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The rheological Pokrovskii-Vinogradov model for flows of solutions or melts of an incompressible viscoelastic polymeric medium is studied in the case of flows in an infinite planar channel with perforated walls. The linear Lyapunov instability is proved for the base solution with constant flow rate in the class of perturbations periodic in the variable varying along the channel wall. Bibliography: 14 titles.

A flat strong discontinuity in a polymer fluid is investigated in the rheological Vinogradov−Pokrovsky model. Relationships for a strong discontinuity are given. The existence of discontinuous stationary solutions of the problem without rotation of the velocity vector at the discontinuity and with rotation (rotational discontinuity) is substantiated. Examples of numerical stationary solutions are given.

Under consideration is some mathematical model describing magnetohydrodynamic motion of viscoelastic polymeric fluid in the cylindrical near-axial zone of a swirl chamber. The absence of steady-state solutions is proved for the cylindrical zone with a fixed lateral boundary. The solutions are also considered in the case of near-axial zone with a free lateral boundary.

Steady-state solutions for the problem of magnetohydrodynamic motion of an incompressible polymer fluid over an infinite rotating disk are considered. The representation of the solution used here is similar to the Von Karman self-similar solution for a viscous fluid. Examples of the numerical steady-state solutions for various values of the problem parameters are presented.

Исследуется плоский сильный разрыв в полимерной жидкости в рамках реологической модели Виноградова-Покровского. Приводятся соотношения на сильном разрыве. Обосновано существование разрывных стационарных решений задачи без поворота вектора скорости на разрыве и с поворотом (вращательный разрыв). Приведены примеры численных стационарных решений.

We study linear stability of a steady state for a generalization of the basic rheological Pokrovskii–Vinogradov model which describes the flows of melts and solutions of an incompressible viscoelastic polymeric medium in the nonisothermal case under the influence of a magnetic field. We prove that the corresponding linearized problem describing magnetohydrodynamic flows of polymers in an infinite plane channel has the following property: For some values of the conduction current which is given on the electrodes (i.e. at the channel boundaries), there exist solutions whose amplitude grows exponentially (in the class of functions periodic along the channel).

The paper considers stationary solutions for the motion problem of a finite layer of an incompressible polymer fluid over an infinite rotating disk. An approximate stationary solution representation is used, similar to the self-similar Karman solution for a viscous fluid. Examples of stationary numerical solutions are given for various values of the problem’s parameters.

We study the linear stability of a resting state for a generalization of the basic rheological Pokrovski–Vinogradov model for flows of solutions and melts of an incompressible viscoelastic polymeri...

We study a new rheological model describing flows of melts and solutions of incompressible viscoelastic polymeric media in an external uniform magnetic field in the presence of a temperature drop and a conduction current. We find an asymptotic representation of the spectrum of the linear problem resulting from the linearization of the initial boundary value problem in an infinite plane channel about a Poiseuille-type flow. For this Poiseuille-type flow we also find the parameter domain of linear Lyapunov's stability., Comment: arXiv admin note: substantial text overlap with arXiv:1912.13195

Рассматриваются стационарные решения для задачи о магнитогидродинамическом движении несжимаемой полимерной жидкости над бесконечным вращающимся диском. Мы используем представление решения, аналогичное автомодельному решению Кармана для вязкой жидкости. Приводятся примеры численных стационарных решений для различных значений параметров магнитного поля.

Equations describing the flow of an incompressible viscoelastic polymer fluid in the presence of a magnetic field are considered. The symmetrization of this system of equations is discussed.

