Arrays of potentiometric sensors including developed solid-contact unmodified and modified sensors based on tetradecylammonium associates with complex compounds of silver (1) and some β-lactam antibiotics (cefazoline, cefuroxime, cefotaxime (n = 3 – 6)) are proposed; polyaniline and copper oxide being modifiers. The main electroanalytic properties of the sensors are determined (the range of the determined concentrations in antibiotic solutions 1 × 10^–4 – 0.1 M, 46.3 < S < 48, C_min = n × 10^–5 М, response time 4 – 10 sec, potential drift 4 – 6 mV/day, service life — 2 months). It is shown that modification of the membrane surfaces brings the steepness of the electrode functions to Nernst-values for single-charged ions of the antibiotics under study; reduces the response time and the detection limits, the linearity intervals of the electrode functions being the same. The potentiometric selectivity coefficients of unmodified and modified sensors based on different electrode active components (EAC) to the studied cephalosporins in the presence of interfering antibiotics are close to unity; cross sensitivity parameters for the considered sensors (the average slope of the electrode function of the sensor S_av, the unselectivity factor F, and the reproducibility factor K) are 46.3 < S (mV/pC) < 48; 0.85 < F < 0.90; 144 < K < 170, respectively. Application of sensors in the multisensory analysis of model mixtures of cephalosporin antibiotics is shown. Method of artificial neural networks (ANN) is used for processing of analytical signals. The correctness of the determination is carried out using «spike tests» on the reference model mixtures (the relative error of the determination does not exceed 12 %).

A method for optimizing the settings of a LIBS device aimed at achieving the maximum intensity of analytical lines of the analyte of constant composition is considered using probabilistic-deterministic design of experiments (PDDE). A mixture of Cr, Mn, Fe, Co, and Ni oxides homogenized and diluted by fusion with a lead-phosphate mixture is used as an analyte. It is shown that data of mathematical processing of 25 spectra by the PDDE method can be used to develop mathematical models which relate the line intensity with the energy of the laser pumping lamp, the lag time of the first and second Q-switches, the time delay of the exposure onset, and the total exposure time. The use of the geometric mean and mathematical model in the form of the product of the partial dependences leads to a good correlation between the calculated and experimental values of the intensity for all the considered spectral lines. The simulation results presented for 16 analytical lines of Cr, Mn, Co, and Ni illustrate the applicability of the method under consideration. The experimentally achieved maximum intensities of analytical lines in the matrix of lead-phosphate glass differ from those calculated using the obtained models by 7 – 12 %. There is a linear correlation between the experimental and calculated values of the intensity at R² = 0.99 and an inclination angle close to 45°. The spectra recorded during the experiment can be used for optimization of other parameters, e.g., the signal-to-noise ratio. The simplicity of calculations and relatively small number of tests in the optimization experiment make the PDDE a promising method for optimizing the LIBS parameters.

The goal is to study the anion-exchange extraction of complex thallium (III) and mercury (II) halides (chlorides, bromides, iodides) by a method of a competing intermediate ion using the anions of various dyes — methyl orange, sodium picrate, 2,4-dinitrophenol, methyl red. Mercury (II) and thallium (III) are poisons of high toxicity. The developed method was used to study the anion-exchange extraction of acidocomplexes A solution of methyl orange trinonyloctadecylammonium (TNODA) in toluene was used as an extractant. The method provides determination of mercury (II) with an accuracy of ±2% when the concentration in the initial solution ranges within 2 – 8 × 10^–8 mol/liter. It is shown that the values of the exchange constants for the same metal are larger for iodide complexes than for bromide and chloride ones. The extractability of metal halide complexes is mainly determined by their mass. Anions with a large mass have a large surface area, a low charge density, and are weakly hydrated, and thus are better extracted. The results of anion-exchange extraction were used to develop a procedure for the extraction-photometric determination of mercury (II) in granosan (ethylmercury chloride a prohibited insectofungicide of the 1^st hazard class) the illegal use and storage of which could be a source of mercury pollution of groundwater in a number of regions of the Republic of Belarus. The relative error of determination does not exceed ±2%.

