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This paper is the first part of the author’s publications cycle devoted to professional stability of future teachers. The article deals with analyzing the essence of the notion of stability/consistency from the position of various sciences: philosophy, mechanics, mathematics, cybernetics, physics, sociology, ecology, psychology. Stability/consistency is considered as a characteristic feature of objects, mechanical and natural systems and their conditions, as a personal characteristic.

The paper presents a study of the dynamics of the oscillatory dissipative system of two elastically connected pendulums in a magnetic field. Nonlinear normal vibration modes of the pendulum system are studied in the paper taking into account the resistance of the medium, and the damping moment created by the elastic element. A system with two degrees of freedom is considered. The masses of the pendulums in that system differ significantly, which leads to the possibility of localization of oscillations. In the following analysis, the mass ratio was chosen as a small parameter. For approximate calculations of magnetic forces, the Padé approximation, which satisfies the experimental data the most, is used. This approximation provides a very accurate description of magnetic excitation. The presence of external influences in the form of magnetic forces and various types of loads that exist in many engineering systems leads to a significant complication in the analysis of vibration modes of nonlinear systems. A study of nonlinear normal vibration modes in this system was carried out, one of the modes is a connected mode, and the second one is localized. Vibration modes are constructed by the multiples scales method. Both regular and complex behavior is studied when changing system parameters. The influence of these parameters is studied for small and significant initial angles of the pendulum inclination. An analytical solution, which is based on the fourth-order Runge-Kutta method, is compared to numerical simulation results. The initial conditions for calculating the vibration modes were determined by the analytical solution. Numerical simulation, which consists of constructing phase diagrams, trajectories in the configuration space and spectra, allows to estimate the dynamics of the system, which can be both regular and complex. The stability of vibration modes is studied using numerical analysis tests, which are an implementation of the Lyapunov stability criterion. The stability of vibration modes is determined by the estimation of orthogonal deviations of corresponding trajectories of vibration modes in configuration space.

The paper proposes a hybrid numerical method for solving a model problem of two-phase nonequilibrium flow of an incompressible fluid in a porous medium. This problem is relevant in the modern theory of the motion of multiphase fluids in porous media and has many applications. The studied model is based on the assumption that the relative phase permeabilities and capillary pressure depend not only on saturation, but also on its time derivative. The saturation equation in this problem refers to the type of convection-diffusion with a predominance of convection, which also includes a third-order term to account for the nonequilibrium effects. Due to the hyperbolic nature of the equation, its solution is accompanied by a number of difficulties that lead to the need for an appropriate choice of the solution method. In contrast to previous works, this paper uses a finite volume element method for solving the problem, the construction of which is based on integral balance equations, and an approximate solution is chosen from the finite element space. To discretize the problem, two different dual grids are used based on the main triangulation. In this paper, a number of a priori estimates are obtained which yields the unconditional stability of the scheme as well as its convergence with the second order. The advantages of the approach used include the local conservatism of the scheme, as well as the comparative simplicity of the software implementation of the method. These results are confirmed by a numerical test carried out on the example of a model problem.

Copyright of Cybernetics & Systems Analysis / Kibernetiki i Sistemnyj Analiz is the property of V.M. Glushkov Institute of Cybernetics of NAS of Ukraine and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This paper aims to examine the functional utility of the Shanghai Cooperation Organization (SCO) for regional stability after the withdrawal of the United States from Afghanistan. The instability in Afghanistan may become a serious regional challenge for the SCO to seek an acceptable solution. The study addresses the question that how the SCO members are dealing with the emerging crisis in Afghanistan. Hence, the prospective role of the SCO in building consensus among member states is unravelled with a conceptual framework, based on two theories of international relations namely regional security complex and functional cooperation theory. These theories provide a conceptual understanding that the interests of states, belonging to a general geographical region, are integrated and their mutual cooperation is more durable than the states outside the region. Subsequently, the study explored the role of the SCO in maintaining regional security and traced its efforts for stability. To explore the complexities within the SCO while managing the nascent government of the Taliban (forbidden in Russia) in Afghanistan, qualitative data has been collected. The data includes government websites, official statements and documents, books, research articles and newspapers, published in different countries. It is found that the worsening security situation in Afghanistan is a common threat to all the members of the SCO, so consensus is required to promote practical measures including the development of Afghanistan. Therefore, the SCO is focusing on addressing the immediate and tangible consequences of the Taliban’s takeover after the withdrawal of the US forces from Afghanistan and supporting regional states to adopt functional cooperation to reconstruct Afghanistan.

Introduction. The Republic of Belarus is one of the first countries on the territory of the CIS, which introduced European design standards (Eurocodes) on its territory, while preserving the effect of building standards developed on the basis of Soviet SNIP. The republic accumulated considerable experience in the practical application and comparative analysis of these two systems of standards. The relevance of this study is contained in the discovery of the most distinctive features of normative documents, on the basis of which it is possible to determine further directions of scientific research and improvement of domestic norms.Materials and methods. Analysis and generalization of experience.Results. The paper presents the results of generalization of the experience of practical application and comparative analysis of Eurocode and CP in relation to the design of steel structures. The analysis of partial factors, classification of cross sections, welded and bolted joints is given.Conclusions. Methodological approaches to checking limit states and ensuring the reliability of steel structures in CP and Eurocodes are very similar, but there are differences in the values and sets of partial factors. When designing steel structures according to Eurocode, the methods of classification of cross-sections of rolled profiles produced according to GOST or TS need to be adjusted. Eurocode 3 provides more possibilities in the design of welded and bolted joints.

Copyright of Automatic Welding / Avtomatitcheskaia Svarka is the property of International Association Welding (Paton Publishing House) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This paper presents a stability analysis of swarm robots, a group of multiple robots. In particular, we focus on robot swarms with heterogeneous abilities, in which each robot has a different sensing range and physical limitations, including maximum velocity and acceleration. In addition, each robot has a unique sensing region with a limited angle field of view. We previously proposed a decentralized navigation method for such heterogeneous swarm robots consisting of one leader and multiple followers. With the decentralized navigation method, a single leader can navigate for followers while maintaining connectivity and satisfying the physical limitations unique to each robot; i.e., each follower has a target robot and follows it without violating its physical limitations. In this paper, we focus on a stability analysis of such swarm robots. When the leader moves at a constant velocity, we mathematically prove that the shape and orientations of all robots eventually converge to the equilibrium state. For this, we must first prove that the equilibrium state exists. Then, we show the convergence of the state to its equilibrium. Finally, we carry out experiments and numerical simulations to confirm the stability analysis, i.e., the convergence of the swarm robots to the equilibrium states.

