Efficient transfer between science and society is crucial for their future development. The rapid progress of information technology and computer systems offers a large potential and new perspectives for solving complex problems. Mathematical modelling and simulation have become important tools not only in scientific investigations but also in analysing, planning and controlling technological and economic processes. Mathematics, imbedded in an interdisciplinary concept, has become a key technology. The book covers the results of a variety of major projects in industrial mathematics following an initiative of the German Federal Ministry of Education and Research. All projects are collaborations of industrial companies and university-based researchers, and range from automotive industry to computer technology and medical visualisation. In general, the projects presented in this volume prove that new mathematical ideas and methods can be decisive for the solution of industrial and economic problems.

Advances in Mathematics for Industry 4.0 examines key tools, techniques, strategies, and methods in engineering applications. By covering the latest knowledge in technology for engineering design and manufacture, chapters provide systematic and comprehensive coverage of key drivers in rapid economic development. Written by leading industry experts, chapter authors explore managing big data in processing information and helping in decision-making, including mathematical and optimization techniques for dealing with large amounts of data in short periods. - Focuses on recent research in mathematics applications for Industry 4.0 - Provides insights on international and transnational scales - Identifies mathematics knowledge gaps for Industry 4.0 - Describes fruitful areas for further research in industrial mathematics, including forthcoming international studies and research

This volume is the first extensive study of the historical and philosophical connections between technology and mathematics. Coverage includes the use of mathematics in ancient as well as modern technology, devices and machines for computation, cryptology, mathematics in technological education, the epistemology of computer-mediated proofs, and the relationship between technological and mathematical computability. The book also examines the work of such historical figures as Gottfried Wilhelm Leibniz, Charles Babbage, Ada Lovelace, and Alan Turing.

Images or discrete objects, to be analyzed based on digital image data, need to be represented, analyzed, transformed, recovered etc. These problems have stimulated many interesting developments in theoretical foundations of image processing. This coherent anthology presents 27 state-of-the-art surveys and research papers on digital image geometry and topology. It is based on a winter school held at Dagstuhl Castle, Germany in December 2000 and offers topical sections on topology, representation, geometry, multigrid convergence, and shape similarity and simplification.

The book titled "RECENT ADVANCEMENT OF MATHEMATICS IN SCIENCE AND TECHNOLOGY" is an edited book that is based on the latest approaches in the area of Engineering and Technology. Understanding the relationship between humans and technology is key to responsible development and acceptance of future technologies in almost every application field, be it energy, mobility, health, work, living, learning, or entertainment. For making understanding more effective. There are 30 chapters in this book that are contributed by different authors to gain a better understanding. The proposed book will demonstrate the applicability of engineering skills and operations in both the Education and Industrial background of several sectors. This book will be ideal for academicians, Industrialist, professionals, researchers and Scientists. Furthermore it could be used as course material at universities covering subjects like Innovations in engineering, Education, and Products etc.

This book constitutes the refereed proceedings of the Second International Conference on Combinatorial Optimization and Applications, COCOA 2008, held in St. John's, Canada, in August 2008. The 44 revised full papers were carefully reviewed and selected from 84 submissions. The papers feature original research in the areas of combinatorial optimization -- both theoretical issues and and applications motivated by real-world problems thus showing convincingly the usefulness and efficiency of the algorithms discussed in a practical setting.

Today's most commonly used circuit models increasingly tend to lose their validity in circuit simulation due to rapid technological developments, miniaturization and increased complexity of integrated circuits. The starting point of this thesis was to tackle these challenges by refining the critical parts of the circuit by combining circuit simulation directly with distributed device models. The approach set out in this thesis couples partial differential equations for electromagnetic devices - modeled by Maxwell's equations -, to differential-algebraic equations, which describe basic circuit elements including memristors and the circuit's topology. First, Maxwell's equations are spatially discretized and a potential formulation is derived, the coupled system is then formulated as a differential-algebraic equation with a properly stated leading term and analyzed. Topological and modeling conditions are presented to guarantee the tractability index of these differential-algebraic equations to be no greater than two. Finally, local solvability, perturbation results and an algorithm to calculate consistent initializations are derived for a general class of differential-algebraic equations with a properly stated leading term having tractability index-2.

These conference proceedings update the use of computer-based techniques, promoting their general awareness throughout the business management, design, manufacture and operation of railways and other advanced passenger, freight and transport systems.

This book deals with the numerical analysis and efficient numerical treatment of high-dimensional integrals using sparse grids and other dimension-wise integration techniques with applications to finance and insurance. The book focuses on providing insights into the interplay between coordinate transformations, effective dimensions and the convergence behaviour of sparse grid methods. The techniques, derivations and algorithms are illustrated by many examples, figures and code segments. Numerical experiments with applications from finance and insurance show that the approaches presented in this book can be faster and more accurate than (quasi-) Monte Carlo methods, even for integrands with hundreds of dimensions.

Simulation based on mathematical models plays a major role in computer aided design of integrated circuits (ICs). Decreasing structure sizes, increasing packing densities and driving frequencies require the use of refined mathematical models, and to take into account secondary, parasitic effects. This leads to very high dimensional problems which nowadays require simulation times too large for the short time-to-market demands in industry. Modern Model Order Reduction (MOR) techniques present a way out of this dilemma in providing surrogate models which keep the main characteristics of the device while requiring a significantly lower simulation time than the full model. With Model Reduction for Circuit Simulation we survey the state of the art in the challenging research field of MOR for ICs, and also address its future research directions. Special emphasis is taken on aspects stemming from miniturisations to the nano scale. Contributions cover complexity reduction using e.g., balanced truncation, Krylov-techniques or POD approaches. For semiconductor applications a focus is on generalising current techniques to differential-algebraic equations, on including design parameters, on preserving stability, and on including nonlinearity by means of piecewise linearisations along solution trajectories (TPWL) and interpolation techniques for nonlinear parts. Furthermore the influence of interconnects and power grids on the physical properties of the device is considered, and also top-down system design approaches in which detailed block descriptions are combined with behavioral models. Further topics consider MOR and the combination of approaches from optimisation and statistics, and the inclusion of PDE models with emphasis on MOR for the resulting partial differential algebraic systems. The methods which currently are being developed have also relevance in other application areas such as mechanical multibody systems, and systems arising in chemistry and to biology. The current number of books in the area of MOR for ICs is very limited, so that this volume helps to fill a gap in providing the state of the art material, and to stimulate further research in this area of MOR. Model Reduction for Circuit Simulation also reflects and documents the vivid interaction between three active research projects in this area, namely the EU-Marie Curie Action ToK project O-MOORE-NICE (members in Belgium, The Netherlands and Germany), the EU-Marie Curie Action RTN-project COMSON (members in The Netherlands, Italy, Germany, and Romania), and the German federal project System reduction in nano-electronics (SyreNe).