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This new volume shows how it is possible to further develop and essentially extend the theory of operators in infinite-dimensional vector spaces, which plays an important role in mathematics, physics, information theory, and control theory. The book describes new mathematical structures, such as hypernorms, hyperseminorms, hypermetrics, semitopological vector spaces, hypernormed vector spaces, and hyperseminormed vector spaces. It develops mathematical tools for the further development of functional analysis and broadening of its applications.
CONTENTS: About the Authors / Editors: Mark Burgin, PhD University of California, Los Angeles, USA; formerly, Head, Assessment Laboratory, Research Center of Science, National Academy of Sciences of Ukraine Dr. Mark Burgin received his MA and PhD in mathematics from Moscow State University, which was one of the best universities in the world at that time, and Doctor of Science in logic and philosophy from the National Academy of Sciences of Ukraine. He was a Professor at several institutions, including the Institute of Education, Kiev; International Solomon University, Kiev; Kiev State University, Ukraine; as well as Head of the Assessment Laboratory in the Research Center of Science at the National Academy of Sciences of Ukraine. Currently he is working at the University of California, Los Angeles, USA. Dr. Burgin is a member of the New York Academy of Sciences and an Honorary Professor of the Aerospace Academy of Ukraine. Dr. Burgin is also a member of the Science Advisory Committee at Science of Information Institute, Washington, DC. Dr. Burgin is doing research, has publications, and taught courses in various areas of mathematics, artificial intelligence, computer science, information sciences, system theory, logic, psychology, social sciences, and methodology of science. He originated such theories as system theory of time, general information theory, theory of named sets, hyperprobability theory, and neoclassical analysis (in mathematics) and has made essential contributions to such fields as foundations of mathematics, theory of algorithms and computation, theory of knowledge, theory of intellectual activity, and complexity studies. He was the first to discover non-diophantine arithmetics; the first to axiomatize and build mathematical foundations for negative probability used in physics, finance, and economics; and the first to explicitly overcome the barrier posed by the Church-Turing Thesis. Dr. Burgin has authored and co-authored more than 500 papers and 21 books, including Structural Reality (2012), Theory of Named Sets (2011), Theory of Information (2010), Neoclassical Analysis: Calculus Closer to the Real World (2008), Super-recursive Algorithms (2005), On the Nature and Essence of Mathematics (1998), Intellectual Components of Creativity (1998), Fundamental Structures of Knowledge and Information (1997), The World of Theories and Power of Mind (1992), and Axiological Aspects of Scientific Theories (1991). Dr. Burgin has also edited eight books. |
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AAP WELCOMES PROF. MOHAMMED KUDDUS, PhD, AS AAP’S NEW ACQUISITIONS EDITOR for books on biotechnology, enzymology, microbiology, bioinformatics, bioremediation, biomedical technology, value-added products etc. Dr. Kuddus is Head of the Department of Biochemistry at the College of Medicine, University of Hail, Kingdom of Saudi Arabia. He is listed in Elsevier/Stanford University World’s Top 2% Scientists. He seeks book proposals from potential editors to consider for publication with Apple Academic Press. Contact: kuddus@appleacademicpress.com for more information. AAP welcomes Dr. Maulin P. Shah as AAP’s new acquisitions editor for books on Applied Microbiology, Environmental Biotechnology and Waste Management. 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Dr. Kulkarni is Adjunct Professor, Faculty of Business, Victorian Institute of Technology, Melbourne, Australia; and Adjunct Professor, Centre of Research Outcome and Impact, Chitkara University, Punjab, India. You can reach him at Email: srkulkarni21@gmail.com for more information. New Book Series: AAP Series on Waste Biomass Valorization will explore the transformation of biomass resources into valuable products, addressing the growing need for sustainable alternatives to fossil fuels and non-renewable resources. For more information and to propose a book, please visit: Click here Congratulations to Hafiz Ansar Rasul Suleria, PhD, for receiving the Dean’s Award for Excellence in Research from the University of Melbourne, Australia, in recognition for his exceptional performance and strong commitment to advanced research in food science. Dr. Suleria is editor of AAP’s book series Innovations in Plant Science for Better Health: From Soil to Fork. 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