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With the development of science and technology, UAV technology and application have become an increasingly important field. The four-rotor aircraft has a simple structure and diverse functions and has been widely used in many fields. In practical applications, it is necessary to strictly ensure the stability of its flight, so it is very important to ensure stability when designing the control system. Knowing that the PID control algorithm can improve the stability of the system by adjusting various parameters, and the response speed is fast and easy to realize, this paper adopts the PID control method to design a stable quadrotor aircraft system. In this paper, the mathematical model of the four-rotor aircraft is first established according to the dynamics theory, and its system composition and working principle are shown, which lays a structural foundation for the subsequent design. After that, the basic principle and function of PID control are expounded, and the corresponding controller is designed based on the algorithm in the four attitude directions of vertical, pitch, roll, and yaw. Finally, the control system is simulated by establishing a model on Simulink and inputting appropriate parameters. The results show that the speed of the PID controller can meet the corresponding control requirements in the simulation of four channels, which indicates that the design method is feasible and can guarantee the stability of the system. This study verifies the effectiveness of PID control of four-wing rotary-wing UAVs and provides a basis for further exploration of algorithm improvement and innovation and improvement of aircraft stability. [ABSTRACT FROM AUTHOR]

In this paper, we describe the dynamics of the spread of the COVID-19 disease. In this paper, a mathematical model of the problem is rewritten. Mathematical models can be used to find strategies to prevent the Coronavirus disease spread. A Susceptible-Exposed-Infected-Recovered (SEIR) mathematical model in the spread of COVID-19 disease is solved using fourth and fifth-order Runge-Kutta methods. The simulation results of the two methods show the same pattern of solution behavior as the results of the reference solution obtained using the ODE45 algorithm in the MATLAB software. Theoretically, the accuracy of the fourth-order Runge-Kutta method is not better than that of the fifth-order Runge-Kutta method. We show the correctness of this theory through simulations in this paper by solving the SEIR mathematical model for the COVID-19 disease. [ABSTRACT FROM AUTHOR]

At the present stage of development of the energy industry of the world, in particular the Republic of Uzbekistan, one of the main directions is connected with the processes of introducing the solar photovoltaic systems into them. The design of such systems involves the selection of the optimal composition of their constituent elements, taking into account the conditions of their long-term operation. Despite the existence, at present, of a number of methods for solving such problem, there are no algorithms based on the use of rigorous mathematical models and optimization methods, taking into account all influencing factors. This paper proposes a mathematical model and algorithm for optimization the composition of elements of autonomous solar photovoltaic systems, taking into account limiting conditions. The results of a study of the effectiveness of this model and the calculation algorithm are presented. Using the development allows you to provide high efficiency by improving the accuracy of optimization. [ABSTRACT FROM AUTHOR]

The paper proposes methods of research and calculation of optimal auger configuration for grain harvesting machinery. The main types of loading on auger supports are analysed when changing auger diameter, pitch, direction and type of helical spiral. The dynamic unbalance of long screw augers is studied. Proposals for the general balancing of the auger during its working operations are formed in order to reduce vibration, noise and increase the service life of the machine. Calculations, methods of determination of technological imbalances, as well as their connection with manufacturing accuracy have formed the basis for creation of information platforms for automated engineering design of highly reliable screws. Proposals for calculation of the main geometrical parameters of screws are formulated. The algorithm of construction of automated calculation processes for selection of optimum geometrical characteristics of long screws on the basis of the received frequency equations and formulas is developed, and also the programme allowing on the basis of available computer technologies to make repeated calculations of critical rotation frequencies of system "long screw supports" at one-time calculation of the screw released from supports is created. A number of proposed design solutions of the elastic-linked suspension of the auger, providing the best characteristics of vibration damping, proposed and implemented in the research work allowed to reduce the level of vibrations transmitted from the auger to the machine structure through the rigid suspension by 15%. [ABSTRACT FROM AUTHOR]

