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Objective. To assess the time-related changes in the titer of virus neutralizing antibodies to SARS-CoV-2 in patients with HIV infection within 6 months after experienced COVID-19, and to identify factors associated with the intensity and duration of the natural humoral immune response.Materials and Methods. А prospective study was performed in 102 HIV-infected patients who had COVID-19 without previous vaccination, the titer of virus neutralizing antibodies to SARS-CoV-2 was identified by microneutralization assay using the standard method, the follow-up period was 6 months. Patients were enrolled in St. Petersburg from October 2020 to January 2022. The possible impact of clinical and laboratory characteristics of HIV infection and the severity of COVID-19 on antibody titer was assessed.Results and discussion. А high antibody titer (>1:160) was detected at 1 month in 15 patients (14.7%), at 3 months — in 5 of 44 patients; at 6 months — in 3 of 26 patients. There was a statistically significant positive correlation of the titer at 1 month with an undetectable HIV viral load and the Cd4+lymphocytes count in the blood. Cases of a late increase in antibody titer (after 3 and 6 months) were registered without COVID-19 re-infection along with improvement of the immune status on antiretroviral therapy.Conclusion. А low incidence of effective humoral immune response 1 month after COVID-19 infection was demonstrated in HIV-infected patients without vaccination against SARS-CoV-2. Single cases of delay in antibody titer increase with an immune status improvement were observed.

Two methods are proposed for assessing the total concentration (cAr) of the most toxic hydrocarbons (arenes) in wastewaters. The procedures include the extraction of petroleum products with n-hexane, the adsorption purification of the extract from phenols, and the measurement of the absorbance of arenes in the UV region. No separation of alkanes and cycloalkanes is required. The first method enables the rapid estimation of cAr in terms of the standard substance Xst (o-xylene or m-xylene) for screening purposes. Absorbance is measured at 250 nm, which decreases the effect of intragroup selectivity and phenols remaining in the extract. The total concentrations of arenes in n-hexane solutions are estimated by this method rather accurately (error δc 50%. The results of cAr estimation in simulations and wastewaters are underestimated, which is mainly due to the loss of arenes during sample preparation. Using the second (more accurate) method, the absorbance of the extract is measured at seven wavelengths in the region 240–280 nm. The cAr value is found by multiple linear regression without recalculation to Xst. Multivariate calibrations are constructed using extracts from 25 simulated solutions (training set) and passing them through all sample preparation operations, which decreases the loss of analytes. At cAr > 1 mg/L, the error in the analysis of simulants from the test set does not exceed 20% at RSD < 12%. The duration of analysis is 1 h. The procedure was tested in the analysis of wastewaters from enterprises of various profiles. The results agree with the results of chromatographic analyses of the same samples.

The purpose of the article is to characterize the problems and prospects of development of volunteer activities in the youth environment of the Orel region. The article provides a brief review of the literature on volunteer activities. The article presents the results of the author’s sociological study “Coordination of volunteer activities among the youth of the Orel region” –materials of interviews with the heads of volunteer organizations (volunteer groups; volunteer groups; volunteer centers (movements)), volunteer projects) of the Orel region. Based on the analysis of the interview materials, groups of problems typical for the development of volunteer activities in the Orel region are identified. A comparison of the materials obtained by the author during the interview with the results of a questionnaire survey of residents of the Orel region, organized by the sociological laboratory of the Central Russian Institute of Management, a branch of the Russian Academy of National Economy and Public Administration, and the results of a VTSIOM study are carried out.The results of the study-the analysis allowed the author to formulate the problems of development of volunteer activity in the youth environment of the Orel region and to identify the prospects for the further existence of this type of activity in the region.