Critical comments on the European standards for designing steel structures including welded and bolted joints have been given on the basis of application experience and executed analysis. Comments are presented in comparison with similar regulatory documents which are in effect in Belarus. European standards concerning loads (determination of calculated load values and drawing up of design load combination) have been also analyzed. Particular attention has been paid to the analysis of European standard requirements to steel and welding materials and their comparison with mechanical characteristics of similar materials used for manufacture of steel structures in Belarus. The paper gives notice to the rules which are accepted in the European norms and the rules being compared with the similar rules used in Construction rules and regulations (SNiP) lead to a significant increase in material consumption of steel structures. First of all, it concerns assignment of partial load factors and classification of sections for ensuring local stability of compressed and partially compressed elements. The paper pays a special notice to the rules of Eurocodes that do not meet requirements of State standards and technical specifications operating in the Republic of Belarus. Significant limitations of some European rules regarding calculation of centrally and eccentrically compressed elements, absence of rules for testing overall stability of through and step columns which are widely used while implementing projects Belarus have been described in the paper. Conclusions have been made on the basis of the analysis results and according to them application of European standards for designing steel structures has significant limitations on the territory of the Republic of Belarus.

The well-known evolutionary equation of mathematical physics, which in modern mathematical literature is called the Kuramoto - Sivashinsky equation, is considered. In this paper, this equation is studied in the original edition of the authors, where it was proposed, together with the homogeneous Neumann boundary conditions. The question of the existence and stability of local attractors formed by spatially inhomogeneous solutions of the boundary value problem under study has been studied. This issue has become particularly relevant recently in connection with the simulation of the formation of nanostructures on the surface of semiconductors under the influence of an ion flux or laser radiation. The question of the existence and stability of second-order equilibrium states has been studied in two different ways. In the first of these, the Galerkin method was used. The second approach is based on using strictly grounded methods of the theory of dynamic systems with infinite-dimensional phase space: the method of integral manifolds, the theory of normal forms, asymptotic methods. In the work, in general, the approach from the well-known work of D.Armbruster, D.Guckenheimer, F.Holmes is repeated, where the approach based on the application of the Galerkin method is used. The results of this analysis are substantially supplemented and developed. Using the capabilities of modern computers has helped significantly complement the analysis of this task. In particular, to find all the solutions in the fourand five-term Galerkin approximations, which for the studied boundary-value problem should be interpreted as equilibrium states of the second kind. An analysis of their stability in the sense of A. M. Lyapunovs definition is also given. In this paper, we compare the results obtained using the Galerkin method with the results of a bifurcation analysis of a boundary value problem based on the use of qualitative analysis methods for infinite-dimensional dynamic systems. Comparison of two variants of results showed some limited possibilities of using the Galerkin method.

This paper is dedicated to the study of «stability» ideas existing in the political sphere as one of the key points of official political power discourse. According to the author, the usage of “stability” concept oriented towards various manipulations of the public opinion is compared with the scientific notions expressed in domestic and foreign developments. The paper includes a comprehensive methodological optics: the author offers detailed analysis of the key contemporary concepts of “stability” with detailed presentation of the relevant requirements for the existing political order. The author makes a conclusion about the discrepancy between the meaning of “stability” in the scientific and political spheres. The paper considers such systematical political circumstances as defects in political communication and existing political language (1); political disenfranchisement and reproducing alienation of citizens from their own political rights and ideas about themselves as political actors (2); and as deliberate transformation of quite specific and instrumental discourse of “stability” and “stabilization” into a vague ethical requirement (3). The author assumes that continuing trends in Russian politics (in many ways similar to similar trends in other countries) – such as the gap between the establishment and the rest of society (a); political apathy and even depression of a large part of the population (b); and the ongoing transformation of the information space (c) – are able to exacerbate the problems of the official authoritative discourse with scientific research and even elementary common sense.

In this paper, the R-functions method is used for the first time to study the stability and vibrations of porous functionally graded (FG) sandwich plates with a complex geometric shape. It is assumed that the face layers of the plate are made of functionally graded materials, and the middle layer is isotropic, namely ceramic. Differential equations of motion were obtained using the first-order shear deformation theory with a given shear coefficient (FSDT). Two models of porosity distribution according to the power (P-law) and sigmoid (S-law) laws were studied. Analytical expressions for calculating the effective mechanical characteristics of functionally graded materials with even and uneven porosity distribution were obtained. Proposed approach takes into account the fact that the subcritical state of the plate can be heterogeneous, and therefore, first of all, the stresses in the middle plane of the plate are determined, and then the eigenvalue problem is solved in order to find the critical load. To determine the critical load and plate frequencies, the Ritz method combined with the R-functions theory was used. Developed algorithms and software are tested on case studies and compared with known results obtained by another methods. A number of problems of stability and vibrations of the porous functionally graded sandwich plates with a complex geometric shape for various layer arrangement schemes, various boundary conditions and laws of porosity distribution have been solved.

