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The purpose of this book is to provide an introduction to numerical modelling of the ocean and the atmosphere. It originates from courses given at Stockholm University and is intended to serve as a textbook for students in meteorology and oceanography with a background in mathematics and physics. Focus is on numerical schemes for the most commonly used equations in oceanography and meteorology as well as on the stability, precision and other properties of these schemes. Simple equations capturing the properties of the primitive equations employed in models of the ocean and atmosphere will be used. These model equations are solved numerically on a grid by discretisation, the derivatives of the differential equations being replaced by finite-difference approximations. The focus will be on the basic numerical methods used for oceanographic and atmospheric modelling. These models are based on the Navier-Stokes equations (including the Coriolis effect) and a tracer equation for heat in both the atmosphere and ocean and tracer equations for humidity and salt in the atmosphere and ocean, respectively. A coupled atmospheric and oceanic general circulation model represents the core part of an Earth System climate model. The book starts by presenting the most common types of partial differential equations and finite difference schemes used in meteorology and oceanography. Subsequently the limitations of these numerical schemes as regards stability, accuracy, presence of computational modes and accuracy the computationally determined phase speed are discussed. The shallow-water equations are discretised for different spatial grids and friction and diffusion terms are introduced. Hereafter implicit and semi-implicit schemes are discussed as well as the semi-Lagrangian technique. Coordinates for atmospheric as well as oceanic models are presented as well as a highly simplified 3D model. A brief description is given of how some atmospheric general circulation models use spectral methods as "horizontal coordinates". Finally, some "pen-and-paper" theoretical exercises and a number of GFD computer exercises are given.

Numerical analysis.

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Rapid advances in modelling research have created new challenges and opportunities for statisticians. Statistical inference in observational studies and many other emerging fields have motivated statisticians worldwide to develop cutting-edge methods and analytical strategies. The aim of this reprint is to showcase the applications and methodological research in all fields of computational statistics. This reprint will provide a forum for computer scientists, mathematicians, and statisticians working in a variety of areas in statistics, including biometrics, econometrics, data analysis, graphics, and simulation.

Numerical analysis.

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Reverse engineering encompasses a wide spectrum of activities aimed at extracting information on the function, structure, and behavior of man-made or natural artifacts. Increases in data sources, processing power, and improved data mining and processing algorithms have opened new fields of application for reverse engineering. In this book, we present twelve applications of reverse engineering in the software engineering, shape engineering, and medical and life sciences application domains. The book can serve as a guideline to practitioners in the above fields to the state-of-the-art in reverse engineering techniques, tools, and use-cases, as well as an overview of open challenges for reverse engineering researchers.

Numerical analysis. --- Mathematical analysis --- Numerical analysis

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Numerical analysis --- Mathematical optimization

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There are three volumes in this body of work. In Volume 1, we lay the foundation for a general theory of organizing. We propose that organizing is a continuous process of ongoing mutual or reciprocal influence between objects (e.g., human actors) in a field, whereby a field is infinite and connects all the objects in it much like electromagnetic fields influence atomic and molecular charged objects or gravity fields influence inanimate objects with mass such as planets and stars. We use field theory to build what we call the Network Field Model. In this model, human actors are modeled as point-like objects in the field. The influence between and investments in these point-like human objects are explained as energy exchanges (potential and kinetic), which can be described in terms of three different types of capital: financial (assets), human (the individual), and social (two or more humans in a network). This model is predicated on a field theoretical understanding of the world we live in. We use historical and contemporaneous examples of human activity and describe them in terms of the model. In Volume 2, we demonstrate how to apply the model. In Volume 3, we use experimental data to prove the reliability of the model. These three volumes will persistently challenge the reader's understanding of time, position and what it means to be part of an infinite field.

Numerical analysis. --- Field theory (Physics)