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This paper presents the results of embolization of popliteal artery branches as an innovative technique to treat pain syndrome not relieved by standard conservative methods for osteoarthritis of the knee joint. The study aimed to evaluate available data on the efficacy and safety of popliteal artery branch embolization in the treatment of pain syndrome in osteoarthritis. Relevant studies on the use of embolization at various degrees of gonarthrosis were analyzed. The results were evaluated using the visual analog scale and Western Ontario and McMaster University Osteoarthritis Index. The performance of patients improved based on both scales, and minor complications resolved on their own. Embolization of the branches of the popliteal artery with insufficiency is a promising and effective treatment method for patients with pain due to osteoarthritis of the knee joint of various degrees, and no serious complications have been identified in the procedures, making it safe.

BACKGROUND: By reason of the high urbanization of the population the mortality rate in combined injury cases remains stably high, despite the CT-scans have appeared in the arsenal of many hospitals. There are a lot of questions: how to reduce the time of diagnosis in favor of therapeutic measures, determine the sequence of actions in different situations? AIM: To determine the degree of informativeness of clinical and instrumental methods for diagnosing combined injuries in an accident. MATERIALS AND METHODS: Were done a retrospective analysis of the results of treatment of 517 patients with combined trauma delivered to the emergency department of the Omsk City Clinical Hospital and the V.P. Demikhovs City Clinical Hospital of the Moscow for 20172019. All patients were examined by a multidisciplinary team using modern diagnostic methods including laparoscopic examination, CT according to the whole body program. RESULTS: The results of the data analysis showed that clinical examination, radiography and ultrasound do not allow the diagnosis to be carried out in full, revealing up to 80% of all injuries. CONCLUSION: FAST protocol has a high degree of informativeness at the early hospital stage (efficiency 83%, reliability 81%). When using modern computed tomographs with subsequent digital analysis of reconstructions, the value of performing radiographs in an urgent situation decreases. MSCT is the gold standard in the diagnosis of combined trauma, has a high diagnostic efficiency compared to other methods of radiation diagnostics.

The paper presents an analysis of the recent studies on the various aspects of surgical management of acute (excluding biliary) pancreatitis. It evaluates the suggestion of interventions in the sterile phase, which are limited to and include enzymatic peritonitis and abdominal compartment syndrome. Surgery is suggested when conservative treatment is ineffective, pain is present, which is associated with pancreatic fluid accumulation, there is a risk of the pancreatic fluid leaking into the abdominal cavity, or compression of the adjacent organs develops due to the disconnected pancre-atic duct syndrome. Infected necrosis is the main indication for surgical intervention in acute pancreatitis. The drainage is preferably delayed for at least 4 weeks following the onset of the disease, and is gradually performed (in a “step-up” manner). The choice of drainage technique is based on the necrosis localization, delimiting wall, surgeon’s expertise, and technical capabilities. Sequestrectomy can be performed starting from mini-invasive percutaneous drainage under endoscopic guidance, or using a covered metal stent. In the cases of early infection or advanced injury of retroperitoneal tissue, it is advisable to combine percutaneous and endoscopic methods, and use multiple transluminal gateway techniques with several draining tracts installed from single or multiple points of access.

