Abstract:
The SL(3,C)-covariant 9-dimensional equation for a free 3-spinor particle is transformed into the Dirac-like form (p_A\delta^A - M)\Psi=0. However, the corresponding \delta matrices do not satisfy the Dirac algebra. It is shown that \delta^A lead to a Finslerian generalization of the Duffin-Kemmer algebra. The Appendix contains an explicit realization of the \delta matrices.

Abstract:
The main facts of the geometry of Finslerian 4-spinors are formulated. It is shown that twistors are a special case of Finslerian 4-spinors. The close connection between Finslerian 4-spinors and the geometry of a 16-dimensional vector Finslerian space is established. The isometry group of this space is described. The procedure of dimensional reduction to 4-dimensional quantities is formulated.

Abstract:
The main facts of the geometry of Finslerian 3-spinors are formulated. The close connection between Finslerian 3-spinors and vectors of the 9-dimensional linear Finslerian space is established. The isometry group of this space is described. The procedure of dimensional reduction to 4-dimensional quantities is formulated. The generalized Duffin-Kemmer equation for a Finslerian 3-spinor wave function of a free particle in the momentum representation is obtained. From the viewpoint of a 4-dimensional observer, this 9-dimensional equation splits into the standard Dirac and Klein-Gordon equations.

Abstract:
New mathematical objects called Finslerian N-spinors are discussed. The Finslerian N-spinor algebra is developed. It is found that Finslerian N-spinors are associated with an N^2-dimensional flat Finslerian space. A generalization of the epimorphism SL(2,C) --> SO^\uparrow(1,3) to a case of the group SL(N,C) is constructed.

Abstract:
We have investigated structure and properties of small metal clusters using all-electron ab initio theoretical methods based on the Hartree-Fock approximation and density functional theory, perturbation theory and compared results of our calculations with the available experimental data and the results of other theoretical works. We have systematically calculated the optimized geometries of neutral and singly charged sodium clusters having up to 20 atoms, their multipole moments (dipole and quadrupole), static polarizabilities, binding energies per atom, ionization potentials and frequencies of normal vibration modes. Our calculations demonstrate the great role of many-electron correlations in the formation of electronic and ionic structure of small metal clusters and form a good basis for further detailed study of their dynamic properties, as well as structure and properties of other atomic cluster systems.

Abstract:
We demonstrate that the angular distribution of photoelectrons from a strongly polarizable target exposed to a laser field can deviate noticeably from the prediction of conventional theory. Even within the dipole-photon approximation the profile of distribution is modified due to the action of the field of alternating dipole moment induced at the residue by the laser field. This effect, being quite sensitive to the dynamic polarizability of the residue and to its geometry, depends also on the intensity and frequency of the laser field. Numerical results, presented for sodium cluster anions, demonstrate that dramatic changes to the profile occur for the photon energies in vicinities of the plasmon resonances, where the effect is enhanced due to the increase in the residue polarizability. Strong modifications of the characteristics of a single-photon ionization process can be achieved by applying laser fields of comparatively low intensities $I_0 \sim10^{10}-10^{11}$ W/cm$^2$.

Abstract:
We review the developments made during the last decade in the theory of polarization bremsstrahlung in the non-relativistic domain. A literature survey covering the latest history of the phenomenon is given. The main features which distinguish the polarization bremsstrahlung from other mechanisms of radiation are discussed and illustrated by the results of numerical calculations.

Abstract:
We review the achievements of the theory of polarization bremsstrahlung of relativistic particles, including the case when both colliders have internal structure. The main features which the relativistic effects bring into the problem are discussed and illustrated by the results of numerical calculations.

Abstract:
New mathematical objects called Finslerian N-spinors are discussed. The Finslerian N-spinor algebra is developed. It is found that Finslerian N-spinors are associated with an N^2-dimensional flat Finslerian space. A generalization of the epimorphism SL(2,C) --> O^\uparrow_+(1,3) to a case of the group SL(N,C) is constructed. Particular examples of Finslerian N-spinors for N=2,3 are considered in detail.