Necessary Conditions For Stability Research Articles

Обеспечение энергетической безопасности России в условиях перехода к зелёному курсу экономики

In modern conditions, each state strives to ensure its economic security, thereby trying to create the necessary conditions for stability and sustainable development. In recent years, the country’s energy security, which is a key component of economic security, has become increasingly important. The relevance of the study lies in the fact that in modern socio-economic conditions of the country’s development it is necessary to develop the energy sector, promptly identify and neutralize existing and emerging threats to Russia’s energy security, which contributes to a gradual transition to a green economic course. The purpose of the work is to study the theoretical aspects of energy security, study its current state in the Russian Federation, as well as develop measures to facilitate the transition to a green economic course. When conducting the research, methods such as the dialectical method of cognition, monographic research, horizontal and vertical analysis, statistical methods, the method of comparing and summarizing information, as well as the method of tabular presentation of information were used. Russia’s energy security is gradually developing, as evidenced by the increase in some indicators and the decrease in others, while there is a need for further development and additional government regulation in order to achieve a higher level of energy security. Reorientation of the energy sector to the use of renewable energy sources is an important strategic task for Russia. Increasing the capacity of generating facilities that operate on the basis of renewable energy sources helps improve the quality of energy supply to the population, reduce environmental pollution and increase the level of energy security. The authors studied the theoretical aspects of energy security. An assessment of the current and future state of energy security in the country was carried out. A conclusion is made about the need for structural changes in the energy sector in order to achieve planned energy security indicators.

Government regulation of the electricity market: foreign experience and prospects for the modernization of domestic legislation

The article is devoted to the study of strategic objectives of reforming the electricity market. Electricity is the basic sector of a national economy, the effective functioning of which is a necessary condition for stabilization and structural transformation of the economy and meeting the needs of the population. The efficient functioning of the electricity market is also a component of the state's energy security. The energy industry of Ukraine is an economic guarantee of state sovereignty, an element of good governance, a reliable basis for the sustainable development of a competitive economy and an integral part of the European energy space. non-discriminatory access to the power grid; timely development of the power grid economy in accordance with the needs of the economy; absence of restrictions on electricity transmission.The article analyzes the possibility of applying the experience of foreign countries in regulating the electricity market in order to increase the efficiency of the electricity industry and the competitiveness of Ukraine in the European market. Comparative characterization of foreign and Ukrainian experience of state regulation of the electricity market is a necessary step towards improving the electricity market. Exchange of experience, conclusion of bilateral and multilateral agreements and other major reforms will help bring the national model of regulation in this area to the next level in order to meet the international and European standards. A detailed analysis of the electricity market and the experience of foreign countries was made, some gaps in regulation and legislation were identified, and therefore the need to improve the legislative regulation of the electricity market was revealed. building market relations and establishing healthy competition.

Modeling and numerical analysis of a fractional order model for dual variants of SARS-CoV-2

This paper considers the novel fractional-order operator developed by Atangana-Baleanu for transmission dynamics of the SARS-CoV-2 epidemic. Assuming the importance of the non-local Atangana-Baleanu fractional-order approach, the transmission mechanism of SARS-CoV-2 has been investigated while taking into account different phases of infection and various transmission routes of the disease. To conduct the proposed study, first of all, we shall formulate the model by using the classical operator of ordinary derivatives. We utilize the fractional order derivative and the model will be extended to a model containing fractional order derivatives. The operator being used is the fractional differential operator and has fractional order Φ1. The model is analyzed further and some basic aspects of the model are investigated besides calculating the basic reproduction number and the possible equilibria of the proposed model. The equilibria of the model are examined for stability purposes and necessary conditions for stability are obtained. Stability is also necessary in terms of numerical setup. The theory of non-linear functional analysis is employed and Ulam-Hyers’s stability of the model is presented. The approach of newton’s polynomial is considered and a new numerical scheme is developed which helped in presenting an iterative process for the proposed ABC system. Based on this scheme, sample curves are obtained for various values of Φ1 and a pattern is derived between the dynamics of the infection and the order of the derivative. Further simulations are presented which show the cruciality and importance of various parameters and the impact of such parameters on the dynamics and control of the disease is presented. The findings of this study will also provide strong conceptual insights into the mechanisms of contagious diseases, assisting global professionals in developing control policies.

