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This essay discusses a potential method for predicting the behavior of various physical processes and uses the COVID-19 outbreak to demonstrate its applicability. This study assumes that the current data set reflects the output of a dynamic system that is governed by a nonlinear ordinary differential equation. This dynamic system may be described by a Differential Neural Network (DNN) with time-varying weights matrix parameters. A new hybrid learning scheme based on the decomposition of the signal to be predicted. The decomposition considers the slow and fast components of the signal which is more natural to signals such as the ones corresponding to the number of infected and deceased patients who suffered of COVID 2019 sickness. The paper results demonstrate the recommended method offers competitive performance (70 days of COVID prediction) in comparison to similar studies.

The effect of the molecular structure of indotricarbocyanine dyes on their luminescence spectral and redox properties was studied. The introduction of a chlorine-substituted bridge into the polymethine chain leads to a significant hypsochromic shift of the absorption and fluorescence spectra, whereas change in the structure of substituents at the indolenine terminal groups only has a weak effect on the spectra. The electrochemical properties of the polymethine dyes were studied by cyclic voltammetry. The oxidation and reduction potentials of the dyes were determined, and the corresponding energies of the highest occupied and lowest unoccupied molecular orbitals were calculated. Reduction of the molecules of the dye is an irreversible process, whereas the reversibility of the oxidation process depends on the structure of the polymethine chain and the nature of the counterion. Introduction of a chlorine–orthophenylene bridge into the polymethine chain leads to a significant increase in the reversibility of the oxidation reaction of the dyes on account of increase in the stability of the dication-radicals. It was shown that oxidation of the bromide ions occurs at lower potentials compared with oxidation of the dyes with a substituted polymethine chain, which probably leads to decrease in the reversibility of electrochemical oxidation of the dyes when bromide ions are present in solution.

Diethyl phthalate (DEP) is a pollutant which can be found on soils as a result of its widespread application in plastic industry. Soil contaminated with DEP requires the application of different chemical methods to attain its remediation. Among these methods, ozonation has proven to be effective against toxic soil pollutants. The presence of metal oxides in soil is a possible source of catalytic effect. In this study, it was analyzed the catalytic effect of goethite (α-FeOOH), hematite (α-Fe2O3), and gibbsite (γ-Al(OH)3) in combination with O3 to achieve DEP decomposition. The DEP elimination efficiency by ozonation on the sand increased according to the following order: without catalyst

This paper suggests a procedure to construct the Pareto frontier and efficiently computes the strong Nash equilibrium for a class of time-discrete ergodic controllable Markov chain games. The procedure finds the strong Nash equilibrium, using the Newton optimization method presenting a potential advantage for ill-conditioned problems. We formulate the solution of the problem based on the Lagrange principle, adding a Tikhonov’s regularization parameter for ensuring both the strict convexity of the Pareto frontier and the existence of a unique strong Nash equilibrium. Then, any welfare optimum arises as a strong Nash equilibrium of the game. We prove the existence and characterization of the strong Nash equilibrium, which is one of the main results of this paper. The method is validated theoretically and illustrated with an application example.

A traditional non-cooperative bargaining situation involves two or more forward-looking players making offers and counteroffers alternately until an agreement is reached, with a penalty according to the time taken by players in the decision-making process. We introduce a game that aids myopic players to reach the equilibrium as if they were forward-looking agents. The key elements of the game are that players are penalized both for their deviation from the previous best-reply strategy and their time taken for the decision-making at each step of the game. It is shown that our game has an equilibrium not only for the traditional processes and utilities used in traditional non-cooperative bargaining literature, but for an expanded and very comprehensive set of stochastic processes (such as Markov processes) and utility functions. Our work not only complements traditional non-cooperative bargaining literature for myopic agents, but also enlarges the class of processes and functions where Rubinstein’s non-cooperative bargaining solutions might be defined and applied.

