{"product_id":"9789814618632","title":"Neurons: A Mathematical Ignition: A Mathematical Ignition","description":"\u003cp\u003eThis 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.\u003c\/p\u003e\u003cp\u003eThis 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.\u003c\/p\u003e\u003cb\u003eContents:\u003c\/b\u003e\u003cul\u003e\n\u003cli\u003eBasics of Discrete Dynamical Systems\u003c\/li\u003e\n\u003cli\u003eCaianiello's Equations\u003c\/li\u003e\n\u003cli\u003eRotation Numbers\u003c\/li\u003e\n\u003cli\u003eClassification of \u003cb\u003eB\u003c\/b\u003e\n\u003c\/li\u003e\n\u003cli\u003eFarey Series\u003c\/li\u003e\n\u003cli\u003eFurther Investigation of ƒ ∈ \u003cb\u003eB\u003c\/b\u003e\u003csub\u003e∞\u003c\/sub\u003e\n\u003c\/li\u003e\n\u003cli\u003eLimit Sets Ω\u003csub\u003eƒ\u003c\/sub\u003e and ω\u003csub\u003eƒ\u003c\/sub\u003e (χ)\u003c\/li\u003e\n\u003cli\u003ePiecewise Linear Maps\u003c\/li\u003e\n\u003cli\u003eOrbital and Itinerary Functions\u003c\/li\u003e\n\u003cli\u003eFarey Structure\u003c\/li\u003e\n\u003cli\u003eα- and β-Leaves\u003c\/li\u003e\n\u003cli\u003eApproximations to Hecke–Mahler Series\u003c\/li\u003e\n\u003c\/ul\u003e\u003cbr\u003e\u003cb\u003eReadership:\u003c\/b\u003e Graduates and researchers interested in dynamical systems, Farey series, Hecke–Mahler series, Diophantine approximation (irrationality measures, transcendental numbers).\u003cbr\u003e\u003cb\u003eKey Features:\u003c\/b\u003e\u003cul\u003e\n\u003cli\u003eA new method to obtain “good” rational approximations to functions with two variables is provided\u003c\/li\u003e\n\u003cli\u003eA number of mostly original exercises is contained in almost all chapters, together with their detailed solutions in the “Hints and Solutions” section\u003c\/li\u003e\n\u003cli\u003eBasic and useful mathematical notions in “discrete dynamical systems”,  “elementary number theory” and in “rational approximation theory” are explained carefully\u003c\/li\u003e\n\u003c\/ul\u003e","brand":"World Scientific Publishing Company, Incorporated","offers":[{"title":"Default Title","offer_id":47186080006384,"sku":"9789814618632","price":38.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0737\/7593\/9824\/files\/9789814618632_p0.jpg?v=1763691283","url":"https:\/\/shop-qa.barnesandnoble.com\/products\/9789814618632","provider":"Barnes \u0026 Noble (DEV)","version":"1.0","type":"link"}