Aim. To assess the effect of metabolic disorders and galectin-3 levels on the progression of liver fibrosis in chronic hepatitis C. Materials and methods. 106 patients with HCV without decompensated liver cirrhosis were examined. Exclusion criteria: age younger than 20 and older than 65 years, diabetes, coronary heart disease, hypertension, alcoholism, drug addiction. Laboratory examination (biochemical blood test, enzyme immunoassay (ELISA) with determination of HCV-Ab antibodies, viral load) was supplemented with liver elastometry (Fibroscan ® ) with fibrosis assessment (kPa, METAVIR scale). The body mass index of Quetelet (kg/m 2 ), the presence of abdominal obesity, insulin resistance were evaluated. Serum levels of insulin and galectin-3 were determined by ELISA. Results. In 45% of patients, an increase in ITM was revealed, in 44% – abdominal obesity, in 62% – insulin resistance. In 75% abdominal obesity was determined in patients with liver fibrosis F 3 –F 4 . Insulin resistance was found more often in patients with fibrosis F 0–1 – 56.7%. Significant correlations between the level of galectin-3 and the degree of liver fibrosis (in kPa) [ r =0,206, p =0,034], as well as the stage of liver fibrosis (on the METAVIR scale) [ r =0,247, p =0,01] were obtained. The level of galectin-3 in liver cirrhosis was 6.32 (4.57; 9.64) ng/ml, which is significantly higher than in F 0 – 3.96 (1.45; 5.30) ng/ml ( p =0.002) and F 1 – 3.85 (2.20; 5.83) ng/ml ( p =0.002). By calculating the specificity and sensitivity of isolated for F 4 stage of liver fibrosis (ROC-curve, the level of galectin-3 is 5.21 ng/ml), the level of specificity of 74.7%, sensitivity of 74% was established. Conclusion. We found a significant relationship between the disturbances of carbohydrate-lipid metabolism and liver fibrosis, the level of galectin-3 and fibrosis stage of the liver. The prognostic value of increasing the level of galectin-3 for predicting the cirrhotic stage of liver fibrosis is substantiated.

We consider an ill-posed problem of localizing (finding the position of) discontinuity lines of a function of two variables, provided that the function of two variables is smooth outside the discontinuity lines and has a discontinuity of the first kind at each point on the line. There is a uniform grid with a step $$\tau$$ . It is assumed that we know the average values of the perturbed function on the square $$\tau\times\tau$$ at each node of the grid. The perturbed function approximates the exact function in space $$L_2(\mathbb{R}^2)$$ . The perturbation level $$\delta$$ is assumed to be known. Earlier, the authors investigated (obtained accuracy estimates of) the global discrete regularizing algorithms for approximating a set of discontinuity lines of a noisy function. However, stringent smoothness conditions were superimposed onto the discontinuity line. The main result of the present study is the improvement of localizing the accuracy estimation methods, which allows replacing the smoothness requirement with a weaker Lipschitz condition. Also, the conditions of separability are formulated in a more general form as compared to previous studies. In particular, it is found that the proposed algorithm makes it possible to obtain the localization accuracy of the order of $$O(\delta)$$ . Estimates of other important parameters characterizing the localization algorithm are also given.

We consider the ill-posed problem of localizing (finding the position of) the discontinuity lines of a function of two variables that is smooth outside the discontinuity lines and has a discontinuity of the first kind at each point of such lines. A uniform square grid with step τ is considered, and it is assumed that the mean values of a perturbed function over squares with side τ are known at each node of the grid. The perturbed function approximates the exact function in the space L2(ℝ2). The perturbation level δ is known. To solve the problem under consideration, we design and study global discrete algorithms that are based on averaging procedures and approximate the discontinuity lines by a set of points of a uniform grid. The main result of the paper is the development of an approach to the global study of localization algorithms. We formulate conditions for the exact function, thus defining a class of correctness. Within this class, we perform a theoretical study of the proposed algorithms, introduce the characteristics to be estimated (the concept of approximating a set of discontinuity lines by a set of points of a uniform grid), and develop methods for deriving the estimates. To achieve this goal, we use a simplified statement: the discontinuity lines are straight line segments, and the proposed localization algorithm has the simplest thinning block. It is established that the localization error of the algorithm has order O(δ). Estimates of other important parameters characterizing the localization algorithm are given.

We consider the problem of localizing (determination of position) the first kind discontinuities of a function of one variable and the problem of localizing q-jumps of a noisy function. In the first case, we assume that the exact function is smooth except for a finite number of discontinuities of the first kind. In the second case, the exact function is smooth except for a finite number of small segments of length 2q. It is required to determine the number of discontinuities (q-jumps) and approximate their positions using the function approximately specified in L2(ℝ) and the level of disturbance. We construct a class of regular averaging methods and obtain estimates of the accuracy of localization, separability, and observability on classes of correctness.

Chronic hepatitis C (CHC) is one of the common chronic viral infections. Current advances in the treatment of chronic hepatitis C have allowed WHO to develop a Global health sector strategy on viral hepatitis for 2016-2021 with the purpose of its elimination by 2030. Antiviral drugs of new generations have therapeutic efficacy of more than 98% and wide indications for use. At the same time, there are special groups of patients in whom the choice of antiviral therapy regimen is limited and its effectiveness differs from the general population of patients with chronic hepatitis C. This review provides data on the epidemiology, pathogenesis, clinical manifestations of CHC, and current approaches to the treatment of the disease. Particular attention is paid to patients with extrahepatic manifestations of chronic HCV infection.

