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Ordered algebraic structures --- Algebraic varieties. --- Intersection theory. --- Local rings.

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Differential topology --- Algebraic geometry --- 512.55 --- Rings and modules --- Curves, Algebraic --- Moduli theory --- Surfaces, Algebraic --- Congresses. --- 512.55 Rings and modules

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Evolution equations --- Kinetic theory of gases --- Transport theory --- Congresses.

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These lecture notes by very authoritative scientists survey recent advances of mathematics driven by industrial application showing not only how mathematics is applied to industry but also how mathematics has drawn benefit from interaction with real-word problems. The famous David Report underlines that innovative high technology depends crucially for its development on innovation in mathematics. The speakers include three recent presidents of ECMI, one of ECCOMAS (in Europe) and the president of SIAM.

Mathematical models --- Mathematics --- Industrial applications --- Congresses --- Mathematics - Industrial applications - Congresses. --- Computer science—Mathematics. --- Calculus of variations. --- Numerical analysis. --- System theory. --- Probabilities. --- Thermodynamics. --- Mathematics of Computing. --- Calculus of Variations and Optimal Control; Optimization. --- Numerical Analysis. --- Systems Theory, Control. --- Probability Theory and Stochastic Processes. --- Chemistry, Physical and theoretical --- Dynamics --- Mechanics --- Physics --- Heat --- Heat-engines --- Quantum theory --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Systems, Theory of --- Systems science --- Science --- Mathematical analysis --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima --- Philosophy --- Mathematical models - Congresses.

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Mathematical analysis --- Stochastic processes --- 51 --- Mathematics --- Functional analysis. --- Geometric measure theory. --- Probabilities. --- 51 Mathematics