The article is devoted to overview of different types of vacuum electronic devices with two or more charged particle beams. There are travelling wave and backward wave tubes, free electron lasers and masers, volume free electron lasers. Two different cases take place in such situation: multiple-beam instability in such devices and multiple-stream instability. In the first case some charged particle beams moves in the system with different velocities. In the second one there are beams with almost equal velocities (streams). Two systems of equations for volume free electron laser with two electron beams are proposed. Some numerical results of VFEL numerical simulation are given and discussed.

Studies of scattering processes at linear colliders of the new generation, when the interaction energy reaches several TeV, make it possible to obtain impressive results. To obtain precise research results, it is important to perform a comparative analysis of the processes of particle interaction on electron-positron, electron-photon and photon-photon beams in order to clarify kinematic features of various processes, as well as possibilities of building a program for studying extended calibration models. The process of production of muon-antimuon, taon-antitaon, and quark-antiquark pairs as a result of high-energy electron and positron annihilation is calculated. A numerical analysis of the differential and total cross sections of the process, as well as the asymmetry of forward-backward departure, has been performed. A study of the ultrarelativistic approximation has been carried out; it has been found that it effectively describes the cross sections of the process. A comparative analysis of the process cross sections for various types of final particles has been carried out.

The expected ATLAS Run 3 data set with time-integrated luminosity of 300 fb−1 and HL–LHC options at the LHC in the diboson channels are used to probe a simple benchmark model with an extended gauge sector, proposed by Altarelli et al. This model accommodates new charged W' and neutral Z' vector bosons with modified trilinear Standard Model gauge couplings, decaying into electroweak gauge boson pairs W Z or W W, where W / Z decay semileptonically. Also presented, from a similar analysis of W' and Z' bosons arising in the EGM, which can decay through W' → lν and Z' → ll , are limits on the W–W' and Z–Z' mixing parameters and the W' and Z' vector boson masses. We present upper limits on the mixing parameters, Z–Z' and W–W', by using the expected Run 3 data and HL–LHC options.

We start with the Stuckelberg tensor system of equations for a boson with spin states S = 1 and S = 0 and fixed intrinsic parity, which is transformed to the matrix form, then generalize this matrix system to the generally covariant case with the use of the tetrad method. This equation is detailed in spherical coordinates in the presence of an external Coulomb field. After separation of the variables we derive the system of 11 radial equations. By diagonalizing the space reflection operator, this system is splitted into two system of four and seven equations for the states with the parities P = (−1) j+1 and P = (−1) j respectively. The system for the states with the parities P = (−1) j+1 leads to the known solution and energy spectrum. The system of seven equations for the states with the parities P = (−1) j is solved for the states with the total angular momentum j = 0 in terms of hypergeometric functions. The system of seven equations for the states with the total angular momenta j = 1, 2, 3, ... turns out to be very complicated, the only nonrelativistic approximation has been studied. The derived nonrelativistic equations are solved in terms of confluent hypergeometric functions, and the corresponding energy spectra are found. In addition, the general form of the nonrelativistic equations for the the Stuckelberg particle is derived in the presence of an arbitrary electromagnetic field.

Energy levels of electrons in semiconductor quantum dots are obtained within the framework of perturbation theory taking into account the Rashba and Dresselhaus spin-orbit interactions and an external magnetic field. The circular quantum dots are simulated by a new smooth confinement potential of a finite depth and width. The dependence of energy levels on a constant uniform magnetic field and potential parameters is presented.

The paper describes methods for theoretical and numerical simulation of the photoacoustic effect that occurs in one-dimensional carbon micro- and nanostructures under an action of pulsed laser radiation. The proposed numerical modeling technique is based on solving the equations of motion of continuous media in the Lagrange form for spatially inhomogeneous media. This model makes it possible to calculate fields of temperature, pressure, density, and velocity of the medium depending on the parameters of laser pulses and characteristics of micro- and nanostructures.

Asymptotic methods are used to study solutions of a modified logistic equation with a delay containing a large parameter. A result on the existence and stability of a relaxation cycle is given.

We show that the new third-order complex nonlinear wave equation, introduced recently by Müller-Hoissen [arXiv:2202.04512], does not pass the Painlevé test for integrability. We find two reductions of this equation, one integrable and one non-integrable, whose solutions jointly cover all solutions of the original equation.

In the unified subquark model of all fundamental particles and forces, the mass of the Higgs boson in the standard model of electroweak interactions (mH) is predicted to be about 2√6 mW / 3 (where mW is the mass of the charged weak boson, W ), which agrees well with the experimental values of about 125 GeV found by the ATLAS and CMS Collaborations at the LHC in 2011. It seems to indicate that the Higgs boson is a composite of the iso-doublet spinor subquark-antisubquark pairs well described by the unified subquark model with either one of subquark masses vanishing or being very small compared to the other. In the unified composite model, there may appear a daughter of the Higgs boson whose mass is predicted to be 2 mW /√3, which agrees well with the experimental values of about 95 GeV for the excess events, found by the LEP experiments and recently by the CMS experiment. This agreement seems to strongly indicate not only the compositeness of the Higgs bosons but also the validity of the unified composite model of all fundamental particles and forces.

Solutions of the spin-weighted spheroidal differential equation are presented in the form of the series involving confluent hypergeometric functions. Relations between solutions with different domains of convergence are derived by considering the confluence of two singularities in an auxiliary equation with four regular singularities. These relations are used to obtain exponentially small corrections to asymptotic expansion of eigenvalues.