In the framework of a new theory of perturbations with converging series, a problem is considered of reconstructing the quantity defined by a finite number of its perturbative expansion terms in a wide range of coupling constant values. As exam.pies of such problems, we consider a zero-dimensional analog of a functional integral and a $\beta$-function of the $g(\varphi^a\varphi^a)^2$ model ($a=1,2,$) in the four-dimensional space-time.
Show AbstractA possible approach to a mathematical description of some financial time series has been suggested. Generally simulation of such series requires a great body of data. In order to solve this problem, a general behavior of trajectories in the vicinity of stationary points has been considered, which made it possible to plot a mathematical model accurate to within a finite number of parBI11eters. An effective technique of estimating these parameters has been described.
Show AbstractVacuum polarization with account of contribution of quarks interacting with interfering electromagnetic and non-Ahelian background gauge fields in an SU(3) model of quantum chromodynamics has been considered. An effective Lagrangian, which is the generalization of the Heisenberg-Euler Lagrangian of quantum electrodynamics and exactly considering the contributions of the fields Hand B for the case of a magnetic field H interfering with a chromomagnetic field B has been calculated in a one-loop approximation.
Show AbstractA numerical algorithm. for processing one class of band sparse matrices arising when calculating waveguide systems by the finite difference method has been suggested.
Show AbstractA pseudospherical surface satisfying the two-soliton solution of the sin-Gordon equation has been studied. The well-known Backlund transform is used for plotting the surface. The expressions for level lines of a two-soliton surface have been obtained in a parametric form and their geometric properties have been studied.
Show AbstractThe Cauchy problem for the two-dimensional Laplace equation under the condition that the exact solution belongs to a certain compact set is considered. For given errors, the method of cutting off convex polyhedra is applied to construct domains containing approximate solutions to some Cauchy problems.
Show AbstractBased on the analysis of experimental data on half-lives of $\alpha$-radioactive even-even nuclei, we have determined the lower bound for the effective-tophysical mass ratio of the alpha particle $m_e/m\approx0.9$.
Show AbstractThe yield and angular distribution of characteristic electromagnetic radiation of channeled ions are studied within the framework of density matrix formalism. Calculations are made for the case of $(2,2)$-resonance in the planar $(100)$ channeling of N$^{6+}$ ions with an energy of $21\div23.5$ MeV in a gold single crystal.
Show AbstractThe spectral-luminescence and lasing characteristics of aqueous solutions of rhodamine 6G dye are studied over a wide range of concentrations and temperatures. The lasing of rhodamine 6G associations has been revealed and investigated. The predominant role has been ascertained of electronic excitation energy transfer from monomer dye molecules to their associations in the course of stimulated emission of radiation
Show AbstractAn experimental setup has been proposed and implemented for exciting and registering shear waves in rubber-like media by means of ultrasound. A shear wave was excited in a sample during the absorption of a powerful focused ultrasonic pulse of sub-millisecond duration. The profile of the originating shear wave and the velocity of its propagation were determined with the help of a focusing converter by. the displacement of a microparticle entrained by the shear wave. The measured value of the shear wave velocity was consistent with the calculated value with consideration of a shear modulus determined by independent techniques.
Show AbstractA nonlinear mechanism of long gravity wave generation in the ocean during rapid oscillations of the ocean floor is investigated. The relationship has been revealed between the wave 81Dplitude and the amplitude, frequency, and duration of the ocean floor oscillations and the horizontal extension of the source.
Show AbstractAn analytical solution describing the evolution of all orbital elements of gravitating bodies in a three-body planetary problem for the first-order orbital cornrnensurability (the Lindblad resonances) has been obtained within the framework of a bounded and an unbounded versions of the problem without any assumption made as to the smallness of orbit eccentricities. The results obtained are generalized to the case where the compression of the central body is taken into consideration.
Show AbstractA supersymmetrical generalization of the Sutherland-Calogero model in an external field has been suggested. The superpotential has been found, supercharges, and the ground state of the system have been constructed.
Show AbstractUsing a computer simulation technique, we have studied the effect of individual contributions from channeled and dechanneled particles to the energy spectrum of fast protons passing through a crystal. Our computations have been made for protons with initial energy of 1 Me V channeled axially in silicon.
Show AbstractAmplitude nonreciprocity arising in a spatially heterogeneous nonlinear medium has been studied both theoretically and experimentally. The theoretical and experimental results obtained are in good qualitative agreement.
Show AbstractA stability criterion has been obtained for an initially planar shock wave propagating along a resting gas with an exponential density distribution. It is shown that the shock wave can also be unstable in a gas with constant adiabatic exponent.
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