Determining the chemical composition of an inhomogeneous body by multi-energy radiography

Under consideration is the problem of determining the chemical composition of an inhomogeneous body consisting of several homogeneous parts by the method of multi-energy radiography. The internal structure of the body is assumed known. At the first stage of the solution, screening of the body is carried by the collimated beam of X-rays along some specially chosen collection of straight lines at a given set of energies; and, by solving a system of linear algebraic equations, the values of the attenuation coefficients are obtained in each homogeneous part of the body. Under some additional assumptions, the possible chemical composition of these parts is found. The analysis is conducted of the influence of measurement errors on the quality of the so-obtained solution. The results are illustrated by some examples of calculations. The proposed method can be used in nondestructive control, customs control, and medicine.     

On Exact Constant in the Generalized Poincare Inequality

Some problems concerning an exact constant in the generalized Poincare inequality with are discussed. In particular, the conjecture that the extremal of this problem is symmetric is confirmed. Bibliography: 7 titles.     

Time-resolved nonlinear surface plasmon optics

A new surface-sensitive method of time-resolved optical studies is proposed. The method consists in the independent excitation of several surface electromagnetic waves (SEW) by two laser femtosecond pulse beams with varied time delay Δτ and distance Δr between corresponding excitation regions on the surface. To fulfill the phase-matching condition for plasmon-photon coupling, metal grating is used. Due to nonlinear plasmon interaction, the optical radiation with ω₁ + ω₂ and 2ω₁ ? ω₂ (where ω₁, ω₂ are corresponding laser beam frequencies) is generated. The intensity of this nonlinear response versus Δτ and Δr are studied. The direct measurements of the SEW temporal properties are presented. Experiments of this type are important for the development of femtosecond surface plasmon optics.     

Eigenoscillations of a string with an additional mass

Dedicated to S. L. Sobolev on the occasion of his 80th birthday.     

Full counting statistics with spin-sensitive detectors reveals spin singlets

We study the full counting statistics of electric current to several drain terminals with spin-dependent entrance conductances. We show that the statistics of charge transfers can be interpreted in terms of single electrons and spin-singlet pairs coming from the source. If the source contains transport channels of high transparency, a significant fraction of electrons comes in spin-singlet pairs.     

Changes in the Seam-Filtration Mode with Stress Redistribution in Country Rock

A mathematical model for the mechanism of increasing oil output of productive seams is developed. The model involves a deliberate conversion of segments of the fault zone of the country rock to a supercritical state, which leads to a local redistribution of stresses in the block massif of rocks and an increase in contour and seam pressures. Based on solving the problem of restricted filtration, it is shown that the use of the proposed mechanism can ensure a relative increase in well production of 5–8%.