A computationally efficient algorithm derives complex digital transmit and receive ultra-wideband radar and communication waveforms with excellent arbitrary frequency band suppression and range sidelobe minimization. The transmit waveform minimizes a scalar function penalizing weighted spectral energy in arbitrary frequency bands. Near constant power results from another penalty function for deviations from constant power, or constant power is enforced by a phase-only formulation. Next, a least squares solution for the receive waveform minimizes a weighted sum of suppressed band spectral energy and range sidelobes (for pulse and continuous wave operation), with a mainlobe response constraint. Both waveforms are calculated by iterative algorithms whose updates require only linear order in memory and computation, permitting quick calculation of long pulses with thousands of samples.

Constitutive equations for a fluid are worked out to the order corresponding to the Burnett approximation of kinetic theory, using the method of time-dependent correlation functions. These equations describe effects such as normal stresses which are characteristic of non-Newtonian fluids. Coefficients of the various terms are identified as integrals of correlation functions; those associated with linear second-order terms involve space and time moments of the same two-point correlation functions which occur in the first-order theory, while the coefficients of nonlinear terms depend in addition on three-point correlation functions.

A simple kinetic theory model is presented for the calculation of atomic hydrogen escape fluxes from earth induced by charge exchange collisions with hot protons. An analytical expression is derived for the nonthermal flux in terms of atmospheric and dynamical variables. The results, which indicate an increase in the nonthermal flux with decreasing exospheric temperature, are in good agreement with the earlier estimates by Bertaux (1975).

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