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Titlebook: Nonlinear PDEs, Their Geometry, and Applications; Proceedings of the W Radosław A. Kycia,Maria Ułan,Eivind Schneider Book 2019 Springer Nat

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Differential Invariants in Thermodynamics is locally determined by the information gain function. We describe the algebra of rational differential invariants of the information gain function under the action of two different Lie groups appearing naturally as a result of measuring random vectors, and we discuss our results in the context of
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Weak Inverse Problem of Calculus of Variations for Geodesic Mappings and Relation to Harmonic Mapsints of the energy functional, on the other hand, geodesic mappings are defined in a more general setting (manifolds with affine connections). Using the well-established formalism of calculus of variations on fibred manifolds, we solve the weak inverse problem for the equation of geodesic mappings a
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Integrability of Geodesics of Totally Geodesic Metrics—hyperbolic and elliptic ones—described in [V.V. Lychagin, V. Yumaguzhin, ., Anal. Math. Phys. 1664-235X 1–9 (2016)] is presented. The cases when geodesic equations are integrable are identified. A similar analysis is performed for the model coupled to electromagnetism described in [V.V. Lychagin, V
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Radosław A. Kycia,Maria Ułan,Eivind SchneiderCollects talks given at the Summer School Wisla 18: Nonlinear PDEs, Their Geometry, and Applications in Wisla, Poland.Presents recent research the applications of nonlinear differential equations to p
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978-3-030-17030-1Springer Nature Switzerland AG 2019
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Contact Geometry, Measurement, and ThermodynamicsThis paper has a long story and goes back to the middle of 80s but its recent version is based on the series of lectures I gave during the Summer school Wisla 18.
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