On the integrability of hyperbolic systems of riccati-type equations

We consider equations of the form U_xy = U * U_x, where U(x, y) is a function taking values in an arbitrary finite-dimensional algebra T over the field ℂ. We show that every such equation can be naturally associated with two characteristic Lie algebras, L_x and L_y. We define the notion of a ℤ-graded Lie algebraB corresponding to a given equation. We prove that for every equation under consideration, the corresponding algebraB can be taken as a direct sum of the vector spaces L_x and L_y if we define the commutators of the elements from L_x and L_y by means of the zero-curvature relations. Assuming that the algebra T has no left ideals, we classify the equations of the specified type associated with the finite-dimensional characteristic Lie algebras L_x and L_y. All of these equations are Darboux-integrable. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 113, No. 2, pp. 261–275, November, 1997.     

Inhibition of the radioactive decay of the isomer 119m Sn with the use of Mössbauer backscattering

In research on the production of beams of coherent γ rays (γ-ray lasers), conditions under which a substantial change Δλ/λ=?(0.114 ±0.027) in the radioactive decay constant λ (the isomeric level 89.53 keV ^119m Sn, T _1/2=293 days) can occur have been found experimentally for the first time. This is made possible by coherent Mo ssbauer (23.87 keV) backscattering from a resonant screen located nearby. An interpretation of the effect observed is proposed on the basis of the idea of dynamic synchronization of oscillations between a nuclear level and a standing wave of Mössbauer radiation. Possibilities for further increasing Δλ/λ up to 0.5 are found.     

Roughness of layer interfaces and phase diagram of magnetic multilayer structures

The dependence of the type of magnetic ordering in multilayer structures on the magnitude of the exchange interaction between the magnetic layers and on the degree of roughness of the interfaces between the layers is investigated. In the case of a three-layer system the regions of existence of the domain structure, of noncollinear ordering of the homogeneous magnetic layers, and of the collinear ferromagnetic phase and collinear antiferromagnetic phase are found. Fiz. Tverd. Tela (St. Petersburg) 39, 1244–1247 (July 1997)     

On one stochastic model that leads to a stable distribution

We consider an integral equation describing the contagion phenomenon, in particular, the equation of the state of a hereditarily elastic body, and interpret this equation as a stochastic model in which the Rabotnov exponent of fractional order plays the role of density of probability of random delay time. We invesgigate the approximation of the distribution for sums of values with a given density to the stable distribution law and establish the principal characteristics of the corresponding renewal process. Ukrainian Mining Academy, Dnepropetrovsk. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 11, pp. 1572–1579, November, 1997.     

New method for the synthesis of 6-amino-4-aryl-3,5-dicyano-3,4-dihydropyridine-2(1H)-thiones by recyclization of 4-aryl-2,6-diamino-4H-thiopyranes

Ammonium 6-amino-4-aryl-3,5-dicyano-1,4-dihydropyridine-2-thiolates were synthesized by recyclization of 4-aryl-2,6-diamino-3,5-dicyano-4H-thiopyranes in the presence of organic bases. On acidification of the products, the corresponding substituted 3,4-dihydropyridine-2(1H)-thiones were obtained which were used in the synthesis of 2-alkylthio-1,4-dihydropyridines, bis-(pyridyl-2)disulfides and thieno[2,3-b]pyridines.Deceased.T. G. Shevchenko Lugansk State Pedagogical Institute, Lugansk 348011. N. D. Zelinskii Institute of Organic Chemistry, Russian Academy of Sciences, Moscow 117913. Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 7, pp. 909–914, July, 1997.     

Resonance method for IR sensing

A highly sensitive method for infrared radiation detection based on thermal resonance in an active bolometer is set forth. An active bolometer is a self-oscillating system consisting of an IR-sensitive cell in a feedback circuit of an adjustable proportional controller. The analysis of an active bolometer autonomous (dark) dynamics reveals that with a generalized gain factor A variation the system evolves from relaxation type towards oscillating and self-oscillating type. When A=A_c, where A_c is a critical value of the generalized gain factor A, the steady state loses stability through self-excited thermal oscillations. The resonance in a system weakly perturbed by IR radiation modulated at self-oscillation frequency q₀[1+exp(iω_ct)] is considered. It is shown that in a small precritical vicinity =(A−A_c)/A_c of the gain factor the amplitude of forced thermal oscillations is proportional to q₀/A_c. The D^* calculation reveals that the detection power of a passive (A=0) bolometer increases with feedback introduction by a factor of 1/||. The detection powers of feasible versions of an active bolometer are compared.     

Reaction of 3,5-diamino-4-nitropyrazole with electrophilic reagents

The interaction of 3,5-diamino-4-nitropyrazole with such electrophilic reagents as acetic anhydride, dimethylformamide acetal, orthoformic ester, and ketones has been studied. Derivatives of pyrazolol[1,5-a]pyrimidines were formed on reaction with 1,3-diketones and some of their properties have been studied.Center for Drug Chemistry, All-Russian Chemical and Pharmaceutical Research Institute (VNIKhFI), Moscow 119815. Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 3, pp. 329–335, March, 1997.