{"product_id":"9783031012907","title":"Synthesis Lectures on Mathematics \u0026 Statistics","description":"\u003ch1\u003eSynthesis Lectures on Mathematics \u0026amp; Statistics\u003c\/h1\u003e \u003ch2\u003eRamm, Alexander G.\u003c\/h2\u003e \u003cp\u003e\u003c\/p\u003e\u003cp\u003eThe inverse obstacle scattering problem consists of finding the unknown surface of a body (obstacle) from the scattering ����(����;����;����), where ����(����;����;����) is the scattering amplitude, ����;���� ���� ����² is the direction of the scattered, incident wave, respectively, ����² is the unit sphere in the ℝ³ and k \u0026gt; 0 is the modulus of the wave vector. The scattering data is called non-over-determined if its dimensionality is the same as the one of the unknown object. By the dimensionality one understands the minimal number of variables of a function describing the data or an object. In an inverse obstacle scattering problem this number is 2, and an example of non-over-determined data is ����(����) := ����(����;����₀;����₀). By sub-index 0 a fixed value of a variable is denoted.\u003c\/p\u003e\n\u003cp\u003eIt is proved in this book that the data ����(����), known for all ���� in an open subset of ����², determines uniquely the surface ���� and the boundary condition on ����. This condition can be the Dirichlet, or the Neumann, or the impedance type.\u003c\/p\u003e\n\u003cp\u003eThe above uniqueness theorem is of principal importance because the non-over-determined data are the minimal data determining uniquely the unknown ����. There were no such results in the literature, therefore the need for this book arose. This book contains a self-contained proof of the existence and uniqueness of the scattering solution for rough surfaces.\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 2019-06-12\u003c\/p\u003e \u003cp\u003eFormat: Paperback\u003c\/p\u003e \u003cp\u003eISBN-13: 9783031012907\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-3-031-02418-4\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x191cm\u003c\/p\u003e \u003cp\u003ePages: 53\u003c\/p\u003e ","brand":"Morgan \u0026 Claypool","offers":[{"title":"Default Title","offer_id":47531954405516,"sku":"9783031012907","price":26.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9783031012907.jpg?v=1776055663","url":"https:\/\/fh90cf-fv.myshopify.com\/products\/9783031012907","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}