Sums of Exponential Functions and Their New Fundamental Properties With Applications to Natural Phenomena

Shestopaloff, Yuri K.

ISBN 10: 098096671X / ISBN 13: 9780980966718

Editore: Akvy Pr, 2008

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Dati bibliografici

• Titolo: Sums of Exponential Functions and Their New Fundamental Properties With Applications to Natural Phenomena
• Editore: Akvy Pr
• Data di pubblicazione: 2008
• Lingua: Inglese
• ISBN 10: 098096671X
• ISBN 13: 9780980966718
• Rilegatura: Brossura
• Edizione: seconda edizione
• Condizione: good

Descrizione articolo

Riassunto

This is an unusual book in many respects. It presents an important study related to adequate mathematical modeling of natural phenomena. The reading is intriguing as if one reads good adventures fiction. The book consists of two parts. The first chapter presents the original consistent paradigm with regard to relationships between the adequacy of some mathematical concepts and physical reality. In particular, the author considers the properties of exponential functions that constitute the foundation of numerous mathematical models, which adequately describe the physical, biological and other types of real phenomena. For instance, the author studies growth and destruction processes in their entirety, as two sides of a single phenomenon, and introduces mathematical concepts that convincingly support his ideas. He commences other interesting concepts, such as a property of rarefaction of discrete spaces, and demonstrates its relation to physical word. It turned out that famous Fermat s Last Theorem has very close relations with physical world, when it is interpreted through the rarefaction property. The book introduces other original concepts and elegant ideas, which the author presents in a well structured and consistent manner, much of which is based on general dialectical vision of natural phenomena. The material is presented in an interesting and entertaining way, sparkled with relevant historical references, facts and original comments. In the second part of the book, the author discovers and proves an important mathematical Theorem. This Theorem and its eight corollaries and one conjecture are also tightly tied to the physical reality and, in fact, represent different aspects of inner working mechanisms governing the evolvement of natural phenomena and Nature in general. The Theorem is stated as follows: "A sum of exponential functions can have a maximum of two points of abscissa intersection, two extremums and two inflection points. Each subsequent derivative of this sum can be equal to zero no more than two times." Behind these concise lines the reader will discover amazing things about the fundamental laws and forces governing Nature and our lives, presented as a rigorous original mathematical study. Although this part requires certain mathematical proficiency, the reader will be rewarded by learning many new important concepts, that the author developed to prove the Theorem, but which have much broader meaning and can be applied in diverse areas of science and technology. In particular, using the Theorem, the author solved a century old enigma how many solutions the IRR equation has. (This equation is a cornerstone of financial mathematics.) Overall, this book is an important, significant research embracing a wide spectrum of real physical problems with regard to their study in entirety by suitable scientific methods, ranging from philosophical doctrines, such as dialectics, to thorough mathematical research of real fundamental mechanisms that govern the evolvement of Nature.

Informazioni sull'autore

Yuri K. Shestopaloff is a professional academic and consultant. He started his academic career as an Applied Mathematician and Engineer-Physicist. He obtained his M.Sc and PhD from prestige Moscow Physical Technological Institute focusing on developing mathematical methods and algorithms for data interpretation. He obtained a Doctor of Sciences degree, the highest academic degree in European countries, for developing advanced mathematical methods for data interpretation and data processing. He worked as Associate Professor, and later Full Professor and Chair at Electrical Engineering Department at Academy of Transport. Simultaneously Yuri held position of Chief Scientist at Institute of Sensor Microelectronics of Russian Academy of Sciences. For the last fourteen years Yuri has done consulting on mathematical methods for data interpretation and mathematical modeling in different areas of science and technology, as well as on computing algorithms. Yuri has published six books and over eighty professional articles in prestige academic and industry journals, with a focus on mathematical methods and algorithms for data interpretation and applied mathematics.