The flow of a gas or liquid can be visualized by detecting and analyzing sequential images of the particle distribution on the surface of the object under study through the determination of the motion parameters. However, this approach does not provide estimation of the mass and density of solid particles along with visualization of their distribution. We present the results of determining the mass and density of suspended particles using additional irradiation of the particle flux with acoustic radiation. The technique is based on the use of the method of visual processing of images of particle flows entrained by an acoustic field of a given frequency and amplitude for at least two periods of acoustic vibrations. Relaxation of the particles in the measuring plane «cut out» by the light «knife» was also taken into account. The basic mathematical expressions required for estimation of the mass, density, velocity field and shape of the particles using digital image processing and temperature measurement in the flow area are presented. The block diagram and design of the device used for the implementation of the proposed diagnostic method are presented. This technique can be used to determine the parameters of suspended particles in medicine, biology, ecology, powder metallurgy and other fields of science and technology.

One of the most critical manufacturing defects of cast metal-matrix composites is a non-uniform porosity distribution over the composite volume. Unevenness of the distribution leads not only to local softening, but also plays a key role in the evolution of the damage process under the external loads. The goal of the study is to apply a new laser-ultrasonic method to in-situ study of a local porosity in reactive cast aluminum-matrix composites. The proposed method is based on statistical analysis of the amplitude distribution of backscattered broadband pulses of longitudinal ultrasonic waves in the studied materials. Laser excitation and piezoelectric detection of ultrasound were carried out using a laser-ultrasonic transducer. Two series of reactive cast aluminum-matrix composites were analyzed: reinforced by in situ synthesized Al₃Ti intermetallic particles in different volume concentrations and by Al₃Ti added with synthetic diamond nanoparticles. It is shown that for both series of the composites, the amplitude distribution of backscattered ultrasonic pulses is approximated by the Gaussian probability distribution applicable for statistics of large number of independent random variables. The empirical dependence of the half-width of this distribution on the local porosity in composites of two series is approximated by the same nearly linear function regardless of the size and fraction of reinforcing particles. This function was used to derive the formula for calculation of the local porosity in the studied composites. The developed technique seems to be promising in revealing potentially dangerous domains with high porosity in reactive-cast metal-matrix composites.

The accuracy of determining the permittivity of the material depends on the thickness of the intermediate layer with variable dielectric characteristics formed on the surface of the sample upon manufacturing. We present the results of studying the influence of the surface roughness of the test sample on the accuracy of determining the permittivity using the resonator method. An algorithm for calculating the permittivity in a volumetric cylindrical resonator is proposed, taking into account the roughness value and the residual gap. Using the matrix method for calculating the wave transmitted through the plate, a model for determination of the dielectric permittivity of a multilayer sample using a measuring resonator is developed. The results obtained can be used to improve the accuracy of the permittivity determination in a volume resonator when testing the samples with a roughness exceeding the required standard.

A comparative analysis of typical stress-strain diagrams obtained for in-plain shear of the 25 unidirectional and cross-ply reinforced polymer matrix composites under quasi-static loading was carried out. Three of them were tested in the framework of this study, and the experimental data on other materials were taken from the literature. The analysis of the generalized shear-strength curves showed that most of the tested materials exhibit the similar deformation pattern depending on their initial shear modulus: a linear section is observed at the beginning of loading, whereas further increase of the load decreases the slope of the curve reaching the minimum in the failure point. For the three parameters (end point the linear part, maximum reduced deviation of the diagram, tangent shear modulus at the failure point) characterizing the individual features of the presented stress-strain diagrams, approximating their dependences on the value of the reduced initial shear modulus are obtained. At the characteristic points of the deformation diagrams, boundary conditions are determined that can be used to find the parameters of the approximating functions. A condition is proposed for determination of the end point of the linear section on the experimental stress-strain curve, according to which the maximum deviation between the experimental and calculated (according to Hooke’s law) values of the shear stress in this section is no more than 1%, thus ensuring rather high accuracy of approximation on the linear section of the diagram. The results of this study are recommended to use when developing universal and relatively simple in structure approximating functions that take into account the characteristic properties of the experimental curves of deformation of polymer composite materials under in-plane shear of the sheet. The minimum set of experimental data is required to determine the parameters of these functions.

