The dependences of the magnetic absorption by spheroidal metal nanoparticles on the ratio between the particle curvature radii and the angle between the spheroid symmetry axis and the magnetic field vector of an incident electromagnetic wave are plotted and theoretically analyzed. An interesting result of the research is the growth of the energy absorbed by a spheroidal nanoparticle, as it becomes more oblate.

The problem of light absorption and scattering has been reduced to the solution of a singular integral equation for the complex vector of electric field intensity inside a nanoparticle. The dipole approximation is chosen as the initial one. The results of computing experiments testify to an acceptable agreement between the approach proposed for the consideration of the electric field inside a spherical nanoparticle and the results available for the optical and emission properties of metal nanoclusters. K e y w o r d s: metal nanoclusters, optical properties, integral equation, computing experiment.

On the example of a specific physical problem of noise reduction associated with losses, dark counts, and background radiation, a summary of methods for regularizing ill-posed problems is given in the statistics of photocounts of quantum light. The mathematical formulation of the problem is presented by an operator equation of the first kind. The operator is generated by a matrix with countable elements. In the sense of Hadamard, the problem of reconstructing the number of photons of quantum light is due to the compactness of the operator of the mathematical model. A rigorous definition of a regularizing operator (regularizer) is given. The problem of stable approximation to the exact solution of the operator equation with inaccurately given initial data can be overcome by one of the most well-known regularization methods, the theoretical foundations of which were laid in the works of A.N. Tikhonov. The selection of an important class of regularizing algorithms is based on the construction of a parametric family of functions that are Borel measurable on the semiaxis and satisfy some additional conditions. The set of regularizers in this family includes most of the known regularization methods. The main ones are given in the work.

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