Climate change has become one of the most pressing global challenges, with carbon dioxide CO2 emissions being key driver of this phenomenon. Understanding the factors influencing CO2 emissions is critical for achieving sustainable development and mitigating the impacts of climate change. This research explores the relationships between CO2 emissions and various economic, social, environmental, energy and technological factors using dataset covering 107 countries from 2000 to 2020. Employing stepwise multiple, non-spatial fixed-effects panel model and spatial regression model, the research incorporates GDP per capita, population density, renewable energy share, and primary energy consumption, with all computations performed using Python and R. By addressing data challenges such as skewness and variability, this research aims to provide a comprehensive understanding of the dynamics of carbon emissions and their determinants. The findings contribute to ongoing discussions on sustainable energy transitions and global efforts to combat climate change, offering insights that can inform policy design and implementation.
This paper is devoted to a stochastic optimal control problem with time inconsistency arising from the presence of an extremal measure in the quality functional. Using the methodology described in K. Miller’s paper, the initial formulation is reduced to a two-level optimization task, in which the inner problem is classical and the outer problem is solved using proximal gradient methods. This study proves a theorem that strengthens a theorem previously formulated and proven in the Miller’s work. This strengthening of the new result stems from the fact that in the current formulation, the performance functional consists of the discounted sum of the performance functional obtained from the classical formulation and the extremal measure, rather than just the extremal measure. This paper also examines control dynamics containing jumps.
Automation of enterprise operations is a relevant development direction for business. This paper describes the goals and results that are pursued when optimizing production processes. Using the example of an oil refinery calendar planning, a step-by-step transition from the conditions of the schedule construction problem to the linear programming problem is demonstrated by means of a formal mathematical record of technical and economic constraints. The quality of the desired production plan is determined by the linear functional. The section on numerical experiments examines the issue of finding inconsistencies in the initial data based on the calculation results of the described model.
This article is carried out in the field of information and measurement technologies and spatial data processing and is dedicated to the assessment of the metrological characteristics of the measuring system. To solve this problem, it is necessary to compare the measurement results with data from another, more accurate (reference) system, which, in turn, implies the need to determine the mutual transition between their coordinate systems. As part of the research, a method has been developed for finding the correct affine transformation between two measurement systems using iterative optimization algorithms. This method acts as a key subtask, providing the possibility of bringing data to a single coordinate system and their subsequent comparison. The practical part of the work is devoted to estimating the accuracy of an optical measuring system based on data from a reference laser system characterized by a negligible error. Repeated application of the proposed approach in the framework of the conducted experiments has confirmed its effectiveness and practical significance.
This paper considers a boundary value problem for a one-dimensional wave equation with Dirichlet boundary conditions. A quadratic Lyapunov — Krasovskii functional is constructed, whose derivative along the solutions coincides with a prescribed negative definite quadratic form. Such functionals are a standard tool in the analysis of stability and robust stability, and they allow to construct estimates for the solutions. To determine the general form of the functional, we use the expansion of the solution of the boundary value problem in terms of eigenfunctions. As a result, an integral representation of the functional is obtained, with the so-called Lyapunov matrix serving as its kernel. A system of conditions under which this matrix yields the prescribed derivative is found, and an explicit analytical formula is derived based on them. The presented results pave the way for similar analyses of problems with multiple space variables and time delays.
The radiation emitted by a charged particle moving with arbitrary acceleration is considered. The field generated by such a particle, described by a potential having both spatial and temporal components, is investigated. To analyze the flow and production of energy, the law of change of momentum in a covariant form, previously obtained based on a covariant analysis of the variation of the electromagnetic field Lagrangian, is applied. It is shown that a charge moving with acceleration transfers energy to the field, which is then carried away by the field into the surrounding space. The presented approach can also be applied to the analysis of the law of change of momentum during the emission of gravitational waves.
A linear game problem for two players is considered. The two players alternately choose their strategies from the corresponding sets. First, the first player chooses their strategy, then, knowing the first player’s strategy, the second player chooses their strategy. The strategy sets of the second player depend on the strategy of the first player. The first player is forbidden from selecting a strategy that results in the strategy sets of the second player being empty. The objective of the first player is to maximize a convex and piecewise-linear function (the minimum function over the second player’s strategy). The objective of the second player is to minimize a linear function. An algorithm is proposed that allows for constructing a locallyoptimal strategy for the first player. An example is provided to illustrate how the algorithm works.
Sufficient conditions for the stability of a linear stationary system with a matrix depending on a small non-negative parameter are considered. Theorems are formulated and proved, providing easy-to-verify conditions for maintaining the stability of the system under study for all sufficiently small positive values of the parameter. The resulting theorems are used to analyze the stability of charged particle motion in a Penning trap with an additional rotating electric field and a buffer gas. The role of the small parameter in the modeling is played by the damping coefficient, which characterizes the effect of the buffer gas on theparticles. The resulting conditions for maintaining stability when adding a buffer gas to the trap can be effectively used to construct stability regions in the space of the trap’s main parameters. Using the proven theorems, the trap stability analysis is significantly simplified, since the characteristic polynomial of the system under study at zero parameter contains only even degrees, which effectively halves (from sixth to third in the general case for the trap) the order of the polynomial for which the root location must be analyzed. Examples of various special trap configurations are also considered, for which the use of the obtained theorems makes it possible to find fairly simple analytical expressions that determine the desired stability region.
