Self-dual Yang-Mills fields ind=4 and integrable systems in 1≤d≤3

The Ward correspondence between self-dual Yang-Mills fields and holomorphic vector bundles is used to develop a method for reducing the Lax pair for the self-duality equations of the Yang-Mills model ind=4 with respect to the action of continuous symmetry groups. It is well known that reductions of the self-duality equations lead to systems of nonlinear differential equations in dimension 1d3. For the integration of the reduced equations, it is necessary to find a Lax pair whose compatibility conditions is these equations. The method makes it possible to obtain systematically a Lax representation for the reduced self-duality equations. This is illustrated by a large number of examples.N. N. Bogolyubov Theoretical Physics Laboratory, JINR, 141980 Dubna, Russia. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 102, No. 3, pp. 384–419, March, 1995.     

The SO(3,3) group as a common basis for Dirac's and Proca's equations

Dirac's and Proca's equations are unified in the sense that the algebras of Dirac -matrices and Duffin-Kemmer-matrices are shown to furnish two distinct matrix representations of the Lie algebra of the SO(3,3)-group. This fact is then interpreted as evidence for the classical picture of particles described by the above-mentioned equations to be a relativistic top. It is also argued that the shape of the top is rod-like.     

Modelling dynamical dialogue processes in evolution systems of automatization

Questions related to the development of a flexible dialogue component automatization system for hightechnology production methods are considered. A formal model of user—system interaction is described. The methods given allow us to approach the problem of the automatization of production of dialogue interactive program packages for SAPR TPP.Translated from Dinamicheskie Sistemy, No. 9, pp. 112–117, 1990.     

Conditions under which a thermal instability arises in friction

We investigate the one-dimensional, stationary problem of the temperature distribution and rate of plastic deformation in a uniform material under the influence of friction on the surface. The temperature distribution in the material is found by numerically solving the nonlinear heat conduction equation taking into account heat released both at the surface and in the sample interior. We modeled the rate of plastic deformation as a power-law function of temperature. We observed a phenomenon in the solution that might be called a thermal instability wherein stable solution exist only for loads lighter than some critical load. The temperature and plastic deformation distribution have a macroscopic character, and cannot be explained by the formation of a thin, highly deformed surface layer that is usually observed experimentally.Institute of Strength and Materials Research Physics, Russian Academy of Sciences, Siberian Branch. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 23–27, February, 1994.     

Generation of Ethyl Metathiophosphate by Thermal Fragmentation of O-Ethyl N-Substituted Phosphoramidothioates

O-Ethyl N-1-adamantylphosphoramidothioate was synthesized and found to fragment on heating in inert solvents to form the pyrophosphate AdNHP(S)(OEt)OP(S)(OEt)OH. The proposed mechanism involves an elimination of the amine portion with release of ethyl metathiophosphate (EtOP(S)O), as was confirmed in previous work for the comparable structure with oxygen. This transient compound then phosphorylates the starting phosphoramidothioate. O-Ethyl N,N-diethylphosphoramidothioate was also synthesized, and while it gave a similar pyro compound on heating, the reaction mixture was more complex. Both phosphoramidothioates, however, served effectively as thiophosphorylating agents toward alcohols, a silanol, and the silanol groups on the surface of silica gel. Exploratory experiments showed that these phosphoramidothioates also could thiophosphorylate the OH group of a monoester of phosphoric acid, as well as that of phosphinic acids, forming anhydrides with the partial structure     

Electroinjection analysis. The introduction of a new variant of flow-injection analysis and comparison with electrophoretically-mediated microanalysis

A new method of mixing sample and reagent due to the difference in their electrophoretic mobilities is introduced. Unlike electrophoretically-mediated microanalysis, sample and reagent are injected from the opposite ends of a capillary tube. This method is compared with electrophoretically-mediated microanalysis. Experiments are performed showing the possibilities of this new method.     

Free vibrations of a thin rectangular plate

An asympototic method developed by V.V. Kucherenko and the author is applied to the problem of free vibrations of a thin plate strip in a state of a plane strain. The first few terms of an asymptotic expansion of the natural frequencies are calculated. The results are compared with those obtained by using the classical and refined theories.