Only a few studies have investigated the complications of laparoscopic cholecystectomy in children. Therefore, relevant case reports will be of interest to pediatric surgeons. The patient was a 10-month-old boy diagnosed with calculous cholecystitis who underwent laparoscopic cholecystectomy. He had peripheral edema and adhesions in the neck of the gallbladder. After 10 h, a clinical picture of intra-abdominal bleeding developed. During relaparoscopy in the area of the gallbladder bed, arterial bleeding from the liver vessel was noted, which was eliminated by coagulation. The postoperative period was uneventful, and the child was discharged on day 8. In the second case, a 10-year-old girl was admitted for chronic calculous cholecystitis, and laparoscopic cholecystectomy was performed, in which a pronounced adhesion process was noted in the gallbladder neck region. On day 8, the child was discharged home; however, after 26 days, the patient was admitted again, with a clinical picture of diffuse biliary peritonitis. During laparoscopy, bile outflow from the gallbladder bed was noted, which only partially eliminated by monopolar electrocoagulation. Drainages were installed, through which bile began to be abundantly secreted in the postoperative period. Laparoscopy with a transition to open surgery was performed, during which a perforation in the wall of the common bile duct was found, and stenting and suturing of the defect were performed. In the postoperative period, active infusional infusion and antibacterial therapy were given. The patient was discharged on day 29. Postoperative complications of the ClavienDindo type IIIb are associated both with the presence of congenital anatomical features and inflammatory-adhesive changes in the Calo triangle zone and with the possibility of latent lesions during monopolar coagulation in both cases. The evaluation of the tactics of eliminating biliary peritonitis in the second patient emphasized the necessity to switch to open laparotomy during the second operation. These cases indicate the need to comply with the principles of safe laparoscopic cholecystectomy, including the availability of modern endoscopic equipment and the experience of surgeons in endosurgery. This requires the concentration of patients with cholelithiasis in specialized clinics.

Dysphagia and progressive swallowing problems due to motoneuron death is one of amyotrophic lateral sclerosis (ALS) symptoms. Malnutrition and body weight loss result in immunological disturbances, fatigability and increase risk of secondary complications in ALS patients, percutaneous endoscopic gastrostomy tube (PEG) placement representing a well-recognized method for malnutrition correction and potentially increasing life expectancy. However, despite nutritional correction, occasional rapid neurological deterioration may develop after PEG placement. We have hypothesized that this decline can be a result of exteroceptive stress during PEG placement and promote neurodegeneration in ALS patients. Intravenous sedation may decrease stress during invasive procedures and it is safe during PEG placement in ALS patients. The aim of the study was comparing different PEG placement protocols of anesthesia (local anesthesia or local anesthesia plus intravenous sedation) in ALS from perspectives of stress load and neurological deterioration profile. During 1.5 years 94 ALS patients were admitted; gastrostomy was performed in 79 patients. After screening according to inclusion and exclusion criteria, 30 patients were included in the prospective consecutive study. All patients were divided in two groups, with local anesthesia and with combination of local anesthesia and intravenous sedation. Routine biochemical indices, neurodegeneration and stress markers were measured. The age of ALS patients was 61 ± 10 years; 20 patients were included at stage 4A and 10 at stage 4B (King’s College staging). PEG was placed at average14 months after the diagnosis and 2.2 years after first symptoms. Mean ALS Functional Rating Scale-Revised was 27.8, mean forced vital capacity of lung 46.3% (19—91%). After one year of observation only 8 patients survived. Mean life duration after PEG was 5 months (5 days—20 months). Comparison of two PEG placement protocols did not reveal differences in survival time, stress load and inflammation level. Higher saliva cortisol levels, serum cortisol, glucose, C-reactive protein and interleukin-6 were detected after PEG placement, confirming considerable stress response. PEG is a stressful factor for ALS patients, PEG placement representing a natural model of exteroceptive stress. Stress response was detected as increased cortisol, C-reactive protein, interleukin-6, and glucose levels. Intravenous sedation did not increase the risk of PEG placement procedure, however, sedation protocol did not affect stress load.