Basing on the rheological mesoscopic Pokrovskii–Vinogradov model, the equations of nonrelativistic magneto-hydrodynamics, and the heat conduction equation with dissipative terms, we obtain a closed coupled system of nonlinear partial differential equations that describes the flow of solutions and melts of linear polymers. We take into account the rheology and induced anisotropy of a polymeric fluid flow as well as mechanical, thermal, and electromagnetic impacts. The parameters of the equations are determined by mechanical tests with up-to-date materials and devices used in additive technologies (as $$3D$$ printing). The statement is given of the problems concerning stationary polymeric fluid flows in channels with circular and elliptical cross-sections with thin inclusions (some heating elements). We show that, for certain values of parameters, the equations can have three stationary solutions of high order of smoothness. Just these smooth solutions provide the defect-free additive manufacturing. To search for them, some algorithm is used that bases on the approximations without saturation, the collocation method, and the relaxation method. Under study are the dependences of the distributions of the saturation fluid velocity and temperature on the pressure gradient in the channel.

A linear problem of small perturbations of the flow of immiscible polymer fluids in a flat channel is formulated. For this problem, the existence of solutions unlimitedly increasing with time, the presence of which means linear instability of the state of rest of a polymer fluid with a strong discontinuity, is studied.

Under discussion is the the so-called acoustic systems (in linear and nonlinear cases) for the system of equations describing the movement of incompressible viscoelastic polymer fluid. We also consider some approximations of these systems.

We study a generalization of the Pokrovski–Vinogradov model for flows of solutions and melts of an incompressible viscoelastic polymeric medium to nonisothermal flows in an infinite plane channel under the influence of magnetic field. For the linearized problem (when the basic solution is an analogue of the classical Poiseuille flow for a viscous fluid described by the Navier–Stokes equations) we find a formal asymptotic representation for the eigenvalues under the growth of their modulus. We obtain a necessary condition for the asymptotic stability of the Poiseuille-type shear flow. For analysis we use new result, that generalizes Birkhoff theorem on the case, when the coefficient matrix of the eigenvalue itself has zero with multiplicity greater than one as an eigenvalue. We also get the necessary condition for Lyapunov stability of the shear Poiseuille-type flow as a result of acquired representation.

In 2016, a multicenter double-blind placebo-controlled randomized clinical trial in parallel groups was completed in the Russian Federation to evaluate the efficacy of the liquid dosage form of Anaferon for children in the treatment of acute respiratory viral infections in children. The design and main results of the study are presented in the largest foreign database ClinicalTrials. gov of the National Library of Medicine of the USA. In November 2018, the collection of reports of the XIII Russian Scientific and Practical Conference with international participation “Health is the basis of human potential: problems and solutions” published the article of the Russian chemist N.N. Khromov-Borisov, where the author questions the reliability of the study of the liquid form of Anaferon for children. The presented article analyzes the legitimacy of the author’s claims. From the point of view of statistics, the analysis of N.N. Khromov-Borisov cannot be considered objective and correct, since it contains gross methodological errors.

Aim: to obtain clinical data on the use of probiotic drugs in infants with functional gastrointesti-nal disorders (FGIDs). Patients and Methods: a retrospective cohort study was conducted on the basis of 7 medical in-stitutions in Moscow. Database of 502 case histories of children with diagnosed disorders of in-testinal microbiocenosis was formed. The children were divided into three groups depending on the probiotic agents and other medications for GI: group 1 — medications containing up to two probiotic strains in a composition; group 2 — medications containing more than two probiotic strains in a composition; group 3 — other medications for symptomatic treatment of FGIDs. Results: 259 case histories of infants were included in the study to analyze the data of the group with FGIDs. The ratio of boys and girls was 50%. In infants on artificial nutrition, the duration of the main symptoms (abdominal pain, flatulence, diarrhea, and changes in stool consistency) was significantly longer (p=0.0002). There was the lowest indicator of the symptoms’ maximum duration in the group of symptomatic treatment for GI without probiotic products. At the same time, the symptoms’ duration in this group differed from multicomponent probiotic medications (p=0.0031), but did not differ from the group of single- and two-component drugs (p=0.15). Adding that, there was a tendency to have differences between single- and two-component drugs and multicomponent ones (p=0.08). Conclusion: multicomponent probiotic medications do not always have the predominance over the single-component. It is necessary to provide a more rational approach to the targeted probi-otic therapy prescription with a possible preference for single-component drugs to avoid a num-ber of effects associated with the multicomponent probiotics use, such as antigenic load on the gastrointestinal mucosa, competitive interaction of strains. KEYWORDS: probiotics, functional gastrointestinal disorders, baby colic, retrospective study. FOR CITATION: Blokhin B.M., Prokhorova A.D., Lobushkova I.P. et al. Pharmacoepidemiology of the probiotics use in infants . Russian Journal of Woman and Child Health. 2020;3(4):309–317. DOI: 10.32364/2618-8430-2020-3-4-309-318.