The aim of this study is to develop robust guidance laws for the control motion of an underwater autonomous vehicle (UAV) in a three-dimensional (3D) space. The control design is based on the use of Averaged Sub-Gradient (ASG) version of a class of dynamic integral sliding mode (ISM) method being sequentially applied to the subsystems of the complete model realizing, the so-called backstepping (or cascade) approach. The mathematical form of the UAV model induces a backstepping formulation for solving the tracking trajectory problem sequentially for the position, translation velocity, angular velocity and actuators (thrusters) dynamics. The solution of the trajectory tracking problem at each stage implements the ASG-version of the ISM method. This problem is treated as the optimization of a suitable convex (not obligatory strongly convex) cost functional, depending on the tracking error and reaching its minimal value at the origin of the error tracking space. This study shows that the minimization of the proposed functional leads to the optimal tracking regime under the presence of uncertainties in the mathematical model description. A numerical example proves the effectiveness of the suggested robust dynamic controller. The comparison between the obtained trajectory tracking results and the outcomes produced by a set of standard proportional integral derivative (PID) controllers, is presented. The proposed controller exhibits a better tracking of the reference trajectory compared with the PID version, showing a smaller mean square estimation for the tracking error.

The carbamazepine (CBZ) abatement is herein evaluated using catalytic ozonation at different NiO concentrations as catalyst: 100, 300, and 500 mg L−1, revealing its total destruction after 5 min of reaction either by conventional or catalytic ozonation. The NiO incorporation in the reactor does not increase the destruction rate, but the catalyst presence enhances the partial mineralization of the contaminant by conversion into oxalic and formic acids and the removal of total organic carbon (TOC) associated with the formation of oxidant species such as hydroxyl radical. Evidence for this behavior is the accumulation rate of the above acids which rise proportionally to the NiO concentration. The highest NiO concentration (500 mg L−1) reached a maximum TOC removal of 79.2%, which exceeds by 50% the outcome of the conventional treatment. The accumulation-decomposition profiles of oxalic and formic acids suggest the occurrence of simultaneous reaction mechanisms (hydroxyl radicals and complex formations) on the catalyst during CBZ ozonation. According to XPS analysis, the presence of nitrogen species in the NiO-ozonated was attributable to byproducts of CBZ decomposition. The toxicity bioassay based on Lactuca sativa seeds demonstrate that ozonated samples attained similar plant germination than the reference substance (water) after 120 min of treatment. This result is comparable with or without the catalyst presence, indicating the formation of non-toxic accumulated byproducts at the end of the ozonation reaction.

The results of research on the possibility of using igneous rock from Belarus for synthesizing glasses, petrositalls, and cast stone are presented. Acomponent of hierarchical modeling—the construction of cluster structures (dendrograms) — was used to optimize the technological processes. The properties, structure, and form of the formed crystalline phases are revealed to be dependent on the chemical-mineral composition of the rock and the temperature-time parameters of heat-treatment as the main criteriological factors in the directed structure- and phase-formation in obtaining glass-ceramic materials.

This paper presents a novel approach for computing the Kalai–Smorodinsky bargaining equilibrium for continuous time and discrete states Markov chains games. To solve the bargaining situation we set the disagreement point as the Nash equilibrium of the problem, then to find the new agreement point we follow the bargaining model presented by Kalai–Smorodinsky employing the utopia point concept. We exemplify the game formulation in terms of nonlinear programming equations implementing the Lagrange principle. The Tikhonov’s regularization method is applied to ensure the convergence of the cost-functions to an equilibrium point. For solving the problem we use a programming method implemented by the extraproximal optimization approach. The proposed method is validated by a numerical example related to the labor market problem for a three-person bargaining problem.

Encapsulated metal nanostructures were prepared using the powerful pulsed discharge method. Metal nanorods were obtained in porous titania and alumina matrix by direct electrodeposition from 1-ethyl-3-methylimidazolium chloride-based ionic liquids. The deposition process was characterized by cyclic voltammetry. Morphology of the encapsulated structures was studied by scanning electron microscope (SEM) and energy dispersive spectrometer (EDS) for morphological and elemental analysis. It was found that the most efficient method for electrodeposition of pure aluminum into titania nanotubes is the potential cycling method, while for deposition of the Al-Ti alloy in alumina pores a pulsed method with three different steps is preferable. Closing the titania nanotubes was found to be possible both with empty and metal-filled pores, whereas in alumina matrix this procedure can be performed only when pores are filled with a conductive material. The obtained results throw light on the mechanism of porous film encapsulation under high-voltage pulses and allow preparing encapsulated nanostructures in the oxide films.

