A matrix is similar to Jordan canonical form over the complex field and the rational canonical form over a number field, respectively. In this paper, we further study the rational canonical form of a matrix over any n...A matrix is similar to Jordan canonical form over the complex field and the rational canonical form over a number field, respectively. In this paper, we further study the rational canonical form of a matrix over any number field. We firstly discuss the elementary divisors of a matrix over a number field. Then, we give the quasi-rational canonical forms of a matrix by combining Jordan and the rational canonical forms. Finally, we show that a matrix is similar to its quasi-rational canonical forms over a number field.展开更多
Various aspects of the influence of the quasi-real photons and the Coulomb resonances on the formation of the crosssection of inelastic scattering of high energy electrons on atomic nuclei are investigated. Emiss is t...Various aspects of the influence of the quasi-real photons and the Coulomb resonances on the formation of the crosssection of inelastic scattering of high energy electrons on atomic nuclei are investigated. Emiss is the energy that disappears in the processes of knocking-on of protons in the reactions . A new hypothesis that interprets the origin of the energy losses is proposed. Specific experiments that can confirm or refute this hypothesis are proposed as well. The “regularized” cross-sections of electro-disintegration of nuclei by high-energy electrons are calculated in the framework of the nuclear shell model. It is shown that for the experimental verification of the existence of Coulomb resonances, it is necessary to investigate the processes at relatively small angles of scattering. The peculiarities of numerical methods that are crucial in the investigation of inelastic scattering of high-energy electrons on nuclei in the framework of the nuclear shell model are analyzed in this work as well. The cross-sections of the scattering of high-energy electrons on the angle are calculated. It is shown that the orthogonality of the wave functions of a knocked-on proton in the initial and final states plays an important role in the interpretation of this process.展开更多
文摘A matrix is similar to Jordan canonical form over the complex field and the rational canonical form over a number field, respectively. In this paper, we further study the rational canonical form of a matrix over any number field. We firstly discuss the elementary divisors of a matrix over a number field. Then, we give the quasi-rational canonical forms of a matrix by combining Jordan and the rational canonical forms. Finally, we show that a matrix is similar to its quasi-rational canonical forms over a number field.
文摘Various aspects of the influence of the quasi-real photons and the Coulomb resonances on the formation of the crosssection of inelastic scattering of high energy electrons on atomic nuclei are investigated. Emiss is the energy that disappears in the processes of knocking-on of protons in the reactions . A new hypothesis that interprets the origin of the energy losses is proposed. Specific experiments that can confirm or refute this hypothesis are proposed as well. The “regularized” cross-sections of electro-disintegration of nuclei by high-energy electrons are calculated in the framework of the nuclear shell model. It is shown that for the experimental verification of the existence of Coulomb resonances, it is necessary to investigate the processes at relatively small angles of scattering. The peculiarities of numerical methods that are crucial in the investigation of inelastic scattering of high-energy electrons on nuclei in the framework of the nuclear shell model are analyzed in this work as well. The cross-sections of the scattering of high-energy electrons on the angle are calculated. It is shown that the orthogonality of the wave functions of a knocked-on proton in the initial and final states plays an important role in the interpretation of this process.