General theoretical aspects of responsibility of civil servants

The article examines the content of the concept of legal responsibility of civil servants as an element of the legal status of civil servants, reveals its normative consolidation, types (disciplinary, administrative, etc.), emphasizes the importance of civil servants aimed at improving law and order in society. Liability of civil servants is allocated as a separate institution, which contains the grounds for prosecuting civil servants, for example, for improper performance of their duties, a civil servant may be prosecuted, for example, disciplinary action and so on
 The domestic legal framework is systematically updated, in particular in the context of the civil service, which is important for the adaptation of the civil service to European standards. An important event for our country was the signing of the Association Agreement between Ukraine and the European Union in 2014, as this document had a great impact on the domestic system of public administration, civil servant status, which includes legal liability, which is a necessary condition for stability, prestige and impartiality of the civil service in general. Nevertheless, the system of legal regulation of the civil service does not yet fully meet the needs of civil society, in particular the need to provide quality public services.
 The problematic aspects of bringing civil servants to justice are analyzed, for example, insufficient publicity of imposing disciplinary sanctions, which can lead to «silencing» the process or avoiding them from legal responsibility, etc .; proposals were made to define the concept of legal liability of civil servants and its main features.

A Stable Condition and Adaptive Diffusion Coefficients for the Coarse-Mesh Finite Difference Method

Coarse-mesh finite difference (CMFD) method is a widely used numerical acceleration method. However, the stability of CMFD method is not good for the problems with optically thick regions. In this paper, a stability rule named the “sign preservation rule” in the field of numerical heat transfer is extended to the scheme of CMFD. It is required that the disturbance of neutron current is positively correlated with that of the negative value of flux gradient. A necessary condition for stability of the CMFD method is derived, an adaptive diffusion coefficient equation is proposed to improve the stability of CMFD method, and the corresponding revised CMFD method is called the rCMFD method. With a few modifications of the code, the rCMFD method was implemented in the hexagonal-Z nodal SN (discrete-ordinates) solver in the NECP-SARAX code system. The rCMFD method and other similar acceleration methods were tested by three fast reactor problems which were obtained by modifying the hexagonal pitches of a benchmark problem. The numerical results indicated that the rCMFD method showed better stability than the traditional CMFD method and the artificially diffusive CMFD (adCMFD) method and a better convergence rate than the adCMFD method and the optimally diffusive CMFD (odCMFD) method for these fast reactor problems.

On stability and instability of stratified elastic solids in a gravity field

Stability and instability of the equilibrium of stratified elastic solids in a uniform gravity field are studied by means of analysis of the second variation of total (elastic and gravitational) potential energy of the solid. By stratification is meant a continuous dependence of density and incremental elastic moduli of the material on vertical coordinate. The unperturbed stress state is supposed to be hydrostatic, whereas the incremental shear stiffnesses for perturbing deformations are nonzero. Obtained analytically both the necessary condition and the sufficient condition for stability demonstrate stabilizing effect of shear stiffness. For shear stiffnesses approaching zero, each of the conditions converts into obtained earlier by the authors the necessary and sufficient stability condition for stratified compressible fluids (having zero shear stiffness).The sufficient condition for stability for given stratifications of density and bulk modulus, and arbitrary dimensions of the domain, occupied by the solid, yields semi-infinite range of values of shear stiffnesses ensuring stability of the solid for conditions under which the corresponding stratified compressible fluid would be unstable.The sufficient condition for instability (negation of the necessary condition for stability) yields such a nonzero value of shear stiffness, that for shear stiffnesses below it the solid is surely unstable. This value (the lower bound for the exact critical value) depends on horizontal dimensions of the domain occupied by the solid, and on thickness of the layer where the stability condition for corresponding stratified fluid would be violated.Possible applications of obtained theoretical results are discussed.