Bio-mathematics is an interdisciplinary subject involving of biology and mathematics, which is broadly applicable for the analysis of biological problems. In this paper, we deliver a mathematical modeling of two phases circulatory system in artery with special reference to Hepatitis A. Main purpose of this study has been to develop a mathematical model in hepatic circulatory system and their analysis and verified clinical data of the hepatitis A patient. The blood flow is thought to be a two-phased process. The clinical data of a Hepatitis A patient (blood pressure and hemoglobin) is gathered. To begin, hemoglobin is transformed into hematocrit, and blood pressure is turned to a decline in blood pressure. For the examination of hepatic arteries in Newtonian and non-Newtonian movements, a mathematical model is constructed. The relationship between two-phase blood flow flux and blood pressure reduction in the hepatic artery is established. For various hematocrit levels, the blood pressure decrease is determined. The patient's states are defined by the slope of the linear relationship between computed blood pressure decrease and hematocrit. [ABSTRACT FROM AUTHOR]

We describe an existing co-dynamics model of the spread of malaria and COVID-19. Mathematical model can be used to find strategies to control the spread of malaria and COVID-19, so that their spread can be minimised in a population. The mathematical model we use is of the type of the SEI (Susceptible-Exposed-Infected) model for malaria and COVID-19 co-dynamics. For this model, we have three compartments of the human population and three compartments of the vector population. The compartments are based on S (Susceptible subpopulation), E (Exposed subpopulation), and I (Infected subpopulation). Solutions to this mathematical model can be obtained using numerical methods. We use the third-order and the fourth-order Runge-Kutta methods to solve the co-dynamics model. From our simulation results, both methods perform quite well. The fourth-order Runge-Kutta method theoretically has a higher accuracy than the third-order one. Our simulations in this paper confirm that, when solving the SEI model of the spread of malaria and COVID-19, the fourth-order Runge-Kutta method performs better than the third-order Runge-Kutta method. [ABSTRACT FROM AUTHOR]

This paper has numerically analyzed the problem of enhanced the dynamic response of an electrohydrostatic actuators used in aerospace systems. Based on physical and mathematical model using both Matlab / Simulink and AMESim Software Student Edition some characteristics of this type of servo actuator were obtained. The results proved that a good tracking of reference is achieved and that the servo actuator meets very well the design requirements imposed in the time domain. [ABSTRACT FROM AUTHOR]

Memory effects are needed to be described in the diffiusion process modelling since there is inconsistent rate with the classical approach. In this paper, a mathematical model is presented for simulation drug release from Metformin Hydrochlo-ride/Vildagliptin tablets based on fractional derivative (FD) and memory-dependent derivative (MDD). Our problem is represented by a set of two numerically solved diffusion equations. For both the tablet and the release medium, the profiles of drug concentration and mass are given and compared to the in vivo profiles. Results indicate that the FD and MDD are better suited for temporal modelling. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to present a unified methodology for the derivation and implementation of the continuous dynamics (equations of motion) and discrete dynamics (transition equations) that comprise the hybrid model of an passive biped robot. A developed general model derivation procedure is presented which generates a complete mathematical model for a selected underactuated bipedal robot. The generated mathematical models are implemented in Simulink using the Stateflow tool. The functionality of the proposed approach has been demonstrated using several case studies. [ABSTRACT FROM AUTHOR]

In the present paper, a mathematical model is proposed to estimate the performances of a Mars Ascent Vehicle as functions of the oxidizer to fuel ratio, propellants properties and mass fractions sent from Earth. The model is then applied to two proposed Mg-CO2 rocket configurations to estimate their performance and verify the convenience of CO2 collection on Mars. [ABSTRACT FROM AUTHOR]

Currently, the problem of reliable design and evaluation of the effectiveness of multistage hydraulic fracturing with the determination of the contribution of each interval of hydraulic fracturing to the total production of the well is urgent. The paper formulates a mathematical model for reducing the dimensionality of the problem of fluid inflow to the fractures of the multistage hydraulic fracturing using a fixed stream tubes model. The limitations under which the proposed approach is applicable for fractures of finite permeability are identified. Two-component and two-phase flow problems approbation has been carried out. It is shown that the proposed low-dimensional model gives a gain of 2-3 orders of magnitude in the counting speed compared to the solution in the original formulation. [ABSTRACT FROM AUTHOR]

