Leptonic constant of the pseudoscalar <Emphasis Type="Italic">B</Emphasis><Subscript><Emphasis Type="Italic">c</Emphasis></Subscript> meson

We calculate the leptonic constant for the pseudoscalar ground state of the B _c meson in the framework of a QCD-motivated potential model taking into account the two-loop anomalous dimension for the heavy quark current in nonrelativistic QCD as matched with full QCD.     

Stress-Strain State in the Zone of Load Transfer in a Composite Specimen under Uniaxial Tension

The stress-strain state in the zone of load transfer in a uniaxially stretched specimen made of a unidirectional epoxy carbon-fiber-reinforced plastic (CFRP) is investigated. A parametric analysis of the influence of geometric and mechanical characteristics of the specimen on its stress-strain state is performed by means of finite-element modeling. The parameters allowing us to significantly reduce the dangerous concentration of transverse and tangential stresses are revealed. The mechanical tensile characteristics of a high-strength pultruded unidirectional CFRP are determined experimentally, and the size effect of its strength is estimated.     

Invariants of Characteristics of Some Systems of Partial Differential Equations

We introduce the notion of an invariant of characteristics for a system of first-order partial differential equations. We prove that the existence of invariants is connected with passiveness of some systems. We describe a few methods for construction of new invariants from those already known. We give a scheme for application of the invariants to reduction and integration of systems of partial differential equations. As an application we consider the equation of gas dynamics.     

Energy Spectrum Width and Nonequilibrium Energy of Rayleigh Waves Scattered on a Two-Dimensional Near-Surface Electron Layer

We obtain expressions for the energy spectrum widths of Rayleigh waves corresponding to their deformational coupling to Fermi and Boltzmann electrons in a two-dimensional layer near the surface of a semibounded solid. We evaluate the nonequilibrium energy of Rayleigh waves that depends on these widths and is caused by the same coupling to the corresponding hot electrons. We show that this energy is independent of the degeneracy degree of the electrons and is given by the mean energy of free Rayleigh waves heated up to temperature of the electrons. We find conditions under which the thermodynamics is determined by this nonequilibrium energy of Rayleigh waves in films of a certain thickness with Fermi electrons near the surface and by the equilibrium energy of bulk phonons in thicker samples. All the results are obtained using the Keldysh diagram technique applied to the case of semibounded media.     

An Algebraic Method for the Exact Solution of the Partition Function of the Canonical Ensemble in Nuclear Multifragmentation

We propose a unified method for deducing recursive relations for the canonical partition function of a system of noninteracting particles with charge conservation if the particles follow the Bose–Einstein, Fermi–Dirac, or Maxwell–Boltzmann statistics or parastatistics. For all these types of statistics, we find recursive relations for the partition function of a new statistical model of nuclear multifragmentation with electric charge and baryon number conservation, accounting for the internal degrees of freedom of the nuclear fragments.     

Periodic Optical Pulses in Nonlinear Optical Fibers

We discuss the problem of transmitting polarized pulses along optical fibers with variable dispersion. The dissipation and mean dispersion are assumed to be zero, which allows using the model of the vector nonlinear Schrödinger equation. We consider an optical fiber consisting of arms of equal length, which is assumed to be large. We propose an asymptotic recursive procedure for calculating the amplitude and the phase of an optical pulse propagating along the optical cable with variable dispersion.     

Probability Interpretation of the Integral of Fractional Order

We establish a relation between stable distributions in probability theory and the fractional integral. Moreover, it turns out that the parameter of the stable distribution coincides with the exponent of the fractional integral. It follows from an analysis of the obtained results that equations with the fractional time derivative describe the evolution of some physical system whose time degree of freedom becomes stochastic, i.e., presents a sum of random time intervals subject to a stable probability distribution. We discuss relations between the fractal Cantor set (Cantor strips) and the fractional integral. We show that the possibility to use this relation as an approximation of the fractional integral is rather limited.     

Structure of Binary Darboux-Type Transformations for Hermitian Adjoint Differential Operators

For Hermitian adjoint differential operators, we consider the structure of Darboux–Bäcklund-type transformations in the class of parametrically dependent Hilbert spaces. By using the proposed new method, we obtain the corresponding integro-differential symbols of the operators of transformations in explicit form and consider the problem of their application to the construction of two-dimensional Lax-integrable nonlinear evolution equations and their Darboux–Bäcklund-type transformations.     

53rd Meeting of the International Society of Electrochemistry

Russian Journal of Electrochemistry -