[en] The analytic properties of the dispersion function of a whistler are investigated in the complex frequency plane. It possesses a pole and a branch point at a frequency equal to the minimum value of the electron gyrofrequency along the path of propagation. An integral equation relates the dispersion function to the distribution of magnetospheric electrons along the path and the solution of this equation is obtained. It is found that the electron density in the equatorial plane is very simply related to the dispersion function. A discussion of approximate formulae to represent the dispersion shows how particular terms can be related to attributes of the electron density distribution, and a new approximate formula is proposed. (author)

[en] This review will stress the importance of using image restoration techniques that deal with incomplete, inconsistent, and noisy data and do not introduce spurious features into the processed image. No single image is equally suitable for both the resolution of detail and the accurate measurement of intensities. A good general purpose technique is the maximum entropy method and the basis and use of this will be explained. (orig.)

[en] Several approximate dispersion formulae are in use for analysing whistlers. We show that the theory of whistler propagation puts constraints on possible formulae for this purpose and suggests development of better ones. It is argued that the nose frequency of a whistler is of no importance in accurate analysis, but the minimum electron gyrofrequency on the propagation path can be found. (author)

[en] The subject is discussed under the topic headings:- parameter fitting, inverse problems, practical approaches to the solution of inverse problems, the maximum entropy criterion, and the maximum entropy in practice. (U.K.)

No abstract available

[en] Using numerical techniques to find approximate solutions to the integral equations for diffractive scattering amplitudes in QCD we examine the hypothesis that renormalization group effects convert the continuum spectrum of singularities in the Mellin transform of the scattering amplitude to a discrete spectrum, the leading pole of which can be associated with the exchange of a pomeron. We find that the gaps between the singularities vanish as one approaches the leading singulairty. This signals the existence of either a cut or a dense distribution of poles, neither of which would simulate the expected pomeron exchange. (orig.)

[en] We introduce a finite-lattice technique for calculating the spectrum of fluctuating Bose theories in the continuum limit. The method gives the continuum spectrum to an estimated approx.1% accuracy in 1+1 dimensions using available computer memory. The spectrum of lambdaphi⁴ theory in 1+1 dimensions is studied as a trial application; we find no bound states in the spectrum between m and 2m

[en] A method has been developed for the inversion of the integral equation connecting whistler propagation times with the distribution of electrons along the propagation path. The path is taken to be a geomagnetic dipole field line, but the method assumes no model for the field aligned distribution of electrons. The calculation is based on the Backus-Gilbert technique and represents the electron density distribution as a sum of orthogonal functions, the coefficients of which are computed from the time delays measured on the whistler trace at a series of frequencies. The application of this method to synthetic and observed whistlers has demonstrated the feasibility of obtaining magnetosphere electron densities. At the same time it is found that some of the approximations of conventional whistler analysis (omission of ionic effects and a term of +1 from the phase refractive index) are inadequate, and lead to certain difficulties in the inversion of higher latitude (L => 3) measured whistlers. (author)

[en] The determination of a particle size distribution p(R) from small-angle scattering data is an example of a practical linear inverse problem for which there is no unique solution. It is shown (I) how the maximum entropy algorithm may be used to extract a unique solution which is the most uniform function compatible with the data set and is necessarily positive, and (II) how the Backus-Gilbert method may be used to judge the significance of features in distributions derived from a data set of given statistical accuracy. As an illustration, void size distributions are presented for a sample of irradiated stainless steel which was successively annealed at increased temperatures. (orig.)

[en] Results are presented of a powerful technique for image reconstruction by a maximum entropy method, which is sufficiently fast to be useful for large and complicated images. Although the examples are taken from the fields of radio and X-ray astronomy, the technique is immediately applicable in spectroscopy, electron microscopy, X-ray crystallography, geophysics and virtually any type of optical image processing. Applied to radioastronomical data the algorithm reveals details not seen by conventional analysis, but which are known to exist. (author)