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In order to improve the driving performance of four-wheel drive electric vehicles and realize precise control of their speed, a Chaotic Random Grey Wolf Optimization-based PID in-wheel motor control algorithm is proposed in this paper. Based on an analysis of the structural principles of electric vehicles, mathematical and simulation models for the whole vehicle are established. In order to improve the control performance of the hub motor, the traditional Grey Wolf Optimization algorithm is improved. In particular, an enhanced population initialization strategy integrating sine and cosine random distribution factors into a Kent chaotic map is proposed, the weight factor of the algorithm is improved using a sine-based non-linear decreasing strategy, and the population position is improved using the random proportional movement strategy. These strategies effectively enhance the global optimization ability, convergence speed, and optimization accuracy of the traditional Grey Wolf Optimization algorithm. On this basis, the CR-GWO-PID control algorithm is established. Then, the software and hardware of an in-wheel motor controller are designed and an in-wheel motor bench test system is built. The simulation and bench test results demonstrate the significantly improved response speed and control accuracy of the proposed in-wheel motor control system. [ABSTRACT FROM AUTHOR]

This paper provides a survey of recent research progress in mathematical modeling and distributed control of wide-area networks. Firstly, the modeling is introduced for two types of wide-area networks, i.e., coopetitive networks and cooperative networks, with the help of algebraic graph theory. Particularly, bipartite network topologies and cluster network topologies are introduced for coopetitive networks. With respect to cooperative networks, an intermittent clustered network modeling is presented. Then, some classical distributed control strategies are reviewed for wide-area networks to ensure some desired collective behaviors, such as consensus (or synchronization), bipartite consensus (or polarization), and cluster consensus (or fragmentation). Finally, some conclusions and future directions are summarized. [ABSTRACT FROM AUTHOR]

The intensive development of photovoltaic (PV) micro-systems contributes to increased interest in energy efficiency and diagnosing the condition of such solutions. Optimizing system energy efficiency and servicing costs are particularly noteworthy among the numerous issues associated with this topic. This research paper addresses the easy and reliable diagnosis of PV system malfunctions. It discusses the original PV system energy efficiency simulation model with proprietary methods for determining total solar irradiance on the plane of cells installed at any inclination angle and azimuth, as well as PV cell temperature and efficiency as a function of solar irradiance. Based on this simulation model, the authors developed procedures for the remote diagnosis of PV micro-systems. Verification tests covered two independent PV systems over the period from April 2022 to May 2023. The obtained results confirm the high credibility level of both the adopted energy efficiency simulation model and the proposed method for diagnosing PV system functional status. [ABSTRACT FROM AUTHOR]

The article deals with a diagnosis of multiple leaks from liquid transmission pipelines using analytical methods. Such solutions, based on advanced mathematical models of pipeline flow dynamics, usually turn out to be very complex and time-consuming. However, under certain operating conditions, a simpler approach may also be useful. Such an idea is presented in this paper, proposing two simplified methods for diagnosing double leakages. In principle, these methods apply to both simultaneous and non-simultaneous leaks. The first one uses a static model of a pipeline involving two leaks and takes advantage of the minimization of the objective function defined as the squared deviation of the modeled pressures from the pressures measured on the pipeline. The second method uses a pipeline flow model of a static type in combination with a gradient indicator aimed at detecting leaks and employing algorithms assigned to determining the location and size of leaks. The results of methods' validation, based on tests carried out with the use of measurement data obtained from an experimental water pipeline, were also presented. The outcomes of the performed tests proved the methods' effectiveness in terms of detection, isolation, localization, and intensity estimation of both simultaneous and non-simultaneous double leakages. [ABSTRACT FROM AUTHOR]

In this paper, we study the system size expansion of a stochastic model for radiation-induced DNA damage kinetics and repair. In particular, we characterize both the macroscopic deterministic limit and the fluctuation around it. We further show that such fluctuations are Gaussian-distributed. In deriving such results, we provide further insights into the relationship between stochastic and deterministic mathematical models for radiation-induced DNA damage repair. Specifically, we demonstrate how the governing deterministic equations commonly employed in the field arise naturally within the stochastic framework as a macroscopic limit. Additionally, by examining the fluctuations around this macroscopic limit, we uncover deviations from a Poissonian behavior driven by interactions and clustering among DNA damages. Although such behaviors have been empirically observed, our derived results represent the first rigorous derivation that incorporates these deviations from a Poissonian distribution within a mathematical model, eliminating the need for specific ad hoc corrections. [ABSTRACT FROM AUTHOR]

