Stress-strain state of a soft braking system

Conclusions It was shown that step-by-step use of models 1 and 2 to determine the stress-strain state of an opening circular parachute on the basis of equations of the theory of soft shells makes it possible to conduct parametric studies of problems of the statics and dynamics of such systems on a computer of moderate capacity and to significantly (by one or two orders of magnitude) reduce computing time.Translated from Mekhanika Kompozitnykh Materialov, No. 5, pp. 839–845, September–October, 1987.     

Laser initiation and early stages of electrical breakdown in charged glasses

A single pulse from a neodymium laser is used to initial electrical breakdown in glasses which accumulate and preserve a space charge induced by a beam of rapid monoenergetic electrons. Laser initiation permits use of high-speed recording apparatus and study of the initial stage of electrical breakdown in the charged glasses. A time delay in electrical breakdown relative to the initiating optical radiation was observed and measured, corresponding to the time of formation of a conductive channel between the region of space-charge localization and the specimen surface. Growth rates of the conductive channel are determined for surface and volume initiation, and possible mechanisms of laser initiation are considered.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 72–77, July, 1988.     

Cycloaddition reaction of quadricyclane and fluoroolefins

Reaction of quadricyclane (1) with fluoroolefins of different structure results in stereoselective formation of polyfluorinated exo-tricyclo[4.2.1.0^2,5]non-7-enes. The reaction of a mixture of trans/cis CF₃CFCFCF₃ with 1 is stereoselective and the resulting cycloadducts 7a, b preserve the original alkene stereochemistry. The relative rate constants of cycloaddition of a series of fluoroolefins to 1 under pseudo first-order conditions measured by kinetic NMR at 109 °C provide a kinetic scale of reactivities of the fluoroolefins in this reaction.These relative rate constants correlate well with the number of fluoroalkyl groups connected to the double bond, reaching a maximum for the tri-substituted olefin: CF₃CFCF₂:CF₃CFCFCF₃:(CF₃)₂CC(CF₃)₂:(CF₃)₂CCFC₂F₅ = 1:1.2-1.9:4:138.     

Extended Antipodal Theorems

In infinite-dimensional Hilbert spaces, we prove that the iterative sequence generated by the extragradient method for solving pseudo-monotone variational inequalities converges weakly to a solution. A class of pseudo-monotone variational inequalities is considered to illustrate the convergent behavior. The result obtained in this note extends some recent results in the literature; especially, it gives a positive answer to a question raised in Khanh (Acta Math Vietnam 41:251–263, 2016).     

Approximating Characteristics of the Nikol’skii–Besov Classes S1,θrBℝd$$ {S}_{1,\theta}^rB\left({\mathrm{\mathbb{R}}}^d\right) $$

Ukrainian Mathematical Journal - We establish the exact-order estimates for the approximation of the classes $$ {S}_{1,\theta}^rB\left({\mathrm{\mathbb{R}}}^d\right) $$ by entire functions of...