Diabetic osteoarthropathy is one of the most difficult complication of diabetes mellitus, requiring the cooperation of a many of specialitys, including traumatologists - orthopedists. However, there is no single approach to the choice of orthopedic treatment tactics for this group of patients. From 2015 to 2018 inclusive, there were 35 patients with diabetic osteoarthropathy that received conservative or surgical orthopedic treatment. 11 patients received conservative orthopedic treatment; 24 patients received surgical treatment. A total of 26 surgical interventions were performed. Two types of surgical interventions were performed: 1) resection of the protruding fragment of one or another bone of the tarsus - 12 operations 2) reconstructive surgery aimed at correcting gross deformation of the middle and / or hindfoot - 14 operations. Along with general clinical examination, all patients underwent orthopedic examination, determining the degree of blood supply disturbance. A differentiated approach to choosing the method of orthopedic treatment of the presented group of patients allowed to restore limb supportability, ensure stability in the ankle joint and joints of the middle foot, create conditions for healing and prevention of relapse of the ulcer. The experience gained allowed us to offer indications for a particular method of orthopedic treatment of foot deformities in diabetic osteoarthropathy, depending on the stage of the pathological process, its location, the severity of the deformation, and the clinical course of this pathology.

Objective. The aim of the study is to analyze the design features of orthopedic appliances used to preserve or restore the transverse arch of the foot and determine the most promising product. Materials and methods. Orthopedic products that were used to correct forefoot flattening in 350 patients aged 1782 years were analyzed. Of the total number of patients, 321 were women, and only 29 were men; 252 people were diagnosed with transverse flatfoot of stages 12, while maintaining high elasticity of the arches, and in 34 cases, there was a pronounced rigidity. Flatness was combined with valgus deformity of one finger in the range of 20300 in 218 patients. The pathological process reached stages 34, and the degree of elasticity of the arches was low in 98 patients. The products were used after various operations in 86 patients, while they were used as a conservative correction in the rest. Results. All orthopedic appliances were divided into groups according to several criteria (design features and functional perspectives). An analysis of the strengths and weaknesses of the first three allowed us to identify the fourth group, which included products that provided the ability to adjust the size of the forefoot and at the same time restored the transverse arch. They were successfully used both in the rehabilitation period, after various reconstructive operations, and with conservative treatment. Conclusion. One of the main goals in the treatment of this category of patients is restoration of the transverse arch of the foot during flattening (surgically, conservatively, or in combination), should be used according to indications and, if necessary, be combined with other corrective elements. All this will allow to achieve both therapeutic and cosmetic results and ultimately improve their quality of life.

In experiments on Wistar rats, a simulated defect in the flat bones of the skull was filled with a collagen sponge of animal origin impregnated with BMP-2 or pure sponge; in control rats, the defect was left open. During follow-up, X-ray density of the collagen sponge in the experimental groups differed significantly. The results attest to the absence of spontaneous remodeling of the bone tissue under conditions modeled focal defect. Moreover, stimulation of reparative processes by the collagen matrix did not lead to positive dynamics. Saturation of the collagen sponge with BMP-2 in a concentration of 0.05 mg/ml allowed increasing Xray density of the bone starting from week 4.

Purpose To improve technique of cortical fixation of quadrupled semitendinosus autograft in anterior cruciate ligament (ACL) reconstruction providing a tight contact of the tendon and bone inside the tunnels. Material and methods Application of the technique offered earlier for preparation and placement of quadrupled semitendinosus autograft in ACL reconstruction for a maximal tendon-bone contact is reviewed. The technique uses cortical buttons for semitendinosus graft fixation. Proximal and distal ends of the graft are corrugated at placement, thus increasing the diameter and providing additional fixation inside the bone tunnels. The modified technique employs same corrugated sutures with an easier placement practice. Potential fixation tightness in the tunnels is assessed by an increase in the diameter at both ends of the prepared graft while tightening corrugated sutures. Six semitendinosus tendons of 3 cadavers were used for testing. Results Diameters of the proximal and distal ends of the graft prepared with modified technique increased by 1.33 ± 0.52 mm and 1.5 ± 0.55 mm, respectively, at tightening the corrugated sutures. The ends of the corrugated sutures were tightened with a force of 50 N with a tension of 80 N applied to the graft. Elastic deformation was observed at 364.83 ± 69.16 N during the tensile test for the graft prepared with earlier technique and cortical fixation thread with the focus on the strength of transverse threads. The modified technique ensured a reliable construct being comparable with that provided by all-inside technique (760 N) by removing the weak link. Tendon graft preparation time reduced by 30 %. Conclusion Modification of the earlier described technique for preparation and placement of quadrupled semitendinosus autograft facilitated tight contact of the tendon and bone inside the tunnels, easier placement practice and improved strength characteristics of the prepared graft.

