On proper accretive extensions of positive linear relations

A linear relation S is called a proper extension of a symmetric linear relation S if S S S^*. As is well known, an arbitrary dissipative extension of a symmetric linear relation is proper. In the present paper, we establish criteria for an accretive extension of a given positive symmetric linear relation to be proper.Published in Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 6, pp. 723–730, June, 1995.     

Controllability of the wave equation with moving point control

This paper deals with approximate and exact controllability of the wave equation in finite time with interior point control acting along a curve specified in advance in the system's spatial domain. The structure of the control input is dual to the structure of the observations which describe the measurements of velocity and gradient of the solution of the dual system, obtained from the moving point sensor. A relevant formalization of such a control problem is discussed, based on transposition. For any given timeinterval [0,T] the existence of the curves providing approximate controllability inH _D ^–[n/2]–1 ()×H _D ^–[n/2]–1 () (wheren stands for the space dimension) is established with controls fromL ²(0,T; R ⁿ +1). The same curves ensure exact controllability inL ²() × H^–1() if controls are allowed to be selected in [L (0,T; R ⁿ+1)]. Required curves can be constructed to be continuous on [0,T).This work was supported in part by NSF Grant ECS 89-13773 and NASA Grant NAG-1-1081.     

Change in structure and properties of carbon steels bombarded by a 10−5 to 10−4 second high-energy electron beam

We consider the hardening characteristics and features of the structural and phase transformations in carbon steel (0.7% C) quenched from the melt using an electron beam with electron energy 130–180 keV, pulse duration 10–200 msec and power density 10⁶ to 10⁷ W/cm². We have observed that maximum hardening is achieved for pulse duration 40 msec. The nonmonotonic character of the dependence of the degree of hardening on the pulse duration is connected with the substantial effect of the beam parameters on the phase composition and morphology of the rapidly quenched structures.Institute of Power Electronics, Siberian Branch, Russian Academy of Sciences; Tomsk State Architectural Design Academy. Institute of the Physics of Strength and Materials Science, Siberian Branch, Russian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, p. 42–50, October, 1995.     

Synthesis of aromatic derivatives of 1,5-benzodiazepine in the reaction of 4-nitro-o-phenylenediamine with chalcone dibromides

The reaction of 4-nitro-o-phenylenediamine with 4-nitro-4-R-chalcone dibromides affords the corresponding -(2-amino-4-nitroanilino)chalcones; x-ray diffraction data indicate that these are the Z-isomers. Experiments have been perfortned to determine the conditions required for cyclization of these compounds into 2, 4-diaryl7(8)-nitro-1, 5-benzodiazepines. In the solid phase or in ethanol solutions, these latter compounds exist primarily in the 3H tautomeric form; but in DMSO solutions, the 1H form predominates.Khar'kov State University, Khar'kov 310077. Institute of Heteroorganic Chemistry, Russian Academy of Sciences, Moscow 117813. Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 7, pp. 950–958, July, 1995. Original article submitted June 30, 1994; revision submitted April 3, 1995.Deceased     

Alkylation of n-methylpyrrole with tert-butanol in the presence of amberlyst 15 ion exchanger

The 2- and 3-tert-butylderivatives of 1-methylpyrrole, hitherto unknown, have been obtained by a single-stage method. The process is characterized by a low positional selectivity with asomewhat predonminating -substitution. The results have been compared with data, obtained by the quantum-chemical calculation of the molecules of pyrrole, N-methylpyrrole, and also of their -complexes with protons, introduced in the - and -position of the rings.Latvian Institute of Organic Synthesis, Riga LV-1006.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 2, pp. 163–167, February, 1995. Original article submitted January 17, 1995.     

Nitroazines 24. stable anionic σ-adducts of condensed nitrotriazines

Stable anionic -adducts of azolo-ring condensed 1, 2, 4-traizines with water were synthesized, and their x-ray structural analysis was carried out.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 1, pp. 52–57, January, 1994.