The classical transfer pricing model considers a cooperative approach taking into account that each division purchases goods from an upstream division in the supply chain. However, divisions of a firm can be decentralized and not necessarily act cooperatively. A conflict in decentralization arises. A lack of coordination between the divisions and central management occurs if the divisions have full autonomy: managers might engage in actions that would benefit their divisions to the detriment of maximizing the well-being of the entire firm. This paper presents a model for transfer pricing that is able to maintain divisional decentralization by computing the Nash equilibrium and at the same time encourage divisions to achieve central management optimal results by computing the strong Nash equilibrium. The resulting strong Nash/Nash equilibrium point involves the computation of a cooperative and non-cooperative behavior. The model is able to provide a measure of the divisional profit maximization of the firm. In addition, we consider a bi-level structure of the company’s supply chain and solve the problem employing a Stackelberg equilibrium approach. For solving the problem we represent the transfer pricing game in terms of a coupled nonlinear programming equations implementing the penalty approach. A regularization method is employed to ensure the convergence of the utility-functions to a unique equilibrium point. For computing the equilibrium point we employ a minimization of the Euclidean distance. Next, we transform the penalty problem into a new system of equations in the Euclidean distance format. For minimizing the Euclidean distance we use a gradient method approach. A numerical example validates the effectiveness and usefulness of the proposed model for transfer pricing.

This paper suggests a new controller exploitation-exploration (CEE) reinforcement learning (RL) architecture that attains a near-optimal policy. The proposed architecture consists of three modules: controller, fast-tracked learning and the actor-critic. The strategies are represented by a probability distribution $$c_{ik}$$ . The controller employs a combination (balance) of the exploration or exploitation using the Kullback–Leibler divergence deciding if the new strategies are better than currently employed immediate strategy. The exploitation uses a fast-tracked learning algorithm, which employs a fix strategy and priori knowledge. The method is (only) asked to find estimated values of the transition matrices and utilities. The exploration employs an actor-critic architecture. The actor is responsible for the computation of the strategies using a policy gradient method. The critic determines the acceptance of the proposed strategies. We show the convergence of the proposed algorithms for implementing the architecture. An application example related to inventory shows the effectiveness of the proposed architecture.

This paper considers the subject of penalty regularized expected utilities and investigates the applicability of the method for computing the mean–variance Markowitz customer portfolio optimization problem. We penalize the large values by introducing a penalty term expressed as least-squares in order to avoid an explosive number of solutions. This penalty term is known as the Tikhonov regularization parameter. Tikhonov’s regularization is one of the most popular approaches to solve discrete ill-posed problems and, in our case, it plays a fundamental role in order to ensure the convergence to a unique portfolio solution. In this sense, we first provide the parameter conditions under which the penalty regularized expected utility of a given optimal portfolio admits a unique solution. A crucial problem concerning Tikhonov’s regularization is the proper choice of the regularization parameter because it can modify (sometimes significantly) the shape of the original functional. The main objective of this paper is to derive a method for regularization in an optimal way. For solving the problem, the parameters of the regularized poly-linear optimization problem are balanced simultaneously. Then, we prove that the original Markowitz portfolio optimization problem converges to an exact solution (with the minimal weighted norm). We consider a projection gradient method for finding the extremal points including the proof of convergence of the method. We show how to select the parameters of the algorithm in order to guarantee the convergence of the suggested procedure. Finally, we present a numerical example to illustrate the practical implications of the theoretical issues of a penalty regularized portfolio optimization problem.

This paper presents a novel algorithm for Simultaneous Localization and Mapping (SLAM) of mobile robots. The proposed algorithm, termed as SLAM using on Attractive Ellipsoid Method (AEM) and Luenberger filter-type application with nonlinear models, under the hypothesis that errors affecting all sensor’s measurements and robot’s motions are unknown-but-bounded. We suggest to select the best parameters of the suggested observer providing a minimal size of this attractive ellipsoid. It is shown that this optimization problem may be converted into the trace optimization of this attractive ellipsoid under some specific constraints of a set of LMI’s (Linear Matrix Inequalities). Simulated indoor experiments are used to demonstrate the performance of the proposed algorithm.

