Appendix

Arik Melikyan
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Arik Melikyan: Institute for Problems in Mechanics, Russian Academy of Science

Chapter 9 in Generalized Characteristics of First Order PDEs, 1998, pp 291-300 from Springer

Abstract: Abstract Consider a system of m equations with respect to m unknowns y1,…, ym: $$ {F_1}\left( {{x_{1,...,}}{x_{n,}}{y_{1,...,}}{y_m}} \right) = 0 $$ $$ {F_2}\left( {{x_{1,...,}}{x_{n,}}{y_{1,...,}}{y_m}} \right) = 0 $$ 9.1 $$ {F_m}\left( {{x_{1,...,}}{x_{n,}}{y_{1,...,}}{y_m}} \right) = 0 $$ which in vector notations looks like: $$ F\left( {x,y} \right) = 0,x \in {\mathbb{R}^n},y,F \in {\mathbb{R}^m} $$ 9.2 $$ F\left( z \right) = 0,z = \left( {x,y} \right) \in {\mathbb{R}^{n + m}} $$ Here the variables xi,…, x n are parameters, z is the extended vector of n + m components.

Keywords: Implicit Function Theorem; Simple Problem; Smooth Hypersurface; Substitution Rule; Contact Transformation (search for similar items in EconPapers)
Date: 1998
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DOI: 10.1007/978-1-4612-1758-9_10

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