The article considered the three types of description of the material behavior model: elastic, elastic–plastic, and viscoelastic. The problem is considered in the framework of deformable solid mechanics. The paper considers the possibility of describing modern polymeric and composite materials used as antifriction sliding layers in the viscoelasticity framework. A numerical procedure for finding the coefficients to describe the viscoelastic material behavior using the Prony model has been implemented. Numerical results and experimental data are compared. The model problem of spherical indenter penetration into polymer half-space is realized. The influence of the system discretization on the numerical solution is analyzed. The influence of the polymer behavior description in static and dynamic problem formulations is analyzed. [ABSTRACT FROM AUTHOR]

This paper explores the concept of Generalized Roughness in LA-Semigroups and its applications in various mathematical disciplines. We highlight the fundamental properties and structures of Generalized Roughness, examining its relationships with Fuzzy Lie Algebras, Order Theory, Lattice Structures, Algebraic Structures, and Categorical Perspectives. Moreover, we investigate the potential of mathematical modeling, optimization techniques, data analysis, and machine learning in the context of Generalized Roughness. Our findings reveal important results in Generalized Roughness, such as the preservation of roughness under the fuzzy equivalence relation and the composition of roughness sets. We demonstrate the significance of Generalized Roughness in the context of order theory and lattice structures, presenting key propositions and a theorem that elucidate its properties and relationships. Furthermore, we explore the applications of Generalized Roughness in mathematical modeling and optimization, highlighting the optimization of roughness measures, parameter estimation, and decision-making processes related to LA-Semigroup operations. We showcase how mathematical techniques can enhance understanding and utilization of LA-Semigroups in practical scenarios. Lastly, we delve into the role of data analysis and machine learning in uncovering patterns, relationships, and predictive models in Generalized Roughness. By leveraging these techniques, we provide examples and insights into how data analysis and machine learning can contribute to enhancing our understanding of LA-Semigroup behavior and supporting decision-making processes. [ABSTRACT FROM AUTHOR]

This paper presents mathematical models to estimate the kinematics and dynamics of wheeled and tracked robots. The models account for the physical–mechanical characteristics of the ground, the influence of the center of gravity displacement on the cornering moment of resistance, and the influence of the interaction of the crawler with the roadway. The results of the models are characterized by defining computational relationships for a robot's equations of motion, longitudinal forces, transverse forces, and resistive turning moments generated via longitudinal forces and transverse forces. [ABSTRACT FROM AUTHOR]

This paper describes a mathematical model of an autowave process in a cell with a ferrocolloid. The model is a system of differential coupled equations of the second order and differs from the previously presented model in terms of its original boundary conditions. The mathematical modeling of autowaves presented in this work constitutes an innovative approach, since the characteristics of the wave process are not initially included in the model but the model demonstrates a wave motion. A 2D solution of the model, which shows the correctness of the described mechanism of the autowave process, i.e., the recharging of magnetic particles in dense near-electrode layers formed near the electrodes under the influence of an electric field, is obtained. The propagation of single and phase autowaves is demonstrated in a computer experiment. [ABSTRACT FROM AUTHOR]