Object and purpose of research. This paper studies electric drives of pod propulsion units installed at heavy-duty icebreakers of the new generations: their electric propulsion systems are based on synchronous motors and static frequency converters. The purpose of this work is to develop a flow chart and investigate electromechanical properties of vector-controlled synchronous propulsion drive that meets stringent requirements to the dynamics of electric propulsion systems aboard new-generation icebreakers. Materials and methods. The study is based on the data available in theoretical literature on electric drives, as well as on personal findings and experience of the authors gained in numerous R&D projects on marine electric propulsion systems. The method followed by the authors is based on the possibility to simulate various electromechanical devices and systems in Simulink application and Sim Power Systems library of MATLAB software package. Main results. The main result of this study is the flow chart of propulsion drive based on 6.5MW synchronous motor: this system is not only as fast and accurate in terms of output coordinates as the best examples of DC and frequency-controlled AC drives, but excels them in terms of power efficiency. Conclusion. Practical findings of the authors could be helpful in development of propulsion drives based on synchronous motors for electric propulsion system of advanced new-generation icebreakers.

In the clinic of the Volga Research Medical University on the basis of Nizhny Novgorod Regional Children’s Clinical Hospital” and “Children’s City Clinical Hospital № 1” from 2014 to 2018 82 newborns including 53 boys (65%) and 29 girls (35%) at the various stages of necrotizing enterocolitis were observed. There were 15 full-term infants (18%), and 67 premature newborns (82%). Symptoms of the disease were manifested in terms from 1 day to 25 days of life. During hospitalization, children were examined by neonatologists and hospital surgeons with the following by instrumental examinations (radiography, ultrasound). The severity of the condition and severity of the process were determined accordingly to the classification by to M.J. Bell (1978). The correlation between the clinical and epidemiological characteristics of newborns and the development of the pathological process was studied using the coefficient of conjugation of characters (φ), on the Wilcoxon, Van der Warden criteria and the sign criterion. Using mathematical analysis, conditionally “weak”, “medium” and “strong” risk factors for the development of NEC are identified. When assessing the occurrence of predictors in different stages of the disease, somatic diseases of the mother, chronic fetal hypoxia, fetal infections (IUI), chronic placental insufficiency (HFPN), weakness of labor, a body weight of the child

Hypoxia is currently considered to be an universal factor involved in the development of complications in many diseases including diabetes mellitus (DM). Acute hypoxia causes a systemic reaction with the large circulatory system developing vasodilation and the lesser circulatory system arteries developinghypoxic pulmonary vasoconstriction (HPV), which demonstrates the arteries' ability to regulate pulmonary circulation and maintain normal ventilation-perfusion ratio. Lack of the adequate response to hypoxic effects may be an additional mechanism for the diabetic complications in the cardiovascular system. Despite years of study, the mechanisms of HPV remain largely unclear, as does the effect of diabetes on pulmonary artery reactivity.The aim of the study was to evaluate the effect of high-fat diet and diabetes on the development of the HPV reaction in vivo and in vitro.Studies in rats divided into three groups (control group, a group of rats on a high-fat diet (HFD), and a group of animals with experimental type 2 diabetes mellitus (T2DM)) showed that in rats kept on the high-fat diet, an injection of streptozotocin leads to significant increase in blood glucose levels. In rats kept on the high-fat diet only, this parameter did not differ from the levels in the control animals. In rats kept on HFD and in rats with T2DM model, the right ventricular pressure was significantly higher compared to the control rats.The lung ventilation with a hypoxic gas mixture led to decrease in blood pressure in the systemic circulation in animals of all groups. In the control rats, the pressure in the right ventricular cavity of the heart increased indicating the development of hypoxic pulmonary vasoconstriction. In HFD rats, hypoxic hypoxiahad virtually no effect on the right ventricular pressure. In T2DM rats, an inversion of the hypoxic pulmonary vasoconstriction reaction with decrease in the right ventricular pressure was observed.These results have been confirmed in the in vitro experiments. In lung sections, the responses of the intrapulmonary arteries to hypoxic effects were multi-directional: the pulmonary artery luminal area decreased in the control animals, almost did not change in HFD animals, and increased in T2DM animals.In the rats with experimental diabetes mellitus, the contractile responses of the pulmonary artery ring segments to hypoxia were significantly suppressed compared to the vessels from the control animals.Finding out the exact mechanisms involved in the inversion of the pulmonary vasoconstriction response in diabetes will contribute to a better understanding of the fundamental pathophysiological processes that will promote development of pathogenetically justified approaches to the treatment of this disease and its complications.