Lyapunov Spectra Behavior for Linear Time-Varying Discrete Systems Under Small Perturbations

We investigate the behavior of the Lyapunov spectrum of a linear time-varying discrete system under the action of small perturbations in order to obtain some verifiable conditions for stability and openness of the Lyapunov spectrum. To this end we introduce the concepts of broken away solutions and splitted systems. The main results obtained are a necessary condition for stability and a sufficient condition for the openness of the Lyapunov spectrum, which is given in terms of the system itself. Finally, examples of using the obtained results are presented.

The mechanical behavior of 2-D lattices with bi-stable springs

Multi-stable structures offer a unique set of mechanical properties, such as the ability to undergo large reversible deformations, the ability to provide mechanical protection and efficient shock absorption, and the ability to retain variety of geometrical configurations after loads have been removed. In addition, the study of lattice-based multi-stable structures is of relevance to a wide range of engineering and physical phenomena, such as atomic models of shape memory materials, mechanics of protein networks, foldable structures for engineering applications, and the development of new meta materials that display extraordinary behaviors. In this paper, we study theoretically and numerically the quasi-static behavior of 2-D multi-stable lattices. Special emphasis is placed on equilibrium configurations, evolution of transition patterns, stability, force-displacement relations, and hysteresis. In addition, the influence of the lattice geometry and the properties of the bi-stable springs on the abovementioned features are investigated. We show that approximating the non-monotonous force-strain relation of the bi-stable springs by a tri-linear relation enables closed-form formulation and analytical insights. These, together with extensive numerical simulations, demonstrate the wealth of equilibrium configurations and that the overall response as well the transition sequence may exhibit an ordered pattern, a disordered pattern, or a combination of both, depending on the lattice parameters. The closed-form analytical formulation has also been found advantageous in analyzing the stability of equilibrium configurations. We show that necessary conditions for stability can be neatly expressed in terms of the Lucas sequence and the corresponding metallic mean, which for some class of lattice parameters, can be replaced by the Fibonacci sequence and the Golden ratio.

The impact of a political shock on foreign exchange markets in a small and open economy: A dynamic modelling approach

Abstract This paper aims to analyse the dynamics of foreign exchange markets in a country facing political uncertainty that prompt capital outflow from the country1. The economic environment under investigation is characterized by dual foreign exchange markets: a formal or official market for foreign exchange with insufficient and volatile foreign exchange flows, and a strong and thriving informal market, with a higher exchange rate2. The findings in the paper indicate a necessary condition for stabilization of the exchange rate system and that is that the return on investment should exceed the depreciation rate of domestic currency in the formal foreign exchange market. This condition implies that the return on investment should at least compensate investors for the opportunity cost of holding domestic money in their private portfolio wealth. Our findings also indicate that stability of the foreign exchange rates is more difficult to achieve under insufficient official reserves as the recovery process from a shock becomes more costly in terms of time period needed for the adjustment process to complete. The dynamic path of the foreign exchange premium shows that under massive capital outflow caused by economic sanctions, the informal market exchange rate overshoots the equilibrium stationary exchange rate, and the size of such overshooting depends on the size of available foreign exchange reserves held by the central bank.

A product form for the general stochastic matching model

AbstractWe consider a stochastic matching model with a general compatibility graph, as introduced by Mairesse and Moyal (2016). We show that the natural necessary condition of stability of the system is also sufficient for the natural ‘first-come, first-matched’ matching policy. To do so, we derive the stationary distribution under a remarkable product form, by using an original dynamic reversibility property related to that of Adan, Bušić, Mairesse, and Weiss (2018) for the bipartite matching model.

Evolutionary stability of behavioural rules in bargaining

I study the evolutionary stability of behavioural rules in a bargaining game. Each individual bargains in a pairwise manner with all other individuals over the division of a pie of fixed size by claiming a share for himself; individuals in a pair receive their respective claims if and only if the sum of the claims does not exceed unity. Each individual is associated with a behavioural rule which determines the share he chooses to claim. A behavioural rule is a correspondence that maps from a set of demands that were claimed by individuals in the recent history of the game into a set of shares, and each share in the latter set is chosen by the individual with positive probability. The evolutionary fitness of a behavioural rule is determined by the shares obtained by individuals who follow that particular rule, and fitter behavioural rules are selected over rules that are less fit. A state, i.e. a profile of claims made by the individuals in the population, is defined to be stable (neutrally stable) if the population continues to be comprised only of the incumbent behavioural rules (all incumbent behavioural rules continue to exist) even in the face of an appearance of a mutant behavioural rule. I formalise this in terms of two conditions. Firstly, internal stability requires the incumbent behavioural rules in the population to be equally fit. Secondly, external stability (neutral external stability) requires incumbent behavioural rules to be fitter (to not be less fit) than any mutant behavioural rule. I show that: (i) a necessary condition for stability of a state is that the state must be such that each individual responds by claiming a time-invariant share of the pie, and (ii) the state where all individuals demand half of the pie is the only state that is both internally stable and neutrally externally stable.