A new mathematical model of an aerosol fibrous filter, composed of a variety of nano- and microfibers, is developed. The combination of nano- and microfibers in a mixed-type filter provides a higher overall quality factor compared with filters with monodisperse fibers. In this paper, we propose a mathematical model of the flow of an incompressible fluid in a porous region consisting of a set of cylinders of various diameters in the range of nano- and micrometers to describe a mixed-type aerosol filter. The flow domain is a rectangular periodic cell with one microfiber and many nanofibers. The motion of the carrier medium is described by the boundary value problem in Stokes flow approximation with the no-slip boundary condition for microfibers and the slip condition for nanofibers. The boundary element method taking into account the slip and non-slip conditions is developed. The calculated velocity field, streamlines, vorticity distribution, and drag of separate fibers and the entire periodic cell are presented. Numerical results for the drag force of the porous medium of a mixed-type filter for the various ratios of mass proportion of nano- and microfibers, porosity, and filtration velocity are presented. The obtained results are compared with the analytical formulas based on the approximate theory of filtration of bimodal filters and with known experimental data. It is shown that with an increase in the mass fraction of nanofibers, the total drag force of the cell increases, while the relative contribution of nanofibers to the total drag force tends toward the value that is less than unity. An approximate analytical formula for the drag coefficient of a mixed aerosol filter is derived. The developed flow model and analytical formulas allow for estimating the aerodynamic drag of a mixed filter composed by nano- and microfibers. [ABSTRACT FROM AUTHOR]

The environmental, economic, and energy problems of the modern world motivate the development of alternative fuel technologies. Multifuel technology can help reduce the carbon footprint and waste from the raw materials sector as well as slow down the depletion of energy resources. However, there are limitations to the active use of multifuel mixtures in real power plants and engines because they are difficult to spray in combustion chambers and require secondary atomization. Droplet micro-explosion seems the most promising secondary atomization technology in terms of its integral characteristics. This review paper outlines the most interesting approaches to modeling micro-explosions using in-house computer codes and commercial software packages. A physical model of a droplet micro-explosion based on experimental data was analyzed to highlight the schemes and mathematical expressions describing the critical conditions of parent droplet atomization. Approaches are presented that can predict the number, sizes, velocities, and trajectories of emerging child droplets. We also list the empirical data necessary for developing advanced fragmentation models. Finally, we outline the main growth areas for micro-explosion models catering for the needs of spray technology. [ABSTRACT FROM AUTHOR]

This paper presents an experimental and numerical investigation of pultruded composite glass fibre-reinforced polymer (pGFRP) cross-arms subjected to flexural creep behaviour to assess their performance and sustainability in composite cross-arm structure applications. The primary objective of this study was to investigate the failure creep behaviour of pGFRP cross-arms with different stacking sequences. Specifically, the study aimed to understand the variations in strain rate exhibited during different stages of the creep process. Therefore, this study emphasizes a simplified approach within the experiment, numerical analysis, and mathematical modelling of three different pGFRP composites to estimate the stiffness reduction factors that determine the prediction of failure. The findings show that Findley's power law and the Burger model projected very different strains and diverged noticeably outside the testing period. Findley's model estimated a minimal increase in total strain over 50 years, while the Burger model anticipated PS-1 and PS-2 composites would fail within about 11 and 33 years, respectively. The Burger model's forecasts might be more reasonable due to the harsh environment the cross-arms are expected to withstand. The endurance and long-term performance of composite materials used in overhead power transmission lines may be predicted mathematically, and this insight into material property factors can help with design and maintenance. [ABSTRACT FROM AUTHOR]

Stochastic modeling of biochemical processes at the cellular level has been the subject of intense research in recent years. The Chemical Master Equation is a broadly utilized stochastic discrete model of such processes. Numerous important biochemical systems consist of many species subject to many reactions. As a result, their mathematical models depend on many parameters. In applications, some of the model parameters may be unknown, so their values need to be estimated from the experimental data. However, the problem of parameter value inference can be quite challenging, especially in the stochastic setting. To estimate accurately the values of a subset of parameters, the system should be sensitive with respect to variations in each of these parameters and they should not be correlated. In this paper, we propose a technique for detecting collinearity among models' parameters and we apply this method for selecting subsets of parameters that can be estimated from the available data. The analysis relies on finite-difference sensitivity estimations and the singular value decomposition of the sensitivity matrix. We illustrated the advantages of the proposed method by successfully testing it on several models of biochemical systems of practical interest. [ABSTRACT FROM AUTHOR]

