Table of contents

The physical properties of atoms, molecules, and solids in ultrahigh magnetic fields B ≫ 10⁹ G that are believed to exist on the surface of neutron stars are discussed. In these fields, atoms are strongly deformed and elongated along the magnetic field lines; the binding energy and ionizing energy of the atoms are substantially increased and the interatomic interaction is dramatically changed. This strongly modifies the properties of matter at the surface of magnetic neutron stars which are crucial for modelling the pulsar magnetosphere. A scenario for magnetosphere evolution is proposed which suggests free emission for a young pulsar and strong binding of the matter to the surface at a later stage. This later stage is due to strongly bound chains of alternate heavy atoms and light atoms accreted on the surface of the star.

A consistent approach to the image restoration problem is presented, wich does not use Bayesian a priori information. Photon noise is taken into account. The unknown object is treated as a multidimensional set of parameters that have to be statistically estimated in an efficient way. The approach is based on an extended notion of feasible estimate (in the sense of information theory) and on Occam's razor rule of choosing the simplest object which is consistent with the data. Occam's rule is applied by transformation to principal components of the inverse (or maximum likelihood) estimate, which are generated by Fisher's information matrix. The same approach can also be applied to various other inverse problems.

Physico-mathematical aspects of fluid flow in elastic thin-walled tubes have been examined and nonlinear equations describing it have been derived and solved. It is shown that an auto-oscillating flow-regime (flutter) can occur and mathematical models of solitons (pulse waves) based on the Korteveg–de Vries equation and on the modified nonlinear Schroedinger equation have been developed. The appropriateness of using the elastic thin-walled tube model for the description of blood flow in major blood vessels is discussed.

Equations for the massive gravitational field have been derived in the framework of the special theory of relativity on the basis of the geometrization principle. Graviton mass has been shown to be crucial for the elaboration of the relativistic theory of gravitation. According to this theory, a homogeneous and isotropic universe develops in a series of alternating cycles, from high to low density, and cannot be anything other than flat. The theory predicts the presence of a large amount of latent mass in the universe and prohibits the existence of 'black holes'. Also, the theory explains all observable events so far known to occur in the Solar system.

The formulation of the equivalence principle underlying the general theory of relativity is considered. Implications of the equivalence principle are discussed with regard to a charge placed in a locally uniform gravitational field or a uniformly accelerated reference frame (the problem was addressed earlier elsewhere, for example by Ginzburg and co-workers in 1962). The criticism by Logunov and co-workers of the canonical equivalence principle in electrodynamics as presented in the earlier review by Ginzburg and co-workers is shown to be irrelevant.

The de Haas–van Alphen effect and the behaviour of a superlattice in a quantising magnetic field can be described in terms of an electronic topological transition. Near the transition, the thermodynamic stability condition is shown to break down, thus eliminating the 1¹/₂-order transition and giving rise to a first-order phase transition. The latter leads to the formation of diamagnetic Condon domains.