In the present paper, the effects of cake thickness and time on the efficiency of brown stock washer of the paper mill are studied by using mathematical model of pulp washing for the species of sodium and lignin ions. The mechanism of the diffusion- dispersion washing of the bed of the pulp fibers is mathematically modeled by the basic material balance and adsorption isotherm is used to describe the equilibrium between the concentration of the solute in the liquor and concentration of the solute on the fibers. To study the parametric effect, numerical solutions of the axial domain of the system governed by partial differential equations (transport and isotherm equations) for different boundary conditions are obtained by the “pdepe” solver in MATLAB source code. The effects of both the parameters are shown by three dimensional graphical representation as well as concentration profiles. [ABSTRACT FROM AUTHOR]

Hoax is an information or explanation with unconfirmed truth. Nowadays, social media is the most used media in hoax propagation. If no action is taken, hoax propagation can cause serious problems. In this paper, a mathematical model representing social media hoax propagation with forgetting mechanism is analyzed in order to study the dynamics of social media hoax propagation in real life. Based on the analysis result, we obtain two equilibria, namely, non-endemic equilibrium and endemic equilibrium whose local stabilities depend on the basic reproduction number or R0. Social media hoax propagation occurs when R0 > 1 and does not occur when R0 < 1. Based on the sensitivity analysis result, the probability that a hoax is considered attractive and the forgetting rate of social media users against hoaxes are the most influential parameters on the dynamics of social media hoax propagation. Next, in order to minimize the number of hoax spreaders and hoax contents on social media, three control variables, namely, anti-hoax campaign, punishment for hoax spreaders, and hoax deletion by authorized parties, are imposed to the mathematical model. The optimal control problem in this paper is solved by using Pontryagin Maximum Principle. The numerical simulation result shows that the bundle implementation of three control strategies is the most effective scenario to minimize the number of hoax spreaders and hoax contents on social media. [ABSTRACT FROM AUTHOR]

In this paper an advanced stochastic approach based a lattice rule with improved generating vector has been obtained and studied. The Unified Danish Eulerian Model (UNI-DEM) is a key element in our investigation since it is one of the most advanced large-scale mathematical models that describes adequately all physical and chemical processes. The calculations are done in a large spatial domain, which covers completely the European region and the Mediterranean, for certain time period. What is more, it studies the transportation of a number of pollutants and all these make it a perfect case study. The paper compares the described lattice rule and demonstrates its superiority over the plain Monte Carlo approach and Fibonacci based lattice rule. The proposed approach is robust and computationally efficient in estimating multidimensional integrals and thus sensitivity indices, which is vital in scientific computing. [ABSTRACT FROM AUTHOR]

This paper consist of mathematical modeling of the Wankel engine simulated in GNU Octave software. Main purpose of this study is to make an algorithm that can simulate a wankel engine that can estimate performance of engine. For any starting initial condition of engine and based on thermodynamic conditions algorithm predict output result from an engine. Simulation code consists of the construction of an engine which consists of radius, thickness and eccentricity of the engine. These construction parameters can be altered to various sizes according to the needs of the user. Code is capable of deriving various engine performance variables, combustion parameters, and cycle parameters such as pressure, temperature, heat transfer coefficient, work done, etc at any rotor angle according to construction parameters. Code is capable of handling various fuel data and conditions. This model can be used to determine values theoretically with any engine size, fuel, rpm, and running condition. Similar to engine size, the condition of the flame propagation can be altered to practically any value. In case of an actual scenario, needs of initial pressure and temperatures can also able to change. As codes are based on a thermodynamic equation model, it benefits low computing power and low simulation time. Codes have been tested by keeping similar conditions of previous research papers and showing good agreement result with this code. [ABSTRACT FROM AUTHOR]

The cylindrical Pirani gauge sensitivity under different conditions is studied in our previous paper. We are modeled the Pirani gauge as cylindrical Couette flow – one dimensional axis symmetrical problem by using a statistical method – Direct Simulation Monte Carlo (DSMC) and the Navier-Stokes-Fourier equations numerical solving. The purpose of this article is to study the cylindrical two-dimensional Taylor-Couette flow with finite length of rarefied gas. The suddenly temperature change of the inner cylinder wall (the fiber) is used to modeling the boundary conditions. The finite volume method and statistical modeling is used to study this problem. This paper is a continuation of our previous work which we extend the study using the NSF model and its numerical solution to assess the applicability of the obtained results. The state of the gas is studied over a long time period close to establishing a steady state in the previous work, while in this paper is studied the initial moment of occurrence and reflection of the wave from the other cylinder. The realization of such conditions is difficult technically feasible in some cases, but their set in mathematical model gives more opportunities to study the stability in the gaseous medium between the cylinders. [ABSTRACT FROM AUTHOR]

