We consider a linear control system with an almost periodic matrix of the coefficients. The control has the form of feedback that is linear on the phase variables. It is assumed that the feedback coefficient is almost periodic and its frequency modulus, i. e. the smallest additive group of real numbers, including all the Fourier exponents of this coefficient, is contained in the frequency modulus of the coefficient matrix. The following problem is formulated: choose a control from an admissible set for which the system closed by this control has almost periodic solutions with the frequency spectrum (a set of Fourier exponents) containing a predetermined subset, and the intersection of the frequency modules of solution and the coefficient matrix is trivial. The problem is called as the control problem of the spectrum of irregular oscillations (asynchronous spectrum) with the target set of frequencies. At present, this problem has been studied only in a very special case, when the average value of the almost periodic coefficients matrix of the system is zero. In the case of nontrivial averaging, the question remains open. In the paper, a sufficient condition is obtained under which the control problem of the asynchronous spectrum of linear almost periodic systems with diagonal averaging of the coefficient matrix has no solution.

The concept of (κ,τ)-regular vertex set appeared in 2004. It was proved that the existence of many classical combinatorial structures in a graph like perfect matchings, Hamiltonian cycles, effective dominating sets, etc., can be characterized by (κ,τ)-regular sets the definition whereof is equivalent to the determination of these classical combinatorial structures. On the other hand, the determination of (κ,τ)-regular sets is closely related to the properties of the main spectrum of a graph. This paper generalizes the well-known properties of (κ,κ)-regular sets of a graph to arbitrary (κ,τ)-regular sets of graphs with an emphasis on their connection with classical combinatorial structures. We also present a recognition algorithm for the Hamiltonicity of the graph that becomes polynomial in some classes of graphs, for example, in the class of graphs with a fixed cyclomatic number.

Herein, we have proven a Fink – Wood conjecture that if Oʹ is the closure of some orientation set O, then a set is a directed O-halfspace if and only if it is a directed Oʹ-halfspace.

Herein, an algorithm is proposed for calculating the Cartesian coordinates of a bilayer nanoscroll rolled from a zigzag graphene nanoribbon (nzGNR) and a commensurate boron nitride nanoribbon (nzBNNR) into two Archimedean spirals. The distance between the layers and the inner radius of the nanoscroll, the length and width of nzGNR, and the length of the chemical bond between the atoms in the ribbon are the parameters used in the algorithm. It is assumed that these parameters are equal both for nzGNR and nzBNNR.

Herein, a spin 1 particle with anomalous magnetic moment in an external Coulomb field is studied. We start with the relativistic tensor system of the Proca type in Cartesian coordinates. In these equations the Γ parameter is present related to an additional characteristic of the particle. In the case of an external magnetic field, it is interpreted as an anomalous magnetic moment. In the presence of an external electric field, additional interaction terms are presented as well; moreover, the terms of the first and second orders in parameter Γ appear. The case of an external Coulomb field is considered in detail. In the nonrelativistic approximation a Pauli type equation is obtained. In the nonrelativistic equation the separation of the variables with the use of spherical vectors is realized. One separate 2-nd order differential equation is found, in which additional interaction terms are missing. Besides, we derive systems of two coupled 2-nd order equations wherein linear and quadratic in parameter Γ interaction terms are presented. Previously, another approach was developed for analyzing the vector particle with anomalous magnetic moment. It was based on the use of tetrad formalism and separation of the variables in the Duffin – Kemmer equation with the help of the Wigner function. The nonrelativistic approximation was performed directly in the system of radial equations. Besides, previously formal Frobenius type solutions for an arising 4-th order differential equation were constructed; however, physically interpretable energy spectra were not found. We have proved that the radial equations derived by different methods are the same up to a simple liner transformation over two radial functions. In this paper, we have obtained a simpler 4-th order equation, the construction of Frobenius solutions becomes technically easier, but physical energy spectra are not found either.

