The aim of the study is to provide multifactor mathematical models suitable for use in automatic control systems of desliming process. For this purpose we described the motion of a two-phase environment regard to the shape the desliming machine and technological parameters of the enrichment process. We created the method for preparation of dependences of the enrichment process quality from the technological and design parameters. To automate the process we constructed mathematical models to justify intensive technological modes and optimal parameters for design of desliming machine.

We consider the modified method of parameter continuation (MMPC) as an asymptotic technique for estimating the frequencies and shapes of nonlinear oscillations of plates with complicated boundary conditions. Unlike the Bolotin’s method, which is usually used for such estimations, MMPC estimations depend from the shape of initial perturbation. When the perturbation coincides with the eigenform of plate vibration, then its frequency close to the relevant eigenfrequency. In another cases, however, it describes real vibration shape of plate with different conditions on its edges. The comparison with numerical calculations confirms the advantages of proposed method and its accuracy.

Nowadays modern requirements to achieving reliable results along with high quality of researches put mathematical analysis methods of results at the forefront. Because of this, evidence-based methods of processing experimental data have become increasingly popular in the biological sciences and medicine. Their basis is meta-analysis, a method of quantitative generalization of a large number of randomized trails contributing to a same special problem, which are often contradictory and performed by different authors. It allows identifying the most important trends and quantitative indicators of the data, verification of advanced hypotheses and discovering new effects in the population genotype. The existing methods of recognizing high molecular substances by gel electrophoresis of proteins under denaturing conditions are based on approximate methods for comparing the contrast of electrophoregrams with a standard solution of known substances. We propose a fuzzy method for modeling experimental data to increase the accuracy and validity of the findings of the detection of new proteins.