Angles between subspaces and their tangents

Principal angles between subspaces (PABS) (also called canonical angles) serve as a classical tool in mathematics, statistics, and applications, e.g., data mining. Traditionally, PABS are introduced via their cosines. The cosines and sines of PABS are commonly defined using the singular value decomposition. We utilize the same idea for the tangents, i.e., explicitly construct matrices, such that their singular values are equal to the tangents of PABS, using several approaches: orthonormal and non-orthonormal bases for subspaces, as well as projectors. Such a construction has applications, e.g., in analysis of convergence of subspace iterations for eigenvalue problems.Comment: 15 pages, 1 figure, 2 tables. Accepted to Journal of Numerical Mathematic

Electronic structure, magnetic and optical properties of intermetallic compounds R2Fe17 (R=Pr,Gd)

In this paper we report comprehensive experimental and theoretical investigation of magnetic and electronic properties of the intermetallic compounds Pr2Fe17 and Gd2Fe17. For the first time electronic structure of these two systems was probed by optical measurements in the spectral range of 0.22-15 micrometers. On top of that charge carriers parameters (plasma frequency and relaxation frequency) and optical conductivity s(w) were determined. Self-consistent spin-resolved bandstructure calculations within the conventional LSDA+U method were performed. Theoretical interpetation of the experimental s(w) dispersions indicates transitions between 3d and 4p states of Fe ions to be the biggest ones. Qualitatively the line shape of the theoretical optical conductivity coincides well with our experimental data. Calculated by LSDA+U method magnetic moments per formula unit are found to be in good agreement with observed experimental values of saturation magnetization.Comment: 16 pages, 5 figures, 1 tabl

The influence of prenatal environmental conditions on the weight of newborn domestic pigs

The weight of newborn piglets in domestic pigs depends on the maternal environment. Using an original algorithm based on the comparison of the coefficients of correlation between the half-nests (the same average genotype and the same conditions of the embryonic environment) and the twin sockets (the same genotype, different conditions of the embryonic environment), it was possible to estimate the relative contribution of the various components to the weight of the newborn in the domestic pigs. Our investigation found that the relative contribution of environmental conditions during prenatal development into newborn weight variation is equal to 0.4717, the contribution of genotypic component is 0.4032; the contribution of interaction between environmental conditions and ambivalence of the “genotype–phenotype” relationships is 0.0846, indeterminacy of phenotypic realization of the littermate’s genotypes is 0.0405. Maternal resource plays the main role amongst factors forming the environmental conditions of prenatal development. The gene pool will remain unchanged in any number of generations, despite a change in the population parameters of the trait. In principle, it can be assumed that when a population reaches a certain level, when the mean value of the trait and the gene pool are optimal (the selection pressure vectors are mutually balanced), selection becomes less effective in transforming the average phenotype than changing environmental conditions. Obviously, therefore, livestock maintenance and feeding are paid as much attention as breeding, and breeds of farmed animals are zoned

RESEARCH OF LINEAR AND NONLINEAR PROCESSES AT FEMTOSECOND LASER RADIATION PROPAGATION IN THE MEDIUM SIMULATING THE HUMAN EYE VITREOUS

The paper deals with mathematical model of linear and nonlinear processes occurring at the propagation of femtosecond laser pulses in the vitreous of the human eye. Methods of computing modeling are applied for the nonlinear spectral equation solution describing the dynamics of a two-dimensional TE-polarized radiation in a homogeneous isotropic medium with cubic fast-response nonlinearity without the usage of slowly varying envelope approximation. Environments close to the optical media parameters of the eye were used for the simulation. The model of femtosecond radiation propagation takes into account the process dynamics for dispersion broadening of pulses in time and the occurence of the self-focusing near the retina when passing through the vitreous body of the eye. Dependence between the pulse duration on the retina has been revealed and the duration of the input pulse and the values of power density at which there is self-focusing have been found. It is shown that the main mechanism of radiation damage with the use of titanium-sapphire laser is photoionization. The results coincide with those obtained by the other scientists, and are usable for creation Russian laser safety standards for femtosecond laser systems