Matrix Correction Minimal with respect to the Euclidean Norm of a Pair of Dual Linear Programming Problems

Abstract. The paper presents problem formulations, theorems and illustrative numerical examples describing conditions for the existence and a form of solutions of the problem of matrix correction minimal with respect to the Euclidean norm of a pair of dual linear programming (LP) problems. The main results of the paper complement classical duality theory and can serve as a tool to tackle improper LP problems, and/or to ensure the achievement of prespecified optimal solutions of the primal and dual problems via the minimal with respect to the Euclidean norm correction of the constraint matrix elements, the right-hand sides of the constraints and the objective functions of the original problems. Keywords: dual pairs of linear programs, improper linear programs, the minimum matrix correction, the Euclidean norm

The problems of utilizing graphite of stopped graphite-uranium reactors

A list of radioactive nuclides, the activity of which forms the main part of total activity of graphite stack and graphite elements of the construction of stopped industrial graphite-uranium reactors has been defined. The analysis of activity part contributed by these nuclides at different moments of time after stopping reactor was carried out. A set of construction graphite elements, in which there is a possibility of self-sustaining release of the energy stored (Wigner's energy) was determined. It was stated that the most value of the Wigner's energy is achieved in graphite constructions operated in low-temperature region or at high values of flux densities of damaging neutrons and concurrent gamma radiation

THERMODYNAMIC ASPECTS OF CORROSION BEHAVIOR OF STEELS IN LEAD MELTS CONTAINING OXYGEN

Термодинамическими расчетами проведена оценка устойчивости оксидов основных легирующих элементов стали в расплавах Pb, содержащих кислород, в диапазоне температур от 400 до 800 оС. Определены границы областей по температуре и содержанию кислорода в Pb, соответствующие существованию однослойных оксидных пленок, состоящих из железо-хромистой шпинели Cr2FeO4 и двухслойных оксидных пленок из магнетита Fe3O4 и шпинели Cr2FeO4. Получены выражения для определения содержания кислорода в Pb, соответствующие линиям равновесия оксидных фаз основных легирующих элементов сталей в зависимости от температуры. Построена диаграмма, позволяющая проводить градацию и группировку экспериментальных данных по механизмам протекания коррозионных процессов.Thermodynamic calculations were used to assess the stability of oxides of the main alloying elements of steel in Pb melts containing oxygen in the temperature range from 400 to 800 °C. The boundaries of the regions by temperature and oxygen content in lead corresponding to the existence of singlelayer oxide films consisting of iron-chromium spinel Cr2FeO4 and two-layer oxide films of magnetite Fe3O4 and spinel Cr2FeO4 are determined. Expressions for determining the oxygen content in Pb corresponding to the equilibrium lines of the oxide phases of the main alloying elements of steels as a function of temperature are obtained. A diagram is constructed that allows gradation and grouping of experimental data on the mechanisms of corrosion processes

Reduction of hepatotoxicity of nimesulide in mechanochemically obtained composition with disodium salt of glycyrrhizic acid

Nimesulide (NIM) is a nonsteroid anti-inflammatory drug which acts as a selective cyclooxygenase 2 inhibitor and is widely used for acute pain treatment. In medical practice, a large amount of data has been collected describing the effect of NIM on the body, while a hepatotoxic side effect of the drug has been found. The exact mechanisms of such NIM-induced hepatotoxicity largely remain unknown but likely involve the intermediate reaction of its metabolism. Reduction of the hepatotoxic side effect of NIM is an actual problem for pharmacology. The aim of the present research was to evaluate the hepatotoxicity of the mechanochemically obtained composition of NIM with glycyrrhizic acid disodium salt (Na2GA) compared to pure NIM and a physical mixture of NIM with Na2GA. Material and methods. CD-1 mice were orally administered for 14 days: 1 group – mechanochemical composition NIM/Na2GA (1:10, m/m) at a dose of 1650 mg/kg; 2 group – physical mixture of NIM with Na2GA (1:10, m/m) at a dose of 1650 mg/kg; 3 group – pure NIM at a dose of 600 mg/kg (which pharmacokinetically corresponds to 1650 mg/kg of NIM/Na2GA); 4 group – vehicle (distilled water). The liver damage was assessed using histological studies and enzymatic activity of the alanine aminotransferase and aspartate aminotransferase in blood serum. Results. Histological analysis did not detect any changes in the liver of NIM/Na2GA-treated animals in comparison with a water-treated group. On the opposite, NIM given alone or as a physical mixture with Na2GA induced severe hepatotoxicity in experimental mice. Biochemical analysis of the blood serum revealed that mechanochemical NIM/Na2GA composition significantly reduced activity of the alanine aminotransferase (about 1.5 times) and aspartate aminotransferase (1.3 times) as compared with the pure NIM. Conclusions. The results obtained indicate a high potential for the practical application of the NIM/Na2GA mechanochemical composition