The paper considers forming interphase adsorption layers in emulsions and foams using a surfactant mixture and milk proteins. The main objective of the study is to substantiate using the surfactant mixture and milk proteins, which define the dispersed system stability. The emulsion formation process at temperatures above the fat crystallization temperature was carried out by determining the boundary shear stress, formed interphase adsorption layers, which was performed in 4×3600 s (interphase adsorption layer formation time that has the largest value of the boundary shear stress at a temperature of 20±1 °C. Behavioral mechanisms of surfactants and milk proteins on the interphase surface were substantiated in the paper in order to determine their rational concentrations. The presented method allows to define the layer strength of the system without surfactants and, with introducing the surfactant mixture, determine the rational composition of the surfactant mixture, which allows to vary the strength of interphase adsorption layers and as a result produce foam-emulsion systems with the high foaming ability, stability and ductility. Research results can be applied by food technologists, as well as technologists specialized pastry shops to create foam-emulsion systems such as creams, souffle, ice-cream, etc. We propose to use milk proteins and surfactant mixture to control the stability of dispersed systems such as foams and emulsions, as well as stable foam-emulsion systems. [ABSTRACT FROM AUTHOR]

The Cauchy problem for a wide class of fractal oscillators is considered in the paper and its numerical investigation is carried out using the theory of finite-difference schemes. Fractal oscillators characterize oscillatory processes with power memory or, in general, with heredity, and are described by means of integro-differential equations with difference kernels — memory functions. By choosing memory functions as power functions, integrodifferential equations are reduced to equations with derivatives of fractional orders. In this paper, using the approximation of the fractional derivatives of Gerasimov-Kaputo, a non-local explicit finite-difference scheme was developed, its stability and convergence are justified, estimates of the numerical accuracy of computational accuracy are presented. Examples of the work of the proposed explicit-finite scheme are given. It is shown that the order of computational accuracy tends to unity as the number of grid nodes increases and coincides with the order of approximation of the explicit finite difference scheme.

This paper is devoted to slowly varying additive fault detection with implementation of the observer-filter to be designed. Sensitivity of the observer to the external disturbance is to be minimized by the choice of its parameters. There are a lot of papers, devoted to fault detection issues, but such problems with initially given spectral features of external disturbances are not a subject of serious attention, in our opinion. External disturbances, which are considered in this research, can be presented as a sum of harmonic oscillations with given central frequency (sea wave disturbance) and a constant signal (ocean currents and wind). A suppression of the polyharmonical oscillations influence is considered as H2-optimization problem, which can be solved with application of the specific spectral approach in frequency domain. This approach is based on polynomial factorization that can improve computational effectiveness of the observer design procedures. This also guaranties nonuniqueness of the optimal solution that makes possible to provide integral action of the residual signal relatively to the external disturbance for the case when at least two sensors are used. The novel algorithm of adaptive fault estimation observer analytical synthesis is proposed and its effectiveness is demonstrated by the numerical example of the fault detection process with implementation of MATLAB package.

A clinical behaviour of the cell-based therapy in recent decades has encouraged a great interest in the culture of cell populations in vitro. One of the directions of cell therapy is transplantation of stem cells. The cell material for transplantation is obtained by culturing the patient’s cells. However, there are often problems because of the genetic mutations of cells in the process of culture, namely, the degeneration of a portion of mutated cells into "immortal" (cancerous) cells, which makes the transplantation of such material unsafe for a patient. To study development dynamics of the cell populations in vitro is quite costly. Such studies are, usually, conducted at the beginning of culture, in the middle of the process, and when completing the process of culture. It is difficult to judge t the cell population development in detail by such data. Here mathematical modelling is of importance.The papers [8-11] propose a cell population system consisting of two types of cells, namely normal (healthy) and abnormal (aneuploid) cells. Interest in such a population system is due to the fact that, although the aneuploid cells have a life time less than the normal ones, a small portion of the aneuploid cells can degenerate into practically "immortal" cancer cells, whose population may, eventually, become dominant.In the qualitative analysis of the nonlinear dynamic systems, a standard component is information on the number of rest points, their nature and location. Earlier, [16] a detailed study of the rest points and their possible nature was performed depending on the biological parameters, such as the proportion of dead cells, the average time of the cell cycle, the proportions of normal cells becoming the population of abnormal ones, etc. However, there is no exhaustive answer, yet, concerning this issueThe paper continues to study the two-component population model considered earlier [9-11, 16]. The study focuses on the zero equilibrium point. The conditions of stability are specified taking into account the fact that the dynamic system, by virtue of its biological content, must be considered in the first quadrant of the plane. In addition, a study of the zero equilibrium point has been conducted in critical cases in which the method to investigate linear approximation stability the does not work.

Optical systems with two-dimensional feedback demonstrate wide possibilities for studying the nucleation and development processes of dissipative structures. Feedback allows to influence the dynamics of the optical system by controlling the transformation of spatial variables performed by prisms, lenses, dynamic holograms and other devices. A nonlinear interferometer with a mirror image of a field in two-dimensional feedback is one of the simplest optical systems in which is realized the nonlocal nature of light fields. A mathematical model of optical systems with two-dimensional feedback is a nonlinear parabolic equation with rotation transformation of a spatial variable and periodicity conditions on a circle. Such problems are investigated: bifurcation of the traveling wave type stationary structures, how the form of the solution changes as the diffusion coefficient decreases, dynamics of the solutions stability when the bifurcation parameter leaves the critical value. For the first time as a parameter bifurcation was taken of diffusion coefficient. The method of central manifolds and the Galerkins method are used in this paper. The method of central manifolds and the Galerkins method are used in this paper. The method of central manifolds allows to prove a theorem on the existence and form of the traveling wave type solution neighborhood of the bifurcation value. The first traveling wave born as a result of the Andronov -Hopf bifurcation in the transition of the bifurcation parameter through the сritical value. According to the central manifold theorem, the first traveling wave is born orbitally stable. Since the above theorem gives the opportunity to explore solutions are born only in the vicinity of the critical values of the bifurcation parameter, the decision to study the dynamics of traveling waves of change during the withdrawal of the bifurcation parameter in the supercritical region, the formalism of the Galerkin method was used. In accordance with the method of the central manifold is made Galerkins approximation of the problem solution. As the bifurcation parameter decreases and its transition through the critical value, the zero solution of the problem loses stability in an oscillatory manner. As a result, a periodic solution of the traveling wave type branches off from the zero solution. This wave is born orbitally stable. With further reduction of the parameter and its passage through the next critical value from the zero solution, the second solution of the traveling wave type is produced as a result of the Andronov -Hopf bifurcation. This wave is born unstable with an instability index of two. Numerical calculations have shown that the application of the Galerkins method leads to correct results. The results obtained are in good agreement with the results obtained by other authors and can be used to establish experiments on the study of phenomena in optical systems with feedback.