This is theoretical study of the ill-posed problem on localization (determination of position) of discontinuities of the first kind of a function of one variable. The exact function x is smooth but has finitely many discontinuities of the first kind. Given some approximate function xδ, ||xδ − x|| L2(ℝ) ≤ δ, and the error level δ, it is required to determine the number of discontinuities and approximate their location with an estimate of the approximation accuracy. Regular localization methods are constructed on the basis of averages that are scaled by the regularization parameter. The investigation of these methods consists in carrying out estimates for their three main characteristics on the classes of correctness: accuracy of localization, separability, and observability. Under consideration is the general formulation of the problem that generalizes the previously obtained results. The necessary conditions are obtained that must be satisfied by the accuracy of localization, separability, and observability. Also, the sufficient conditions close to the necessary are found, under which a localization method is constructed with the specified accuracy, observability, and separability. The concept of optimality of the localization methods is introduced in terms of the order of accuracy, separability, and observability (in the whole) and the methods are constructed that are optimal in order in the whole.

We consider the problem of localizing (finding the position of) discontinuity lines of a noisy function of two variables. Such problems arise in image processing, because the boundaries of objects are often discontinuity lines. It is assumed that the function of two variables is smooth in a neighborhood of discontinuity lines and has discontinuity of the first kind at each point of these lines. Instead of the exact function, its approximation in the space L2 and the measurement error level δ are known. In this case, the problem belongs to the class of nonlinear ill-posed problems, and regularization algorithms should be constructed for its solution. We construct and study regularizing discrete algorithms of averaging “with a turn.” New rules are proposed for choosing regularization parameters, and the methods of deriving localization error bounds are improved. Error bounds are found for the localization of singularities of order O(δ4/3) under stricter separability conditions: the separability threshold in the present paper has order O(δ2/3), whereas in the authors’ previous papers devoted to this problem the bounds for the localization error and separability threshold have order O(δ). In addition, the discretization of the algorithms of averaging “with a turn” is investigated theoretically for the first time (conditions for the discretization step are specified).

The aim of the research. Evaluation of the structure of viral hepatitis in patients with oncohaematological diseases and activity of ALT and AST during various methods of treatment of the main disease.Materials and methods. Retrospective analysis of data from 2000 patients treated during 2001–2014 in Raisa Gorbacheva Memorial Research Institute for Pediatric Oncology, Hematology and Transplantation Pavlov of the First Saint Petersburg State Medical University was carried out. The dynamics of cytolytic enzymes during therapy (polychemotherapy, transplantation of hematopoietic stem cells, symptomatic) of oncohematological diseases was evaluated between the patients with concomitant chronic viral hepatitis (N=175) and without liver pathology (N=203). Analysis was performed with SAS software. Results. Over a 10-year follow-up period, 9% of the oncohematological patients of the specialized center identified markers of hemocontact viral hepatitis. The results of the study showed that in patients with concomitant viral hepatitis, in contrast to a group without hepatitis the activity of ALT and AST significantly increased compared to baseline values after the treatment of hematological malignancy. It was twofold increase of the activity of enzymes after transplantation of hematopoietic stem cells and 3–4- fold incease after courses of polychemotherapy. In patients without viral hepatitis, changes in enzyme activity after such therapy were not observed. Summary. Thus, the associated effect of concomitant viral hepatitis and toxic effects of treatment methods with the use of polychemotherapy and transplantation of hematopoietic stem cells was proven on the development of cytolytic syndrome in oncohematological patients.

We consider the ill-posed problem of localizing (finding the position of) discontinuity lines of a noisy function of two variables. New regularizing methods of localization are constructed in a discrete form. In these methods, the smoothing kernel is varying, which simplifies the implementation of the algorithms. We obtain bounds for the localization error of the methods and for their separability threshold, which is another important characteristic.

We consider an ill-posed problem of localization of discontinuities of the first kind of a one-dimensional function, when knowing only its approximation and the error level δ in the metric of L 2(−∞,+∞). We propose a new statement of the problem when all discontinuities are divisible into subsets, and the localization takes place for subsets of discontinuities. Assuming additionally that all discontinuities in each subset have jumps of one sign, we construct a new regular method that allows to determine the number of subsets of discontinuities, to approximate their boundaries, and to estimate the approximation accuracy.

