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### MIXED PROBLEM FOR ONE QUASILINEAR PARABOLIC EQUATION WITH HYSTERESIS

The paper considers an initial-boundary value problem for a quasilinear parabolic equation with a memory operator in a bounded domain with a sufficiently smooth boundary. A theorem on the existence of solutions of the initial-boundary value problem with a memory operator is proved. We used the method of discretization with respect to time to prove this theorem. The uniqueness of the solutions of this problem is also proved if the memory operator is a hysteresis nonlinearity of the generalized backlash type.

Read More### ON SOLVABILITY OF CAUCHY PROBLEM FOR SYSTEMS OF NON-LINEAR INTEGRO-DIFFERENTIAL EQUATIONS IN PARTIAL DERIVATIVES WITH PARAMETERS

It is possible to carry out the method of transforming solutions to study the problem of solvability of the Cauchy problem for non-linear integro-differential partial differential equations. The essence of this approach is the transformation of the initial Cauchy problem into an equivalent Volterra integral equation of the second kind, to which one can apply the topological method – the principle of condensed mappings. Sufficient conditions are defined for given functions for which the original problem is solvable from the conditions of contraction of the operator u.

In this paper we study the solvability of the Cauchy problem for systems of non-linear integro-differential partial differential equations of the first order with a parameter and an integral representation of the solutions obtained. Further, for a new class of systems of non-linear integro-differential partial differential equations of the third order, sufficient conditions for the existence of solutions of the Cauchy problem are found, and, in addition, an integral representation of such solutions is constructed. In view of the non-linearity of the initial problems, sufficient conditions do not guarantee the uniqueness of the solutions obtained.

Read More### CONSTRUCTION OF LABELED MULTITUDES USING POTENTIAL FUNCTIONS

In this paper, based on earlier papers, we constructed a labeled area using potential functions. The definitions and designations of labeled areas are given, specific cases of labeled areas are considered. The paper also introduces the concept of oriented labeled areas. Examples of oriented labeled areas are given. We consider a linear singularly perturbed ordinary differential equation of the first order as an example of the application of labeled area. A labeled area is constructed to study the asymptotic behavior of the solution of the initial problem. It is proved that there is a part of the labeled area that is the area of the attraction of the solution of the degenerate equation.

Read More### CORRECTION OF PROLONGED HEMOFILTRATION OF LIPID PEROXIDATION IN ABDOMINAL SEPSIS

Continuous hemofiltration was used in combination therapy of 27 patients with abdominal sepsis, with developing multichannel insufficiency or septic shock. Indicators of oxidative stress were studied. The enhancement of lipid peroxidation and the decrease in the content of α-tocopherol are established. Continuous hemofiltration improved the performance of antioxidant protection. The calculated coefficient of oxidative “K” stress in the serum and erythrocytes, normally approaching unity, was initially increased by 2.8 and 2.59 times, respectively. This index improved significantly after prolonged hemofiltration but remained elevated 1.28 and 1.72 times in plasma and erythrocytes.

Read More### DETERMINATION OF LOCAL SANITATION ACTIVITIES ALGORITHM IN CHILDREN WITH THE EMPIEMA OF PLEUR

In order to improve the results of treatment of children with pleural empyema and to evaluate the effectiveness of various methods of local sanatorium interventions, the results of treatment in this pathology in children who were treated with drainage of the pleural cavity and thoracoscopic sanitation were analyzed. Fifty six children with destructive pneumonia complicated by empyema of the pleura were on examination and treatment from 2014 to 2018 in the Department of Pediatric Surgery in Vladimirsky Moscow Regional Research Clinical Institute. All children were treated with draining of the pleural cavity with an aspiration system connected. Five patients underwent videotoracoscopic sanation of the pleural cavity. Adequate and timely drainage of the pleural cavity in combination with enzyme and antibacterial therapy has proved to be an effective method of treating pleural empyema. In the absence of pulmonary dilatation after drainage, formation of confined purulent cavities for 10-12 days, rational use of thoracoscopic sanation of the pleural cavity is rational.