Stability of non-conservatively loaded elastic and inelastic bodies – a classic section of deformable solid mechanics that has been of interest for many years. In this paper, we study the motion stability of a free rod subjected to a constant tracking force on one of its ends. The defining ratio of the rod material is the Kelvin-Voigt model. The solution is presented in the form of an expansion in terms of beam functions. The number of terms of this expansion is substantiated. The values of the critical load in the presence and absence of viscosity are determined. The given analytical results are confirmed by numerical calculations.

The paper deals with the problem of estimation of stability parameters of light commercial vehicle. In contrast to previously published works of domestic and foreign scientists in this publication the evaluation the stability of vehicle is made with considering of the angular stiffness of vehicles bearing system.The paper presents the results of computer simulation of conditions of bench and road tests that allow evaluating the stability of the vehicle. A feature of the simulation is that the support system in the model (chassis, cab, body) is not a set of rigid bodies, but the finite element model, which can be deformed as a result of loads acting (as it happens in reality). Positive results of a comparative analysis of simulation results and experimental data have shown that this approach allows getting more accurate results in predicting the parameters of stability of commercial vehicles.The study allows developing a method of estimating of commercial vehicles parameters of stability. The methodology focuses on using of computer modeling capabilities, but requires the adequacy of the computer models by means for comparison of the simulation results with the data of bench and road tests.

A three-mass system is defined by six parameters (three weights and three rigidity), and these six parameters are fixed. Relevance. The problem of defining the maximum stability degree is an essential and urgent topic of the linear theory of automatic control. The paper considers the maximum stability degree for a class of objects which are considered most often as models. Research objectives. Any three-mass system, that is any masses and rigidity, is considered as a control object. This three-mass system is considered as a singlechannel, operated by a regulator 3/3 (polynomial of a degree no more than 3 is the numerator of a transfer function, and a denominator is a polynomial of degree 3). Steering force is applied to the weight closest to the motionless basis; adjustable size is a deviation of the third weight. The paper considers as well the case when the steering force is applied to the weight most remote from the basis, and the adjustable size is a deviation of the first weight. The maximum (limiting) stability degree is investigated. The paper is guided first of all by the following statement proved in earlier and more volume research: for any three mass systems the maximum stability degree is provided by controllers for which the roots of a characteristic polynomial with the greatest material part form quadruple complex pair. Methods. For any fixed object, running controllers 3/3, the characteristic polynomials form some class of polynomials of the ninth degree with the senior factor 1 with two linear communications. In the class of these polynomials the steady polynomial with the maximum stability degree is sought. Then the controller providing this stability is restored by this polynomial. Results. The position of the ninth root depends only on value of an object one parameter. The paper introduces the instruction on calculation of this parameter of the object, the maximum stability degree, a characteristic polynomial and a controller 3/3 providing this stability. The calculations were carried out on the following example: weights and rigidity are equal to a unit. It turned out that in this case the ninth root of a characteristic polynomial is not the most right. Conclusions. The paper can form a basis of a technique of calculating the maximum stability degree and lower-order controllers providing this stability, and for other operated singlechannel lower-order systems.

Copyright of Proceedings of the National Academy of Sciences of Armenia. Mechanics is the property of National Academy of Sciences of the Republic of Armenia and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Sharp wave treatment for 1-D gas dynamic problem is still a chellenge for modern numerical methods. They often require too many space and time steps, produce spurious oscillation of solution, exhibit a strong numerical dissipation or divergence of results. This paper is further extension of authors’ idea of employment the analytical solution for space coordinate, where time step is a parameter which used in the space solution. Its peculiarity consists in development of additional procedure of linearization of dependence between the pressure and density. It is performed in premise that actual pressure for each space element is close to the basic pressure, attained at previous moment of time. The efficiency of method is tested on the very popular task of Sod, where two different ideal gases in a tube are separated by diaphragm, which is suddenly broken. The problem considered in Lagrangian coordinates formulation. The results obtained show the very good efficiency of method, which requires the essentially lesser time and space steps, leads to no spurious oscillation and give consistent and predictable results with respect to meshing. The accuracy of method is mostly controlled by time step, which should be larger than clearly stated theoretical lower limit. Other advantage of method is that it can calculate the process to any desired moment of time, and space meshing can be variable in time and space and can be easily adapted during the process of calculation.

In modern natural sciences, the term of a dynamic system plays an important role and is a common type of mathematical models. Dynamical systems are rarely come to simple functional dependencies. Therefore, qualitative analysis methods of dynamical systems are crucial. In the paper, we consider the simplest type of dynamic systems | continuous dynamical systems described by the systems of ordinary differential equations.Qualitative analysis of differential equations systems usually starts with a search for equilibrium points and a study of the behaviour of a dynamic system in the neighborhood of each equilibrium points. The main attention is paid to the stability of equilibrium, as well as their behaviour type classification. Effective qualitative analysis of differential equations systems is best approached through the bifurcation theory which explains modification of quality in the behaviour of a dynamic system if its parameters are changed.In the behavior of dynamic systems, in addition to the equilibrium points, other bounded trajectories (for example, boundary cycles or separatrix) and their certain conglomerates (such as attractors, invariant tori) play an important role. Investigation of bounded trajectories, in particular, attractors is a difficult task and a lot of scientific articles deal with this problem.In this paper, we study a continuous Lorenz-type system. For this system, all of the equilibrium points are defined and the analysis of equilibrium points types are performed in accordance with the system parameters. The analysis of some bifurcations of equilibrium points are carried out. In particular, the Andronov | Hopf bifurcation is determined and it is shown that it leads to a bifurcation of boundary cycles.DOI: 10.7463/mathm.0315.0789497

