In the 19th century, pure mathematics research reached a climax in Germany, and Carl Friedrich Gauss (1777–1855) was an epochal example. August Ferdinand Möbius (1790–1868) was his doctoral student whose work was profoundly influenced by him. In the 18th century, it had been mostly the French school of applied mathematics that enabled the rapid developments of science and technology in Europe. How could this shift happen? It can be argued that the major reasons were the devastating consequences of the Napoleonic Wars in Central Europe, leading to the total defeat of Prussia in 1806. Immediately following, far-reaching reforms of the entire state system were carried out in Prussia and other German states, also affecting the educational system. It now guaranteed freedom of university teaching and research. This attracted many creative people with new ideas enabling the “golden age” of pure mathematics and fundamental theory in physical sciences.

Möbius’ legacy reaches far into today’s sciences, arts, and architecture. The famous one-sided Möbius strip is a paradigmatic example of the ongoing fascination with mathematical topology. This is the first book to present numerous detailed case studies on Möbius topology in science and the humanities. It is written for those who believe in the power of ideas in our culture, experts and laymen alike.

In the 19th century, pure mathematics research reached a climax in Germany, and Carl Friedrich Gauss (1777–1855) was an epochal example. August Ferdinand Möbius (1790–1868) was his doctoral student whose work was profoundly influenced by him. In the 18th century, it had been mostly the French school of applied mathematics that enabled the rapid developments of science and technology in Europe. How could this shift happen? It can be argued that the major reasons were the devastating consequences of the Napoleonic Wars in Central Europe, leading to the total defeat of Prussia in 1806. Immediately following, far-reaching reforms of the entire state system were carried out in Prussia and other German states, also affecting the educational system. It now guaranteed freedom of university teaching and research. This attracted many creative people with new ideas enabling the “golden age” of pure mathematics and fundamental theory in physical sciences.

Möbius’ legacy reaches far into today’s sciences, arts, and architecture. The famous one-sided Möbius strip is a paradigmatic example of the ongoing fascination with mathematical topology. This is the first book to present numerous detailed case studies on Möbius topology in science and the humanities. It is written for those who believe in the power of ideas in our culture, experts and laymen alike.

Understanding the major factors determining the specificity of transmembrane transfer processes in proteins is now a hot topic in molecular bio-science. Advanced electron paramagnetic resonance (EPR) at high magnetic fields is a powerful technique for characterizing the transient states of proteins in action. High-Field EPR Spectroscopy on Proteins and their Model Systems: characterization of Transient Paramagnetic States offers a comprehensive overview of experimental techniques in, and paradigmatic examples of, the application of high-field EPR spectroscopy in biology and chemistry. The book’s focus is on the use of the technique in conjunction with site-specific mutation strategies and advanced quantum-chemical computation methods to reveal protein structure and dynamics. This yields new insights into biological processes at the atomic and molecular level. The theoretical and instrumental background of high-field EPR is described and examples of paradigmatic protein systems, such as photosynthetic reaction centres, are discussed in the light of recent investigations. Aspects of structure dynamics-function relations that are revealed by studying site-specific mutants are highlighted, thereby combining high-field EPR with genetic engineering techniques. The information obtained complements that obtained from protein crystallography, solid-state NMR, infrared and optical spectroscopy. The book documents both background knowledge and results of the latest research in the field. Unique features include comparisons of information content of EPR, ENDOR, Triple resonance, ESEEM and PELDOR taken at different microwave frequencies and magnetic fields. Coherent treatment of the subject by the leading Berlin high-field EPR laboratory covers the theoretical background as well as state-of-art research both in terms of instrumentation and application to biological systems. The book provides an outlook to future developments and references for further reading and is essential reading for postdoctoral scientists, professionals, academics and graduate students working in this field.

In the 19th century, pure mathematics research reached a climax in Germany, and Carl Friedrich Gauss (1777–1855) was an epochal example. August Ferdinand Möbius (1790–1868) was his doctoral student whose work was profoundly influenced by him. In the 18th century, it had been mostly the French school of applied mathematics that enabled the rapid developments of science and technology in Europe. How could this shift happen? It can be argued that the major reasons were the devastating consequences of the Napoleonic Wars in Central Europe, leading to the total defeat of Prussia in 1806. Immediately following, far-reaching reforms of the entire state system were carried out in Prussia and other German states, also affecting the educational system. It now guaranteed freedom of university teaching and research. This attracted many creative people with new ideas enabling the “golden age” of pure mathematics and fundamental theory in physical sciences.

Möbius’ legacy reaches far into today’s sciences, arts, and architecture. The famous one-sided Möbius strip is a paradigmatic example of the ongoing fascination with mathematical topology. This is the first book to present numerous detailed case studies on Möbius topology in science and the humanities. It is written for those who believe in the power of ideas in our culture, experts and laymen alike.

In the 19th century, pure mathematics research reached a climax in Germany, and Carl Friedrich Gauss (1777–1855) was an epochal example. August Ferdinand Möbius (1790–1868) was his doctoral student whose work was profoundly influenced by him. In the 18th century, it had been mostly the French school of applied mathematics that enabled the rapid developments of science and technology in Europe. How could this shift happen? It can be argued that the major reasons were the devastating consequences of the Napoleonic Wars in Central Europe, leading to the total defeat of Prussia in 1806. Immediately following, far-reaching reforms of the entire state system were carried out in Prussia and other German states, also affecting the educational system. It now guaranteed freedom of university teaching and research. This attracted many creative people with new ideas enabling the “golden age” of pure mathematics and fundamental theory in physical sciences.

Möbius’ legacy reaches far into today’s sciences, arts, and architecture. The famous one-sided Möbius strip is a paradigmatic example of the ongoing fascination with mathematical topology. This is the first book to present numerous detailed case studies on Möbius topology in science and the humanities. It is written for those who believe in the power of ideas in our culture, experts and laymen alike.

Understanding the major factors determining the specificity of transmembrane transfer processes in proteins is now a hot topic in molecular bio-science. Advanced electron paramagnetic resonance (EPR) at high magnetic fields is a powerful technique for characterizing the transient states of proteins in action. High-Field EPR Spectroscopy on Proteins and their Model Systems: characterization of Transient Paramagnetic States offers a comprehensive overview of experimental techniques in, and paradigmatic examples of, the application of high-field EPR spectroscopy in biology and chemistry. The book’s focus is on the use of the technique in conjunction with site-specific mutation strategies and advanced quantum-chemical computation methods to reveal protein structure and dynamics. This yields new insights into biological processes at the atomic and molecular level. The theoretical and instrumental background of high-field EPR is described and examples of paradigmatic protein systems, such as photosynthetic reaction centres, are discussed in the light of recent investigations. Aspects of structure dynamics-function relations that are revealed by studying site-specific mutants are highlighted, thereby combining high-field EPR with genetic engineering techniques. The information obtained complements that obtained from protein crystallography, solid-state NMR, infrared and optical spectroscopy. The book documents both background knowledge and results of the latest research in the field. Unique features include comparisons of information content of EPR, ENDOR, Triple resonance, ESEEM and PELDOR taken at different microwave frequencies and magnetic fields. Coherent treatment of the subject by the leading Berlin high-field EPR laboratory covers the theoretical background as well as state-of-art research both in terms of instrumentation and application to biological systems. The book provides an outlook to future developments and references for further reading and is essential reading for postdoctoral scientists, professionals, academics and graduate students working in this field.