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Analysis and Synthesis in Mathematics

Analysis and Synthesis in Mathematics
Author: Michael Otte
Publisher: Springer Science & Business Media
Total Pages: 476
Release: 1997
Genre: History
ISBN: 9780792345701
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The book discusses the main interpretations of the classical distinction between analysis and synthesis with respect to mathematics. In the first part, this is discussed from a historical point of view, by considering different examples from the history of mathematics. In the second part, the question is considered from a philosophical point of view, and some new interpretations are proposed. Finally, in the third part, one of the editors discusses some common aspects of the different interpretations.

The Cambridge Companion to Newton

The Cambridge Companion to Newton
Author: I. Bernard Cohen
Publisher: Cambridge University Press
Total Pages: 785
Release: 2002-04-25
Genre: Philosophy
ISBN: 1139826026
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Sir Isaac Newton (1642–1727) was one of the greatest scientists of all time, a thinker of extraordinary range and creativity who has left enduring legacies in mathematics and the natural sciences. In this volume a team of distinguished contributors examine all the main aspects of Newton's thought, including not only his approach to space, time, mechanics, and universal gravity in his Principia, his research in optics, and his contributions to mathematics, but also his more clandestine investigations into alchemy, theology, and prophecy, which have sometimes been overshadowed by his mathematical and scientific interests.

The Fundamentals of Analysis for Talented Freshmen

The Fundamentals of Analysis for Talented Freshmen
Author: Peter M. Luthy
Publisher: Springer Nature
Total Pages: 84
Release: 2022-05-31
Genre: Mathematics
ISBN: 3031024095
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This book assumes the students know some of the basic facts about Calculus. We are very rigorous and expose them to the proofs and the ideas which produce them. In three chapters, this book covers these number systems and the material usually found in a junior-senior advanced Calculus course. It is designed to be a one-semester course for "talented" freshmen. Moreover, it presents a way of thinking about mathematics that will make it much easier to learn more of this subject and be a good preparation for more of the undergraduate curriculum.

Sound Analysis and Synthesis with R

Sound Analysis and Synthesis with R
Author: Jérôme Sueur
Publisher: Springer
Total Pages: 637
Release: 2018-06-06
Genre: Medical
ISBN: 3319776479
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Sound is almost always around us, anywhere, at any time, reaching our ears and stimulating our brains for better or worse. Sound can be the disturbing noise of a drill, a merry little tune sung by a friend, the song of a bird in the morning or a clap of thunder at night. The science of sound, or acoustics, studies all types of sounds and therefore covers a wide range of scientific disciplines, from pure to applied acoustics. Research dealing with acoustics requires a sound to be recorded, analyzed, manipulated and, possibly, changed. This is particularly, but not exclusively, the case in bioacoustics and ecoacoustics, two life sciences disciplines that attempt to understand and to eavesdrop on the sound produced by animals. Sound analysis and synthesis can be challenging for students, researchers and practitioners who have few skills in mathematics or physics. However, deciphering the structure of a sound can be useful in behavioral and ecological research – and also very amusing. This book is dedicated to anyone who wants to practice acoustics but does not know much about sound. Acoustic analysis and synthesis are possible, with little effort, using the free and open-source software R with a few specific packages. Combining a bit of theory, a lot of step-by-step examples and a few cases studies, this book shows beginners and experts alike how to record, read, play, decompose, visualize, parametrize, change, and synthesize sound with R, opening a new way of working in bioacoustics and ecoacoustics but also in other acoustic disciplines.

Sequential Logic

Sequential Logic
Author: Joseph Cavanagh
Publisher: CRC Press
Total Pages: 912
Release: 2018-10-03
Genre: Computers
ISBN: 1420007858
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Until now, there was no single resource for actual digital system design. Using both basic and advanced concepts, Sequential Logic: Analysis and Synthesis offers a thorough exposition of the analysis and synthesis of both synchronous and asynchronous sequential machines. With 25 years of experience in designing computing equipment, the author stresses the practical design of state machines. He clearly delineates each step of the structured and rigorous design principles that can be applied to practical applications. The book begins by reviewing the analysis of combinatorial logic and Boolean algebra, and goes on to define sequential machines and discuss traditional and alternative methods for synthesizing synchronous sequential machines. The final chapters deal with asynchronous sequential machines and pulse-mode asynchronous sequential machines. Because this volume is technology-independent, these techniques can be used in a variety of fields, such as electrical and computer engineering as well as nanotechnology. By presenting each method in detail, expounding on several corresponding examples, and providing over 500 useful figures, Sequential Logic is an excellent tutorial on analysis and synthesis procedures.