Problem. The determination of the stages of stability for vehicles as technical systems when moving uphill on an inclined section of the road and their possible longitudinal roll back is considered. The considered stages ensure the safe operation of vehicles in various conditions and with various combinations of the values of the parameters that are included in the proposed equations characterizing the stability of the vehicle. Goal. The purpose of the paper is to improve the method of researching the physical foundations of the stability of vehicles when moving uphill on an inclined plane, the formation of mathematical models, which allows to significantly improve the mathematical support of the methods of calculating the stability of two-axle vehicles (cars, trucks, tractors, special and specialized vehicles, etc.) Methodology. The approaches adopted in the work to achieve the set goal are based on the classical laws of the mechanics of free-standing or moving objects, namely: the principle of possible movements, where calculated dynamic and mathematical models with their solutions are able to preserve the given conditions and parameters, and characterize the state of stability of the vehicle in case of its longitudinal roll back. Results. It was established and confirmed by a numerical examples that the longitudinal stability of a vehicle moving uphill depends on the longitudinal road slope, the vehicle design, the elasticity of the road surface, the critical overturning angle of the vehicle and its weight parameters. Originality. The proposed mathematical model of the longitudinal stability of the vehicle when moving uphill showed that its solution significantly depends on the values of the geometric parameters of the uphill and the vehicle, and also depends on the position of the center of gravity of the vehicle relative to the surface of the road surface. Practical value. The obtained equations for determining the values of the stability parameters of the vehicle when moving uphill on an inclined road section make it possible to specify the parameters for ensuring the logistics of vehicles in the conditions of their operation on uphill.

In modern natural sciences, the term of a dynamic system plays an important role and is a common type of mathematical models. Dynamical systems are rarely come to simple functional dependencies. Therefore, qualitative analysis methods of dynamical systems are crucial. In the paper, we consider the simplest type of dynamic systems | continuous dynamical systems described by the systems of ordinary differential equations.Qualitative analysis of differential equations systems usually starts with a search for equilibrium points and a study of the behaviour of a dynamic system in the neighborhood of each equilibrium points. The main attention is paid to the stability of equilibrium, as well as their behaviour type classification. Effective qualitative analysis of differential equations systems is best approached through the bifurcation theory which explains modification of quality in the behaviour of a dynamic system if its parameters are changed.In the behavior of dynamic systems, in addition to the equilibrium points, other bounded trajectories (for example, boundary cycles or separatrix) and their certain conglomerates (such as attractors, invariant tori) play an important role. Investigation of bounded trajectories, in particular, attractors is a difficult task and a lot of scientific articles deal with this problem.In this paper, we study a continuous Lorenz-type system. For this system, all of the equilibrium points are defined and the analysis of equilibrium points types are performed in accordance with the system parameters. The analysis of some bifurcations of equilibrium points are carried out. In particular, the Andronov | Hopf bifurcation is determined and it is shown that it leads to a bifurcation of boundary cycles.

The paper is devoted to the problem of additive fault detection observer design for discrete LTI plants with scalar measurement and external disturbance with the known spectral features. Choice of the observer-filter parameters should maximize its sensitivity to the faults effect and minimize its response to the external disturbance signal. These features are provided by the special filter, generating the corrective signal. The specific spectral approach to discrete H2 optimization in frequency domain, based on the polynomial factorization, is applied with the aim to improve computational effectiveness of the synthesis. Some theoretical aspects are discussed and the novel algorithm of discrete adaptive fault detection observer analytical design is formulated and its effectiveness is demonstrated by the numerical example with implementation of MATLAB package.

Nonlinear discrete-time repetitive processes with Markovian jumps are considered. For such processes stability analysis is developed and this result is then applied to iterative learning control design.Stability of nonlinear repetitive processes has not been developed previously in the current literature. This paper proposes and characterizes a stability theory for nonlinear repetitive processes that includes stability along the pass of linear examples as a special case.For considered systems the second Lyapunov method cannot be used. Because repetitive processes belong to a class of 2D systems in which state variables are depend on two independent variables and cannot be solved using all first differences of state variables. It is not allow us to find a first difference of Lyapunov function along the trajectory of the system without finding solution of a system of equations that fully excludes a main advantage of second Lyapunov method. At the same time the use of vector Lyapunov functions and discrete-time counterpart of the divergence operator of this function along the trajectories of system instead of first difference allow us to obtain constructive results.In this paper based on vector Lyapunov function approach sufficient conditions for pass profile exponential stability are obtained which in the linear case are obtained in terms of linear matrix inequalities and in the linear case without failures these conditions are reduced to known conditions of stability along the passA major application area where repetitive process stability theory can be used is Iterative Learning Control (ILC). The idea of ILC is following.If the system repeats the same finite duration operation over and over again, it is reasonable to use the input and output variables on the current pass for improving accuracy of performance of operations on the next pass.The new theoretical stability results are applied to ILC design under possible information failures. The ILC law convergence reduces to pass profile stability analysis. Computation and modeling of the system have been carried out using a simplified model of a vertical axis dynamics of a gantry robot.

In this paper, we propose a new method for synthesizing the control of multi-input multi output linear plants with a guarantee of finding controlled signals in given sets under conditions of unknown bounded disturbances. The problem is solved in two stages. At the first stage, the coordinate transformation method is used to reduce the original constrained problem to the problem of studying the input-to-state stability of a new extended system without constraints. At the second stage, the control law for the extended system is obtained by solving a series of linear matrix inequalities. To illustrate the effectiveness of the proposed method, simulation in the MATLAB/Simulink is given. The simulation results show the presence of controlled signals in the given sets and the boundness of all signals in the control system. The proposed method is recommended for use in control problems where it is required to maintain controlled signals in given sets, for example, control of an electric power network, control of the reservoir pressure maintenance process, etc.

In this paper, our primary result is on the existence of non-empty fixed point sets for a new multivalued function defined here. An admissibility condition is also postulated and used in the main theorem. In two separate sections, we present data dependence and stability results for the non-empty fixed-point sets of these mappings. Some consequences of the main theorem are discussed. The analysis is in the most general setting of metric spaces. An illustrative example is discussed, which shows that our existence theorem effectively extends some results in this line of research.