We consider an ill-posed problem of localizing the discontinuity lines of a function of two variables. It is assumed that, instead of a precisely given function f, the values are available of the averages on the square of the perturbed function fδ at the points of a uniform grid as well as the error level δ so that \({\left\| {f - {f^\delta }} \right\|_{{L_2}}}{(_\mathbb{R}}^2)\) ≤ δ. An algorithm is constructed for localizing the discontinuity lines, its convergence is proved with the estimates of the approximation accuracy, which coincide in the order of magnitude with the estimates obtained earlier by the authors for the case when, instead of the average values of the function fδ, the function itself is given. Also, we substantiate the estimates for an important characteristic of localization methods, i.e. separability threshold.

We construct and study the methods of localization (positioning) of the lines in whose neighborhoods a measured function of two variables is smooth, whereas at each point of the lines it has discontinuity of the first kind (i.e., lines of discontinuity). Assume that the function has countably many discontinuity lines: on finitely many of them the function has a “large” jump, whereas the jump values on the other lines satisfy some smallness condition. Given a noise-contaminated function and an error level in L2, it is required to determine the number and localize the position of discontinuity lines from the first set for the exact function. This problem belongs to the class of nonlinear ill-posed problems and, to solve it, we need to construct some regularizing algorithms. Some simplified theoretical approach is proposed in the case when the conditions on the exact function are imposed in a narrow strip intersecting the discontinuity lines.We constructed the averaging methods and obtained accuracy estimates for the localization of discontinuity lines.

In this paper, we propose a regular iterative method of identifying a numerical parameter in the kernel of the integral equation of the first kind of the convolution type. It is shown that an unambiguous identification of the parameter is possible if the exact solution has discontinuities of the first kind. The convergence theorem is proved, and an example of the equation with a parameter, for which the method constructed is applicable, is given.

To assess the influence of informing patients with postmenopausal osteoporosis about the their probability of 10-year absolute fracture risk calculated by FRAX tool on the patient ’s decision to start treatment and their adherence to therapy during 3 years of follow-up. Materials and Methods. Multicenter open randomized trial included 417 women (mean age 65.9 years). Patients of the 1 group (n=191) were informed about the value of their absolute risk of fracture by FRAX. Patients of the 2 group (the control; n=196) got usual advice and recommendations without calculating FRAX. All patients were recommended to take alendronate in a standard dose (70 mg a week) and calcium/vitamin D supplements. Results. During the first three months after initial visit 96.4% of patients started their treatment. The adherence to treatment at sixth month was 7% higher in the group 1; the compliance in the group 1 was 8% higher, than in the control group. 6.4% of patients developed adverse drug reactions, which led to cancellation of therapy in only 2.9% of patients.

Methods of the localization (detection of positions) of discontinuities of the first kind for a univariate function of bounded variation are constructed and investigated. Instead of an exact function, its approximation in L2(-∞,+∞) and the error level are known. We divide the discontinuities into two sets, one of which contains discontinuities with the absolute value of the jump greater than some positive Δmin; the other set contains discontinuities satisfying a smallness condition for the value of the jump. It is required to find the number of discontinuities in the former set and localize them using the approximately given function and the error level. Since the problem is ill-posed, regularizing algorithms should be used for its solution. Under additional conditions on the exact function, we construct regular methods for the localization of discontinuities and obtain estimates for the accuracy of localization and for the separability threshold, which is another important characteristic of the method. The (order) optimality of the constructed methods on the classes of functions with singularities is established. © 2013 Pleiades Publishing, Ltd.

A function of two variables with lines of discontinuity of the first kind is considered. It is assumed that outside the discontinuity lines the function is smooth and has a bounded partial derivative. An approximation to the function in L2 and a perturbation level are known. The problem in question belongs to a class of nonlinear ill-posed problems, which are solved by constructing some regularizing algorithms. We propose a simple theoretical approach to solving the problem of localizing the discontinuity lines of a function that is noisy in the space L2. Some conditions on the exact function are imposed “in the small.” Methods of averaging are constructed, and error estimates of localizing the lines (in the small) are obtained.

In the paper, the methods are constructed and investigated of localization (determination of the location) of the line in a neighborhood of which a measured function of two variables is smooth, whereas it has a discontinuity of the first kind on this line. Instead of the exact function, there is available some of its approximations in L2 and the perturbation level. The problem under consideration belongs to the class of nonlinear ill-posed problems, and to solve it some regularization algorithms are needed. A simplified theoretical approach is suggested to the problem of localization of the discontinuity line of a noisy function, when the conditions on the exact function are imposed on an arbitrary small strip intersecting the discontinuity line. Some averaging methods are constructed, and estimates for the precision of the line localization are obtained.