The results of full-scale experiment (M. D. Trifunak, S. S. Ivanovich, M. I. Todorovska, E. I. Novikova, and A. A. Gladkov, Soil Dynamics and Earthquake Engineering, 18, No. 3, 169–187 (1999)) are discussed. The actual wave pattern in foundation bed of a sevenstory building that shows the nonuniformity of the soil properties and the displacement of the center of stiffness of the foundation, resulting in appreciable torsional oscillations, was obtained in the course of the experiment. Analysis of the experimental results will be helpful in the calculation of the earthquake-resistance of the foundations and foundation beds and monitoring their state after strong earthquakes.

Acompounded mixture of fritted white, bright, glass ceramic, glaze coating for household majolica in the system Na2O–K2O–CaO–B2O3–Al2O3–ZrO2–SiO2 is developed. The structure of the coating is distinguished by homogeneity and uniformity of the distribution of the crystalline formations over the entire volume of the glaze. The physical and chemical properties of the glaze coating (CLTE = (50.2 – 50.5) × 10 –7 K–1, thermal resistance 150°C, whiteness 80 – 82%, brightness 87 – 89%, microhardness 5350 – 5400 MPa) attest an appropriate ratio of the crystalline and glassy phases in the glass ceramic coating formed.

This paper proposes a new approach for designing a nonlinear optimal controller with an integral sliding mode component employing a generalization of the saddle point method which consists on controlling a controllable nonlinear system. Based on the initial and final conditions of the dynamical system, we consider an open-loop control such that the state of the system can be moved to a neighborhood of the equilibrium state corresponding to the given final condition. The implementation of the method for solving the problem involves a two-step iterated procedure: (i) The first step consists of a “prediction” which calculates the preliminary position approximation to the steady-state point, and (ii) the second step is designed to find a “basic adjustment” of the previous prediction. We apply the controller to a Cartesian 3D-crane. The formulation of the 3D-crane is in terms of nonlinear programming problems implementing the Lagrange principle. We transform the problem in a system of equations where each equation is itself an optimization problem. For designing the controller we suggest to employ an integral sliding mode method which suppress the model uncertainties consequence of moving the trolley and the bridge, lifting the cargo as well as external forces. As a result, the optimal controller will be simultaneously able to lift the cargo, suppressing the payload vibration, tracking the trolley and moving the bridge. A numerical example involving the simulation of a 3D-crane shows the effectiveness of the controller.

In this paper, we present a multi-objective solution of the Pareto front for a certain class of discrete-time ergodic controllable Markov chains. For solving the problem, we transform the original multi-objective problem into an equivalent nonlinear programming problem implementing the Lagrange principle. We then propose to adopt the Tikhonov’s regularization method to ensure the convergence of the cost functions to a unique point into the Pareto front. We show that Pareto policies are characterized as optimal policies. One of the fundamental problems related to the construction of the Pareto front is the existence and characterization of both, Pareto and strong Pareto policies. By introducing the Tikhonov’s regularizator, we ensure the existence of strong Pareto policies. This paper proposes a real solution to this problem. We formulate the original problem considering several constraints: (a) we employ the c-variable method for the introduction of linear constraints over the nonlinear problem and (b) restrict the cost functions, allowing points in the Pareto front to have a small distance from one another. The constraints imposed by the c-variable method make the problem computationally tractable and the restriction imposed by the small distance change ensures the continuation of the Pareto front. The resulting equation in this nonlinear system is an optimization problem for which the necessary and efficient condition of a minimum is solved using the projected gradient method. Moreover, we also prove the convergence conditions and compute the estimate rate of convergence of variables corresponding to the Lagrange principle and the Tikhonov’s regularization, respectively. We provide all the details needed to implement the proposed method in an efficient way. The usefulness of the method is successfully demonstrated by a numerical example.

