In the present paper we propose a doubly orbitally degenerate narrow-band model with correlated hopping. The peculiarity of the model is taking into account the matrix element of electron-electron interaction which describes intersite hoppings of electrons. In particular, this leads to the concentration dependence of the effective hopping integral. The cases of the strong and weak Hund's coupling are considered. By means of a generalized mean-field approximation the single-particle Green function and quasiparticle energy spectrum are calculated. Metal-insulator transition is studied in the model at different integer values of the electron concentration. With the help of the obtained energy spectrum we find energy gap width and criteria of metal-insulator transition.

In the present paper the ground state of a double orbitally degenerate model at weak intra-atomic interaction is studied using the Green functions method. Beside the diagonal matrix elements of electron-electron interactions the model includes correlated hopping integrals and inter-atomic exchange interaction. The influence of orbital degeneracy with Hund's rule coupling, correlated hopping and inter-atomic direct exchange on the ferromagnetic ordering is investigated. The expressions for ground state energy and magnetization, the criterion of transition from paramagnetic to ferromagnetic ground state as functions of the model parameters are obtained. The obtained results are compared with some experimental data for magnetic materials.

In the present work ferromagnetic ordering in the Hubbard model generalized by taking into account the inter-atomic exchange interaction and correlated hopping in a partially filled band is considered. In the mean-field approximation the ground state energy and condition of ferromagnetic state realization are found by using the Green function technique. The obtained results indicate the important role of correlated hopping.

The use of augmented reality-enabled scenarios in cybersecurity teaching is proposed in the article to respond to new requirements for the rapid adoption of new technologies and profound knowledge of cybersecurity issues by professionals. Implementation of project-type activities based on real cybersecurity issues in application fields of cyber-physical systems is suggested to improve the competence forming. A use-case of agricultural cyber-physical system of systems is discussed as a viable example of augmented reality-enabled prototyping of cybersecurity risk-aware architecture. The necessary steps are analysis of general and business-specific tasks on cybersecurity, creation of a list of competencies, formalized in educational standards and curricula, development of gaming scenarios for the formation of hard and soft skills, development of the scenario management system for AR interfaces. The system using AR tools can be easily adapted to different cybersecurity training activities. Industrial cyber-physical systems may be vulnerable due to insecure wireless connectivity, lack of encryption, inadequate access policy. The project-based learning complex is focused on the implementation of a data acquisition, storage and processing platform for new sensor networks and instruments. Representing all the diverse information on different layers will be greatly improved by use of the developed holographic projection AR tools.

The electron correlations in narrow energy bands are examined within the framework of the modified form of polar model. This model permits to analyze the effect of strong Coulomb correlation, inter-atomic exchange and correlated hopping of electrons and explain some peculiarities of the properties of narrow-band materials, namely the metal-insulator transition with an increase of temperature, nonlinear concentration dependence of Curie temperature and peculiarities of transport properties of electronic subsystem. Using a variant of generalized Hartree-Fock approximation, the single-electron Green's function and quasi-particle energy spectrum of the model are calculated. Metal-insulator transition with the change of temperature is investigated in a system with correlated hopping. Processes of ferromagnetic ordering stabilization in the system with various forms of electronic DOS are studied. The static conductivity and effective spin-dependent masses of current carriers are calculated as a function of electron concentration at various DOS forms. The correlated hopping is shown to cause the electron-hole asymmetry of transport and ferromagnetic properties of narrow band materials.