Исследуется обобщение модели Покровского-Виноградова для течений растворов и расплавов несжимаемой вязкоупругой полимерной среды на случай неизотермических течений в бесконечном плоском канале при воздействии магнитного поля. Для линеаризованной проблемы (основное решение - аналог течения Пуазейля для вязкой жидкости в модели Навье-Стокса) найдено формальное асимптотическое представление для собственных чисел при возрастании их модуля. Получено необходимое условие асимптотической устойчивости аналога сдвигового течения Пуазейля. Библиография: 22 названия.

A new rheological model, an extension of the Pokrovskii-Vinogradov rheological model, describing the flows of melts and solutions of incompressible viscoelastic polymeric media in external uniform magnetic field in the presence of a temperature drop and conduction current is studied. An asymptotic representation of the linear problem spectrum resulting from the linearization of the initial boundary value problem in an infinite plane channel about a Poiseuille-type flow is obtained. For this Poiseuille-type flow the parameter domain of linear Lyapunov’s stability is determined.

This work is focused on the topical problem of developing efficient software tools to design intelligent systems, in particular, integrated expert systems (IESs), which have powerful functionality and scalable architecture. Automated planning methods are employed to facilitate IES development at the design and requirement analysis stages. General problems of developing a modern software tool base for IES design are discussed. In this context, the intelligent software environment of the AT-TECHNOLOGY workbench for IES development based on the problem-oriented methodology is described. The problem of planning the IES prototyping process is investigated, which forms the basis for implementing the basic components of the intelligent software environment (intelligent planner and technological knowledge base). An automation method based on heuristic search is proposed. The use of the intelligent software environment is illustrated by the development of a dynamic IES prototype for controlling and planning medical resources in serious road traffic accidents.

The stability of the flow of an incompressible polymer fluid with a strong discontinuity when the fluid can flow through the discontinuity is discussed. Particular solutions of the linearized problem that increase with time are constructed numerically.

Acute respiratory infections (ARI) are major causes of morbidity in children. Symptomatic treatment is insufficiently effective and requires additional drugs with etiotropic action. This multi-center double blind placebo-controlled randomized clinical study with superiority model design considers a liquid formulation of Anaferon for children.Methods. The study included 142 children from 1 month to 3 years 11 month 29 days old with ARI of the upper respiratory tract. They were randomized into Anaferon for children and Placebo groups (71 in each group) via interactive voice randomization system. The treatment period was 5 days, observation period – 14 days. The average duration of the symptoms and the severity of the respiratory disease were used as primary efficacy endpoints.Results. All 142 patients were randomized and included into ITT (Intention to treat) analysis. 140 patients (70 patients in each group) were included into PP-analysis. The patients in the Anaferon for children group had better results with average duration of ARI as compared to the Placebo group (87.7±31.5h vs. 103.3±19.4h; p =0.007). The authors marked efficacy of Anaferon for children in such parameters as disease severity (ITT-analysis: p=0.0004), total severity of disease symptoms (ITT-analysis: ANOVA: “Group” factor p=0.0004; “Day” factor pConclusion. Anaferon for children proved their efficiency and safety in young children with ARI.

