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On Higher Derivatives as Constraints in Field Theory: a Geometric Perspective
Higher Derivative Field Theory Fiber Bundles Jet Bundles
2010/12/15
We formalize geometrically the idea that the (de Donder) Hamiltonian formu-lation of a higher derivative Lagrangian field theory can be constructed under-standing the latter as a first derivative theo...
Higher-order derivatives of the QR and of the real symmetric eigenvalue decomposition in forward and reverse mode algorithmic differentiation
univariate Taylor polynomial arithmetic higher-order derivatives QR decomposition real symmetric eigenvalue decomposition
2010/12/15
We address the task of higher-order derivative evaluation of computer programs that contain QR
decompositions and real symmetric eigenvalue decompositions. The approach is a combination of univariate...
Loss of derivatives for systems of complex vector fields and sums of squares
Loss of derivatives for systems complex vector fields sums of squares
2010/11/29
We discuss, both for systems of complex vector fields and for sums of squares, the phenomenon discovered by Kohn of hypoellipticity with loss of derivatives.MSC: 32W05, 32W25, 32T25
We discuss loss of derivatives for degenerate vector fields obtained from infinite type exponentially non-degenerate hypersurfaces of C2.