Remark on bilinear operations on tensor fields

Two-Lipschitz operator ideals

By extending linear systems theory to include bilinear functionals, it is shown that the output of any power detector is given by the contraction of two tensor fields: one of which describes the spatio-temporal state of coherence of the incoming radiation, and the other characterizes the partially coherent response of the detector. A detector's coherence tensor is Hilbert–Schmidt, and can be decomposed into a superposition of natural spatio-temporal modes. It follows that any single power detector can be regarded as a number of independent power detectors acting in parallel; each of which is sensitive to radiation in some particular state of coherence; and each of which has a reception pattern that comprises an incoherent superposition of fully coherent beams. The work can be extended to allow the fluctuations in the output, and the correlations between the fluctuations in the outputs of two detectors, say in an array, to be calculated. The model has numerous applications in areas as diverse as pulsed communications systems, THz imaging, astronomical detectors, and insect and animal vision.

A linearlized mass-conservative fourth-order block-centered finite difference method for the semilinear Sobolev equation with variable coefficients

Dependence of solutions of nonsmooth differential-algebraic equations on parameters