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The fusion of algebra, analysis and geometry, and their application to real world problems, have been dominant themes underlying mathematics for over a century. Geometric algebras, introduced and classified by Clifford in the late 19th century, have played a prominent role in this effort, as seen in the mathematical work of Cartan, Brauer, Weyl, Chevelley, Atiyah, and Bott, and in applications to physics in the work of Pauli, Dirac and others. One of the most important applications of geometric algebras to geometry is to the representation of groups of Euclidean and Minkowski rotations. This aspect and its direct relation to robotics and vision will be discussed in several chapters of this multi-authored textbook, which resulted from the ASI meeting. Moreover, group theory, beginning with the work of Burnside, Frobenius and Schur, has been influenced by even more general problems. As a result, general group actions have provided the setting for powerful methods within group theory and for the use of groups in applications to physics, chemistry, molecular biology, and signal processing. These aspects, too, will be covered in detail. With the rapidly growing importance of, and ever expanding conceptual and computational demands on signal and image processing in remote sensing, computer vision, medical image processing, and biological signal processing, and on neural and quantum computing, geometric algebras, and computational group harmonic analysis, the topics of the book have emerged as key tools. The list of authors includes many of the world's leading experts in the development of new algebraic modeling and signal representation methodologies, novel Fourier-based and geometric transforms, and computational algorithms required for realizing the potential of these new application fields.
As urban areas keep growing, water infrastructure ages, and the requirements on environmental protection become more rigorous, there is a continual need for upgrading water pollution control facilities and restoring degraded urban waters. Such issues are addressed in this book by focusing on five major topics: (a) Upgrading stormwater management facilities, (b) Retrofitting / upgrading combined sewer overflow (CSO) facilities, (c) Optimising/upgrading sewage treatment plant performance, (d) Urban stream restoration, and (e) Challenges in restoring urban environment. Each chapter contains some overview papers followed by research or case study papers. Besides presentations of new approaches and accomplishments in the field of upgrading and restoration, several papers provide analysis of vast needs in this field in several countries of Central and Eastern Europe, which either recently joined the European Union (EU) or are preparing for accession, and need to comply with the existing EU directives dealing with environmental protection. As such, this book will be of primary interest to researchers and university lecturers dealing with environmental upgrading and restoration, environmental planners from all levels of government, municipal engineers and politicians, and finally the private industry representatives (consultants, private utilities and environmental technology suppliers) searching for new business opportunities among the new or aspiring members of EU.