Purpose: to study the potentialities of orthopaedic surgery in foot deformities as a method for prevention and treatment of diabetic foot syndrome (DFS). Patients and methods. During the period from 2014 to 2017 thirty seven patients (13 men and 24 women aged 47 - 75 years) with DFS were operated on for feet deformity. According to Texas University classification 4 patients had grade 0, 7 - grade 3 and 26 patients - grade 4a pathology. Primary deformities were observed in 13 cases, secondary deformities resulting from DFS - in 24 cases. Forty seven different surgical interventions were performed. All interventions were grouped according to D.G. Armstrong classification for DFS surgical treatment. The surgical task was the correction of biomechanics, unloading of foot segments that were subjected to high mechanical effect caused by the deformity. Results. The follow up period was from 2 moths to 3 years. Primary healing of the ulcers was observed after 32 surgical interventions. In 2 cases revision (more radical) surgical intervention was performed. No deformity relapse was noted. Postoperative wound suppuration was recorded in 1 case. Ulcer relapse was observed in 1 case. Conclusion. The study results allow suggesting a significant role and wide-ranging potentialities of surgical orthopaedics for the effective and functional treatment of patients with DFS.

Based on the analysis of morphological and morphometric data, the clinical and experimental results of the effect of hypoxia on the wall of the small and large intestine in newborns are presented. The clinical part is based on the study of 58 case histories of patients with necrotizing enterocolitis, which the operating material (resected sections of the small intestine, large intestine) was studied in detail. The experimental work included the modeling of chronic hypobaric hypoxia in different trimesters of pregnancy in 4 groups of white rats (24 females). The offspring was taken out of the experiment at 4-5 days after birth, followed by collection of the small and large intestine areas to study histoarchitectonics. It is proved that hypoxia affects the number of newborn offspring, its weight. The small intestine is most vulnerable to the effect of this factor. Analysis of the morphological and morphometric picture of the operating and experimental material convincingly proves that under the influence of hypoxia the destruction of the intestinal mucosa occurs and the growth of the connective tissue component in the muscle layer occurs. Changes from the microcirculation of blood and lymph provoke the development of pre-ulcerative, ulcerative defects and the formation of necrosis. Disturbance of the drainage function promotes the spread of destruction in the intestinal wall.

