## Vol 23, No 4 (2019)

**Year:**2019**Articles:**14**URL:**https://journals.eco-vector.com/1991-8615/issue/view/1968

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The equations that describe a new type of wave motion arise in the course of mathematical modeling for continuous media with memory. This refers to differential equations of fractional order, which form the basis for most mathematical models describing a wide class of physical and chemical processes in media with fractal geometry. The paper presents a qualitatively new equation of moisture transfer, which is a generalization of the Aller–Lykov equation, by introducing the concept of the fractal rate of change in humidity clarifying the presence of flows affecting the potential of humidity. We have studied the second boundary value problem for the Aller–Lykov equation with the fractional Riemann–Liouville derivative. The existence of a solution to the problem has been proved by the Fourier method. To prove the uniqueness of the solution we have obtained an a priori estimate, in terms of a fractional Riemann–Liouville using the energy inequality method.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2019;23(4):607-621

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**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2019;23(4):622-645

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**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2019;23(4):646-656

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**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2019;23(4):657-670

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**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2019;23(4):671-704

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**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2019;23(4):705-723

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Our findings follow:

– Stretching one-step prediction and measurement update operations are wise to perform at the Decision Making Center; computation operations aimed to minimize the instrumental performance index are to be done in this place, too.

– Uncompounded procedures of adaptive data scaling are advisable to complete at the sensors' location in the network.

– Adaptation algorithms may be implemented based for filter structures taken in different forms: Kolmogorov–Wiener, Kalman covariance, or Kalman information forms.

– Computational operations for minimizing the instrumental performance index would be beneficial to develop as versions to implement the modern practical optimization methods of different levels of complexity.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2019;23(4):724-743

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Forecasting is performed on the basis of a comparison of the pre- andpostoperative condition of the patient, assessed according to variousordinal and quantitative scales as a result of interviewing the patient.

With a relatively small number of analyzed cases of the disease (severaltens or hundreds) and a small number of indicators (no more than two orthree dozen), the use of neural networks seems premature for two reasons: asmall amount of data allows analyzing them with classical methods ofmathematical statistics, and identifying dependencies on a given stagerequires constant “manual” intervention, taking into account informationfrom the subject area.

The application of statistical analysis methods to data on the treatment ofchronic injuries showed the presence of standard problems for medical data.This is the presentation of the initial information in nominal or ordinalscales, the subjective nature of some indicators, as well as theinterdependence of the presented characteristics, which reduces the qualityof research.

The search for the objective function that characterizes the quality ofsurgical treatment has shown the ambiguity of solving this problem even fora highly specialized situation.

The identification of objectively present relationships also revealed alarge number of problems, especially related to the choice of the type ofsurgical treatment, which is largely determined by the experience of thesurgeon.

Based on the study, it was proposed to build a model for predicting thequality of surgical treatment, based on expert assessments in the form of aforecast tree with recommended surgical treatment options and a statisticalforecast based on the available experience. It is assumed that the modelwill be dynamic with feedback and be able to self-update.

To predict the quality of surgical treatment in reconstructive surgery ofthe spine and pelvic complex, it is advisable to use a forecast tree, which allows usto recommend the type of surgery for a specific case of injury or diseaseand calculate the predicted values of quality of life indicators.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2019;23(4):744-755

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Depending on the electrolytic concentration,the electric conductivity of the liquid and, accordingly, the electrostatic fieldarising from friction in fluid are determined. The effect of the electrostaticfield on the dynamics of the bubble formation has shown that the radius ofgas bubbles and expansion dynamics formed by the pressure drop can beregulated by the potential difference parameter. It is presented that one of themain factors affecting the flow of two-phase fluids is the nature of the liquidphase and the concentration of electrolyte added. The results of regulation ofthe bubble formation dynamics in the gas–liquid system via the electrostaticfield and a number of physical parameters can be applied in the oil and gasindustry, chemical processes, biomechanics.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2019;23(4):756-763

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**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2019;23(4):764-770

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**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2019;23(4):771-776

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**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2019;23(4):777-788

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The problem under investigation is reduced to a non-local problem for an ordinary second-order differential equation with respect to the trace of the unknown function in the line of the type changing. The existence and uniqueness theorem for the solution of the problem has been proved; the solution is written out explicitly in the hyperbolic part of the domain. In the parabolic part, the problem under study is reduced to the Volterra integral equation of the second kind, and the solution representation has been found.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2019;23(4):789-796

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**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2019;23(4):797-808