Neurons:A Mathematical Ignition (Series on Number Theory and Its Applications) by Masayoshi Hata 0000-00-00 00:00:00

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by Masayoshi Hata
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Neurons:A Mathematical Ignition (Series on Number Theory and Its Applications) by Masayoshi Hata
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Masayoshi Hata
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This unique volume presents a fruitful and beautiful mathematical world hidden in Caianiello's neuronic equations, which describe the instantaneous behavior of a model of a brain or thinking machine. The detailed analysis from a viewpoint of "dynamical systems", even in a single neuron case, enables us to obtain amazingly good rational approximations to the Hecke-Mahler series with two variables. Some interesting numerical applications of our rational approximations are also discussed.

This book is fundamentally self-contained and many topics required in it are explained from the beginning. Each chapter contains a number of instructive and mostly original exercises at various levels.

Readership: Graduates and researchers interested in dynamical systems, Farey series, Hecke Mahler series, Diophantine approximation (irrationality measures, transcendental numbers).

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