Object and purpose of research. This paper studies automated frequency-controlled electric drive of a ship mechanism (thruster) in the electric propulsion system of various advanced ships. The purpose of this work is to develop a flow chart of frequency-controlled electric drive of ship mechanism (a thruster, as an example) that would feature, instead of currently used generator-based braking, the dynamic braking that offers significant gains in weight and size of the whole drive. Materials and methods. Scientific and technical information, as well as personal findings and experience of the authors, gathered over the years of various R&D projects in electric drives for various ship machinery. The solution to the challenge discussed in this paper is based on the method of developing a frequency-controlled electric drive, where static converter can convert the system of three-phase voltage with constant parameters into the one with smoothly-adjustable parameters, as well as to convert the said system into the system of constant, smoothly-adjustable voltage. Main results. The authors have developed a flow chart of frequency-controlled electric drive for ship mechanism (thruster) with dynamic braking, as well as enumerated other ship machinery items where electric drives are also practicable to feature this system. Their results are confirmed by simulations of electromechanical processes taking place in given electric drive of ship thruster. The diagrams of these processes, as well as their analysis, are also given in this paper. Conclusion. These solutions can be implemented in development of electric drives for machinery of advanced ships.

Aim. To show the difficulties in identification of pathogenic organisms of catheter-associated biliary infection and to demonstrate the differences in antibiotic sensitivity of microbes in biofilms and planktonic form. Materials and Methods. The patient with pancreatic head pseudocyst complicated by obstructive jaundice underwent two-stage surgery. Ultrasound-assisted cholecystostomy was performed followed by cholecystectomy. Further there were pancreatic head resection with cystopancreato- and hepaticojejunal anastomosis on excluded jejunal loop and common bile duct drainage through the cystic duct. The postoperative period was complicated by recurrent cholangitis. We carried out the microbiological analysis of drainage discharge with the assessment of antibiotic sensitivity according to conventional technique. The drainage surface was studied using scanning electron microscopy. Mass spectrometry was applied for microorganisms’ identification. Biofilms were modeled based on isolates obtained from the catheter; antibiotic sensitivity of microorganisms in biofilm was determined. Results. Pseudomonas aeruginosa and Candida аlbicans were isolated in the discharge from cystic duct drainage. The biofilm found on drainage surface consisted of Streptococcaceae strains except for those mentioned above. P. aeruginosa strain could not form biofilm, though it could be built in the biofilm formed by C. albicans. P. aeruginosa and C. аlbicans as part of biofilm lost their sensitivity to antimicrobial agents they had when being in plankton. Conclusion. Bile ducts drainage is associated with biofilm formation on catheter surface. Routine microbiological study does not always enable to evaluate the range of microbial pathogens. Traditionally determined antibiotic sensitivity of planktonic forms does not correspond that when microorganisms are in biofilm. External bile draining eliminates cholestasis rather than bacteriocholia. Adequate treatment of biliary infection should take into consideration all the above mentioned factors; restoration of bile outflow in small intestine is the most important condition

Object and purpose of research. The object of this study is electric propulsion drive of the electric propulsion system aboard Project 22220 multi-purpose nuclear icebreaker now under construction. The purpose of the study is to developcomputer-based model of electric propulsion drive for this icebreaker. The drive is frequency-regulated and has vector control algorithm. The model is intended to both analyse electromechanical processes taking place in the channels of the electric drive and to synthesize its control system. Materials and methods. The study was based on scientific & technical information available in literature on electric drive theory, as well as on personal findings of the authors and on their profound experience accumulated over many years of R&D in the sphere of marine electric propulsion systems. Solution to this problem is based on the possibility to simulate various electromechanical equipment and systems by means of Simulik application software and Sim Power Systems block library of MatLab package. Main results. The computer-based model developed under this work and representing electric propulsion drive of Project 22220 multi-purpose nuclear icebreaker makes it possible to investigate electromechanical processes taking place in different operational conditions of this drive. Virtual oscillograms were obtained for currents, voltages, RPM, power, electromagnetic moment, etc. These oscillograms characterize operation of the electric drive in the conditions of RPM regulation, power regulation, change of rotation direction, shaft cranking, ice milling, propeller jamming, decrease and increase of static load moment. The model can also be used to update the software governing microchip-based control system of the electric drive (this update becomes necessary during pre-commissioning set-to-work activities). Conclusion. The model of electric propulsion drive for Project 22220 icebreaker is an engineering tool that enables, already at early design stages, investigation and analysis of electromechanical processes: these data are necessary for proper selection of electric drive equipment. After corresponding update, this model can be used in detailed design of electric propulsion plants for ice-breaking ships of other designs.

