Spatial structure of perturbations and origin of galactic rotation in fluctuation theory

We derive the magnitude of fluctuations in total synchrotron intensity in the Milky Way, both from observations and from theory under various assumption about the relation between cosmic rays and interstellar magnetic fields Given the relativ e magnitude of the fluctuations in the Galactic magnetic field suggested by the Faraday rotatio n and polarization data, the observations are inconsistent with local energy equipartiti on between cosmic rays and magnetic fields Our analysis of synchrotron fluctuations suggests th at the distribution of cosmic rays is nearly uniform at scales of order 100pc, in contrast to that of the interstellar magnetic field A conservative upper limit on the relative variations in the cosmic ray number density is 02‐04 at the scales of order 100 pc Our results are consist ent with a mild anticorrelation between cosmic-ray and magnetic energy densities at these scales Energy equipartition between cosmic rays and magnetic fields still may hold, but at scales e xceeding 1 kpc

An observational test for correlations between cosmic rays and magnetic fields

The application of identification methods in the U.S.S.R.-A survey

Monitoring of Fine Particulate Air Pollution as a Factor in Urban Planning Decisions

An optimal control problem with quadratic cost functional for a linear stochastic system with pointwise and distributed time delays in the state variable is considered. The case where the cost functional does not contain a control cost is treated. The latter means that the problem under consideration is a singular optimal control problem. This control problem is associated with a new optimal control problem for the same equation of dynamics. The cost functional in this new problem is the sum of the original cost functional and an integral of the square of the control with a small positive weighting coefficient. Thus, the new problem is a regular optimal control problem. Moreover, it is a cheap control problem. By using the control optimality conditions, the solution of this problem is reduced to solution of the set of four equations: one Riccati-type matrix ordinary differential equation, two Riccati-type matrix partial differential equations of the first order, and one trivial scalar ordinary differentia...

P. Whittle

Papers

Applied Methods of the Theory of Random Functions. By A. A. Sveshnikov. Pp. ix, 321. 1966. (Pergamon.)