. The problem of real bremsstrahlung calculation is considered using the modern methods of regularization of divergencies. In particular, we calculate soft photon bremsstrahlung in the most general form using the method of dimensional regularization of infrared divergences. The general calculation algorithm of hard photon bremsstrahlung is described. It is shown that the contribution of hard bremsstrahlung can be separated into the finite and divergent parts. The divergent part can be factorized with the contribution of the initial process in the Born approximation. It is shown that a good choice of kinematic variables makes an analytic covariant calculation of the divergent part of the hard bremsstrahlung possible. In a particular case, an algorithm for determining the kinematic constraints on the invariants is described. A numerical analysis of the radiative corrections for gauge bosons production processes in the case of electron-photon collisions is performed. It is discovered that the contribution of the finite part of bremsstrahlung at high collision energies reaches 20 per cent and must be taken into account in calculations of radiative corrections. The results obtained can be used in various calculations, including covariant ones, performed in the context of confirmation of the Standard Model theoretical predictions or searching for manifestations of alternative gauge models.

The cross section of the process e+ e– → π+ π– π0 was measured with the CMD-3 detector at the electron-positron collider VEPP-2000 in the energy region from 750 MeV to 800 MeV in c.m.s. This measurement was based on the data collected in 2013 and related to an integrated luminosity of about 7.8 pb–1. The procedure for obtaining the Born cross section and determining the parameters of the ω-meson was worked out. The preliminary ω-meson parameters mω = 782.70 ± 0.02 ± ± 0.11 MeV, Гω = 8.74 ± 0.05 ± 0.22 MeV, σ0(ω → π+ π– π) = 1545 ± 4 ± 39 nb were obtained. The results were compared with previous data and proven to demonstrate a good agreement with them.

In this paper, we present the results of the study of the statistics of pulse energy fluctuations in a Raman laser under optical pump by the multimode nanosecond pulses. A system of coupled differential equations for slowly varying envelopes of the pump field and first three Stokes lines was integrated numerically with taking into account spatial inhomogeneity of the pump beam, spontaneous noise, and optical feedback. Data of the numerical simulation revealed a sharp increase in the fluctuation amplitude in the nonlinear regime of Raman frequency conversion when the optical length of the Raman cavity was matched with the cavity length of the multimode pump laser. At a mean 1st Stokes conversion efficiency of 3.5–3.8 %, the calculations showed an increase in the coefficient of variation (CV) of a random value from 9 % to 118 %. In the linear regime of Raman frequency conversion, when the conversion efficiency was 0.2–0.03 %, a further increase in the CV value up to 270–500 % was predicted. It is also numerically shown that the fluctuation statistics under the conditions of the cavity length matching is essentially non-Gaussian and described by the L-type probability density distributions (PDDs) with long tails and maxima located near zero. The numerical data were quantitatively confirmed by an experiment for a Raman laser on a barium nitrate crystal operated near the Raman threshold, when the 1st Stokes conversion efficiency did not exceed 0.3 %. A Raman cavity was formed by two flat mirrors providing a double-pass pump configuration. The Raman laser was excited by the linearly polarized frequency-doubled radiation of a Q-switched Nd:YAG laser generating multimode pulses with a duration of 7–8 ns. A Raman laser operating regime characterized by the hyperexponential PDDs with CVs reaching 480 %, which is 2–2.5 times higher than those observed earlier for the single-pass conditions of stimulated Raman scattering, was realized.