In-depth studies of the topological properties of information and telecommunication networks contribute to the understanding of their functional capabilities, including stability. The study of the stability of complex networks to failures in operation when their components fail is based on modeling by sequentially removing nodes or edges of the network (percolation). The paper presents a comparative analysis of sequential and stochastic variants of percolation of network nodes and statistical estimates of the complex two-criterion network stability coefficient. During the study, methods for calculating the average path length based on graph theory were used. In the statistical analysis of the network stability, we applied the analysis of variance and pairwise comparisons according to the Tukey criterion, based on the provisions of the theory of mathematical statistics. The simulation is performed using the Barabashi–Albert and Erdős–Rényi random graph models. The difference between the method of stochastic percolation and sequential percolation is shown. The performed statistical analysis proved the influence of the factor changing the structure of networks on their stability due to stochastic percolation. The dynamics of network stability reduction under stochastic percolation for different types of networks is shown. It is revealed that in some cases, for example, in networks with high density, the stochastic percolation method is the most preferable one. The study shows the possible options for assessing the stability of networks without a priori knowledge about the type of connections between nodes and with a priori knowledge about the type of connections between nodes. In the former case, knowing the number of network nodes, one can calculate the limit values of stability, in the same way as if the nodes were deleted accidentally. The latter option can be used to calculate the stability of networks that are subject to random node failures, for example, when diagnosing technical systems.

The purpose of the article is to implement a systematic analysis of the factors of the formation of a stable system of political governance. To clarify the functions and structure of a stable political system, the characteristics of stability are highlighted, according to which the political system: has signs of legitimacy; is able to cope with the threat of illegitimate violence; supports the constitu-tional system; reproduces a model of behavior based on stability. Methodologically, the article is based on the works of classical and modern scientists (P. M. Khomyakov, M.A. Gaydes, I.B . Rodionov, A. A. Khomiakov). Makarycheva), devoted to the systematic analysis of political systems. The paper also uses morphological analysis, analysis of political efficiency, and in the final part — the method of state-management design. The author comes to the conclusion that the functions and structure of the modern political system should be considered from the point of view of the defini-tions of “political stability”, viewed through the prism of the absence of political threats, adaptive irremovability of political subjects and the balance of political forces. Political stability implies that the distribution of resources in society involves not only the institutional subsystem of the political system, but also the functional, regulatory and ideological subsystems. Morphological analysis demonstrates that a stable political system is characterized by a balanced interaction of subsystems, in which at least the institutional, regulatory and functional subsystems jointly determine the process of functioning and development of the political system. Stability is the basis and guarantee of po-litical development in the modern world, and stability is not contrary to innovative development or development in general. Both stability and development are the basic conditions for the development of a modern political system, methods of avoiding negative adaptation in the global environment. Stability is not synonymous with closeness — on the contrary, it implies horizontal and vertical mobility, a constitutional system, and a focus on maintaining the activity of political actors. At the same time, all these processes cannot be allowed to take their course and develop outside the political control of the vertical structures of power. Integrity as a system-wide property is an integral basis for the stability of the political system.

The paper presents comparative test results of 12 domestically produced diagnostic kits/PCR test systems for DNA detection of the African swine fever virus with regard to the following parameters: completeness and correctness of instructions for use; labeling and package contents; convenience of using the kit; shelf life stability of reagents; stability of reagents after transportation and repeated freezing – thawing; batch-to-batch repeatability; sensitivity of various test materials and specificity of kits. The study of the instructions for use and kit contents revealed incompleteness of some instructions. It was noted that some manufacturers make serious errors in the instructions, which can significantly affect the interpretation of test results. It was also observed that there is insufficient control of the manufacturing process, which results in the production of faulty kits, as well as kits with poor-quality components and errors in the labeling. Thus, during the study, one kit showed its inactivity, demonstrating the absence of accumulation curves of the fluorescent signal during amplification of both positive controls and DNA of ASFV isolates. When the specificity was assessed, all the kits showed absence of non-specific reactions and acceptable sensitivity when testing various types of ASFV-containing material (blood, suspensions of pork spleen and pork casings used in sausage production). The stability test showed a sharp deterioration in the quality of operation of one kit within the shelf life period, and a significant decrease in the fluorescence signal was detected during repeated freeze – thaw cycles for another kit. Comparison of the repeatability results of different kit batches of the same manufacturer showed significant discrepancies for 41.5% of all kits. It was found that only 33% of the studied kits for ASFV DNA detection were compliant. The results of this study demonstrate the need for control of the manufactured diagnostic kits used in state programs for animal disease monitoring.

In this paper, we study an initial boundary value problem for a differential equation with a fractional order derivative in time in the Caputo-Fabrizio sense. This equation is of great practical importance in modeling the processes of fluid motion in porous media and anomalous dispersion. The uniqueness and continuous dependence of the solution of the problem on the input data in differential form is proved. A computationally efficient implicit difference scheme with weights isproposed. A priori estimates are obtained for the solution of the problem under the assumption that the solution exists in the class of sufficiently smooth functions. The uniqueness of the solution and the stability of the difference scheme with respect to the initial data and the right-hand side of the equation follows from the obtained estimates. The convergence of the difference problem solution to the differential problem solution with the second order in time and space variablesis proved. The results of computational experiments confirming the reliability of the theoretical analysis are presented.

The presented paper is devoted to the problem of the fault estimation observers design in case of plants with the Lipschitz system nonlinearity. Insensitivity of the observer to external disturbances, including ones with the given spectral properties, is to be guaranteed by the choice of its parameters. The proposed method is based on the special spectral approach in frequency domain, using parametrization of the set of transfer functions of the closed-loop system, Nevanlinna-Pick rational function interpolation and the condition of asymptotic stability of the zero equilibrium position of the estimation error dynamics. A novel approach to analytical synthesis of the adaptive nonlinear fault estimation observer is proposed, and its effectiveness is demonstrated on the practical example – the marine ship horizontal motion with the constant longitudinal speed under the sea waves action. The MATLAB package is used for numerical simulation of the ship dynamics.