This paper presents a genetic algorithm for vector optimization, PAND-ES (Pareto Adaptive Normal Distribution Evolution Strategy). The approximate Pareto set is being clarified and completed over successive generations. The method uses normal distribution, but generating sample points in the parameter space is performed without covariance matrix calculating. The algorithm is simple to implement and demonstrates high convergence rate. The proposed algorithm is applied to the problem of multiobjective optimization of electron beam longitudinal motion in a linear accelerator. A representative Pareto set is obtained. Beam dynamics investigation shows the Pareto-optimal solutions to be promising. The vector optimization results are validated using the NSGA-II algorithm (Nondominated Sorting Genetic Algorithm II). However, the latter was found to be slower both in generation formation and convergence speed compared to the PAND-ES algorithm.
Using quantum mechanical methods, the ionization potentials of a number of polyacenes, phthalocyaninates, and composite materials were calculated. It was shown that, in accordance with Koopmans’ theorem, the ionization potentials are well approximated by the highest occupied molecular orbital of the system. This assessment is relevant for determining the work function of composite materials consisting of many atoms, for which ionized states are difficult to calculate. Calculations were performed using the Hartree — Fock method and the electron density functional theory with the B3LYP hybrid potential, taking into account various basis sets. The obtained results are in good agreement with existing experimental data. It has been theoretically shown that applying carbon-containing structures to the metal surface reduces the electron work function of the heteromaterial surface. The proposed method can be applied to determining the ionization potentials and work functions of other nanostructures.
A comparative analysis of various operating modes of a vibration cone crusher as a type of dual-mass dynamic system was conducted. An asynchronous electric motor was used as the unbalance drive. A mathematical model of the crushing process was developed based on stochastic differential equations, taking into account the random nature of the incoming rock composition and time. During the operation, two unstable Sommerfeld thresholds were identified, and the changes in the key crushing parameters upon passing through them were calculated. As the values of some parameters were found to be best at the Sommerfeld thresholds, two types of stabilizing controls were applied to maintain them. Both proved successful.
The long-wave dynamics of a rotating layer of an ideal incompressible electrically conducting fluid bounded by a rigid impermeable surface at the top and a free surface at the bottom is studied. A mathematical model is constructed on the basis of the magnetohydrodynamic equations, taking into account the effects of gravity, the Coriolis force, and magnetic interactions. For long waves of small amplitude, the original system of magnetohydrodynamic equations is reduced to an equation for a modified perturbation function of the free surface. Two boundary-value problems are considered, depending on the structure of the external magnetic field. A numerical algorithm is developed for solving the dispersion equations. In the case of a frozen-in magnetic field, periodic oscillations of the Alfven type are formed in the liquid medium, whereas for finite values of the magnetic Reynolds number, a transition to decaying or unstable regimes is possible depending on the values of the magnetohydrodynamic parameters. The obtained results make it possible to estimate the influence of boundary effects and magnetic diffusion on the qualitative nature of the dynamics of the conducting medium and can be used in modeling processes in geophysics, astrophysics, oceanology, and technological systems with liquid metals.
In this paper, we consider two independent systems based on epidemics. The evolutionaryepidemic system focuses on human decision behavior, while the impulse control-epidemic system focuses on allocation management in government departments. Evolutionaryepidemic system contains two procedures corresponding to human protection decisions during the period without vaccine and vaccination decisions during the period with vaccine. Factors such as the ability of the virus to spread, the cost of taking protective measures, and the side effects of vaccination all influence people’s decisions. Factors that artificially influence epidemic behaviour are not only the individuals decision, but also the involvement of the Epidemic Prevention and Control Centre. Although medicine can be effective in suppressing the spread of epidemics, mass delivery of medicine depletes enormous resources. We use regular treatment as a means of control, attenuating infection rates and transmission, thus slowing the progression of the epidemic. Based on the maximum principle of pulse control, we derived the optimal set of solutions for discrete-time impulse control. Finally, numerical simulations are used to confirm the theoretical results.
The structure of a linear stationary control system with a system matrix in Jordan form is investigated. For such a system, its Kalman controllability matrix consists of string blocks corresponding to all Jordan cells of the system matrix. Each individual string block consists of vectors of several invariant cyclic chains formed by a common Jordan cell and the corresponding string part of its column of the control matrix. Using the structural representation of the vector matrices of these cyclic chains, a constructive representation of the Kalman controllability matrix is obtained, which determines the distribution of controllability of the system over all different eigenvalues. The concept of the controllability matrix of the eigenvalue of the Jordan canonical form control system is formulated. These matrices are made up directly from the elements of the control matrix. In the case of transferring the initial system to the Weir basis, the form of equivalent eigenvalue control matrices acquires a lower triangular block structure, which clearly confirms the correctness of the well-known controllability criterion.
