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This guide offers a practical introduction to building web applications from scratch, focusing on JavaScript and its widely-used frameworks like Node.js and React.js. It is designed for beginners, providing step-by-step instructions and hands-on projects to help readers gain confidence in web development and understand the core concepts essential for creating dynamic web applications.

Explore the mathematical theory of hyperelliptic functions of the first order with this classic text, written in German. Beginning with basic principles and definitions, the author delves deep into the properties and applications of these functions, culminating in a detailed exposition of transformation theory. A must-have for researchers and students of number theory.

A combined investigation based on numerical analysis and experimental examination of SCRamjet intake geometries is undertaken within the Research Training Group (GRK) 1095/1. It is the purpose of this thesis to focus on the examination of laminar to turbulent transition for hypersonic boundary layers and its influence on the shock wave/boundary layer interaction for intake flows. First, the work presents a summary of the flow phenomena that have to be considered for hypersonic intake flows. It is followed by a general introduction of the research that has been done over the last decades in many different countries. For a better understanding of the conceptional design issues of SCRamjet intakes a review of existing and examined configurations is provided together with an evaluation of the advantages and disadvantages of the different designs. Second, the physical basis of laminar to turbulent transition is explained and the different reasons for this phenomenon are discussed in detail. After this a review of the possible numerical methods for predicting as well as modelling transition is given. Direct Numerical Simulation (DNS) and Large Eddy Simulation (LES) are described in general and their ability of predicting transition for macro three-dimensional industrial applications is pointed out. It is concluded that the only appropriate way of modelling transition for flow problems investigated within this project is using Reynolds-Averaged Navier-Stokes equations (RANS). Therefore, the governing equations are presented together with the closure mechanism to get a complete set of equations to perform simulations of Newtonian fluid flow. Additionally, the time averaged techniques are shortly introduced. Furthermore, the boundary conditions as well as time integration methods are presented. Finally, several transition models for RANS equations are described to give an overview of their applicability to 3D hypersonic transitional flow. The Langtry/Menter transition model is selected and described in detail together with the SST turbulence model that forms the basis for the transition equations. The Langtry/Menter transition model has not been published completely in technical literature when this work was done. Two correlations that describe the transition length and onset are missing. Therefore, this thesis shows how to create own correlations for subsonic as well as super- and hypersonic flow conditions. Due to the topic of this work the focus is put on the correlations for the super- and hypersonic flow regime.

This book is devoted to a generalization of the classical Fredholm theory of operators, namely the Fredholm theory in Banach algebras and paraalgebras. An element in a Banach algebra (or paraalgebra), which is invertible modulo a given ideal, is called a Fredholm element with respect to this ideal and these elements are studied in the present work. In the first chapter the foundations of Fredholm theory in paraalgebras are developed and the following three chapters deal with applications of the abstract theory to interpolation theory, majorized operators and triangular operators. Generally speaking, the examples show that the characterization of abstract Fredholm elements in the various situations lead to properties which fit astonishingly well tu the respective cases and thus characterize a natural class of operators.