The aim of this paper was to design a repeated drug administration strategy to reach and maintain the requested drug concentration in the body. Conservative designs require an exact knowledge of pharmacokinetic parameters, which is considered an unrealistic demand. The problem is usually resolved using the trial-and-error open-loop approach; yet, this can be considered insufficient due to the parametric uncertainties as the dosing strategy may induce an undesired behavior of the drug concentrations. Therefore, the presented approach is rather based on the paradigms of system and control theory. An algorithm was designed that computes the required doses to be administered based on the blood samples. Since repeated drug dosing is essentially a discrete time process, the entire design considers the discrete time domain. We have also presented the idea of applying this methodology for the stabilization of an unstable model, for instance, a model of tumor growth. The simulation experiments demonstrated that all variants of the proposed control algorithm can reach and maintain the desired drug concentration robustly, i.e., despite the presence of parametric uncertainties, in a way that is superior to that of the traditional open-loop approach. It was shown that the closed-loop control with the integral controller and stabilizing state feedback is robust against large parametric uncertainties. [ABSTRACT FROM AUTHOR]

In this paper, we take physical and health integration as the entry point. Firstly, based on the transformation mechanism of adolescent idiopathic scoliosis we construct a time delay differential model. Moreover, using the theory of characteristic equation we discuss the stability of a positive equilibrium under the delays of τ = 0 and τ ≠ 0 . Furthermore, through numerical simulation, it has been verified the delay, τ , exceeds a critical value, the positive equilibrium loses its stability and Hopf bifurcation occurs. Lastly, we determine that sports have a positive effect on adolescent idiopathic scoliosis, directly reducing the number of people with adolescent idiopathic scoliosis. [ABSTRACT FROM AUTHOR]

The paper investigates a model of a k-out-of-n system, the residual lifetime of which changes after failures of any of its components. The problem of a Preventive Maintenance (PM) organization as advice to the Decision Maker (DM) for such a system is considered. The purpose of this paper is to propose a mathematical model of the k-out-of-n system to support DM about PM. For most practical applications, it is usually possible to estimate the lifetime distribution parameters of the system components with limited accuracy (only one or two moments), which is why special attention is paid to the sensitivity analysis of the system reliability characteristics and decisions about PM to the shape of system components lifetime distributions. In the numerical examples, we consider the 3-out-of-6 model discussed in our previous works for two real systems. The novelty, significance, and features of this study consist of the following, after the failure of one of the system components, the load on all the others increases, which leads to a decrease in their residual lifetime. We model this situation with order statistics and study the quality of PM strategies with respect to the availability maximization criterion. At the same time, we are focusing on the study of the sensitivity of decision-making to the type of lifetime distribution of system components. [ABSTRACT FROM AUTHOR]

Image coding technology has become an indispensable technology in the field of modern information. With the vigorous development of the big data era, information security has received more attention. Image steganography is an important method of image encoding and hiding, and how to protect information security with this technology is worth studying. Using a basis of mathematical modeling, this paper makes innovations not only in improving the theoretical system of kernel function but also in constructing a random matrix to establish an information-hiding scheme. By using the random matrix as the reference matrix for secret-information steganography, due to the characteristics of the random matrix, the secret information set to be retrieved is very small, reducing the modification range of the steganography image and improving the steganography image quality and efficiency. This scheme can maintain the steganography image quality with a PSNR of 49.95 dB and steganography of 1.5 bits per pixel and can ensure that the steganography efficiency is improved by reducing the steganography set. In order to adapt to different steganography requirements and improve the steganography ability of the steganography schemes, this paper also proposes an adaptive large-capacity information-hiding scheme based on the random matrix. In this scheme, a method of expanding the random matrix is proposed, which can generate a corresponding random matrix according to different steganography capacity requirements to achieve the corresponding secret-information steganography. Two schemes are demonstrated through simulation experiments as well as an analysis of the steganography efficiency, steganography image quality, and steganography capacity and security. The experimental results show that the latter two schemes are better than the first two in terms of steganography capacity and steganography image quality. [ABSTRACT FROM AUTHOR]