We consider the problem of the localization of singularities (delta-functions) of a solution to a convolution-type equation of the first kind with a step kernel. We propose a regularization method which allows one to calculate the number of singularities, to approximate their location, and to estimate the approximation error. We also adduce bounds for an important characteristic of the method, namely, the separability threshold. We prove the order optimality of the proposed method on classes of functions with singularities both with respect to the accuracy and the separability.

For a problem of localizing singularities (discontinuities of the first kind) of a noisy function in Lp (1 ≤ p < ∞), new classes of regularizing methods are constructed. The methods determine the number of discontinuities and approximate their positions. The upper and lower bounds of the localizing singularities and the separability threshold are also obtained. It is proved that the methods are order-optimal by accuracy and separability on some classes of functions with discontinuities.

The problem of localizing the singularities (breakpoints) of functions that are noisy in the spaces Lp, 1 < p < ∞, or C is considered. A wide class of smoothing algorithms that determine the number and location of breakpoints is constructed. In addition, for the case when a function is noisy in C, a finite-difference method is constructed. For the proposed methods, convergence theorems are proved and approximation accuracy estimates for the location of breakpoints are obtained. The lower estimates obtained in this paper show the order-optimality of the methods. For all the methods constructed, their capacity of separating close breakpoints is investigated.

The problem of detecting singularities (discontinuities of the first kind) of a noisy function in L2 is considered. A wide class of regularizing algorithms that can detect discontinuities is constructed. New estimates of accuracy of determining the location of discontinuities are obtained and their optimality in terms of order with respect to the error level δ is proved for some classes of functions with isolated singularities. New upper bounds for the singularity separation threshold are obtained.

Previously studied reactions of the formation of ion associates between polyallyldimethylammonium chloride (PADAC) and triphenylmethane dyes were used in the determination of the residual concentration of polymeric flocculants. Rapid procedures were developed for analyzing hydrochemical objects of different types without the separation of PADAC and the effect of interferents was taken into account. The analysis of process solutions of water treatment was performed using the reaction with Xylenol Orange; the analysis of potable water and purified sewage waters was based on the reaction with Erythrosine. The precision of the procedures is at a level of RSD ≤ 20%. The systematic error does not exceed the tolerable level if the concentrations of metals and surfactants in the studied water are lower than their maximum permissible concentrations.

In many applied problems, one has not only to find the desired function, but also to characterize its singularities (to define their type, location, etc). It seems that such problems first arose in the spectroscopy (see references in [1–3]). One can find several problem definitions and additional references, for example, in recently published monographs [4–5]. Further we consider an one-dimensional function x which has a finite number of discontinuities of the first kind. We assume that outside the discontinuities the function is sufficiently smooth; the number and the locations of discontinuities are unknown. We need to define the number of discontinuities, their approximate locations, and the jump value for each of them, using an approximately defined function xδ. The problem on the approximation of discontinuities and other problems which imply the characterization of singularities of solutions to ill-posed problems are theoretically investigated in several papers [6–7] (see also [8]). In these papers an algorithm is proposed which approximately calculates the location of discontinuities and the jumps values; the accuracy of calculations is estimated theoretically. In order to substantiate the algorithm efficiency and to estimate the accuracy, in these papers, one introduces a lower bound for the proximity of discontinuity points. Note that these restrictions guarantee the efficiency of any algorithm for discontinuities separation. It is well-known that in practical calculations, a restriction on the minimal distance between discontinuities also arises. If the distance between singularities is less than a certain threshold value, then the number of singularities is defined incorrectly, and the accuracy of approximation of their locations essentially decreases (with a fixed error level). In practice one usually defines this threshold by systematic numeric calculations. This problem was theoretically investigated in [1–3]. In the statistical statement, one considers a solution to the integral Fredholm equation of the first kind, defining a function x which represents a finite sum of δ-functions (one can multiply each one of them by a certain constant). A threshold value which is called the resolving power of a device is introduced and the calculation methods for the latter are proposed. This value is a lower estimate of the minimal distance which, in principle, enables one to solve the “problem on the separation of neighboring peaks” with the help of any algorithm appropriate for the equation under consideration. In this paper for an arbitrary algorithm for separation of discontinuities we define the separability threshold as the minimal distance which enables the algorithm to restore the number of discontinuities and their locations. In addition, we estimate this distance from above and study the algorithm for discontinuities separation described in [6]. The statement of the main theorem in this paper formally coincides with theorem 1 in [6]. However, we essentially weaken the a priori restriction imposed on the proximity of the locations of discontinuities. We replace the condition min k =j |sk − sj| > h, where sk are