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This brief monograph is the first one to deal exclusively with the quantitative approximation by artificial neural networks to the identity-unit operator. Here we study with rates the approximation properties of the "right" sigmoidal and hyperbolic tangent artificial neural network positive linear operators. In particular we study the degree of approximation of these operators to the unit operator in the univariate and multivariate cases over bounded or unbounded domains. This is given via inequalities and with the use of modulus of continuity of the involved function or its higher order derivative. We examine the real and complex cases. For the convenience of the reader, the chapters of this book are written in a self-contained style. This treatise relies on author's last two years of related research work. Advanced courses and seminars can be taught out of this brief book. All necessary background and motivations are given per chapter. A related list of references is given also per chapter. The exposed results are expected to find applications in many areas of computer science and applied mathematics, such as neural networks, intelligent systems, complexity theory, learning theory, vision and approximation theory, etc. As such this monograph is suitable for researchers, graduate students, and seminars of the above subjects, also for all science libraries. |
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Business Process Model and Notation: Third International Workshop, BPMN 2011
The Business Process Model and Notation (BPMN) has seen a huge uptake in
both academia and industry over the past years. It is seen by many as the de
facto standard for business process modeling and has become very popular with
business analysts, tool vendors and end users. As of version 2.0, the BPMN
contains a comprehensive set of... | | Beginning Hibernate
Beginning Hibernate, Third Edition is ideal if you’re experienced in Java with databases (the traditional, or "connected," approach), but new to open-source, lightweight Hibernate, a leading object-relational mapping and database-oriented application development framework.
This book packs in information... | | Maya Secrets of the ProsFeaturing completely original material from a new team of Maya know-it-alls, this second edition of an award-winning book is sure to inform and inspire even the most seasoned Maya user. In this distinctive Maya Press title, a cadre of professionals led by two acclaimed Maya pros, reveal the precious secrets they’ve... |
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