The most commonly used model of solar cells is the single-diode model, with five unknown parameters. First, this paper proposes three variants of the single-diode model, which imply the voltage dependence of the series resistance, parallel resistance, and both resistors. Second, analytical relationships between the current and the voltage expressed were derived using the Lambert W function for each proposed model. Third, the paper presents a hybrid algorithm, Chaotic Snake Optimization (Chaotic SO), combining chaotic sequences with the snake optimization algorithm. The application of the proposed models and algorithm was justified on two well-known solar photovoltaic (PV) cells—RTC France solar cell and Photowatt-PWP201 module. The results showed that the root-mean-square-error (RMSE) values calculated by applying the proposed equivalent circuit with voltage dependence of both resistors are reduced by 20% for the RTC France solar cell and 40% for the Photowatt-PWP201 module compared to the standard single-diode equivalent circuit. Finally, an experimental investigation was conducted into the applicability of the proposed models to a solar laboratory module, and the results obtained proved the relevance and effectiveness of the proposed models. [ABSTRACT FROM AUTHOR]

In this article, a class of scalar nonlinear integro-differential equations of first order with fading memory is investigated. For the considered fading memory problem, we discuss the effects of the memory over all the values of the parameter in the kernel of the equations. Using the Lyapunov–Krasovski functional method, we give various sufficient conditions of stability, asymptotic stability, uniform stability of zero solution, convergence and boundedness, and square integrability of nonzero solutions in relation to the considered scalar nonlinear integro-differential equations for various cases. As the novel contributions of this article, the new scalar nonlinear integro-differential equation with the fading memory is firstly investigated in the literature, and seven theorems, which have novel sufficient qualitative conditions, are provided on the qualitative behaviors of solutions called boundedness, convergence, stability, integrability, asymptotic stability and uniform stability of solutions. The novel outcomes and originality of this article are that the considered integro-differential equations are new mathematical models, they include former mathematical models in relation to the mathematical models of this paper as well as the given main seven qualitative results are also new. The outcomes of this paper enhance some present results and provide new contributions to the relevant literature. The results of the article have complementary properties for the symmetry of integro-differential equations. [ABSTRACT FROM AUTHOR]

This paper deals with the alternative mathematical modeling of the two-side platform. Two-sided platforms are specific multi-sided platforms that bring together two distinct groups of a model. The stochastic modeling by adapting various innovative mathematical methods including the first exceed theory and the stochastic pseudo-game theory has been applied for describing a two-sided platform more properly. A stochastic pseudo-game model is newly introduced to solve the two-sided platform more effectively. Analytically tractable results for operation thresholds for maximizing profits are provided and it also delivers the optimal balance of a two-sided platform. The paper includes how these innovative models are applied into various two-sided market situations. Additionally, users could conduct these multi-sided models to real business developments and the case practices of these unique models shall help the readers who want to find recommendations of their business situations easily even without having any mathematical background. [ABSTRACT FROM AUTHOR]

The mathematical model of a fragment of a high-voltage electric network is developed in this paper. The network consists of a long power line with distributed parameters and an equivalent three-phase active-inductive load. Neumann and Robin—Poincare boundary conditions were used to identify the boundary conditions for the long line equation. The parameter output voltage (voltage at the end of the line) is introduced into the paper for further universal use of the developed line model. On the basis of the developed mathematical model, the program code is written in the algorithmic language Visual Fortran. By means of it, oscillograms of transient electromagnetic processes of voltages and currents in the form of spatial, temporal and temporal-spatial distributions during remote two-phase short circuits in the transmission line of high voltage are obtained. Two transient electromagnetic processes are analyzed in the present work. The first one was analyzed during the switching on of the line to the normal mode of operation with the subsequent transition to the emergency mode. The second one was analyzed during the switching on the line in the mode of a remote two-phase short circuit to the ground. The results of transient electromagnetic process simulation in the form of analyzed figures are shown. All the results presented in this paper were obtained exclusively using numerical methods. [ABSTRACT FROM AUTHOR]