The paper considers the process of filtration of water and oil phases, taking into account the deformation of the medium. A suitable mathematical model of the process is proposed. Using the proposed model, the influence of medium deformation on hydrodynamic parameters was analyzed. The problem was solved numerically by the large particle method. Based on the obtained results, the influence of environmental deformation on reservoir pressure, porosity, permeability, oil saturation and oil production was studied. [ABSTRACT FROM AUTHOR]

In the paper an active solute transport problem in a fractured-porous medium is considered with taking into consideration linear and non-linear non-equilibrium adsorption, corresponding to Henry and Freundlich isotherms at equilibrium state. The problem is numerically solved and the influence of non-equilibrium adsorption on solute transport characteristics is established. [ABSTRACT FROM AUTHOR]

The paper examines optimization problems for underground structures based on algorithmic methods, develops mathematical models, and specifies algorithms for solving them. Solving these problems allowed us to achieve significant savings in materials and costs compared to existing projects. The possibility of designing vault structures with minimal consumption of materials is being explored. The results of calculations for the optimization of underground structures are presented. [ABSTRACT FROM AUTHOR]

A difference equation is an equation that contains a difference in one or more than one variable. It has significant applications in the mathematical models of the applications of engineering and science. In this paper, we proposed a method for solving ordinary difference equations using discrete Sumudu transform. Some properties of the discrete Sumudu transform have been introduced. The implementations for the test examples of initial value problems of difference equations examined the efficiency of the proposed method. The approximated solutions of initial value problems of ordinary difference equations in discrete domain with different orders have been evaluated and compared with exact solutions of these problems. [ABSTRACT FROM AUTHOR]

Control the air flow in the engine cylinder is very important to maintain the performance of the vehicle. This performance is maintained by a device called electronic throttle (ET) that lower the emission of exhaust meeting the emission norms. The control of ET is quite challenge exercise due its multiple nonlinearities such as transmission friction, spring set (limp-home), backflash of the gear as well as external. The simulation of tracking performance ET openings angle using hybrid sliding mode control (SMC)is presented in this paper. The integration of two control algorithms is proposed using integral SMC and super twisting SMC that is applied on mathematical model of ET. The stability of the controller is examine using Lyapunov theorem. Theoretically, Lyapunov theorem has proven that the proposed control law satisfies sufficient condition of stability. The effectiveness of the proposed controller has been evaluated against integral SMC and super twisting SMC. The results of the simulation have demonstrated the controller proposed in work has enhanced the transient response, decreased steady-state error, and removed chattering effects in control input as well as sliding surface. [ABSTRACT FROM AUTHOR]

From a practical point of view, an urgent task in the formation of fresh water reserves is to study the process of changing the water level and salt concentration in the underground aquifer. In this paper work on the issues of groundwater movement and salt migration, changes in groundwater levels and mineralization processes were considered together. For a detailed and comprehensive study of the process of changing the level of groundwater and salt concentration, an improved three-dimensional mathematical model was developed that describes the main features of the object. This task was expressed in the form of nonlinear differential equations for monitoring geofiltration processes through mathematical and numerical modelling and the development of proposals and recommendations. Since the problem is represented by nonlinear differential equations with free variables, it is not possible to solve it analytically. To solve these problems, an absolutely stable implicit scheme with high approximation accuracy, finite differences, direct and inverse protraction methods was used, an efficient numerical algorithm was presented. [ABSTRACT FROM AUTHOR]

In this paper, a mathematical model, a numerical algorithm for the process of transfer and diffusion of harmful substances, is developed, which takes into account the wind speed in three directions and the rate of deposition of aerosol particles on the underlying surface, as well as the capture of particles by vegetation elements, which play a significant role in the dynamics of the object of study. In order to integrate the task, an implicit finite-difference scheme and an algorithm with the second order of approximation in terms of time and space variables were developed with the help of which numerical calculations can be carried out on a computer system, on the basis of which it is possible to investigate and predict the ecological state of the industrial region under consideration. To investigate the adequacy of the developed mathematical apparatus, computational experiments were carried out on a computer, the results of which were compared with full-scale data of a real production facility located in the Tashkent region of Uzbekistan. [ABSTRACT FROM AUTHOR]

