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Quasiconformal Mappings in the Plane and Complex Dynamics
This book comprehensively explores the foundations of quasiconformal mappings in the complex plane, especially in view of applications to complex dynamics.Besides playing a crucial role in dynamical systems these mappings have important applications in complex analysis, geometry, topology, potential theory and partial differential equations, functional analysis and calculus of variations, electrostatics and nonlinear elasticity .The work covers standard material suitable for a one-year graduate-level course and extends to more advanced topics, in an accessible way even for students in an initial phase of university studies who have learned the basics of complex analysis at the usual level of a rigorous first one-semester course on the subject.At the frontier of complex analysis with real analysis, quasiconformal mappings appeared in 1859-60 in the cartography work of A.Tissot, well before the term “quasiconformal” was coined by L.Ahlfors in 1935. The detailed study of these mappings began in 1928 by H.Grötzsch, and L. Ahlfors’ seminal work published in 1935 significantly contributed to their development and was considered for awarding him the Fields Medal in 1936.The theory further evolved in 1937 and 1939 with O. Teichmüller’s contributions, and subsequent advancements are partially covered in this book. Organized into ten chapters with eight appendices, this work aims to provide an accessible, self-contained approach to the subject and includes examples at various levels and extensive applications to holomorphic dynamics.Throughout the text, historical notes contextualize advancements over time.A sequel to the author’s previous book, ‘Complex Analysis and Dynamics in One Variable with Applications,’ also published by Springer, this volume might be suitable for students in mathematics, physics, or engineering.A solid background in basic mathematical analysis is recommended to fully benefit from its content.
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Stein Manifolds and Holomorphic Mappings : The Homotopy Principle in Complex Analysis
This book, now in a carefully revised second edition, provides an up-to-date account of Oka theory, including the classical Oka-Grauert theory and the wide array of applications to the geometry of Stein manifolds. Oka theory is the field of complex analysis dealing with global problems on Stein manifolds which admit analytic solutions in the absence of topological obstructions.The exposition in the present volume focuses on the notion of an Oka manifold introduced by the author in 2009.It explores connections with elliptic complex geometry initiated by Gromov in 1989, with the Andersén-Lempert theory of holomorphic automorphisms of complex Euclidean spaces and of Stein manifolds with the density property, and with topological methods such as homotopy theory and the Seiberg-Witten theory. Researchers and graduate students interested in the homotopy principle in complex analysis will find this book particularly useful.It is currently the only work that offers a comprehensive introduction to both the Oka theory and the theory of holomorphic automorphisms of complex Euclidean spaces and of other complex manifolds with large automorphism groups.
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The Collected Works of Kenneth White, Volume 2 : Mappings: Landscape, Mindscape, Wordscape
Three collections of essays whose aim is to express the cartography and the experience of a live, open worldThese essays all explore Scottish subjects and the wider issues of geopetics.This volume starts with On Scottish Ground by delving into forgotten cultural resources.Ideas of Order at Cape Wrath explores more socio-political considerations before opening out to a larger space of cosmological meditation in The Wanderer and his Charts.
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Food Engineering Automation with Robotics and AI
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When are mappings?
Mappings are typically used in the context of data transformation or conversion, where they define the relationship between elements in two different data structures. Mappings are created during the design phase of a data integration process, where the transformation logic is defined. They are then executed during the data integration process to convert data from the source format to the target format. Mappings are essential for ensuring that data is accurately and efficiently transformed from one system to another.
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What are chained mappings?
Chained mappings refer to a series of mappings or transformations that are applied sequentially to a dataset or input. Each mapping takes the output of the previous mapping as its input, creating a chain of operations. This allows for complex data processing tasks to be broken down into smaller, more manageable steps. Chained mappings are commonly used in data science and machine learning pipelines to preprocess and transform data before feeding it into a model.
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What are linear mappings?
Linear mappings, also known as linear transformations, are functions between vector spaces that preserve the algebraic structure of the spaces. In other words, a linear mapping T: V -> W between vector spaces V and W satisfies two properties: (1) T(u + v) = T(u) + T(v) for all u, v in V, and (2) T(kv) = kT(v) for all k in the field of the vector spaces and all v in V. This means that linear mappings preserve vector addition and scalar multiplication. Linear mappings are fundamental in linear algebra and have applications in various fields such as physics, engineering, and computer science.
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'Functions or not, which mappings?'
Functions are a specific type of mapping where each input has exactly one output. Not all mappings are functions, as some mappings may have multiple outputs for a single input, making them not functions. It is important to distinguish between functions and non-functions when analyzing relationships between variables or solving mathematical problems.