Drying is a complex process of simultaneous heat, mass, and momentum transport phenomena with continuous phase changes. Numerical modelling is one of the most effective tools to mechanistically express the different physics of drying processes for accurately predicting the drying kinetics and understanding the morphological changes during drying. However, the mathematical modelling of drying processes is complex and computationally very expensive due to multiphysics and the multiscale nature of heat and mass transfer during drying. Physics-informed machine learning (PIML)-based modelling has the potential to overcome these drawbacks and could be an exciting new addition to drying research for describing drying processes by embedding fundamental transport laws and constraints in machine learning models. To develop such a novel PIML-based model for drying applications, it is necessary to have a fundamental understanding of heat, mass, and momentum transfer processes and their mathematical formulation of drying processes, in addition to data-driven modelling knowledge. Based on a comprehensive literature review, this paper presents two types of information: fundamental physics-based information about drying processes and data-driven modelling strategies to develop PIML-based models for drying applications. The current status of physics-based models and PIML-based models and their limitations are discussed. A sample PIML-based modelling framework for drying application is presented. Finally, the challenges of addressing simultaneous heat, mass, and momentum transport phenomena in PIML modelling for optimizing the drying process are presented at the end of this paper. It is expected that the information in this manuscript will be beneficial for further advancing the field. [ABSTRACT FROM AUTHOR]

In this paper, a mathematical analysis of the HIV/AIDS deterministic model studied in the paper called Mathematical Model of HIV/AIDS Considering Sexual Preferences Under Antiretroviral Therapy, a case study in the previous works preformed by Espitia is performed. The objective is to gain insight into the qualitative dynamics of the model determining the conditions for the persistence or effective control of the disease in the community through the study of basic properties such as positiveness and boundedness; the calculus of the basic reproduction number; stationary points such as disease-free equilibrium (DFE), boundary equilibrium (BE) and endemic equilibrium (EE); and the local stability (LAS) of disease-free equilibrium. The findings allow us to conclude that the best way to reduce contagion and consequently reach a DFE is thought to be the reduction in the rate of homosexual partners, as they are the most affected population by the virus and are therefore the most likely to become infected and spread it. Increasing the departure rate of infected individuals leads to a decrease in untreated infected heterosexual men and untreated infected women. [ABSTRACT FROM AUTHOR]

Transformer-less connection schemes can provide a feasible solution for lowering the economic cost, occupied space, and device weight of modular multilevel converter (MMC) systems. However, due to the reduction in the converter transformer, the current flow loop is changed; as a result, the existing MMC model is not suitable. In this paper, the ac- and dc-side equivalent circuit models of the MMC system using a transformer-less connection scheme are established in both a–b–c stationary and d–q rotating coordinate systems. Then, a highly accurate mathematical analysis model is proposed, in which the interactions among the electrical quantities can be fully seen. The mathematical model is established in the time domain, and hence the amplitude and phase angle of every harmonic component in each quantity can be directly obtained. The proposed model is verified under various typical situations by comparing the calculated values with the actual waveforms. The comparison results prove that the calculation error is small enough to be negligible. The mathematical model in this paper can provide a powerful tool in terms of the performance analysis and the main circuit parameter design for MMCs in transformer-less applications. [ABSTRACT FROM AUTHOR]

A new mathematical model of Coronavirus (2019-nCov) using piecewise hybrid fractional order derivatives is given in this paper. Moreover, in order to be consistent with the physical model problem, a new parameter μ is presented. The boundedness, existence, and positivity of the solutions for the proposed model are discussed. Two improved numerical methods are presented in this paper. The Caputo proportional constant nonstandard modified Euler–Maruyama method is introduced to study the fractional stochastic model, and the Grünwald–Letnikov nonstandard finite difference method is presented to study the hybrid fractional order deterministic model. Comparative studies with real data from Spain and Wuhan are presented. [ABSTRACT FROM AUTHOR]

This paper presents the design of a planar parallel manipulator with a pneumatic drive. Such manipulators are used in production lines for sorting, selecting, packing, and palletizing workpieces. This paper presents simulation studies of the designed manipulator in Matlab/Simulink software and using the SimMechanics library. A simple kinematics problem and an inverse kinematics problem were solved in order to carry out simulation studies of the designed manipulator. Simulation studies were also carried out on the dynamics of the manipulator using a mathematical model describing the physical phenomena occurring during the operation of the manipulator's electro-pneumatic servo-drives. The main objective of the simulation study was to determine the manipulator working space and the possibility of positional control of the manipulator end-effector using a fuzzy logic controller. [ABSTRACT FROM AUTHOR]