In this presentation we evaluate nonlinear control systems on a finite time interval. We also discuss application of the invariance features and weak invariant sets in the procedures of constructing solutions for approach problems. These problems are closely connected with evaluation of reachability sets and integral funnels of control systems. We revise several problems of approaching and one general scheme of constructing solutions for these problems. Scheme consist of two stages: at the first stage we construct approximate reachability set of the approach problem; at the second stage in one way or another we construct control on a given time interval that solves the approach problem.

Object and purpose of research. This paper studies automated frequency-controlled electric propulsion drive being an element of electric propulsion system aboard a multi-purpose nuclear icebreaker currently under construction. The purpose of this work is to develop a flow chart of electric drive control system based on vector control algorithm that meets a number of tough requirements to dynamic properties of electric propulsion drive. Materials and methods. Input data for this work were scientific and technical data given in the literature on electric drive theory, as well as personal findings and multi-year experience of the authors in the R&D activities related to electric propulsion of ships. Solution to this problem is based on designing a frequency-controlled electric propulsion drive as a closed-loop automatic regulation system with several control channels, each of these, in its turn, consisting of several circuits synthesized as per cascade compensation principles. Main results. The result of this work is a control system for frequency-regulated electric propulsion drive based on 20 MW squirrel-cage rotor that equals the best Russian and foreign electric drives in terms of response speed and accuracy of maintaining specified output coordinates. Conclusion. The value of the practical results obtained by the authors is development of the control system for electric propulsion drive as a totality of units performing mathematical operations with both controllable parameters and non-observable physical coordinates. This system is the basis for development of the software to be used in the microchip-based control system of electric propulsion plant for Project 22220 multi-purpose nuclear icebreaker currently under construction.

A differential inclusion (d.i.) with a parameter α ∈ ℒ, where ℒ is a compact set in a finite-dimensional Euclidean space is considered. The problem under study is one of guiding a d.i. to a given compact set M in the phase space of the d.i. at a fixed moment of time. Issues concerning the unification of the d.i. with a parameter are discussed. A specific feature of the present unification is that it is performed for a parameterdependent d.i. that cannot be initially structured by a vector function similar to those determining the dynamics of systems in control and conflict control problems.

In this paper, a finite-dimensional nonlinear control system is considered on a finite time interval. Research deals with the problem of approach of the system with a target set in the system phase space at a fixed moment of time. A discrete approximation scheme is proposed for solution of the approach problem. Model examples of mechanical systems are given with application of the proposed scheme.