We propose and describe in detail an effective numerical algorithm for finding the stationary solution of charge transport problem in a DG-MOSFET. Hydrodynamical models describing the process of charge transport in semiconductors are sets of nonlinear PDE's with small parameters and specific conditions on the boundary of transistor that essentially complicates the process of numerical simulations. We construct a new algorithm based on the stabilization method and ideas of approximation without saturation and pseudo-spectral methods that enables one to overcome all of the mentioned difficulties. The proposed algorithm enables us to obtain the solution for different geometrical characteristics of DG-MOSFET and boundary conditions (including the non-symmetric cases) with extremely small values of dimensionless doping density and dielectric constant that are used in practice.

We study a generalization of the Pokrovski–Vinogradov model for flows of solutions and melts of an incompressible viscoelastic polymeric medium to nonisothermal flows in an infinite plane channel under the influence of magnetic field. For the linearized problem (when the basic solution is an analogue of the classical Poiseuille flow for a viscous fluid described by the Navier–Stokes equations) we find a formal asymptotic representation for the eigenvalues under the growth of their modulus. We obtain a necessary condition for the asymptotic stability of the Poiseuille-type shear flow.

In this study, we consider a rheological Pokrovski–Vinogradov model of the flows of solutions and melts of an incompressible viscoelastic polymeric medium for a flow in an infinite plane channel with perforated walls. We prove the linear Lyapunov instability of the base solution with a constant flow rate in a perturbation class, which is periodic with respect to the variable and changing along the channel wall.

Studying the problem of a stationary supersonic van der Waals gas flow around an infinite plane wedge, we prove the local-in-time well-posedness of the generalized statement of the problem.

In this paper, we study a new rheological model (a modification of the well-known Pokrovskii–Vinogradov model) which is shown by computational experiments to take into account the nonlinear effects occurring during melt flows and polymer solutions in regions with complex boundary geometry. For the case where the main solution is an analogue of the Poiseuille flow in an infinite flat channel (viscoelastic polymer fluid considered), an asymptotic formula is obtained for the distribution of points of the spectrum of the linear problem. It is shown that small perturbations have the additional property of periodicity in the variable that runs along the axis of the channel.

The temporally growing particular solutions of linearized equations of an incompressible polymeric liquid with strong discontinuities were constructed.

An algorithm for solving a stationary nonlinear problem of a nonisothermal flow of an incompressible viscoelastic polymer fluid between two coaxial cylinders is developed on the basis of Chebyshev approximations and the collocation method. In test calculations, the absence of saturation of the algorithm is shown. A posteriori estimates of two error components in the numerical solution—the error of approximation method and the round-off error—are obtained. The behavior of these components as a function of the number of nodes in the spatial grid of the algorithm and the radius of the inner cylinder is analyzed. The calculations show exponential convergence, stability to rounding errors, and high time efficiency of the algorithm developed.

We study the motion of an incompressible polymeric fluid with volume charge and construct stationary solutions of the electrohydrodynamical equations.

The time-dependent mathematical model describing the vortex motion of an incompressible polymeric liquid is discussed. In the steady-state case certain particular solutions are found. In the case of the steady-state pressure along the axis of cylinder, a version of deriving this model for both fixed and free boundaries is given.

A problem of an incompressible polymer fluid flow past an infinite flat wedge is considered. The flow moves parallel to the plane of symmetry of the wedge and normal to the wedge rib. It is demonstrated that two surfaces of strong discontinuities are needed for the no-slip condition to be satisfied on the wedge surface. Steady solutions of the problem are studied, and the flow is shown to be asymmetric with respect to the plane of symmetry of the wedge.

An asymptotic formula for the spectrum of a linearized problem of the stability of stationary flows of a polymer fluid with a space charge is obtained.

We deduce a formula of spectral asymptotics of the linearized problem for stationary flows of an incompressible weakly conducting polymeric fluid.

The existence of partial solutions, increasing with time, of the linearized equations of a nonisothermal incompressible polymer liquid is established.