This article is devoted to extended Caputo fractional derivative of various Trigonometric cardinal functions. Recently, fractional derivatives and Mathematical Models involving fractional derivatives have found many applications in several branches of sciences. Trigonometric cardinal functions play significant roles in many theories of mathematics. These are special functions that are used in signal analysis which includes sound recording and radio transmission. Sine cardinal function found its existence in the theory of Fourier analysis. In this paper, we have established general expression of fractional derivative of different cardinal function using extended Caputo approach. [ABSTRACT FROM AUTHOR]

The performance of PV systems in fractional or complicated fractional shading situations is impacted by erratic irradiance, temperature, and unpredictable weather patterns. In these conditions, maximizing the O\P of PV schemes becomes challenging. This work investigates the tracking mechanism in HOM under fractional shade environments and complex partial shade conditions to obtain maximum power (MPP) in PV system, and capture global peak (GP) instead of local peak (LP) to make the system Photoelectric stable and high efficiency. Also studying the results obtained from the newly proposed (HOA) and comparing them with smart and traditional swarm optimization techniques such as p&o, improved cuckoo search (ACS), particle swarm optimization (PSO) and dragonfly algorithm (DA). For gradient optimization with regard to PV panels, MPPT use mathematical models Comparison shows HOA outperforms other technologies and achieves the best results in terms of fast tracking and effectiveness, for stability under variable weather factors and the ability to get maximum power. This paper compares the effectiveness of a number of MPPT performances over a broad variety of shading speeds using MATLAB, and proposes a PV array configuration for various systems under various partial shading advances. [ABSTRACT FROM AUTHOR]

For the uncertainty data problem, traditional methods are incapable of handling them that caused inaccuracy in data analysis and prediction. Uncertainty data often occurs during the data collection phase and cannot be used to generate geometric models directly. Therefore, this paper discusses the B-Spline curve interpolation modeling using intuitionistic alpha cut for the uncertainty data. Fuzzy set theory, intuitionistic fuzzy set, and geometry modeling are used and integrated with one each other to solve the data with uncertainty and generate the mathematical model. In detail, there are three main processes employed, the first of which is the fuzzy set theory applied to defined uncertainty data followed by the intuitionistic fuzzy set, which is used to consider the membership and non-membership values of the alpha before proceeding to the fuzzification and defuzzification process. Next, geometric modeling is utilised to construct mathematical geometry in the form of curves, which is the B-spline curve interpolation function. As a result, various numerical examples, as well as their algorithms for generating the desired curve, are shown. [ABSTRACT FROM AUTHOR]

In this paper, mathematical modeling and numerical formulations are developed to predict the overall behavior of fractional visco-electroelastic composites. The modeling is based on Riemann-Liouville's fractional derivative formulation, Carson-Laplace transform, the frequency Green's functions, and integral equation formulations. The micro-macro modeling is elaborated for various heterogeneous visco-electroelastic composites. The inclusion problem and a micromechanical method are used to obtain the localization and the concentration tensors expressions. The block decomposition procedure is used to address the draw-back of the ill-conditioned problem caused by the localization tensor inverses. The effective fractional visco-electroelastic behavior is expressed based on the regularized concentration tensor and the Mori-tanaka method. Numerical results of effective fractional visco-electroelastic properties are obtained and examined for various fractional parameter, volume fraction and shapes of inclusions in frequency domain. [ABSTRACT FROM AUTHOR]

Theoretical analysis to predict the crack propagation of Al 2024 is required and validated by experiment. This theoretical analysis was developed through a mathematical model that is based on the development of the Paris equation. The Paris equation is used to analyze crack propagation against a constant amplitude load. In this paper, a mathematical model based on the Paris equation is developed for the load spectrum, where the effective results are obtained at stage 2 when conditions are stable. The results of the development of this mathematical model are quite promising to be used as a reference for further experiments with the same material [ABSTRACT FROM AUTHOR]