In this paper, we studied the dynamics of transient absorption spectra of a hybrid nanostructure (Ag–CuPc)6 Ag based on island silver films and copper phthalocyanine thin films, as well as individual structural units of this system, by femtosecond transient absorption spectroscopy. It is found that the effects observed for a hybrid nanostructure reflect the existing mutual influence of the plasmonic and organic subsystems on the spectral-kinetic characteristics of each other. The characteristic time of the main component of induced optical density kinetics at a wavelength λ = 525 nm (τ ~ 15 ps) that is caused by singlet-triplet relaxation of the excited electronic states of the organic subsystem of the hybrid structure is noticeably shorter than the relaxation time (τ ~ 50 ps) at the same wavelength for a pure copper phthalocyanine film of 40 nm thickness, just the same as the total thickness of the organic subsystem in the hybrid structure. It is assumed that the presence of silver nanoparticles in the hybrid structure (Ag–CuPc)6 Ag, affects the probability of intersystem conversion in the organic subsystem, accelerating the transition of CuPc molecules to a long-lived triplet state due to a strong local field near the surface of the plasmon particle. The triplet-triplet absorption spectrum of copper phthalocyanine in the spectral range 470–750 nm was obtained.

The isotopic content of natural silicon (28Si (92.23 %), 29Si (4.68 %) и 30Si (3.09 %)) affects noticeably the shape of IR absorption bands related to the oxygen impurity atoms. In the present work an attempt is undertaken to determine the positions of local vibrational modes (LVMs), related to quasimolecules 28Si16OS29Si and 28Si16OS30Si (OS – substitutional oxygen atom), for the absorption spectra measured at room temperature. An estimation of the isotopic shifts of corresponding modes is done by fitting the shape of the experimentally measured absorption band related to the vacancy–oxygen center in irradiated Si crystals. The LVM isotope shifts are found to be equal 2,2 ± 0.25 cm–1 for 28Si-16OS29Si and 4,3 ± 0,9 см–1 for 28Si-16OS30Si in relation to the basic band due to 28Si-16OS28Si, and the full width at half maximum of the A-center absorption band (28Si-16OS28Si) is 5,3 ± 0.25 cm–1. By means of infrared absorption spectroscopy a clear correlation between the disappearance of the divacancy (V2) in the temperature range 200–275 ºС and appearance of two absorption bands with their maxima at 825.8 and 839.2 cm–1 in irradiated oxygen-rich Si crystals is found. The band positioned at 825.8 cm–1 is assigned to a divacancy-oxygen defect V2O formed via an interaction of mobile V2 with interstitial oxygen (Oi ) atoms. The 839.2 cm–1 band is much more pronounced in neutron irradiated samples as compared to samples irradiated with electrons. We argue that it is related to a trivacancy–oxygen defect (V3O) formed via an interaction of mobile V3 with Oi atoms.

For decreasing the radiation effects of the cosmic environment on the electronic components of spacecraft, local protection shields are used. They are manufactured on the basis of materials with high density and large atomic numbers (tungsten, tantalum, the W-Cu composite etc.) and then integrated into the ceramic-and-metal package of electronic components with an insufficient level of radiation resistance. On the basis of the Monte Carlo approach we considered the methods of decreasing the level of the dose absorbed by the crystals of active elements if using the radiation shields based on the W-Cu composite in hybrid metal cases under the action of electrons of a circular orbit with an inclination angle of 30° and an altitude of 8000 km. The electron spectra at the maximum and minimum solar activity were obtained using OMERE 5.3 software. It was established that an increase in the mass thickness of the base and cover of cases with shields up to 1.67 g / cm2 makes it possible to reduce the dose load by 3.5–3.7 times at the minimum and by 3.9–4.1 times at the maximum of solar activity. The optimization of protection by lowering the upper layer of the W-Cu composite to the base to a height of 1.2 mm reduces the absorbed dose by 6.8–9.3 times at the minimum and by 7.6–10.7 times at the maximum solar activity.

Applications of the most common adaptation of Fourier analysis in spherical coordinate systems used to solve a number of problems in structural biology, namely, flat wave decomposition (flat waves are represented as spherical functions decomposition), are herein considered. Arguments in favor of this decomposition are compared with other decompositions in superposition of special functions. A more general justification for the correctness of this decomposition is obtained than that existing today. A method for representing groups of atoms in the form of a Fourier object is proposed. It is also considered what opportunities give such a representation. The prospects for the application of Fourier analysis in structural biophysics are discussed.