The main idea of statistical convergence is to demand convergence only for a majority of elements of a sequence. This method of convergence has been investigated in many fundamental areas of mathematics such as: measure theory, approximation theory, fuzzy logic theory, summability theory, and so on. In this monograph we consider this concept in approximating a function by linear operators, especially when the classical limit fails. The results of this book not only cover the classical and statistical approximation theory, but also are applied in the fuzzy logic via the fuzzy-valued operators. The authors in particular treat the important Korovkin approximation theory of positive linear operators in statistical and fuzzy sense. They also present various statistical approximation theorems for some specific real and complex-valued linear operators that are not positive. This is the first monograph in Statistical Approximation Theory and Fuzziness. The chapters are self-contained and several advanced courses can be taught. The research findings will be useful in various applications including applied and computational mathematics, stochastics, engineering, artificial intelligence, vision and machine learning. This monograph is directed to graduate students, researchers, practitioners and professors of all disciplines.
The main idea of statistical convergence is to demand convergence only for a majority of elements of a sequence. This method of convergence has been investigated in many fundamental areas of mathematics such as: measure theory, approximation theory, fuzzy logic theory, summability theory, and so on. In this monograph we consider this concept in approximating a function by linear operators, especially when the classical limit fails. The results of this book not only cover the classical and statistical approximation theory, but also are applied in the fuzzy logic via the fuzzy-valued operators. The authors in particular treat the important Korovkin approximation theory of positive linear operators in statistical and fuzzy sense. They also present various statistical approximation theorems for some specific real and complex-valued linear operators that are not positive. This is the first monograph in Statistical Approximation Theory and Fuzziness. The chapters are self-contained and several advanced courses can be taught. The research findings will be useful in various applications including applied and computational mathematics, stochastics, engineering, artificial intelligence, vision and machine learning. This monograph is directed to graduate students, researchers, practitioners and professors of all disciplines.
Health interpreters and translators often face unpredictable assignments in the multifaceted healthcare setting. This book is based on the very popular international publication (Crezee, 2013) and has been supplemented with commonly asked questions and glossaries in Turkish. Turkish is the home language of a very significant number of (now often elderly) migrants in countries outside of Turkey and this book provides an invaluable resource to those interpreting for these migrants in the healthcare setting. The book will also be invaluable to those interpreting for medical tourists from Turkey travelling to other countries for treatment. In short, this is an exceptionally useful and easily accessible handbook, in particular for interpreters, translators, educators, cultural mediators, health professionals and other practitioners working between Turkish and English - or other languages. Speakers of Turkish represent a rich and diverse range of historical, religious and cultural traditions. This book covers some of those, while also describing the Turkish healthcare system and touching on cultural beliefs and traditional approaches to health. This unique book is an indispensable vade mecum ("go with me") for anyone wishing to navigate language access involving speakers of Turkish in the healthcare setting.
The book describes the direct problems and the inverse problem of the multidimensional Schrödinger operator with a periodic potential. This concerns perturbation theory and constructive determination of the spectral invariants and finding the periodic potential from the given Bloch eigenvalues. The unique method of this book derives the asymptotic formulas for Bloch eigenvalues and Bloch functions for arbitrary dimension. Moreover, the measure of the iso-energetic surfaces in the high energy region is construct and estimated. It implies the validity of the Bethe-Sommerfeld conjecture for arbitrary dimensions and arbitrary lattices. Using the perturbation theory constructed in this book, the spectral invariants of the multidimensional operator from the given Bloch eigenvalues are determined. Some of these invariants are explicitly expressed by the Fourier coefficients of the potential. This way the possibility to determine the potential constructively by using Bloch eigenvalues as input data is given. In the end an algorithm for the unique determination of the potential is given.
This book investigates community interpreting services as a market offering that satisfies the needs of Culturally and Linguistically Diverse (CALD) members of the Australian community, with an additional chapter on the Turkish context. Bringing together the disciplines of interpreting studies and management, the author analyses a variety of challenges which still arise in various fields of interpreting and suggest possible solutions, as well as future directions for other global contexts where changing demographics mean that community-based interpreting is increasingly relevant. Based on interviews with various stakeholders including directors, interpreters, and trainers in the private sector or state-run institutions, the book's main focus is the real experiences of people working on the ground in community interpreting. This book will be of interest to students and scholars of translation, interpreting and migration studies, as well as interpreters and their trainers, and government policy-makers.
This book gives a complete spectral analysis of the non-self-adjoint Schrödinger operator with a periodic complex-valued potential. Building from the investigation of the spectrum and spectral singularities and construction of the spectral expansion for the non-self-adjoint Schrödinger operator, the book features a complete spectral analysis of the Mathieu-Schrödinger operator and the Schrödinger operator with a parity-time (PT)-symmetric periodic optical potential. There currently exists no general spectral theorem for non-self-adjoint operators; the approaches in this book thus open up new possibilities for spectral analysis of some of the most important operators used in non-Hermitian quantum mechanics and optics. Featuring detailed proofs and a comprehensive treatment of the subject matter, the book is ideally suited for graduate students at the intersection of physics and mathematics.
Thank you for visiting our website. Would you like to provide feedback on how we could improve your experience?
This site does not use any third party cookies with one exception — it uses cookies from Google to deliver its services and to analyze traffic.Learn More.