This paper dispenses a study on sustainability of TiN-TiCN-Al2O3−ZrCN coated tungsten carbide (WC) cutting inserts during dry condition turning of T6 tampered AA7075, through investigation of influence of cutting factors on tool flank wear (Fw), followed by their significance prediction on the desired output through analysis of variance (ANOVA) and prediction of mathematical model through regression analysis. Fw was optimized following signal to noise (S-N) ratio concept of Taguchi, and finally some confirmatory experiments were executed. Results revealed augmentation of Fw on enhancing spindle speed (N) and feed (f), but it reduced slightly on incrementing the cutting depth (d). N was the highest significant factor for Fw, taken after by f, whereas d was non-significant. The predicted model was significant, and possessed high determination coefficient. Optimization results revealed that the factorial combination N = 250 rpm, f = 0.05 mm.rev−1 and d = 0.2 mm was optimal for Fw, which was further validated through confirmatory experiments, resulting an improvement of S-N ratio by 7.1446 dB. [ABSTRACT FROM AUTHOR]

This paper dispenses influence of cutting factors on surface quality of AA7075 while turning with tungsten carbide (WC) tools coated with TiN-TiCN-Al2O3−ZrCN in dry cutting environment, followed by their significance prediction on the desired output through analysis of variance (ANOVA) and prediction of mathematical model through regression analysis. Average surface roughness (Ra) was optimized following signal to noise (S-N) ratio concept of Taguchi, and finally some confirmatory experiments were executed. Results revealed augmentation of Ra on enhancing spindle speed (N) or feed (f), but on incrementing the depth of cut (d), Ra reduced first, then increased and again reduced on further increase of d. The highest factor of significance for Ra was f, taken after by N. The predicted model was significant, and possessed high determination coefficient. Optimization results revealed that the factorial combination N = 250 rpm, f = 0.05 mm.rev−1 and d = 0.2 mm was optimal for Ra, which was further validated through confirmatory experiments. [ABSTRACT FROM AUTHOR]

The new coronavirus that is the source of the pandemic respiratory infection known as COVID-19 poses a major risk to the public's health. In this paper, we present a mathematical model of the spread of an infectious disease according to the characteristics of the COVID-19 pandemic. The proposed improvedmodel is developed on the AnyLogic system, which will be referred to as the SEAIR (Susceptible-Exposed-Asymptomatically Infected-Symptomatically infected-Recovered) model. The paper considers mathematical models that are used to analyze and predict the development of the COVID-19 pandemic, including time series analysis, equations of mathematical physics and simulation models, their various combinations and generalizations. Due to the novelty and complexity of the COVID-19 disease, the parameters of most mathematical models are usually unknown, and this leads to the need to consider and solve inverse problems. [ABSTRACT FROM AUTHOR]

This paper provides healthy lifestyle of diabetic patients by using mathematical modeling. In this paper we construct a mathematical model of diet planning for diabetes. The formulated mathematical model is the application of linear programming and integer programming. All the requirements and restrictions were fulfilled in the mathematical model which was developed in this paper. An optimal and feasible solution was produced by using linear and integer programming. This optimal solution gives the diet problem of diabetic patients. All the constraints and objective functions are defined in the diet problem. To provide daily needs of supplement for the particular age of diabetic patients. [ABSTRACT FROM AUTHOR]

Two stroke engines is comparatively small, simple in operation with less cost because of absence of valve mechanism. The performance of the engine is such that it has low brake thermal efficiency and higher exhaust emission because of incomplete combustion which results into high emission and fuel consumption. Scavenging is important for improvement of the engine performance by removing the exhaust gases from the engine. The paper details the modification in the engine for enhancing the scavenging process so that performance of engine in terms of brake power and thermal efficiency will increase. The modification in the two stroke engine is done by providing hole in transfer port for air aspiration. The general concept in using external air aided scavenging is to improve scavenging characteristics of base engine by reducing short-circuiting phenomenon. Investigation of the modified engine were done by evaluating the brake power and thermal efficiency of two stroke engine using the mathematical tools such as mathematical modeling, sensitivity and optimization. The paper highlights the modification in the engine to enhanced the performance of engine and the formulation of mathematical model. The formulated mathematical model predicts the performance of engine with the help of indices of each pie term formed with input variables. The positive indices of the pie term indicate the most influencing pie terms responsible for variation in the output variable such as brake power and thermal efficiency. The negative indices of the pie term indicate the inverse effect on the output variables as it is inversely proportional to the output variables brake power and thermal efficiency. Thus the exact mathematical model help to investigate the performance of the engine at lower cost with less time involved in experimentation. [ABSTRACT FROM AUTHOR]

