By Jean A. Dieudonne
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L. a. matematica informa, in modo consapevole e inconsapevole, anche i più semplici e automatici gesti quotidiani. Avreste mai pensato che l. a. matematica ci può aiutare consistent with lavorare a maglia? E che esistono numeri fortunati according to giocare al lotto, enalotto e superenalotto? E che addirittura esiste una formulation consistent with scegliere correttamente los angeles coda al casello?
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Additional info for A Panorama of Pure Mathematics (Pure and Applied Mathematics (Academic Pr))
As a result, the displacement at the present state can be expressed as the sum UK∗ (XJ ,t) = UK0 (XJ ) +UK (XJ ,t). (36) The equation of motion of the material at the present state ∗ ∗ ∗ (δkL + δkM UM,L )],K −ρ0 δkM UM,tt =0 [TKL (37) is derived on the basis of the laws of conservation (22), (23) and expressions (28) and (35). In Eq. (37) ρ0 denotes the density of the material in the natural prestressfree state, and δkL and δkM are Euclidean shifters, which connect the Lagrangian Cartesian coordinates XK and the Eulerian Cartesian coordinates xk .
20. : Leçons sur la Theorie Mathématique de l’Elasticité des Corps Solides. Bachelier, Paris (1852) 21. : A Treatise on the Mathematical Theory of Elasticity. Cambridge University Press (1906) 22. : Internal variables and dissipative structures. J. Non-Equilib. Thermodyn. 15, 173–192 (1990) 23. : Thermomechanics of Plasticity and Fracture. Cambridge University Press (1992) 24. : Material Inhomogeneities in Elasticity. Chapman & Hall, London (1993) 30 Jüri Engelbrecht 25. : Thermodynamics with internal variables, Part I: general concepts, Part II: applications.
The problem (40), (42) is solved under the assumption that the strain evoked in the material by the prestress and wave motion is small but finite and plastic deformations are not allowed. This leads to the idea to solve Eqs. (40) and (42) making use of the perturbation theory. Thus a small parameter | ε | 1 that has the physical meaning of a small strain is introduced. Solutions of equations (40) and (42) are sought assuming that the displacement of the prestressed state can be expressed by the series UK0 = ∞ ∑ m=1 0 (m) ε m UK , (43) 42 Arvi Ravasoo and the displacement due to the wave motion can be expressed by the series ∞ U1 = ∑ ε n U1 (n) (44) .
A Panorama of Pure Mathematics (Pure and Applied Mathematics (Academic Pr)) by Jean A. Dieudonne