In the article the approach to modeling of MEMS devices using the method of structural matrices is presented. The structure of the subsystem to determine the basic characteristics of a broad class of devices.
In the paper the model of integrated accelerometer is presented. Obtained in an analytical form solution of the differential equation describing this model.
The method of solving problems of mathematical physics, in particular for pressure distribution finding in the water in the underground gas storage layers on the basis of the biorthogonal polynomials constructed by the authors is proposed in the paper. The way of the problem solving by the method of separation of variables on the basis of the biorthogonal polynomials is studied. The solution of the problem is found in the form of the series sum of the biorthogonal and quasi-spectral polynomials. The comparative analysis for the different values of parameters is performed. The impact of
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.
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.
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.
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.
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.
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.