Read More### USE OF METHYLENE BLUE IN INTRAOPERATIVE SEARCH OF PARATHYROID GLANDS

The original technique for intraoperative identification of parathyroid glands with the use of aniline dyes was proposed and tested in this work. This technique implies the introduction of a 0.1% aqueous solution of methylene blue into the lower thyroid artery. The procedure is simple and does not require additional costs for special equipment and other expensive dyes. This method can be taken for everyday use in the work of endocrinology surgeons. Thus, a simple and inexpensive study can significantly reduce the time of surgery, keep the parathyroid glands and the recurrent laryngeal nerve under visual control when resecting the thyroid gland.

Read More### USE OF VISUAL CONTENT TO BOOST MOTIVATION OF CHILDREN TO GET ORTHODONTIC TREATMENT

The article presents the results of a study aimed at increasing motivation of children to get orthodontic treatment by means of showing thematic cartoons. Using the elements of visual pedagogics (visual content) allowed raising interest and the level of the patients’ motivation for further orthodontic treatment (100% of children in the experimental group). An increase in the level of hygiene was noted in 67.6% compared with the baseline, and the level of dental compliance rose by 30.6%. This, in turn, has improved the children’s self-esteem, the level of their sociability and, in general, the quality of life.

Read More### ALTERNATIVE WAY OF STORING COLLECTION OF GENETIC RESOURCES OF FODDER CROPS

The article analyzes the results of 25-year storage of 575 samples of creeping alfalfa seeds (Medicago sativa L.) and 127 samples of meadow clover seeds (Trifolium pratense L.) in the branch of N.I.Vavilov Research Institute of Plant Industry of the Kuban genetic seed bank at a temperature of 4 °C. Seeds were stored in hermetically sealed containers; the initial moisture content of the seeds was 4.0-6.9%. It was found that 95% of the samples of creeping alfalfa and 93% of clover had germination above 80% after the storage. Clover specimen showed a tendency for the increase in terms of keeping high viability with a decrease in the initial moisture of seeds. In 2018, a method was developed to produce ultra-dry seeds of clover meadow and creeping alfalfa potentially suitable for long-term storage without the use of low temperatures, which is an alternative way to store plant genetic resources. Using silica gel in the ratio of seeds: silica gel = 1:10, in 7 weeks we managed to dry the clover meadow to 2.8%, and creeping alfalfa to 1.9-2.0% without reducing their germination. These values are below the recommended standards for gene banks; such seeds can be referred to as ultra-dry. An important point in the technique is the weekly replacement of the used silica gel with the fresh one. The next stage of the work is to test the effectiveness of this mode of drying the seeds of clover meadow and creeping alfalfa in experiments on long-term storage, as well as in model experiments on accelerated aging of seeds.

Read More### ANGLE OF MOUTH GAPING OF THE NILE CROCODILE CROCODYLUS NILOTICUS AT BASKING

One of the aspects of the behavioral thermoregulation of the Nile crocodile Crocodylus niloticus Laurenti, 1768 (Crocodylidae, Crocodylia) under the conditions of a crocodile farm in Djerba Explore Park (Djerba Island, Tunisia) was considered. Observation of the basking was carried out for 12 adult individuals on June 3, 2018, in the daytime at an air temperature of + 29°C. It was established that the degree of mouth gaping during basking was determined by the angle between the open jaws, which on average was 26 ± 1°, varying from 18° to 32°.

Read More### ESTIMATION OF INTER-OSCILLATORY COHERENCE IN THE ELECTROENCEPHALOGRAMS BY USE OF THEIR MATHEMATICAL MODELING

In our previous studies, a model of the electroencephalogram (EEG), based on integral nonlinear equations for averaged brain membrane potentials in neuronal ensembles, was developed. In areas of EEG stability, characteristic equations, constructed for a set of oscillations with negative decrements and their convolution with discrete (evenly discontinuous) white Gaussian noise, satisfyingly simulated the EEG. The methods for calculation of the EEG decrements through correlation functions were suggested earlier and tested on EEG from rats and mice. In present study on transgenic 5xFAD mice (a model of the Alzheimer’s disease), we analyze the relationships between different brain areas using coherence of oscillations in their EEG with decrements and frequencies revealed from our EEG model.

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