Promising direction of heat-transfer intensification is modification of the liquids used as coolants or working bodies for various kinds of equipment. Within this framework the usage of nanofluids (suspensions of nano-size particles (up to 100 nm) in a base fluid) is proposed. The results obtained have shown that the additive of Al2O3 nanoparticles to isopropanol increases the heat transfer coefficient during pool boiling up to 10-26%. However, such effect was found only at the low heat flux densities. At the high heat flux densities the presence of the nanoparticles in isopropanol leads to decreasing the heat-transfer coefficient. According to the authors, this is the result of nanofluid destabilization. It is shown that the complex nature of nanoparticles Al2O3 effect on the changes in heat-transfer coefficient is related to a combined contribution of different factors: interaction of nanoparticles with heating surfaces, changing in thermal properties of nanofluids compared to the base fluid, hydrodynamic radius of nanoparticles and their concentration in isopropanol. According to the authors, the possible reason of nanofluid destabilization during pool boiling may be the destruction of heterogeneous micelles on the heater surface. Therefore, the study of nanofluids pool boiling and correct interpretation of the collected data should consider the stability, concentration changes of nanofluid and heating surface properties. The study on hydrodynamic radius of nanoparticles was carried out using experimental setup wherein DLS method has been realized. The results has shown increasing in hydrodynamic radius from 53 to 86 nm with an increasing in the mass fraction of nanoparticles from 0.036 to 4.2 wt.%. The experiments to determine the stability of nanofluid has shown that the system remains stable throughout the period of the experiment (100 hours), temperatures interval (20-70 °C) and the mass fraction of nanoparticles (0.036-4.2 wt.%). In addition, in this paper, the dependence of the mass fraction of Al2O3 nanoparticles in isopropanol on the value of the transmitted light through the nanofluid was obtained. The magnitude of the transmitted through the nanofluid light is proportional to the mass fraction of nanoparticles. [ABSTRACT FROM AUTHOR]

Mine surveying in mining operations is of particular importance, since all technological processes of the full life cycle of a mining enterprise and, ultimately, its competitiveness depend on the surveying quality, efficiency and reliability. Organizations independently determine the structure of mine surveying services, taking into account the methods applied and the scale of mining. To ensure safe open-pit mining of minerals, it is necessary to permanently assess and monitor the pit bench and wall rock mass condition. Misjudgement of rock physical and mechanical properties, non-observance of the minerals mining and transportation process cycle, changes in climatic conditions and other problems lead to loss of stability of rocks in all parts of an open pit, including in the areas of ore production and mining and transport equipment operation. The existing practice shows that the effectiveness of an open pit wall and bench stability calculation can be achieved using a technique that should take into account the slope deformation and failure mechanism, as well as the nature of the stress-strain state of the open pit rock mass. The studies presented in the paper are based on comparative analysis of the sliding wedge parameters for benches, dumps and roads at open pits using analytical and graphical software packages, and taking into account the static load produced by dump trucks. The study findings allow to establish that: determination of the bench slope stability and the sliding wedge width, performed by the analytical method, gives higher accuracy results than those obtained by the graphical method; the bench slope stability and the sliding wedge width depend not only on the rock physical and mechanical condition, but also on the bench height, the dump truck (plus its freight load) weight per 1 linear meter of the placement area, the distance from the slope edge and other factors; the rock mass is stable and not subject to landslide phenomena for as long as the sum of the holding forces is greater than or equal to the sum of the shearing forces; when using large-sized transport equipment of nonstandard weight in open-pit mining, it is necessary to calculate the safe width of the sliding wedges, taking into account the loads on them (per 1 linear meter), the values of which can be 1.5–2.0 times higher than those calculated for the circular-cylindrical sliding surface.

In this paper, an initial-boundary value problem for the equation of forced vibrations of a cantilever beam is studied. Such a linear differential equation of the fourth order describes bending transverse vibrations of a homogeneous beam under the action of an external force in the absence of rotational motion during bending. The system of eigenfunctions of the one-dimensional spectral problem, which is orthogonal and complete in the space of square-summable functions, is constructed by the method of separation of variables. The uniqueness of the solution to the initial-boundary value problem is proved in two ways: (i) using the energy integral; (ii) relying on the completeness property of the system of eigenfunctions. The solution to the problem was first found in the absence of an external force and homogeneous boundary conditions, and then the general case was considered in the presence of an external force and inhomogeneous boundary conditions. In both cases, the solution of the problem is constructed as the sum of the Fourier series. Estimates of the coefficients of these series and the system of eigenfunctions are obtained. On the basis of the established estimates, sufficient conditions were found for the initial functions, the fulfillment of which ensures the uniform convergence of the constructed series in the class of regular solutions of the beam vibration equation, i.e. existence theorems for the solution of the stated initial-boundary value problem are proved. Based on the solutions obtained, the stability of the solutions of the initial-boundary value problem is established depending on the initial data and the right-hand side of the equation under consideration in the classes of square-summable and continuous functions.

To effectively solve the problems of operational dispatch control of the operating modes of the unified power system, its individual power systems and power districts, in particular, oil production power districts, it is required to carry out calculations of the established modes of electrical networks. In addition, along with the calculations of steady-state regimes, it is important to study the stability of the power grid operation. The convergence and rate of convergence of widely used iterative methods for calculating steady-state modes depend on many operating and design factors determined by the network and mode parameters, the choice of initial approximations, and the method for specifying the initial data. Therefore, the development of new methods that make it possible to calculate all steady-state regimes are of significant practical interest.One of the promising techniques is the holomorphic imbedding method. In this method, the unknown parameters of the nodes are represented in the form of holomorphic functions, which can be written in the form of power series, the coefficients of which are calculated using recurrent expressions, and the problem is reduced to finding the coefficients of the power series. In a previously published article by the authors, the method is considered for a circuit with load nodes. For a complete correct analysis of the modes of real power systems, it is necessary to show how to calculate for generating units. The paper presents recurrent expressions for calculating the unknown coefficients of the holomorphic functions of the unknown parameters of the system of steady-state equations for the load and generator nodes. The expressions obtained, in contrast to those proposed in the works of other authors, are more general. The principle of forming a matrix equation for finding unknown coefficients with the division of complex parameters into real and imaginary parts is shown. A method for obtaining converging power-law in some cases is proposed. On the example of a test power system, the advantage over the Newton–Raphson method is shown. We consider the question of evaluating the existence of a solution to the system of equations of the steady state for a multinode network based on a sigma-graph. An approach is proposed to determine the indicator of the static stability margin of the power system, based on the Fabry criterion. The aim of the research isto apply the analytical method of holomorphic imbedding to calculate an electrical circuitcontaining load and generator units; to evaluate the influence of the number of calculated power series coefficients on the accuracy of the obtained solution, and also to consider ways to increase the numerical accuracy of the solution, consider the question of evaluating the existence of a solution to the system of equations of the steady state for a multi-node network based on the analysis of power series. Methods: Taylor expansion, analytic continuation, Padé approximation, solving algebraic equations by the recursive method. Results. Using the example of a scheme with a poorly conditioned Jacobi matrix, in which the Newton–Raphson method does not converge from a flat start, the advantage of the holomorphic immersion method is shown. The influence of the number of members of the power series on the calculation error is shown. For the considered scheme, a graphical estimate of the existence of a solution to the system of equations is performed. Conclusions. For load and generator nodes, the unknown parameters can be represented as holomorphic functions, which can be written down as a Taylor series, the coefficients of which are calculated using recurrent expressions. Partial consideration of shunts to the ground in the diagonal elements of the matrix of successive conductances makes it possible to obtain converging power series in some cases. The considered graphical method for assessing the possibility of the regime existence allows us to make a rough estimate. Unlike classical iterative methods, an initial approximation is not specified for the holomorphic immersion method.