This paper strives to achieve a comprehensive review of chaos in analog circuits and lumped electronic networks. Readers will be guided from the beginning of the investigations of simple electronic circuits to the current trends in the research into chaos. The author tries to provide the key references related to this issue, including papers describing modern numerical algorithms capable of localizing chaotic and hyperchaotic motion in complex mathematical models, interesting full on-chip implementations of chaotic systems, possible practical applications of entropic signals, fractional-order chaotic systems and chaotic oscillators with mem-elements. [ABSTRACT FROM AUTHOR]

A general sampling problem can be described by an Ellsberg urn, which is a mathematical model that assumes that balls are randomly drawn from an urn with an uncertain numbers of colored balls. This means that the Ellsberg urn is essentially an intricate model with simultaneous randomness and epistemic uncertainty, and this is the core problem discussed in this paper. Since practical sampling is usually processed in an intricate environment, the solution for an equivalent mathematical problem is necessary. Suppose an Ellsberg urn contains three unknown numbers of colored balls (i.e., a two-degrees-of-freedom Ellsberg urn), and three balls are randomly drawn from the urn. Compared to the published papers, this paper first constructs a chance space with two-dimensional uncertainty space and three-dimensional probability space to rigorously calculate the color distributions for those drawn balls by uncertainty theory, probability theory, and chance theory. Moreover, it is interesting to find that all cases of the drawn balls are symmetric in such a specific situation of a sample problem with epistemic uncertainty. [ABSTRACT FROM AUTHOR]

In this paper, a one-dimensional mathematical model for investigating the vibrations of structures consisting of elastic and weakly curved rods is proposed. The three-dimensional structure is replaced by a limit graph, on each arc of which a system of three differential equations is written out. The differential equations describe the longitudinal and transverse vibrations of an elastic rod, taking into account the influence of longitudinal and transverse vibrations on each other. Describing conjugation conditions at joints of four or more rods is an important problem. This article assumes new conjugation conditions that guarantee the all-around decidability and symmetry of the resulting boundary value problems for systems of differential equations on a star graph. In addition, the paper proposes a physical interpretation of the conjugation conditions found. Thus, the work presents one more area of knowledge where symmetry phenomena occur. The symmetry here is manifested in the preservation of conjugation conditions when passing to the conjugate operator. [ABSTRACT FROM AUTHOR]

In this paper, in order to understand the development process and influencing factors of coal underground gasification, taking the two-dimensional underground gasification area of the plane as the simulation object, the characteristics of the multi-physical field coupling process of exudate mass heat transfer and combustion gasification reaction in the process of horizontal coal seam underground gasification are analyzed, and a two-dimensional mathematical model of thermal-hydrological-mechanical-chemical coupling of a porous medium is established. The temperature distribution of coal rock from the gasification point, the distribution of gas water vapor pressure and stress-strain, the temperature contour distribution of fractured coal rocks of different densities of heterogeneity, and the influence of different water-oxygen ratios and different fractured coal rocks on the gas components generated by the gasification reaction were studied. The results show that the tensile damage caused by the tensile strain volume expansion of the coal underground gasification center, the shear damage caused by the compression of the edge compressive strain volume, and the temperature conduction rate decrease with the increase in the coal rock fracture, but in the heterogeneous coal rock, the greater the fracture density, the faster the temperature conduction rate, which has a certain impact on the gasification combustion reaction. The ratio of CO2, H2 and CO in the case of simulating that the water-to-oxygen ratio is 1:2, 1:1, and 2:1 is 1:0.85:0.73, 1:1.1:0.97, and 1:1.76:1.33, respectively. At a water-oxygen ratio of 2:1, the concentration ratio is the most ideal, and the main gases, CO, CO2, and H2, are 32%, 21%, and 37%. Furthermore, the reaction rate increases with the increase of fracture density. The gas component concentration simulated in this paper has good consistency with the results of the previous experimental data, which has important guiding significance for the underground coal gasification project. [ABSTRACT FROM AUTHOR]

