mathematical model

Modelling of the Articulated Vehicle Dynamics Taking into Account the Elastically Fastened Freight

In this article, some methodological statements of the formation of mathematical models in the problems of machine dynamics are elucidated. The presence of a cushioned freight in the form of the fastened vehicle complicates the system, so that the equations describing its oscillations are too complicated and unsuitable for practical usage. It is shown that with all the complexity of the research object, it is expedient to form the mathematical model at the level of the design diagram (model) with a relatively small number of degrees of freedom.

Modeling of Sewer Networks by Means of Directed Graphs

The paper presents an analysis of the known theoretical models of drainage network of the city as directed graphs of different types. It is proved that ringing sewer networks increases reliability of their work and improves maneuverability and regulation of drainage system as a whole. A theory of solving the optimization problem “capacity – economic efficiency” was proposed to design optimization schemes for sewage system, using the straightdual algorithmproposed by Saharovych.

Comparative Analysis of Models, Methods and Tools of Personal Authentication in Informational Systems After Keyboard Rhythm

The article analyzes the models, methods and means of authentication of computer users by their handwriting keyboard. Identified deficiencies of existing mathematical models and methods of data processing keyboard writing. Formulated topical problems of further research in the field of information security.

Model i metod rozrakhunku poperechno-kutovykh kolyvan bitumo-shchebenevoho ahrehatu z rozihritym ridkym bitumom [Model and calculation method for transverse-angular oscillations of bitumen crushed stone aggregate with hot liquid bitumen]

Mathematical model of oscillations in the transverse and vertical space of trail of bitem and broken stone aggregate with independent torsions suspension with of motion warming up of bitems are developed.

Auxiliary model of parametric sensitivity

The two-point boundary value problem of the differential equations of parametric sensitivity in addition to solving a two-point boundary value problem of the differential equations of state is solved. A joint monodromy matrix is defined by the product of matrix coefficients of the equations of state and the matrix of so-called auxiliary model of parametric sensitivity as the equations of first variation of the incomplete equations of state. The computational results are presented.

Solving of differential equations systems in the presence of fractional derivatives using the orthogonal polynomials

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.

Identification of Controlled Plant and Development of Its Model by Means of PLC

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.

Механіка дислокацій під час різання та її моделювання методами скінченних елементів

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.

Модель формування необхідного рельєфу відповідальних поверхонь енергоощадних машин комбінованим торцевим фрезеруванням

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.

Математичне моделювання процесу модифікації окиснених нафтових бітумів нафтополімерною смолою з флуорвмісними функціональними групами

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).