Application of the variational method for studying stability of the 3D Lotka — Volterra system

The paper investigates the stability of the Lotka — Volterra dynamic system ≪predator — two preys≫ with the help of variational method. This method is applicable for studying equilibrium stability non-linear dynamical systems of any kind and in any dimension. It approves its effectiveness even in cases where the use of the Lyapunov function causes great difficulties (for example, when solving tasks of large dimension). The proposed method is based on a variation method for estimating the rate of phase-state metric change for the perturbed system when the variable t → ∞. The disadvantage of the variation method is the fact that this method provides only the necessary conditions of stability. However, its it forms the first step in studying the stability of non-linear dynamical systems of any kind and any dimension.

Stability Conditions for Coupled Autonomous Vehicles Formations

In this article, we give necessary conditions for the stability of coupled autonomous vehicles in $\mathbb {R}$ . We focus on linear arrays with decentralized vehicles, where each vehicle interacts with only a few of its neighbors. We obtain explicit expressions for necessary conditions for stability in the cases where a system consists of a periodic arrangement of two or three different types of vehicles, i.e., configurations as follows:... 2-1-2-1 or... 3-2-1-3-2-1. Previous literature indicated that the (necessary) condition for stability in the case of a single vehicle type (...1-1-1) held that the first moment of certain coefficients of the interactions between vehicles has to be zero. Here, we show that this does not generalize. Instead, the condition (necessary) in the cases considered is that the first moment plus a nonlinear correction term must be zero.

A compact higher-order finite-difference scheme for the wave equation can be strongly non-dissipative on non-uniform meshes

We study necessary conditions for stability of a Numerov-type compact higher-order finite-difference scheme for the 1D homogeneous wave equation in the case of non-uniform spatial meshes. We first show that the uniform in time stability cannot be valid in any spatial norm provided that the complex eigenvalues appear in the associated mesh eigenvalue problem. Moreover, we prove that then the solution norm grows exponentially in time making the scheme strongly non-dissipative and therefore impractical. Numerical results confirm this conclusion. In addition, for some sequences of refining spatial meshes, an excessively strong condition between steps in time and space is necessary (even for the non-uniform in time stability) which is familiar for explicit schemes in the parabolic case.

Stability and Stabilization of Steady Rotations of a Spherical Robot on a Vibrating Base

This paper addresses the problem of a spherical robot having an axisymmetric pendulum drive and rolling without slipping on a vibrating plane. It is shown that this system admits partial solutions (steady rotations) for which the pendulum rotates about its vertical symmetry axis. Special attention is given to problems of stability and stabilization of these solutions. An analysis of the constraint reaction is performed, and parameter regions are identified in which a stabilization of the spherical robot is possible without it losing contact with the plane. It is shown that the partial solutions can be stabilized by varying the angular velocity of rotation of the pendulum about its symmetry axis, and that the rotation of the pendulum is a necessary condition for stabilization without the robot losing contact with the plane.

Empirical stability criteria for parametrically driven solitons of the nonlinear Schrödinger equation

