Negative Schemes Research Articles

Investigation of stress-strain state of pipeline hoist taking into account installation displacements

Stress-deformed state of a technological equipment at oil and gas refinery facilities has an ambiguous character and may depend on such factors as, for instance, operating conditions, design feature, material degradation rate, different deviations during assembly and installation etc. Moreover, the maximum level of working stress can be changed either according to linear or nonlinear laws depending on operating machinery and determining parameter of technical condition. This aspect is highly important at forecasting the further safe operation. In a modern world it is very important and urgent to build up equipment model and its parts which are digital analogue of a real facility. Application of such digital models allows to forecast future behavior of facility at the present and for the future depending on change rate of specific parameters, to determine positive and negative schemes from high stress formation point of view in the structure. Such digital model can be applied on each stage of an equipment service life and make forecasts of an equipment transfer to critical state, to determine possible reasons of changes and to carry out prevention activities. This article considers the stress-deformed state of a technological pipe operated under vacuum at different locations of its fixation on nozzle pipes of technological apparatuses.

Negative modal schemes

We deal with the question of whether solutions of modal propositional negative schemes are definable on Kripke models. It is shown that there exists a formula by which a solution of such a scheme is defined in every Kripke model with the ascending chain condition, in which the solution exists. We present an algorithm for constructing such a defining formula.