Computation of the Morse Spectrum

The Morse spectrum is a limit set of Lyapunov exponents of periodic pseudo-trajectories. This notion is especially important in the case where a dynamical system has infinitely many periodic trajectories of large period. A method for estimating the Morse spectrum was suggested by the first author in J. Math. Anal. Appl., 252 (2000). This method is based on ideas of symbolic dynamics which reduces the study of a dynamical system to the study of a certain graph, called a symbolic image. Within the framework of this method, the computation of the Morse spectrum is connected with searching simple closed paths and extracting contours with suitable characteristics. However, under iterations of the symbolic image, the number of such paths sharply increases, which leads to huge expenses of memory and time. We suggest an algorithm for constructing contours with the maximal and minimal mean values. This algorithm is based on a special version of the simplex method. Numerical tests are also described. Bibliography: 13 titles. Illustrations: 3 figures.     

Optimal reconstruction of the solution of the wave equation from inaccurate initial data

In the present paper, we consider the problem of the optimal reconstruction of the solution of the wave equation from the approximate values of the Fourier coefficients of the function specifying the initial form of the string. For an operator defined on the weight space of vectors from l ₂, we present the solution of the more general problem of reconstruction from the approximate values of the coordinates of these vectors.     

Fracture initiation in the contact region under shear

In the contact region between sliding elastic bodies, there are subregions where the interacting shores are bonded and subregions where they can slide along each other. It is convenient to interpret the latter as transverse shear cracks with slip resistance forces acting on their closed shores. In the end regions of such a crack, stress concentration may lead to fracture initiation in the contacting bodies. Experimental results and an analytic model of the phenomenon are given for a situation where the fracture intersects the contact plane tilted with respect to the direction of the loads.     

Compilation and analysis of charge asymmetry measurements from electron and positron scattering on nucleon and nuclei

World data on the lepton-charge asymmetry in the elastic and inelastic lepton scattering off the proton and nuclei are compiled and discussed. After reviewing the published results, we compare the elastic data to a model calculation of the two-photon-exchange mechanism. We show that the existing data do not provide any evidence for enhancement of the two-photon contribution. At confidence level 95% the data allow to exclude the two-photon exchange as an explanation for the difference between Rosenbluth and polarization transfer measurements of proton electromagnetic form factors.     

Mean Convergence of Periodic Pseudotrajectories and Invariant Measures of Dynamical Systems

Mathematical Notes -     

Structure, dielectric, magnetoelectric, and dissipative properties of AFe2/3W1/3O3 (A = Ba, Sr, Pb) ceramics in wide frequency and temperature ranges

High-density impurity-free AFe_2/3W_1/3O₃ (A = Ba(BWF), Sr(SWF), Pb(PWF)) ceramics with well-developed microstructures were synthesized. Their structures and dielectric properties were investigated over wide temperature (10–973 K) and frequency (25 Hz-1 MHz) ranges. These materials are found to be almost transparent in the microwave range. They were characterized by weak magnetoelectric interactions; ?(BWT) ≈ 50 up to 400 K and ?(BWT) and ?(PWT) have second maxima between 400 and 600 K. All properties are easily reproduced, regardless of slight variations in synthesis conditions.     

Optimal Recovery of the Derivative of Periodic Analytic Functions from Hardy Classes

LetS_β{z : |Im z|<β}. For 2π-periodic functions which are analytic inS_βwithp-integrable boundary values, we construct an optimal method of recovery off′(ξ), ξS_β, using information about the valuesf(x₁), mldr;, f(x_n), x_j[0, 2π).     

Infrared and electron paramagnetic resonance spectra of the products of condensation of o- dihydroxybenzene with formaldehyde

The curing of heat-treated pyrocatechol — formaldehyde resins was studied by means of IR (infrared) and EPR (electron paramagnetic resonance) spectra. A hypothesis about the mechanism of resin curing is offered on the basis of the experimental data obtained.     

Thermal conductivity of alloys of the systems Sn-Pb and Sn-In in the solid and liquid states

Results are presented of the measurement of the thermal conductivity of alloys of the eutectic systems Sn-Pb and Sn-In in the solid and liquid phases from 100 to 600 °C by a steady-state method. The thermal conductivity of the investigated alloys depends linearly on the temperature. The contribution of the phonon and electron components to the thermal conductivity are estimated. It is concluded from the results that the presence of foreign atoms in the investigated alloys has no significant effect on the thermal conductivity, which is determined principally by the scattering of the electrons by the phonons.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 25–28, December, 1970.     

Photoproduction of the omega meson on the proton at large momentum transfer

The differential cross section, dsigma/dt, for omega meson exclusive photoproduction on the proton above the resonance region (2.6相似文献