Azaindole derivatives

In addition to normal nucleophilic substitution, redox processes to form dehalogenation products of 7-azaindoline and the corresponding oxidized compounds — 6-amino-7-azaindole derivatives — occur during the reactions of various primary and secondary amines with 6-chloro-7-azaindolines. The quantitative ratios of the products of nucleophilic substitution and the redox reaction depend mainly on the nucleophilicity of the attacking amine and, by selecting the amine component of the reaction, one can accomplish either predominantly nucleophilic substitution or direct the process primarily along the path of the redox reaction.See [1] for communication XXXVIII.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 6, pp. 789–794, June, 1971.     

Linear stationary control systems over a Boolean semiring: Geometric properties and the isomorphism problem

In the present paper, we consider linear stationary dynamical systems over a Boolean semiring B. We analyze the complete observability, identifiability, reachability, and controllability of such systems. We define the notion of a “graph of modules” of completely controllable, completely reachable Boolean linear stationary systems by analogy with the spaces of modules in the case of systems over fields. We give a graph-theoretic interpretation of systems of this class. We solve the isomorphism problem in this class of systems.     

Convective combustion of aerosuspensions in fuel that contains the oxidant

The convective combustion of porous gunpowder and high explosives is an intermediate stage in the transition from layered combustion to detonation [1, 2]. The theory of convective combustion of such systems is developed in [3–6]. It has now become necessary to analyze the possibility of convective combustion of aerosuspensions. The present paper develops the theory of the combustion of such systems on the basis of an analysis of the equations of gas dynamics with distributed supply of mass and heat; the problem of nonstationary motion of a convective combustion front is formulated. In the homobaric approximation [7], when the pressure is assumed to be spatially homogeneous, an analytic solution to the problem is found; this determines the law of motion of the front and the distribution of the parameters that characterize the gas and the particles in the combustion zone. Necessary conditions for the transition from convective combustion to explosion are obtained.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 49–56, September–October, 1980.I thank R. I. Nigmatulin for helpful comments and advice, and also V. A. Pyzh and V. K. Khudyakov for discussing the work.     

Quantum chromodynamics and charm photoproduction

It is shown that charm photoproduction can be consistently described within an asymptotically free field theory. Quantum chromodynamics is used to derive sum rules for the total cross section σ_c^γ which includes both production of mesons with hidden charm (J/ψ, ψ′ and so on) and of charmed particles (pairs $\text{D}\text{D}$, $\text{F}\text{F}$ and so on). An estimate of σ_c^γ as a function of energy is given and fast growth is discovered up to energies ～ 1000 GeV. In this energy range σ_c^γ turns out to be equal to several μb. It is argued that measurements of charm photoproduction would give the most direct information on the gluon distribution within a nucleon. All the results are generalized to production of heavier particles containing new quarks. In particular, a simple rescaling law is derived connecting the cross sections for charm and beauty.     

Instanton effects in supersymmetric theories

We calculate some simplest n-point functions in supersymmetric Yang-Mills theories contributed by instantons. The result is not vanishing and we discuss some implications of this. In particular, the dynamics of the supersymmetric theories must exhibit some unusual features.