Mathematical Analysis and Applications

Mathematical Analysis and Applications
Author: Michael Ruzhansky
Publisher: John Wiley & Sons
Total Pages: 1050
Release: 2018-04-11
Genre: Mathematics
ISBN: 1119414334
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An authoritative text that presents the current problems, theories, and applications of mathematical analysis research Mathematical Analysis and Applications: Selected Topics offers the theories, methods, and applications of a variety of targeted topics including: operator theory, approximation theory, fixed point theory, stability theory, minimization problems, many-body wave scattering problems, Basel problem, Corona problem, inequalities, generalized normed spaces, variations of functions and sequences, analytic generalizations of the Catalan, Fuss, and Fuss–Catalan Numbers, asymptotically developable functions, convex functions, Gaussian processes, image analysis, and spectral analysis and spectral synthesis. The authors—a noted team of international researchers in the field— highlight the basic developments for each topic presented and explore the most recent advances made in their area of study. The text is presented in such a way that enables the reader to follow subsequent studies in a burgeoning field of research. This important text: Presents a wide-range of important topics having current research importance and interdisciplinary applications such as game theory, image processing, creation of materials with a desired refraction coefficient, etc. Contains chapters written by a group of esteemed researchers in mathematical analysis Includes problems and research questions in order to enhance understanding of the information provided Offers references that help readers advance to further study Written for researchers, graduate students, educators, and practitioners with an interest in mathematical analysis, Mathematical Analysis and Applications: Selected Topics includes the most recent research from a range of mathematical fields.

Analysis and Synthesis of Logics

Analysis and Synthesis of Logics
Author: Walter Carnielli
Publisher: Springer Science & Business Media
Total Pages: 612
Release: 2008-01-22
Genre: Mathematics
ISBN: 1402067828
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Starting with simple examples showing the relevance of cutting and pasting logics, the monograph develops a mathematical theory of combining and decomposing logics, ranging from propositional and first-order based logics to higher-order based logics as well as to non-truth functional logics. The theory covers mechanisms for combining semantic structures and deductive systems either of the same or different nature. The issue of preservation of properties is addressed.

Hadamard Matrix Analysis and Synthesis

Hadamard Matrix Analysis and Synthesis
Author: Rao K. Yarlagadda
Publisher: Springer Science & Business Media
Total Pages: 120
Release: 2012-12-06
Genre: Technology & Engineering
ISBN: 1461563135
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Hadamard Matrix Analysis and Synthesis: With Applications to Communications and Signal/Image Processing presents the basic concepts of Sylvester's construction of Hadamard matrices, the eigenvalue-eigenvector decompositions, along with its relationship to Fourier transforms. Relevant computational structures are included for those interested in implementing the Hadamard transform. The 2-dimensional Hadamard transform is discussed in terms of a 1- dimensional transform. The applications presented touch on statistics, error correction coding theory, communications signaling, Boolean function analysis and synthesis, image processing, sequence theory (maximal length binary sequences, composite sequences, and Thue-Morse sequences) and signal representation. An interesting application of the Hadamard transform to images is the Naturalness Preserving Transform (NPT), which is presented. The NPT provides a way to encode an image that can be reconstructed when it is transmitted through a noisy or an unfriendly channel. The potential applications of the Hadamard transform are wide and the book samples many of the important concepts among a vast field of applications of the transform. Hadamard Matrix Analysis and Synthesis: With Applications to Communications and Signal/Image Processing serves as an excellent reference source and may be used as a text for advanced courses on the topic.

Network Analysis and Synthesis

Network Analysis and Synthesis
Author: Brian D. O. Anderson
Publisher: Courier Corporation
Total Pages: 560
Release: 2013-01-30
Genre: Technology & Engineering
ISBN: 0486152170
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This comprehensive look at linear network analysis and synthesis explores state-space synthesis as well as analysis, employing modern systems theory to unite classical concepts of network theory. 1973 edition.