Overview
- For the first time the theory of hyper-random phenomena developed by the author is presented in English, in an extensive and coherent way
- Broadens our understanding of statistical stability
- An original contribution to measurement theory
Part of the book series: Mathematical Engineering (MATHENGIN)
Access this book
Tax calculation will be finalised at checkout
Other ways to access
Table of contents (21 chapters)
-
Front Matter
-
Features of the Phenomenon of Statistical Stability
-
Front Matter
-
-
Experimental Study of the Statistical Stability Phenomenon
-
Front Matter
-
-
The Theory of Hyper-random Phenomena
-
Front Matter
-
-
Principles of the Mathematical Analysis of Divergent and Many-Valued Functions
-
Front Matter
-
Keywords
About this book
This monograph investigates violations of statistical stability of physical events, variables, and processes and develops a new physical-mathematical theory taking into consideration such violations – the theory of hyper-random phenomena. There are five parts. The first describes the phenomenon of statistical stability and its features, and develops methods for detecting violations of statistical stability, in particular when data is limited. The second part presents several examples of real processes of different physical nature and demonstrates the violation of statistical stability over broad observation intervals. The third part outlines the mathematical foundations of the theory of hyper-random phenomena, while the fourth develops the foundations of the mathematical analysis of divergent and many-valued functions. The fifth part contains theoretical and experimental studies of statistical laws where there is violation of statistical stability.
The monograph should be of particular interest to engineers and scientists in general who study the phenomenon of statistical stability and use statistical methods for high-precision measurements, prediction, and signal processing over long observation intervals.
Authors and Affiliations
About the author
He worked at the Kiev Research Institute for Hydroequipment, participating in a number of developmental and research programmes. He was in charge of algorithms for several sonar systems, was a research adviser for two scientific expeditions to the Pacific to study hydroacoustic signals, was the first deputy to the Chief Designer and Chief Designer of the sonar complexes.
Since 1993 he has been working at the Institute of Mathematical Machines and Systems Problems, National academy of Sciences of Ukraine, as Principal Scientist and Deputy Director for Research.
Igor I. Gorban is the author of more than 200 scientific publications and several books devoted to:
• the theory of space-time processing of hydroacoustic signals under complex dynamic conditions,
• the theory of fast multi-channel processing of hydroacoustic signals, and
• the physical-mathematical theory of hyper-random phenomena that takes into account violations of statistical stability.
Bibliographic Information
Book Title: The Statistical Stability Phenomenon
Authors: Igor I. Gorban
Series Title: Mathematical Engineering
DOI: https://doi.org/10.1007/978-3-319-43585-5
Publisher: Springer Cham
eBook Packages: Engineering, Engineering (R0)
Copyright Information: Springer International Publishing AG 2017
Hardcover ISBN: 978-3-319-43584-8Published: 25 October 2016
Softcover ISBN: 978-3-319-82863-3Published: 28 June 2018
eBook ISBN: 978-3-319-43585-5Published: 17 October 2016
Series ISSN: 2192-4732
Series E-ISSN: 2192-4740
Edition Number: 1
Number of Pages: XXXIX, 322
Number of Illustrations: 108 b/w illustrations, 7 illustrations in colour
Additional Information: Originally published by Naukova Dumka Publishing House of National Academy of Sciences of Ukraine, Kiev, 2014
Topics: Mathematical and Computational Engineering, Measurement Science and Instrumentation, Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences, Complex Systems, Mathematical Applications in the Physical Sciences, Statistical Physics and Dynamical Systems