Research Topics in Analysis, Volume II PDF Download

Author: Shouchuan Hu
Publisher: Springer Nature
ISBN: 3031641892
Category :
Languages : en
Pages : 731

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Author: Shouchuan Hu
Publisher: Springer Science & Business Media
ISBN: 1461546656
Category : Mathematics
Languages : en
Pages : 941

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Book Description
In volume I we developed the tools of "Multivalued Analysis. " In this volume we examine the applications. After all, the initial impetus for the development of the theory of set-valued functions came from its applications in areas such as control theory and mathematical economics. In fact, the needs of control theory, in particular the study of systems with a priori feedback, led to the systematic investigation of differential equations with a multi valued vector field (differential inclusions). For this reason, we start this volume with three chapters devoted to set-valued differential equations. However, in contrast to the existing books on the subject (i. e. J. -P. Aubin - A. Cellina: "Differential Inclusions," Springer-Verlag, 1983, and Deimling: "Multivalued Differential Equations," W. De Gruyter, 1992), here we focus on "Evolution Inclusions," which are evolution equations with multi valued terms. Evolution equations were raised to prominence with the development of the linear semigroup theory by Hille and Yosida initially, with subsequent im portant contributions by Kato, Phillips and Lions. This theory allowed a successful unified treatment of some apparently different classes of nonstationary linear par tial differential equations and linear functional equations. The needs of dealing with applied problems and the natural tendency to extend the linear theory to the nonlinear case led to the development of the nonlinear semigroup theory, which became a very effective tool in the analysis of broad classes of nonlinear evolution equations.

Author: Shouchuan Hu
Publisher: Springer Nature
ISBN: 3031178378
Category : Mathematics
Languages : en
Pages : 544

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Book Description
This book, which is the first of two volumes, presents, in a unique way, some of the most relevant research tools of modern analysis. This work empowers young researchers with all the necessary techniques to explore the various subfields of this broad subject, and introduces relevant frameworks where these tools can be immediately deployed. Volume I starts with the foundations of modern analysis. The first three chapters are devoted to topology, measure theory, and functional analysis. Chapter 4 offers a comprehensive analysis of the main function spaces, while Chapter 5 covers more concrete subjects, like multivariate analysis, which are closely related to applications and more difficult to find in compact form. Chapter 6 deals with smooth and non-smooth calculus of functions; Chapter 7 introduces certain important classes of nonlinear operators; and Chapter 8 complements the previous three chapters with topics of variational analysis. Each chapter of this volume finishes with a list of problems – handy for understanding and self-study – and historical notes that give the reader a more vivid picture of how the theory developed. Volume II consists of various applications using the tools and techniques developed in this volume. By offering a clear and wide picture of the tools and applications of modern analysis, this work can be of great benefit not only to mature graduate students seeking topics for research, but also to experienced researchers with an interest in this vast and rich field of mathematics.

Author: Georg Polya
Publisher: Springer Science & Business Media
ISBN: 1475762925
Category : Mathematics
Languages : en
Pages : 400

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Author: Elias M. Stein
Publisher: Princeton University Press
ISBN: 1400831156
Category : Mathematics
Languages : en
Pages : 398

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With this second volume, we enter the intriguing world of complex analysis. From the first theorems on, the elegance and sweep of the results is evident. The starting point is the simple idea of extending a function initially given for real values of the argument to one that is defined when the argument is complex. From there, one proceeds to the main properties of holomorphic functions, whose proofs are generally short and quite illuminating: the Cauchy theorems, residues, analytic continuation, the argument principle. With this background, the reader is ready to learn a wealth of additional material connecting the subject with other areas of mathematics: the Fourier transform treated by contour integration, the zeta function and the prime number theorem, and an introduction to elliptic functions culminating in their application to combinatorics and number theory. Thoroughly developing a subject with many ramifications, while striking a careful balance between conceptual insights and the technical underpinnings of rigorous analysis, Complex Analysis will be welcomed by students of mathematics, physics, engineering and other sciences. The Princeton Lectures in Analysis represents a sustained effort to introduce the core areas of mathematical analysis while also illustrating the organic unity between them. Numerous examples and applications throughout its four planned volumes, of which Complex Analysis is the second, highlight the far-reaching consequences of certain ideas in analysis to other fields of mathematics and a variety of sciences. Stein and Shakarchi move from an introduction addressing Fourier series and integrals to in-depth considerations of complex analysis; measure and integration theory, and Hilbert spaces; and, finally, further topics such as functional analysis, distributions and elements of probability theory.

