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Kac-Moody Lie algebras 9 were introduced in the mid-1960s independently by V. Kac and R. Moody, generalizing the finite-dimensional semisimple Lie alge­ bras which we refer to as the finite case. The theory has undergone tremendous developments in various directions and connections with diverse areas abound, including mathematical physics, so much so that this theory has become a stan­ dard tool in mathematics. A detailed treatment of the Lie algebra aspect of the theory can be found in V. Kac's book [Kac-90l This self-contained work treats the algebro-geometric and the topological aspects of Kac-Moody theory from scratch. The emphasis is on the study of the Kac-Moody groups 9 and their flag varieties XY, including their detailed construction, and their applications to the representation theory of g. In the finite case, 9 is nothing but a semisimple Y simply-connected algebraic group and X is the flag variety 9 /Py for a parabolic subgroup p y C g.

Kac-Moody algebras. --- Representations of groups. --- Flag manifolds. --- Kac-Moody, Algèbres de --- Représentations de groupes --- Variétés de drapeaux (Géométrie) --- Representations of groups --- Flag manifolds --- Kac-Moody algebras --- Kac-Moody, Algèbres de --- Représentations de groupes --- Variétés de drapeaux (Géométrie) --- Algebraic topology. --- Topological groups. --- Lie groups. --- Algebra. --- Algebraic geometry. --- Group theory. --- Algebraic Topology. --- Topological Groups, Lie Groups. --- Algebraic Geometry. --- Group Theory and Generalizations. --- Groups, Theory of --- Substitutions (Mathematics) --- Algebra --- Algebraic geometry --- Geometry --- Mathematics --- Mathematical analysis --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups --- Groups, Topological --- Continuous groups --- Topology

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Soft Computing Approach to Pattern Classification and Object Recognition establishes an innovative, unified approach to supervised pattern classification and model-based occluded object recognition. The book also surveys various soft computing tools, fuzzy relational calculus (FRC), genetic algorithm (GA) and multilayer perceptron (MLP) to provide a strong foundation for the reader. The supervised approach to pattern classification and model-based approach to occluded object recognition are treated in one framework , one based on either a conventional interpretation or a new interpretation of multidimensional fuzzy implication (MFI) and a novel notion of fuzzy pattern vector (FPV). By combining practice and theory, a completely independent design methodology was developed in conjunction with this supervised approach on a unified framework, and then tested thoroughly against both synthetic and real-life data. In the field of soft computing, such an application-oriented design study is unique in nature. The monograph essentially mimics the cognitive process of human decision making, and carries a message of perceptual integrity in representational diversity. Soft Computing Approach to Pattern Classification and Object Recognition is intended for researchers in the area of pattern classification and computer vision. Other academics and practitioners will also find the book valuable.

Artificial intelligence. --- Computer science. --- Computer vision. --- Machine learning. --- Pattern recognition systems. --- Soft computing. --- Pattern perception --- Soft computing --- Engineering & Applied Sciences --- Computer Science --- Applied Physics --- Pattern perception. --- Design perception --- Pattern recognition --- Pattern classification systems --- Pattern recognition computers --- Image processing. --- Computer Science. --- Image Processing and Computer Vision. --- Signal, Image and Speech Processing. --- Artificial Intelligence (incl. Robotics). --- Cognitive computing --- Electronic data processing --- Computational intelligence --- Form perception --- Perception --- Figure-ground perception --- Computer vision --- Artificial Intelligence. --- AI (Artificial intelligence) --- Artificial thinking --- Electronic brains --- Intellectronics --- Intelligence, Artificial --- Intelligent machines --- Machine intelligence --- Thinking, Artificial --- Bionics --- Cognitive science --- Digital computer simulation --- Logic machines --- Machine theory --- Self-organizing systems --- Simulation methods --- Fifth generation computers --- Neural computers --- Machine vision --- Vision, Computer --- Artificial intelligence --- Image processing --- Pattern recognition systems --- Optical data processing. --- Signal processing. --- Speech processing systems. --- Computational linguistics --- Electronic systems --- Information theory --- Modulation theory --- Oral communication --- Speech --- Telecommunication --- Singing voice synthesizers --- Pictorial data processing --- Picture processing --- Processing, Image --- Imaging systems --- Optical data processing --- Processing, Signal --- Information measurement --- Signal theory (Telecommunication) --- Optical computing --- Visual data processing --- Integrated optics --- Photonics --- Computers --- Optical equipment

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Metallurgy --- corrosie

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