Entropy is one of the important concepts in physics and thermodynamics and it is one of the quantities surrounded by amount of mystery. The ambiguity of this concept is due to several reasons, including the mathematical and physical interpretation of the concept as presented by Clausius. This ambiguity is also due in part to the widening of the use of the term entropy to represent several physical concepts that are not related to the basic concept of entropy as introduced by Clausius himself. In this paper, the mathematical and physical modeling of this term will be reviewed. Furthermore, this paper will show how does this term has been used to describe some physical concepts which are not related to the original use of it. And finally, in order to remove the confusion and ambiguity surrounded this term, the paper will show how should the entropy explained and understanding from the macroscopic thermodynamics point of view. [ABSTRACT FROM AUTHOR]

The pollution considerations and the economic view of reliable and cheap production have pushed the permanent magnet machines to stand in proceed position in many fields of machines industrial applications. Whereas the sensorless controllers become mature day after day to support and satisfy the beneficial applications for these machines. This paper employs only measurements of the machine terminal voltages to establish a mathematical model whose function is to present sensorless standstill position estimation of one-degree resolution and approximately 5% error estimation. No current measurements are required, therefore the current sensing sensors are eliminated. No position sensors and techniques for magnet polarity detection of the rotor are required as well. The proposed paper strategy was applied on a non-salient synchronous machine and tested by the (MATLAB-Simulink-R-2018). It can be modified to be applicable for any other type of permanent magnet machine. [ABSTRACT FROM AUTHOR]

A process to give teaching assignments for the teachers or lecturers to the available days and times by meeting certain goals is called timetabling. The lecturer's availability, number of courses, type of courses, number of course credits, classroom availability, course start time, and course end time are the factors that affect the learning schedule that makes timetabling complicated especially in university. Therefore, by using a mathematical optimization model, timetabling process becomes easier. Although many mathematical models have been made to do timetabling, there is no general model that can use in every university. In this paper, Binary Integer Programming is used to build the learning schedule in the Mathematics Study Program of Bandung Institute of Technology (ITB). The compulsory courses do not overlap, the courses with the same year are evenly distributed, the lecturer's schedule being unable to teach, the lecturer's schedule shouldn't be teaching, and the lecturer's schedule should be teaching become the consideration in this paper. Then, based on the given data, there are three outputs, that is the schedule of the lecturers, the schedule based on the course year, and the schedule based on the day. The schedule that has been made based on the model is quite good and can be implemented in the daily life. [ABSTRACT FROM AUTHOR]

The task of developing effective granular aggregates, as well as the creation of a mathematical model and management of this process, is the most promising and relevant. The paper deals with the construction of mathematical models based on the results of experimental studies of granular aggregates (GA). We present the processing of the results of experimental studies on the production of granular aggregates using the classical method with the use of the high-level general-purpose Python programming language. The processing of research results is fully object-oriented. This approach to the generation of the obtained results allowed us to automate the processing of the array of data for the planning of the experiment. The results of mathematical modeling and nomograms reflecting the variability of the developed compositions, which allowed to obtain samples with the required technological, physical-mechanical and operational characteristics are presented. The paper calculates the values of reproducibility dispersions: for sand fraction ≤0.16 mm - 0.889; for sand fraction ≤0.315 mm - 0.967; for sand fraction ≤0.63 mm - 0.981. The analysis of nomograms has shown that the greatest strength values have the compositions with the sand fraction of 0.16 mm and the minimum content of sand (as an aggregate). For mixtures with sand fractions ≤0.315 mm it is established that the strongest will be the mixture with the minimum content of aggregate. It is revealed that when using sand fraction ≤0.63 mm the strength is reduced. [ABSTRACT FROM AUTHOR]

Based on the materials of specific agricultural formations in the Almaty region, this paper presents a methodological approach to assessing the effectiveness of using a resource potential. Approved economic-mathematical model of optimizing production and industrial structure, justifying the optimal parameters of elements of the resource potential through which there are revealed reserves for increasing efficiency of using a resource potential. The research results show that the use of economic and mathematical optimization models will significantly increase the efficiency of production and the use of the resource potential of specific agricultural formations. Practical recommendations are given to substantiate the optimal parameters of the resource potential of all types of agricultural enterprises in the Almaty region based on this methodology. [ABSTRACT FROM AUTHOR]

