mathematical model

The mathematical model of the gas motion in the pipelines for the case where unstable process is described by the fractional time derivative is constructed in the paper. The boundary value problem is formulated. The solution of the problem is founded by the spectral method on Chebyshev-Laguerre polynomials bases with respect to the time variable and Legendre polynomials with respect to the coordinate variable. The finding of the solution eventually is reduced to the system of algebraic equations. The numerical experiment is conducted.

The results of experimental and theoretical investigation of dynamic and static characteristics of a thermal object (electric oven) as a controlled plant are presented in the paper. The up-to-date microprocessor instruments were applied during the investigation. The experimental study of the plant was made by obtaining the step response curves for the controlling action channel and for the disturbance channel. Fifteen step response curves were recorded during the study.

In the article the analysed bases of theory of distributions are from the point of view of the use in the reologycal models of cutting. Given results over of imitation design of Burgers criterion. Described mathematical model over that describes behavior of the thermal and tense state of plastic purveyance in the cutting process.

Mathematical model which allows to solve a problem necessary relief formation the surface processed by the combined face milling for the purpose of maintenance of necessary operational properties of a product is offered.

The article present the empirical mathematical model of receiving oxidized oil bitumen modified by polymeric petroleum resin with fluorine-containing functional groups. The given model allows to predict oxidized oil bitumen performance (penetration, ductility, softening temperature) without any additional experiment while changing certain process managing factors. Запропонована емпірична математична модель одержання окиснених нафтових бітумів модифікованих нафтополімерною смолою з флуорвмісними функціональними групами (НПСФ).

This paper is devoted to the method of extraction unit calculation of periodical action for direct flow and return flow of extraction processes based on an analysis of the kinetics of extraction of components of the porous structures of minerals and seeds plant material under a constant driving force. Запропонована методика розрахунку прямотечійного та протитечійного екстракторів безперервної дії на основі аналізу кінетики екстрагування цільових компонентів з пористих структур мінеральної сировини та насіння рослинної сировини в умовах постійної рушійної сили. 

Automatic dosing system for loose materials is widely used in construction, food and pharmaceutical industries to prepare various mixtures. The main criterion for optimization of such systems is the accuracy of dosing of each component of the mixture, which depends on the speed component dosing and other process factors. Technological requirements for product quality in production and the high cost of individual components of the mixture strictly regulate the developers of the automated system loose materials size dosing errors.

Досліджено вплив довжини світлової хвилі на швидкість поглинання вуглекис-
лого газу мікроводоростями. Описано механізм транспорту вуглекислого газу із повітря
у внутрішнє середовище клітини мікроводорості. На основі математичної моделі
приросту мікроводоростей визначено коефіцієнт приросту. Отримано аналітичну залеж-
ність коефіцієнта приросту мікроводоростів від довжини світлової хвилі. Встановлено
оптимальні довжини світлових хвиль для проектування технологічних схем

The method of solving problems of mathematical physics, in particular for calculating a non-stationary gas flow in pipelines, is proposed in this article on the basis of the biorthogonal polynomial constructed by the authors. The method of solving the problem by means of the separation of variables in the base of biorthogonal polynomials is investigated. The analytical-approximate and approximate solutions of the problem as the sum of some biorthogonal and quasi-spectral polynomials are found.