a chapter on sums of independent random variables and vectors, with maximal inequalities and sharp estimates on moments which are later used to develop and interpret decoupling inequalities. Decoupling is first introduced as it applies in two specific areas, randomly stopped processes (boundary crossing problems) and unbiased estimation (U-- statistics and U--processes), where it has become a basic tool in obtaining several definitive results. In particular, decoupling is an essential component in the development of the asymptotic theory of U-- statistics and U--processes. The authors then proceed with the theory of decoupling in full generality. Special attention is given to comparison and interplay between martingale and decoupling theory, and to applications. Among other results, the applications include limit theorems, momemt and exponential inequalities for martingales and more general dependence structures, results with biostatistical implications, and moment convergence in Anscombe's theorem and Wald's equation for U--statistics. This book is addressed to researchers in probability and statistics and to graduate students. The expositon is at the level of a second graduate probability course, with a good portion of the material fit for use in a first year course. Victor de la Pe$a is Associate Professor of Statistics at Columbia University and is one of the more active developers of decoupling.

Stochastic processes --- Decoupling (Mathematics) --- Decoupling (Mathematics). --- Probabilities. --- Statistics . --- Probability Theory and Stochastic Processes. --- Statistics, general. --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Mathematics --- Econometrics --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Inequalities (Mathematics)

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The paper documents an intriguing development in the emerging world in the 2000s: a decoupling from the business cycle of advanced countries, combined with the strengthening of the co-movements in the main emerging market assets that predates the synchronized sell-off during the crisis. In addition, the paper tests the hypothesis that financial globalization, to the extent that it creates a common, global investor base for emerging markets, could lead to a tighter asset correlation despite the weaker economic ties. While an examination of the impact of alternative financial globalization proxies does not yield conclusive results, a closer look at global emerging market equity and bond funds shows that the latter indeed foster financial recoupling during downturns, reflecting the fact that they trade near their respective benchmarks and respond to withdrawals by liquidating holdings across the board.

Bond funds --- Currencies and Exchange Rates --- Debt Markets --- Decoupling --- Economic Theory & Research --- Emerging economies --- Emerging Markets --- Finance and Financial Sector Development --- Financial globalization --- Financial recoupling --- Mutual Funds --- Private Sector Development

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Energy consumption and economic growth have been of great interest to researchers and policy-makers. Knowing the actual causal relationship between energy and the economy with respect to environmental degradation has important implications for modeling environmental and growth policies. The eleven chapters included herein aim to help researchers, academicians, and especially decision-makers to understand relevant issues and adopt appropriate methods to tackle and solve relevant environmental problems. Various methods from different disciplines are proposed and applied to various environmental and energy issues.

expected utility maximization --- decoupling theory --- urban utility tunnel --- sensitivity analysis --- environmental Kuznets curve (EKC) --- economic systems --- structural decomposition analysis --- thermodynamic cycles --- sustainable wind energy management --- environmental engineering --- energy commodities --- hedging strategies --- energy consumption --- industrialization --- energy --- waste --- Analytic Hierarchy Process --- panel data --- rank reversal --- economy --- industrial CO2 emission --- sustainability --- sustainable development --- energy-related carbon emissions --- Multi-Criteria Decision Analysis --- Shapley value --- Kaya identity --- circular economy --- minimum-variance hedge ratio --- MESSAGE model --- fixed assets investment --- life cycle cost --- Analytic Network Process --- environmental efficiency --- Pakistan --- data envelopment analysis --- embodied energy --- carbon emissions --- district distributed power plants --- economic benefit evaluation --- differential GMM estimation --- linearization --- effectiveness --- dynamic hybrid input–output model --- environment quality cointegration --- cost allocation --- risk aversion --- environment --- 3E --- financial development --- LMDI approach --- differential games --- energy recovery --- resource dependence theory --- open-loop control systems --- Tapio decoupling model --- uncertain dynamic systems

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In this book, nine papers focusing on different fields of power electronics are gathered, all of which are in line with the present trends in research and industry. Given the generality of the Special Issue, the covered topics range from electrothermal models and losses models in semiconductors and magnetics to converters used in high-power applications. In this last case, the papers address specific problems such as the distortion due to zero-current detection or fault investigation using the fast Fourier transform, all being focused on analyzing the topologies of high-power high-density applications, such as the dual active bridge or the H-bridge multilevel inverter. All the papers provide enough insight in the analyzed issues to be used as the starting point of any research. Experimental or simulation results are presented to validate and help with the understanding of the proposed ideas. To summarize, this book will help the reader to solve specific problems in industrial equipment or to increase their knowledge in specific fields.

soft-switching --- Superjunction MOSFET --- LLC resonant converter --- zero voltage switching --- COSS hysteresis --- COSS intrinsic energy losses --- SiC devices --- antiparallel diode --- dual active bridge --- power electronic transformer --- high-frequency transformer --- Artificial Neural Networks (ANN) --- fault diagnosis --- Fast Fourier Transform (FFT) --- Multilevel Inverter (MLI) --- LabVIEW --- magnetics modeling --- variable inductor --- hysteresis --- eddy currents --- saturable core --- AC/AC conversion --- decoupling control --- modulation --- DC–DC converter --- phase shift PWM --- ZVS --- inrush current --- MOSFET --- telecom server --- modular multilevel converter (MMC) --- total harmonic distortion (THD) --- universal mathematical model (UMM) --- switching state --- nearest level modulation (NLM) --- DC-DC converter --- IGBT --- averaged model --- electrothermal model --- SPICE --- power electronics --- converter control --- power factor correction --- total harmonic distortion --- flyback --- solid-state lighting