The paper presents the results of radiation surveying and determination of radionuclide and elemental composition in water objects (soil, bottom sediments, water) of the transboundary rivers Shu, Shor-Koo, Aksu, Karabalta, Toktas as well as of Tasotkel water-storage in Kazakhstan in vicinity of the border with Kyrgyzstan. Increased contents of natural radionuclides of 238U and 232Th series, As, Co, Cs, Cu, Hf, Mo, Pb, Sb, Sc, Zn, Zr and rare earth elements were observed in soil and bottom sediment samples. Increased contents of the following toxic elements were revealed in water samples: B, As, Mo, Ba, U. Negative influence of radiation-hazardous sites in Kyrgyzstan on the contamination of the transboundary rivers with natural radionuclides and toxic elements was revealed.

The paper describes the development of nuclear-physical methods of analysis and their applications in Kazakhstan for geological tasks and technology. The basic methods of this complex include instrumental neutron-activation analysis, x-ray fluorescent analysis and instrumental γ-spectrometry. The following aspects are discussed: applications of developed and adopted analytical techniques for assessment and calculations of rare-earth metal reserves at various deposits in Kazakhstan, for technology development of mining and extraction from uranium-phosphorous ore and wastes, for radioactive coal gasification technology, for studies of rare metal contents in chromite, bauxites, black shales and their processing products.

In this paper we generalize two models for chemical reactions, based on continuous-time Markov chains, into continuous-time Markov decision process. We propose a mathematical optimization approach for solving an average optimality criterion in state-discrete continuous-time Markov decision process. Our proposal extends the c-variable method used in discrete-time decision process by introducing a new linear constraint for continuous time. The advantage of our approach is that it reduces the continuous-time Markov decision process to a discrete-time Markov decision process where the linear constraints make the problem computationally tractable. The usefulness of the method is illustrated in chemical reactions where the concentration dynamics is modelled as a continuous-time Markov chain. The first application is a single reversible reaction for the formation of the amidogen radical where we found the optimal temperature that minimizes the average expected rate of H formation at steady state. The second is a chemical reaction network for the proton transfer, hydration and tautomeric reaction of anthocyanin pigments, in this case we found an optimal strategy over a set of values of $$\hbox {H}^{+}$$ that minimizes the average expected total number of molecules at steady state.

Naphthalene (NA) is a polycyclic aromatic hydrocarbon with toxic properties in aquatic systems. Ozonation (O3) and catalytic ozonation (O3-cat) processes are attractive alternatives of degradation for this kind of compound. NA (20 mg L−1) degradation by conventional and catalytic ozonation in the presence of a cosolvent (ethanol) was the aim of this study. This solution was proposed to simulate some aspects of real wastewaters where not only water acts as solvent. Two proportions of the mixture ethanol/water were selected (30:70 and 50:50) with the purpose of studying the cosolvent effect on NA degradation system by ozonation. O3-cat process used nickel oxide as catalyst (0.1 g L−1). The degradation analysis of NA by O3-cat in two different proportions of cosolvent showed that in the case of 30:70 (ethanol/water), a 95 % of NA elimination in 60 min was obtained, while in the case 50:50 (ethanol/water), only 55 % was achieved. The O3 process showed similar results of degradation to the initial compound in comparison with catalytic system. According to these results, there is an inhibition effect in pollutant removal by ethanol due to the higher ethanol concentration; the lower elimination rate of NA was obtained (by 40 % during the 60 min). The by-products analysis of ozonation process detected oxalic and formic acids. Treatments with NiO presented less production of organic acids in comparison with conventional ozonation process. The high concentration of ethanol has a relevant factor in the elimination of NA and formation of organic acids; samples with 50 % of cosolvent have showed a higher concentration of organic acids. X-ray photoelectron spectroscopy (XPS) study of O3-cat of diluent (O3-NiO control) and O3-NA-NiO showed the presence of –CO3 absorbed on catalyst due to ethanol decomposition.

A method for the simultaneous calculation of three rotational components using available translational motion accelerograms is examined, allowing a universal analytical relationship to be obtained between Fourier coefficients for rotational and translational motion. The method has been implemented in Eurosoft Odyssey software (published by JSC Eurosoft) and verified by carrying out seismic calculations at the Kurchenko Central Scientific-Research Institute of Structural Engineering.

The results of research on the possibility of using galvanic sludge as components of the raw material composition for the manufacture of furnace tiles are reported and it is shown that the sludge affects the thermophysical characteristics of the articles. The introduction of the sediments of the industrial sewage from the galvanic production at Atlant JSC and Belorussian MetallurgicalWorks JSC in the amount 9% promotes the formation of ceramic structure with a rational ratio of the crystalline, liquid, and gas phases, which decreases the thermal conductivity of the material while preserving the required mechanical strength and heat resistance.

