Some linear Bäcklund transformations

Dirac's equation is a first-order auto-Bäcklund transformation for the Klein-Gordon equation in 4 variables, this equation being second-order in each of the 4 variables. Here first-order auto-Bäcklund transformations are given for any linear equation of arbitrary (possibly different) order in each of n variables (n arbitrary). This class of equations includes, for example, any of the linearised versions of the KdV hierarchy or equations, and the n-dimensional diffusion equation.     

Estimation of minimum detectable sample concentrations obtained with near and middle infrared detectors for infrared absorption spectrophotometry

An expression is given to allow estimation of the minimum detectable sample concentration of a molecular absorber measured by any infrared spectrophotometer using photon or thermal detectors. Typical plots are given of minimum detectable sample concentration vs. wavelength for a hypothetical absorber with a molar absorptivity of unity and for several different photon and thermal detectors. Such plots, used along with the general expression, are useful for selecting the optimum detector for a given infrared measurement and for estimation of the minimum detectable sample concentration measured by a specific spectrometric system.