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Identification problem for nonlinear beam -- extension for different types of boundary conditions

Radová, Jana, Machalová, Jitka (2023)

Programs and Algorithms of Numerical Mathematics

Identification problem is a framework of mathematical problems dealing with the search for optimal values of the unknown coefficients of the considered model. Using experimentally measured data, the aim of this work is to determine the coefficients of the given differential equation. This paper deals with the extension of the continuous dependence results for the Gao beam identification problem with different types of boundary conditions by using appropriate analytical inequalities with a special...

L 2 -estimates for the d -equation and Witten’s proof of the Morse inequalities

Bo Berndtsson (2007)

Annales de la faculté des sciences de Toulouse Mathématiques

This is an introduction to Witten’s analytic proof of the Morse inequalities. The text is directed primarily to readers whose main interest is in complex analysis, and the similarities to Hörmander’s L 2 -estimates for the ¯ -equation is used as motivation. We also use the method to prove L 2 -estimates for the d -equation with a weight e - t φ where φ is a nondegenerate Morse function.

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