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Industrial Automation and Robotics : Techniques and Applications
This book discusses the radical technological changes occurring due to Industry 4.0, with a focus on offering a better understanding of the Fourth Industrial Revolution.It also presents a detailed analysis of interdisciplinary knowledge, numerical modeling and simulation, and the application of cyber–physical systems, where information technology and physical devices create synergic systems leading to unprecedented efficiency.The book focuses on industrial applications of automation and robotics.It covers recent developments and trends occurring in both computer-aided manufacturing techniques, as well as computer-aided assembly techniques.Robots using embedded systems and artificial intelligence applications are also covered.Industrial Automation and Robotics: Techniques and Applications offers theoretical results, practical solutions, and guidelines that are valuable for both researchers and those working in the area of engineering.
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Robotics and Automation in Healthcare : Advanced Applications
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Technology Innovation in Manufacturing
This text identifies and discusses different technology innovation initiatives (TIIs) such as entrepreneurial capability, technology infrastructure capability, organizational culture and climate, and government initiatives.It further evaluates the relationship between various technology innovation initiatives and manufacturing performances using multi-criteria decision-making techniques such as fuzzy set theory (FST), structural equation modeling (SEM), and analytic hierarchy process (AHP).It will serve as an ideal reference text for graduate students and academic researchers in the field of industrial engineering, manufacturing engineering, mechanical engineering, automotive engineering. This book:• Discusses technology innovation initiatives such as entrepreneurial capability, technology infrastructure capability, and organizational culture. • Highlights technology innovation-strategy model in assisting manufacturing industries for enhancing their performance in today’s competitive environment. • Examines the effect of technology innovation initiatives on the performance of manufacturing industries. • Covers multi-criteria decision-making techniques such as fuzzy set theory, structural equation modeling, and analytic hierarchy process. • Explores the validation of fuzzy-based technology innovation model through structural equation modeling.
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Mediating Innovation Policy Delivery : The Regional Innovation Centres of Ontario
Report cards and academic scholarship have been critical of innovation policy in Canada.But what if these reports have done a profound injustice to the story of knowledge-driven economic reinvention and the actual transformation taking place in the country?Spotlighting what is happening in cities and regions across Ontario, Mediating Innovation Policy Delivery argues that it is far more nuanced and exciting than what has been captured in scorecards and report cards.The book explores the intermediary institutions, the organizational brokers at the frontline of Canada’s innovation race, that are shepherding the process of economic reinvention in regions large and small. The book draws on case studies to explore three central themes.The first is about innovation, innovation policy, and their delivery systems.The second is that of regions as the frontlines of technological and socioeconomic change in the Canadian federation.The third covers the role of intermediary institutions as innovation platforms, highlighting their triumphs and tribulations as they strategically navigate through the shifting currents of change.The book’s main lessons apply not just to Ontario and Canada but also to other industrialized democracies worldwide.Ultimately, the book advances our knowledge of organizational instruments of innovation policy delivery that operate at the strategic interface between the state, market, and society.
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Are functions or not, mappings?
Yes, functions are mappings. A function is a relation between a set of inputs and a set of possible outputs, where each input is related to exactly one output. This can be thought of as a mapping from the input set to the output set, where each input is mapped to a unique output. Therefore, functions can be considered as a type of mapping.
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What are subspaces of mappings?
Subspaces of mappings refer to the spaces that are formed by the collection of all possible outputs of a given mapping function. These subspaces are subsets of the codomain of the mapping and can include vectors, functions, or other mathematical objects. By studying these subspaces, mathematicians can gain insight into the properties and behavior of the mapping function, helping to analyze its structure and relationships with other mathematical objects. Understanding subspaces of mappings is crucial in various fields of mathematics, such as linear algebra, functional analysis, and differential equations.
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What are well-defined mappings?
Well-defined mappings are functions or transformations that are clearly defined and unambiguous. This means that for each input, there is exactly one output, and the mapping is consistent and does not depend on the way the input is represented. In other words, a well-defined mapping produces the same output for the same input, regardless of how the input is described or presented. This ensures that the mapping is reliable and can be consistently applied.
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Are the following mappings functions?
To determine if the following mappings are functions, we need to check if each input has a unique output. 1. Mapping 1: {(1, 2), (2, 3), (3, 2), (4, 5)} This mapping is a function because each input (1, 2, 3, 4) has a unique output (2, 3, 2, 5). 2. Mapping 2: {(1, 2), (2, 3), (3, 2), (4, 2)} This mapping is not a function because the input 4 has two different outputs (2 and 5). Therefore, Mapping 1 is a function, while Mapping 2 is not a function.
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