On some optimum problems of vibration theory

Some optimum problems of vibration theory and the variational approach to their solution are discussed. The results of construction of optimum solutions obtained by means of necessary conditions of the calculus of variations are presented.     

3-Azabicyclo[3.3.1]nonane Derivatives: IX. Synthesis and Molecular Structure of 3-Azabicyclo[3.3.1]nonane-1,5-diamines in Solution and in Solid State

During catalytic reduction with hydrogen on nickel of a series of 3-substituted 1,5-dinitro-3-azabicyclo-[3.3.1]non-6-enes alongside nitro groups reduction occurred also hydrogenation of the double bond. New diamines of the 3-azabicyclo[3.3.1]nonane series were synthesized, and their structure was established by means of IR, ¹H and ¹³C NMR spectroscopy and X-ray diffraction study.     

Mathematical models of the initial stage of the thermal degradation of poly(vinyl chloride). II. The thermal degradation of poly(vinyl chloride) with effective removal of HCl

The dehydrochlorination of different samples of PVC under vacuum with continuous removal of HCl by freezing, has been studied at 180–210°C. The comparison of the kinetic curves of the dehydrochlorination of various samples of PVC which were obtained by us and other investigators, with the theoretical curves for the thermal degradation of idealized PVC in the absence of HCl has been carried out. This had made it possible to evaluate the influence of unstable fragments present in the original polymer on the initial rate of PVC degradation quantitatively. It has been shown that the distinction between the stationary rates of the dehydrochlorination of various samples of PVC is determined by the difference of the values of the average length of dehydrochlorination chain, l_av. The most probable interval of the values of l_av has been ascertained to be 4–12. It is established that the most probable value of the constant of the rate of dehydrochlorination of normal links of PVC, k₀, is 2.1 × 10^?7?2.5 × 10^?7 s^?1 at 200°C. © 1993 John Wiley & Sons, Inc.     

Deposition of silicon dioxide antireflection coatings on glass by sol-gel method in the presence of Pluronic® F127 block-copolymer

Hydrolysis of tetraethoxysilane in the presence of Pluronic® F127 block-copolymer in a water-alcohol mixture was used to obtain sol-formulations from which antireflection coatings were deposited onto silicate glass by the dip-coating method and then calcined at high temperatures (200–500°C). Electron spectroscopy was used to study the dependence of the optical transmission of glass samples with a coating on the concentration of Pluronic® F127 in the starting sol, introduction of organic additives (toluene) into the sol, and calcination temperature of the glasses obtained. The refractive index and hardness of the film coatings were determined and their surface structure was assessed.     

Variational problems in the theory of optimum processes

This paper presents a review of the optimization problems for control processes described by ordinary differential equations and of the variational methods for solving these problems. The following cases are studied: problems with constraints on the controls or the coordinates, problems described by equations with discontinuous right-hand sides, problems with functionals depending on intermediate coordinates, and problems with given discontinuities in the coordinates. Variational problems of synthesis of optimal systems are also discussed. The method of solution is based on the multiplier rule and the Weierstrass necessary condition for the strong minimum of a functional. In some cases, the Legendre-Clebsch necessary condition for the weak minimum of a functional is used.