A circular hole of a nanometer radius in an infinite elastic plate with a nanometer sized thickness under the uniaxial remote tension is considered. The surface stresses and residual surface tension are assumed to exist at the hole surface and the faces of the plate according to the Gurtin - Murdoch surface elasticity model within the framework of continuum mechanics. Besides of the external loading, the biaxial stress field is induced at infinity by the uniaxial remote tension due to incorporating surface stresses in the faces of the plate. The corresponding boundary value problem under the assumption of the plane stress state of the plate is solved using Goursat-Kolosov's complex potentials and Muskhelishvili's representations. The way of the problem solution leads to the system of two singular integral equations which are evaluated in terms of power functions. Explicit formulas for the complex potentials are derived. Based on these formulas and Muskhelishvili's relations, numerical investigations of the stress field dependence at the hole boundary on the hole radius and plate thickness under different ratios of the radius to the thickness are performed.
This study examines a differential game involving n players focused on optimizing collaborative development of non-renewable natural resources. A distinctive feature of this model is its consideration of random state transitions in the system, necessitating specialized analytical methods. The methodological framework employs optimal cooperative solutions constructed using the zeta-characteristic function, facilitating effective distribution of benefits among resource extraction participants. Solutions are developed across two strategic classes open-loop and closed loop strategies enabling comprehensive assessment of system control capabilities. Characteristic function calculation formulas are derived. Numerical simulations and comparative analyses of solutions across strategy classes demonstrate the practical applicability of proposed approaches to managing joint non-renewable resource development.
The paper considers the functioning of a generalized multi-level supply chain consisting of several successive links: manufacturer, supplier, distributor and retailer. Two approaches to inventory management in the chain are proposed: centralized and decentralized. In first control is constructed in the form of a piecewise constant function using the positional optimization method in real time for a supply chain described using a system of differential equations. In this case, information on the current state of stocks in the system at fixed points in time is taken into account. This control allows to take into account the current inventory volume and parry external impacts on the system. In second the model takes into account that each participant of supply chain makes decisions on the size of an order from a higher link based on its own stocks, incoming orders, and expected demand. Here control is constructed using a heuristic approach, Monte Carlo Tree Search (MCTS). This approach is based on the sequential construction of a decision tree using simulation modeling to assess the prospects of various options. It can be used to determine sub-optimal inventory control strategies that minimize logistics costs. The use of MCTS allows to effectively work with large solution spaces in dynamically changing conditions, which is especially important when managing complex supply chains.
In this paper the conditional optimization problem for table functions is considered. The minimum (maximum) of the function f is to find under restrictions on the function g. The tables of these function values are experimentally obtained. When examining these tables, it's possible to single out areas, supposed to contain the optimal point. When approximating with basis functions by the least squares method the discrepancy decreases with decreasing of these areas. In the limit we obtain the interpolation problem. But when taking into account measuring errors, dispersion of the approximation coefficients estimates increases. The article presents the combined criterion, that takes into account both these factors. The algorithm for finding an area, that satisfies this criterion, is given. As an example the problem of optimizing the properties of the coolant is considered. The function f is the freezing point and the function g is solution viscosity. In this case f and g are functions of two arguments: NaCl concentration and mass fraction of propylene glycol. They are approximated by polynomials of the second degree.
The article is devoted to the construction of a kinemo-dynamic model of a space robot that takes into account the reactionary motion of the body. The controlled robot operates near the space station and consists of a free-floating base and a three-link manipulator fixed to it. The space robot is controlled in the translation-flying mode, in which the position of the system's center of mass and the angles of rotation of the links are taken as controlled coordinates, while the reactive motion of the base is not compensated for, but taken into account in the mathematical model. A solution to the inverse kinematics problem is presented, performed using the annealing simulation method. The solution is based on the theorem on the change in kinetic momentum relative to a moving point. Illustrations of the resulting motions for particular cases of transferring a tool from point to point in the acceleration braking mode are given.
This paper combines the intergenerational income mobility with the dynamic network games and constructs a model that includes a network formation stage and a two-stage game. This model is used to discuss the impact of changes in social networks on the income of the children. Firstly, in the network formation stage, the players build an initial social network. In the game stage, the players change their connections with other players to maximize their own payoffs. This paper's payoff function definition incorporates four factors: parental income, quantity of neighbors, the differences in social status, and the evolution of the network structure. These factors are taken into account in the payoff function. This paper analyzes the situations of non-cooperative games and cooperative games respectively. In the non-cooperative game, it is proven that under certain conditions, the network structure and the social status of the players and their neighbors have an impact on their payoffs. In the cooperative game, a characteristic function is constructed and the Shapley value is used to allocate the coalition payoffs. Finally, it is proven that the imputation distribution procedure is subgame consistent.