The relevance of the study is caused by the need to develop the effective technologies to ensure the preservation of the design position of the main pipeline sections in the areas with permafrost distribution. The workis of particular relevance, taking into account active development of the northern and Arctic gas and oil regions of Russia. The main aim of the research is to develop a design solution and the construction of underground supports for fixing non-heat-insulated sections of the pipeline in seasonally thawing and insular permafrost. Objects: main pipeline fixed in frozen soils. Results. The paper considers the existing types of supports and suspensions of pipelines in the context of their applicability for the fixing underground sections of oil and gas pipelines in permafrost and seasonally thawing soils, including at the intersection of insular permafrost, ice lenses and pingos. Based on the results of the analysis of the possible loads and limitations of existing supporting structures of pipelines with the risks of emersion and sagging of underground sections in the melted trench, the design of underground anchor supports is proposed and conclusions are made about the advantages of their use. To calculate the loads and determine the required dimensions and number of anchors, cross-sections of stretch ropes and a mounting clamp, a finite-element model was developed. Its effectiveness was confirmed analytically and experimentally on the developed test bench.

The paper substantiates the conditions of seismic stability in the rock mass with cavities, on which protected objects are located, under constant seismic effects of mass explosions in quarries. Based on the ray-tracing method, a mathematical model of the interaction between longitudinal and transverse waves with a spherical cavity has been developed. An algorithm has been elaborated for determining the total static and dynamic loads along the spherical cavity perimeter from seismic explosion waves falling on the interface. The regularities of joint action of static loads have been determined, when located above the objects cavity, with allowance for the effect of the mass of cavity ceiling, the mass of the protected object above it and dynamic loads in the rock mass, and under the plane wave front fall on the cavity from different directions. The dependences of the change of total stresses referred to the incident wave stress at the interface of the rock mass and the cavity depending on the coordinate on its surface have been set. It has been established that the most dangerous points of cavity surface, in which destruction is likely to occur, are the cases when the seismic wave front falls on the cavity from the bottom directions typical for blasting operations in deep quarries. Under the arbitrary angles of the wave incidence on the cavity the stresses rearrange along the perimeter, which under different circumstances might lead to the mass breach and the fall of the protected objects, located above it, under the ground. [ABSTRACT FROM AUTHOR]

An upcoming anniversary of the USSSR dissolution raises the opportunity to overview the tendencies of the development of the state systems, emerged on its fragments. A retrospective view of this process, which has received various (sometimes contradictory) political and expert assessments, raises the main question – the viability and prospects of sustainable development of the former USSR countries.The shared past continues to have a significant impact through the Soviet legacy, making these countries difficult to analyze and raise questions about the effectiveness of common tools for assessing their resilience and stability.The paper describes the application of the model of resilience and stability of the state systems, developed earlier in a co-authorship within the framework of joint research. The estimates obtained make it possible to form the profile of some countries and determine the structural imbalances in the development of their state systems in terms of resilience and stability.

The paper is devoted to the construction and research of a mathematical model of self-oscillations of an aerodynamic pendulum in the flow of a medium. As a model of the influence of the medium on the body, the model of quasi-static flow around the plate by the medium is adopted. According to this hypothesis, the aerodynamic forces acting on the body are applied at the center of pressure. In this problem, the center of pressure is mobile relative to the plate. The equations of motion for the body under consideration are obtained. The transition to new dimensionless variables is performed. Violation of uniqueness in determining the angle of attack is shown. Parametric analysis of ambiguity areas is performed. All stationary points that are solutions of the equilibrium equations are found. It is shown that there is no ambiguity in the most characteristic equilibrium position corresponding to the state of rest. A study of the stability of various equilibrium positions in which the Hurwitz criterion is implemented and the stability regions are depicted. It is shown that the forces of aerodynamic action for bodies with some shapes can contribute to the development of self-oscillations, and for others to damping. In the Matlab 18 mathematical package, a set of programs is written that allows you to build stability regions and perform numerical integration of equations describing body vibrations in order to confirm the adequacy of the constructed model.

The paper focuses on measuring and evaluating the impact of selected technical and technological factors -the height of adjustable guides and stretching force - on the side deflection of the saw band of a joinery band saw. There is a detailed description of the ways the side deflection can be measured. In order to find out the intensity of the stretching force was used portable tension meter SANDVIK 5000, enabling to check the tensile stress in the saw blades of a gang saw or in the saw bands of a band saw. The actual experiment was conducted on a joinery band saw, at the cutting rate vc = 15 m·s-1. The results of the measurements confirmed the theoretical assumption of the impact of the selected technical and technological factors on the stability of the saw band, where the side deflection decreases with increasing stretching force and increases with increasing height of the guides. The stability of the saw band affects the quality of the surface to be treated, thus saving the cost of machining the workpiece and making work productivity more efficient.