Estimation of the scatter of the durability at the second stage of fatigue, namely at the stage of crack propagation is a problem of scientific and obvious practical importance: machines operate according to their technical condition, which means monitoring of the actual crack length during their service life. The limits of the spread of the strength values at the stage of crack propagation in aluminum samples are studied using published data and a previously developed model. In view of the great importance of this problem, a special simulation model was used to generate the extrema of a random sequence based on target Markov matrices. On the one hand, this simulation method guarantees the characteristic traits of real sequence in exploitation (TWIST standard in this example). On the other hand, it contains reasonable randomness — these two parts together provide an opportunity to study the variability of the crack growth rate. For the simulation experiment, literature data on aluminum and steel samples were used along with popular fatigue crack growth models (Paris, Foreman and Willenborg models). In addition, the Miner’s summation rule was quantitatively tested to estimate the crack growth resistance coefficient under various loads. The agreement with the literature experimental data is shown. Preliminary data on the effect of the type of loading (random or block) on the durability are given on the basis of scientific literature data. The proposed simulation method can be useful for testing various models. It is also intended to develop an experimental design for laboratory testing in the future.

The possibility of determining the degree of damage to flat samples in the area of low-cycle fatigue at the stage of accumulation of scattered damage before the appearance of a macroscopic crack is demonstrated. Flat samples were tested for cantilever bending at room temperature with a constant loading amplitude until a fatigue crack appeared. Austenitic steel 12Cr18Ni10Ti was used as a test material. The velocity (propagation time) of elastic waves in the material and the coercive force were measured upon testing at intervals of 500 cycles. The zone of damage development was analyzed and value of hardening (based on microhardness measurements) was determined within 15 mm of the developed crack. The analysis of the images of the alloy microstructures in the zone of the most likely crack propagation was performed following different number of cycles at the same point on the sample surface. The structural changes (γ – α transition (formation of martensite deformation)) that occur during cyclic loading, as well as nucleation and development of damage, followed by the formation of fatigue cracks, inevitably lead to changes in the elastic and magnetic properties of the material. At the initial stages of loading, we observed changes in the initial (both acoustic and magnetic) characteristics of the material, which later became stable or changed slightly. When operating time exceeded 80 % of the number of cycles before failure, a significant change in the measured parameters occurred. The obtained dependences of the acoustic and magnetic characteristics of the material provide reliable information about the current damage and can be used in estimating the residual life of the structures made of 12Cr18Ni10Ti steel.

A problem of estimating linear regression equations by the least absolute deviations method is considered. The exact methods of implementation of the method are significantly inferior in performance to the least square method. The fastest algorithm based on coordinate descent along nodal straight lines has a computational complexity proportional to the square of the number of observations, which limits the practical application of the method to monitoring and diagnostic tasks. The goal of the study is to describe a faster version of the descent along the nodal straight lines, as well as to evaluate the performance. Reduction of the computational costs is achieved due to the fact that instead of calculating the values of the objective function at nodal points, we find the derivative of the objective function in the vicinity of these points along the nodal line. The computational efficiency of gradient descent along nodal straight lines is estimated. For a typical computer, a comparative analysis of the average calculation time for various algorithms of descent along nodal straight lines is performed. A simple example is given to illustrate the implementation of a gradient descent procedure. Along with reduction of the computational costs, we also eliminated the possibility of accumulating computational errors when determining the values of the objective function for large samples. Moreover, gradient descent is quite simple for implementation. This makes it possible to use the method of least absolute deviations as an alternative to the least square method in various practical applications.

When analyzing statistical data in biomedical research, insurance, demography, as well as in other areas of practical research, random variables of interest take on certain values depending on the occurrence of certain events, e.g., when testing physical systems (individuals), the values of their operating time depend on the failures of subsystems; in the insurance business, the payments of insurance companies to their customers depends on insured events. In such experimental situations, the problems of studying the dependence of random variables on the corresponding events become rather important thus entailing the necessity to study the limiting properties of empirical processes indexed by classes of functions. The modern theory of empirical processes generalizes the classical results of the laws of large numbers, central and other limit theorems uniformly over the entire class of indexing under the imposition of entropy conditions. These theorems are generalized analogs of the classical theorems of Glivenko – Cantelli and Donsker. Special empirical processes are proposed in the study to check the independence of a random variable and an event. The properties of convergence of empirical processes to the corresponding Gaussian processes are analyzed. The results obtained are used to test the validity of the random right censoring model.