In this paper, we present a new method for finding a fixed local-optimal policy for computing the customer lifetime value. The method is developed for a class of ergodic controllable finite Markov chains. We propose an approach based on a non-converging state-value function that fluctuates (increases and decreases) between states of the dynamic process. We prove that it is possible to represent that function in a recursive format using a one-step-ahead fixed-optimal policy. Then, we provide an analytical formula for the numerical realization of the fixed local-optimal strategy. We also present a second approach based on linear programming, to solve the same problem, that implement the c-variable method for making the problem computationally tractable. At the end, we show that these two approaches are related: after a finite number of iterations our proposed approach converges to same result as the linear programming method. We also present a non-traditional approach for ergodicity verification. The validity of the proposed methods is successfully demonstrated theoretically and, by simulated credit-card marketing experiments computing the customer lifetime value for both an optimization and a game theory approach.

A differential scheme of a seismic effect with assignment of the spatial ground motion in the form of a field of kinematic parameters in a coherent of incoherent (considering the dispersive properties of the ground) statement is used to analyze the earthquake resistance of lengthy structures. The feasibility of using a spatial-coherency function for analysis of concordance of seismic-wave motion with respect to the ground surface is discussed. The properties of the function are cited, and questions concerning its practical use in engineering analyses are examined.

We obtained optically transparent n-type semiconductor films of lead zirconate titanate Pb(ZrxTi1–x)O3 by reaction of individual sols of hydrated titanium dioxide and zirconium dioxide with lead ions, followed by heat treatment at 500–800°C. We established that these films, when in contact with an aqueous electrolyte, can generate a photopotential and a photocurrent when exposed to UV radiation (250–400 nm). The average values of the bandgap energy from optical absorption and photocurrent spectroscopy data are slightly dependent on the composition of the lead zirconate titanate solid solution (they increase by 0.07–0.12 eV on going from Pb(Zr0.2Ti0.8)O3 to Pb(Zr0.52Ti0.48)O3), which may be connected with features of the band structure in these materials.

This article describes the application of the so-called attractive ellipsoidal method to solve the trajectory stabilization problem for a class of genetic network systems modelled by a stochastic model. The genetic network model is described by a stochastic quasi-linear system affected by additive and multiplicative noises simultaneously. The solution of the control design provided in this study is based on a linear feedback structure. In this paper the algorithm to construct a suboptimal gain for adjusting the control design is introduced. The attractive ellipsoidal method is the key stone for designing the so-called suboptimal gain. Moreover, the practical stability of the genetic network trajectories is demonstrated on the mean and in almost sure senses. Some numerical simulations show how a set of stochastic trajectories are stabilized by the controller suggested in this study and how the predicted ellipsoid region is achieved by these trajectories.

Terephthalic acid (TA) is considered as a refractory model compound. For this reason, the TA degradation usually requires a prolonged reaction time to achieve mineralization. In this study, vanadium oxide (VxOy) supported on titanium oxide (TiO2) served as a photocatalyst in the ozonation of the TA with light-emitting diodes (LEDs), having a bandwidth centered at 452 nm. The modified catalyst (VxOy/TiO2) in combination with ozone and LEDs improved the TA degradation and its by-products. The results obtained by this system were compared with photolysis, single ozonation, catalytic ozonation, and photocatalytic ozonation of VxOy/TiO2 with UV lamp. The LED-based photocatalytic ozonation showed almost the same decomposition efficiency of the TA, but it was better in comparison with the use of UV lamp. The oxalic acid accumulation, as the final product of the TA decomposition, was directly influenced by either the presence of VxOy or/and the LED irradiation. Several by-products formed during the TA degradation, such as muconic, fumaric, and oxalic acids, were identified. Besides, two unidentified by-products were completely removed during the observed time (60 min). It was proposed that the TA elimination in the presence of VxOy/TiO2 as catalyst was carried out by the combination of different mechanisms: molecular ozone reaction, indirect mechanism conducted by ·OH, and the surface complex formation.