Introduction. Prosthetic plastic with the use of polymeric materials has become main practice in modern herniology. Issues of application of synthetic endoprosthesis under condition of bacterial contamination are the point at discussion. The potential and justification of such approach are arguable, while the closest and more remote outcomes are actively being examined.Aim of the work is to study the opportunities of synthetic materials application under conditions of compromising area interference of patients with urgent surgery pathology. Materials and methods. 2152 patients have been operated on hernia and prosthetic plastics of abdominal wall have been carried out to 1537 patients with the use of synthetic materials in Surgery of Municipal Hospital № 35 in Nizhny Novgorod. Moreover, the outcomes of constricted hernia treatment of 445 persons have been reviewed. Patients with constricted hernia were included to the main group and were carried out prosthesis plastics (n = 281). Patients, who were carried out plastics with their own tissue, have been ascribed to the control group (n = 164). The groups were comparable by sex, age, characteristic of the main and concomitant pathology. Potential for application of synthetic materials for open abdomen for widespread peritonitis (n = 82) has also been analyzed. Two options have been used – polyethylene perforated film and polymeric coating made of reperen by patent RF № 102192. The findings of treatment of patients with eventration (n = 57), including with application of filigree, have been examined. Findings and their discussion. Frequency of complication of the disease after hernia surgery was significantly higher among persons with urgent pathology. There were no considerable differences in this regard between the categories of persons with ventral and inguinal hernia. Frequency of complications didn’t have clear correlation with age. During the treatment of patients with constricted hernia this indicator didn’t differ significantly in the main and control groups. The application of prosthesis plastics didn’t impact significantly on the frequency of infections in the area of surgical interference. Utilization of special polymeric coating for open abdomen while treating patients with widespread peritonitis enabled to exclude contact of suture with knuckle, provide adequate drainage of abdominal space, sustain allowed limits of abdominal pressure, observe the character and quantity of exudate and assess the situation dynamically prior to performing regular revision and sanitation, and timely make tactical decisions. The usage of synthetic materials of eventration treatment allowed to fully exclude the development of occasional eventrations. Increase in frequency of pyoinflammatory complications and formation of intestinal fistula were not observed. Conclusion. Application of tension-free technique for constricted hernia allows to perform reconstruction and correction, fast and firmly close hernia defect, and at the same time frequency of systematic complications decreases, whereas pyoinflammatory complications don’t increase. The usage of synthetic materials for open abdomen for widespread peritonitis allows to provide exudate outflow, control abdominal pressure, and avoid a number of complications or timely reveal them. Implantation of filigree for final closure of abdominal space and tension-free plastic on eventration are possible on availability of experience and under a number of conditions.

We study the problem of making a control system in a finite-dimensional Euclidean space approach a compact set at a fixed instant of time. The technique presented in the paper for solving the approach problem is based on constructions involving solvability sets. To construct approximately the solvability set, we apply a backward (in time) procedure that involves storing controls selected during the construction of this set. We also give examples of simulation of approach problems for mechanical systems.

A differential inclusion with parameter on a finite time interval is studied. Questions related to determining the solvability set in the problem of guiding a differential inclusion to a compact target set in the phase space are discussed.

This article considers the problem of approximate calculation of reachability set of a nonlinear dynamical system at the fixed moment v. This paper presents one of the methods of approximate calculation of reachability set which allows to avoid the perfomance degradation of calculation speed for large values of v.

The problem of the approach of a nonlinear control system to a compact target set in the phase space at a fixed time is studied. An algorithm for constructing a solution of this problem based on maximum attraction of the system’s motion to the feasibility set is proposed.

The research considers the numerical solution method of the reachability set construction problem for non-linear dynamical system in n-dimensional Euclidean space. The study deals with the dynamical system on the finite time interval, which is described by differential equation satisfying a set of defined conditions. The existing step-by-step pixel methods are based on the time interval sampling and applying the step-by-step reachability set constructing procedure to every time moment in partition. These methods allow us to solve the approximate reachability set constructing problem for the complex non-linear systems, which do not have analytical solutions. However, applying these methods causes a sharp increase of number of points used for reachability set constructing on the next step of time partition. This results in increase of calculation time as well as lack of computing device memory. To reduce the calculation time and satisfy the existing constraints of used device memory, we developed the set fi...

The research considers the problem of constructing the reachability sets of non-linear dynamical system in n-dimensional Euclidean space on the fixed time interval. The approximate solution methods of the reachability sets constructing are considered in this research as well as the accuracy estimation for this methods is given. The research contains the computational experiments on computer modeling of described reachability sets constructing methods, which use the algorithms implemented for two computation technologies CPU as well as GPU (using CUDA technology). In this research the description and comparison of approaches to the computer modeling of the problem are given. Furthermore, the CPU-based computer modeling result comparison with the result obtained on GPU based on CUDA technology are presented. Besides, this research discusses some the side issues appeared during computer modeling, the issues raised during the computer algorithms implementation, as well as the ways to eliminate these issues or...