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.
Introduction.- Your First Groundwater Model with PMWIN.- Modeling Environment.- The Advective Transport Model PMPATH.- Modeling Tools.- Examples and Applications.- Supplementary Information.
The purpose of this book is to provide a practical approach for IT professionals to acquire the necessary knowledge and expertise in data modeling to function effectively. It begins with an overview of basic data modeling concepts, introduces the methods and techniques, provides a comprehensive case study to present the details of the data model components, covers the implementation of the data model with emphasis on quality components, and concludes with a presentation of a realistic approach to data modeling. It clearly describes how a generic data model is created to represent truly the enterprise information requirements.
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