The paper proposes a variant of describing the propagation of speech signals under ideal conditions using the mathematical apparatus of Radon in the interests of their subsequent identification. The task of describing the propagation of speech signals has been formulated and it has been shown that the main goal of its solution is to develop a universal mathematical apparatus based on a generalized mathematical model of acoustic wave propagation, which is considered as a spherically symmetric function from the distance to the wave source, described by the Radon transform, which provides automation identification and increases the efficiency of the removal of speech information. The concept of ideal conditions for the propagation of speech signals is described, under which it is necessary to have a point omnidirectional sound source, the constancy of the parameters of acoustic receiving devices, a homogeneous unlimited environment limited only by a flat earth's surface and described by a mathematical model with the Radon transform, where the Fourier transform is understood as the corresponding equivalent norm. A variant of describing the propagation of speech signals under ideal conditions using the mathematical apparatus of Radon is proposed, which makes it possible to identify the received signals, in which all the properties and features of the emitted speech signals that determine their belonging to a fixed object of generation of these signals, propagating under ideal conditions for unlimited distances before registration receiving devices retain all these properties and features. The presence in the database and knowledge of mappings of these properties and features, accumulated and replenished during the execution of applied tasks for the removal of speech information, makes it possible to automate the identification of received signals and fixed objects of their generation. [ABSTRACT FROM AUTHOR]

Mathematical models appear in many forms, such as instantaneous dynamics (ordinary differential equations) or time-lags dynamics (delay differential equations). It is important to investigate the effect on the model outputs when a perturbation is applied to the initial or boundary conditions, time delay parameters, or any model parameters in the governing equations. In this paper, we study the general theory of sensitivity analysis based on the direct differential method for systems governed by delay differential equations. Problems governed by ordinary differential equations can also be considered as a particular case of delay differential equations with the absence of delays. The normalized forward sensitivity indices are then computed to identify the important model inputs. To show the efficiency of the methodology, we apply the theory and numerical computations to immunology and infectious disease models. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to develop the Coronavirus disease (COVID-19) transmission model using the fractional-order differential equation defined by Caputo. This model is developed based on the susceptible-exposed-infected-recovered model, commonly known as the SEIR model. The basic reproduction number, denoted by R0, is computed using the next-generation matrix method. The disease-free equilibrium point is evaluated, and local stability analysis is performed. The analysis shows that the disease-free equilibrium is locally asymptotically stable when R0<1 and unstable when R0>1. In other words, the COVID-19 disease can be eliminated when R0< 1. Finally, numerical results are presented based on the real data of COVID-19 cases in Malaysia. [ABSTRACT FROM AUTHOR]

The emerging growth of edge devices and the expansion of IoT systems produced the demand to enhance their security algorithms to run on diverse applications and appliances. Lightweight cipher algorithms are mainly designed for IoT-constrained devices. Thus, due to the new services and applications of IoT that require extensive networks and devices, the need for efficient lightweight cipher algorithm implementations is a critical issue. In this paper, an enhanced cipher LED-128 algorithm based on Galois Fields (GF) operations is presented. The mathematical model of the LED algorithm simply requires a slight execution time for encryption-decryption processing. The Enhanced LED algorithm is applied with 64 bits of block plaintext and 128 bits of the key size which turn out 64 bits block size of ciphertext. The proposed algorithm is presented to advance the randomness of cipher text by enhancing the key schedule based on GF operations. The developed key schedule is enhanced to generate a robust key for the proposed algorithm. The NIST statistical tests have been examined and experimented for the proposed enhanced algorithm by utilizing diverse keys with distinct cipher text, which passed the randomness for each test. The proposed algorithm demonstrated a high confusion and diffusion based on the correlation coefficient analysis. The executed time for the encryption and decryption processes of the proposed enhanced LED algorithm is concentrated at minimum compared to the original LED-128 cipher algorithm. Hence, the proposed enhanced algorithm can be implemented for diverse IoT systems and can reach the trade-off between cost and performance as an efficient lightweight algorithm. The results of the enhanced algorithm are benchmarked with the current LED 64/128 algorithms and presented significant improvements in the performance compared to original design of the LED cipher algorithm. [ABSTRACT FROM AUTHOR]