For the parametrically driven nonlinear Schrödinger equation, two criteria for the dynamical stability of solitons are presented, using the driving force f(x, t) = a exp[2 i K(t) x]. Both criteria are based on the results of a collective coordinate theory. In this theory, the parameters of the 1-soliton solution are allowed to depend on time and a variational approach yields a set of coupled nonlinear ODEs for the collective coordinates. The solutions of these ODEs are used to compute the soliton’s normalized momentum p(t), velocity v(t), and a parametric plot p(v). The first criterion states that a sufficient condition for instability is fulfilled if the curve p(v), or a piece of it, has a negative slope. If the slope is positive then a necessary condition for stability is fulfilled. For constant K, a second criterion is presented. Here a complex wavefunction is calculated and a parametric plot of its imaginary part vs its real part is made. This yields a closed orbit in the complex plane. If this orbit has a negative sense of rotation with respect to a fixed point, then a sufficient condition for instability is fulfilled, whereas a positive sense is a necessary condition for stability. The ensemble of orbits and fixed points is a so-called phase portrait, which is very helpful for the classification of the different types of solutions of the ODEs. Finally, the validity of the two criteria is tested by comparing with simulations for the driven nonlinear Schrödinger equation. Both criteria make correct predictions about the stability and instability of the solitons, with the exception of a few cases at the border between stability and instability regions.

Practical Regulation of Nonholonomic Systems Using Virtual Trajectories and LaSalle Invariance Principle

This paper investigates the regulation problem for a class of nonholonomic systems that includes power form systems and an approximated system of the rolling sphere as special cases. The basic idea is first to introduce a virtual periodic moving trajectory that satisfies certain persistent excitation condition (PE) and has the zero value at some time instants. Based on LaSalle invariance principle, the associated tracking problem is then solved under a necessary condition for stabilization and particularly true for the power form systems and the rolling sphere. With the help of virtual trajectory, the achieved tracking result is applied to the regulation problem and used to guarantee practical stability. The proposed controllers have a simple and explicit form, and hence are easily implemented. Simultaneously, fast convergence is guaranteed, thanks to the K-exponential convergence. More interestingly, the used approach is adding sufficiently exciting signals to the systems by considering virtual tracking signals so that the attractivity of the origin can be guaranteed based on LaSalle invariance principle. Thus, it is possible to extend the proposed results to more general systems. To verify the effectiveness of the proposed scheme, interesting simulation results are presented.

Stability of synchronous regimes in unbalanced rotors on elastic base

The stationary dynamics of an unbalanced rotor (vibrator) on a movable base (linear oscillator) under excitation by a driving torque is studied with focusing on the stability of 1:1 stationary regimes of rotation and oscillation. This problem was well studied previously in the first approximation, dealing, in fact, with averaged regimes, mainly in the framework of asymptotic procedures. We use an efficient analytical procedure, proposed in our previous works for another problem, which sequentially separates the averaged regimes and deviations from them. Describing in the first approximation the known features of the synchronous stationary regimes under consideration, this approach in the second approximation results in the analytical solution for nonuniform rotation whose exactness is confirmed in the numerical simulation. The solution enables us to reveal possibility of parametric instability for oscillations of the rotor angular velocity and to describe two possible mechanisms of this instability. It is shown that the known condition of stability of stationary synchronous rotation-oscillation regimes is only necessary but not sufficient criterion, and two additional necessary conditions of stability are obtained and confirmed by the numerical simulation.

On the stability of certain motions of a rigid body-gyrostat in an incompressible ideal fluid

This work is devoted to investigating the stability of motion of a rigid body-gyrostat in an incompressible ideal fluid. This motion is assumed to happen under the action of neutral forces (buoyancy and gravity) whose centers are not coincide. The equations of motion are introduced, and they are expressed by means of the Hamiltonian function in the framework of the Lie-Poisson system. We prove that the problem of motion of a gyrostat in an incompressible ideal fluid is equivalent to the general problem of the motion of a rigid body under the action of a combination of potential and gyroscopic forces. We endeavor for studying the stability of two possible types of stationary solutions which describe the spin motion and non-spin motion of a gyrostat. For the non-spin motion, we consider two stationary solutions for which the translation motion is either in direction of the gravity or in the perpendicular direction on it. For the spin motion, we consider an stationary solution describing physically translation along and rotation about the same axis, say, the third one. The linear approximation method is applied to get the sufficient conditions for instability or in other words, the necessary conditions for stability. The energy-Casimir method is utilized to provide sufficient conditions for stability.

Stability of Polytropic Stars in Palatini Gravity

We will briefly discuss the necessary conditions for stability of polytropies in $f(\hat R)$ Palatini gravity and the differences with the General Relativity ones.