Author: Antonio Bova
Publisher: Frontiers Media SA
ISBN: 2832519962
Category : Science
Languages : en
Pages : 206

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Author: Jeng-Shyang Pan
Publisher: Springer
ISBN: 3319077732
Category : Technology & Engineering
Languages : en
Pages : 583

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This volume presents the proceedings of the First Euro-China Conference on Intelligent Data Analysis and Applications (ECC 2014), which was hosted by Shenzhen Graduate School of Harbin Institute of Technology and was held in Shenzhen City on June 13-15, 2014. ECC 2014 was technically co-sponsored by Shenzhen Municipal People’s Government, IEEE Signal Processing Society, Machine Intelligence Research Labs, VSB-Technical University of Ostrava (Czech Republic), National Kaohsiung University of Applied Sciences (Taiwan), and Secure E-commerce Transactions (Shenzhen) Engineering Laboratory of Shenzhen Institute of Standards and Technology.

Author: Amar Sahay
Publisher: Business Expert Press
ISBN: 1631574809
Category : Business & Economics
Languages : en
Pages : 321

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This business analytics (BA) text discusses the models based on fact-based data to measure past business performance to guide an organization in visualizing and predicting future business performance and outcomes. It provides a comprehensive overview of analytics in general with an emphasis on predictive analytics. Given the booming interest in analytics and data science, this book is timely and informative. It brings many terms, tools, and methods of analytics together. The first three chapters provide an introduction to BA, importance of analytics, types of BA-descriptive, predictive, and prescriptive-along with the tools and models. Business intelligence (BI) and a case on descriptive analytics are discussed. Additionally, the book discusses on the most widely used predictive models, including regression analysis, forecasting, data mining, and an introduction to recent applications of predictive analytics-machine learning, neural networks, and artificial intelligence. The concluding chapter discusses on the current state, job outlook, and certifications in analytics.

Author: Pang-Ning Tan
Publisher: Springer
ISBN: 3642302203
Category : Computers
Languages : en
Pages : 468

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The two-volume set LNAI 7301 and 7302 constitutes the refereed proceedings of the 16th Pacific-Asia Conference on Knowledge Discovery and Data Mining, PAKDD 2012, held in Kuala Lumpur, Malaysia, in May 2012. The total of 20 revised full papers and 66 revised short papers were carefully reviewed and selected from 241 submissions. The papers present new ideas, original research results, and practical development experiences from all KDD-related areas. The papers are organized in topical sections on supervised learning: active, ensemble, rare-class and online; unsupervised learning: clustering, probabilistic modeling in the first volume and on pattern mining: networks, graphs, time-series and outlier detection, and data manipulation: pre-processing and dimension reduction in the second volume.

Author: Jessica N. Lester
Publisher: SAGE Publications
ISBN: 1506351255
Category : Social Science
Languages : en
Pages : 313

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Focusing on applied conversation analysis (CA), Applied Conversation Analysis: Social Interaction in Institutional Settings by Jessica N. Lester and Michelle O’Reilly offers practical insights and guidelines for CA scholars studying social interactions in institutional settings. Written in an accessible style and packed with case studies, examples, activities, and practical tips, the book takes readers through the entire process of planning and carrying out an applied CA research study. By highlighting challenges, debates, and important questions, each chapter provides the theoretical foundation necessary for making informed decisions at every stage of a research project. The book is divided into three sections (context and planning, doing a project using conversation analysis, and disseminating your research) to mirror the research process.