The morphofunctional and biochemical characteristics of opisthorchiasis-associated cholangiocarcinoma in a Syrian hamster model

The validity of experimental models of pathologies is one of the key challenges in translational medicine. Cholangiocarcinoma, or bile duct cancer, ranks second among oncological diseases of the liver. There is a strong association between bile duct cancer and parasitic infestation of the liver caused by trematodes in the family Opisthorchiidae. We have recently demonstrated that cholangiocarcinoma can develop in Syrian hamsters (Mesocricetus auratus) infected by Opisthorchis felineus and administered with dimethylnitrosamine. However, there is still no description of how this experimental model can possibly be used in translational research. The aim of this work was to study the morphological, functional and biochemical characteristics during cholangiocarcinoma development in Syrian hamsters infected by O. felineus and administered with dimethylnitrosamine. The experi­ment lasted 30 weeks with combined exposure to dimethylnitrosamine in drinking water at a dose of 12.5 ppm and a single injection of 50 metacercariae O. felineus. It was shown that the development of cholangiocarcinoma (18 weeks) increased the total number of basophils, eosinophils and monocytes, the relative number of granulocytes, the amount of total and direct bilirubin, and cholesterol and ALT levels, but reduced the relative number of lymphocytes. Based on pathological, morphometric and biochemical analyses, our model has characteristics similar to those in patients with opisthorchiasisassociated cholangiocarcinoma. Thus, this model can be used to test anticancer drugs, to study the mechanisms of cholangiocarcinogenesis and to search for molecular markers for early diagnosis of bile duct cancer

INVESTIGATION OF STEEL CORROSION RATE IN MOLTEN SALTS USING NEUTRON ACTIVATION METHOD

The paper gives experimental results of investigation of EP-823 steel corrosion in molten salts using neutron activation method. Unoxidized and thermally oxidized in the air to ~12.5 μm thick oxide film EP-823 steel samples, irradiated in IVV-2M reactor to neutron fluence of ~2.9·1017 n/cm2, underwent static corrosion tests in KCl-LiCl and KCl-LiCl-nPbCl2 molten salts at 500 and 650 °С during 24 h. It shows that corrosion and corrosion product transfer to molten salts are selective in terms of steel elements

TRAJECTORY CONTROL OF A SOLID BODY RELATIVE TO THE MOVABLE OBJECT

The paper deals with the problem of dynamic tracking of an external movable object. These problems arise when designing tracking control systems for unmanned aircrafts following ground movable objects. A dynamic model of a solid body in three-dimensional space is selected as a control object model. An external object is described by the kinematic model of a solid body on the plane. Smooth trajectory is defined as an implicit curve associated with an external movable object. The desired height of movement is selected separately. Relative dynamics of the plant and an external movable object is considered for the synthesis of control algorithm, and methods of differential geometric transformation of the original model to the task-oriented coordinate system are applied. The original problem is formulated in terms of a longitudinal motion and two orthogonal deviations after transformation. The main results are represented by task-oriented model of spatial movement and the corresponding nonlinear control algorithms. An example of solid body motion along a circular trajectory with respect to a given rectilinear motion of an external object is given for the illustration of the proposed method performance

ALGORITHM FOR ESTIMATING THE TIME WINDOW SIGNAL " WHITE NOISE" IN THE PROBLEMS OF ACOUSTIC SPECTROMETRY ELASTOMERS

Summary. In article the problem of choice of an optimum time interval and a quantization step at measurement of spectral characteristics of objects with using «white noise» signal with restrictions by technical possibilities of signal registration is considered. In the application of "white noise" as a stationary perturbing signal problems arise with the presence of distortions in the frequency spectrum due to the limited resolution of the digital recording device. When used in experimental studies of digital technology there is the possibility of distortion due to restrictions on the time signal "white noise" for a fixed number of points of the signal due to limited recording memory oscilloscope. For small time intervals distortion occurs in the low frequency region of the spectrum and at large intervals signal is distorted in the high-frequency area due to the lower sampling rate and, accordingly, the loss of information. To minimize distortions in the spectrum of the emitted signal it is proposed selection algorithm of the time window signal type "white noise" fixed (in the sense of the amount of sampling points) in terms of sample tasks for acoustic spectrometry based on the estimation of parameters of a linear function that approximates the spectrum and characterizing the linear trend