Aiming at maritime infrared target detection with low contrast influenced by maritime clutter and illumination, this paper proposes a Modified Histogram Equalization with Edge Fusion (MHEEF) pre-processing algorithm in backlight maritime scenes and establishes Local-Contrast Saliency Models with Double Scale and Modes (LCMDSM) for detecting a target with the properties of positive and negative contrast. We propose a local-contrast saliency mathematical model with double modes in the extension of only one mode. Then, the big scale and small scale are combined into one Target Detection Unit (TDU), which can approach the "from bottom to up" mechanism of the Visual Attention Model (VAM) better and identify the target with a suitable size, approaching the target's actual shape. In the experimental results and analysis, clutter, foggy, backlight, and dim maritime scenes are chosen to verify the effectiveness of the target detection algorithm. From the enhancement result, the LCMDSM algorithm can achieve a Detection Rate (DR) with a value of 98.26% under each maritime scene on the average level and can be used in real-time detection with low computational cost. [ABSTRACT FROM AUTHOR]

In this paper, we consider a retrial queue with a state-dependent service rate as a mathematical model of a node of FANET communications. We suppose that the arrival process is Poisson, the delay duration is exponentially distributed, the orbit is unlimited, and there is multiple random access from the orbit. There is one server, and the service time of every call is distributed exponentially with a variable parameter depending on the number of calls in the orbit. The service rate has an infinite number of values. We propose the asymptotic diffusion method for the model study. The asymptotic diffusion approximation of the probability distribution of the number of calls in the orbit is derived. Some numerical examples are demonstrated. [ABSTRACT FROM AUTHOR]

In this paper, a mathematical model is presented to identify the direct dynamic coefficients (kxx, kzz, cxx, czz) of a pressurized bearing in a rotor-bearing system. The presented mathematical model for online identification is the result of the application of the algebraic identification approach to a two-degree-of-freedom rotor-bearing model. The proposed identification model requires only the vibration response as the input data. The performance of the model was assessed by theoretically and experimentally testing the proposed identifier at different shaft frequencies and, for the experimental test, a pressurized bearing that has hydrodynamic and hydrostatic characteristics at a support pressure of 10 psi was considered. The working fluid is Chevron GST 32 oil. The results show negligible differences between the vibration response of the experimental rotor and those obtained numerically using the identified direct dynamic coefficients of the pressurized bearing. In addition, it is observed that the algebraic identifier determines the identified parameters in a time less than 0.2 s. The proposed identifier can be used in other types of bearings, which is a great advantage over other identifiers. [ABSTRACT FROM AUTHOR]

Detecting small targets and handling target occlusion and overlap are critical challenges in weld defect detection. In this paper, we propose the S-YOLO model, a novel weld defect detection method based on the YOLOv8-nano model and several mathematical techniques, specifically tailored to address these issues. Our approach includes several key contributions. Firstly, we introduce omni-dimensional dynamic convolution, which is sensitive to small targets, for improved feature extraction. Secondly, the NAM attention mechanism enhances feature representation in the region of interest. NAM computes the channel-wise and spatial-wise attention weights by matrix multiplications and element-wise operations, and then applies them to the feature maps. Additionally, we replace the SPPF module with a context augmentation module to improve feature map resolution and quality. To minimize information loss, we utilize Carafe upsampling instead of the conventional upsampling operations. Furthermore, we use a loss function that combines IoU, binary cross-entropy, and focal loss to improve bounding box regression and object classification. We use stochastic gradient descent (SGD) with momentum and weight decay to update the parameters of our model. Through rigorous experimental validation, our S-YOLO model demonstrates outstanding accuracy and efficiency in weld defect detection. It effectively tackles the challenges of small target detection, target occlusion, and target overlap. Notably, the proposed model achieves an impressive 8.9% improvement in mean Average Precision (mAP) compared to the native model. [ABSTRACT FROM AUTHOR]

The modeling of biological processes has increasingly been based on fractional calculus. In this paper, a novel fractional-order model is used to investigate the epidemiological impact of vaccination measures on the co-dynamics of viral hepatitis B and COVID-19. To investigate the existence and stability of the new model, we use some fixed point theory results. The COVID-19 and viral hepatitis B thresholds are estimated using the model fitting. The vaccine parameters are plotted against transmission coefficients. The effect of non-integer derivatives on the solution paths for each epidemiological state and the trajectory diagram for infected classes are also examined numerically. An infection-free steady state and an infection-present equilibrium are achieved when R 0 < 1 and R 0 > 1 , respectively. Similarly, phase portraits confirm the behaviour of the infected components, showing that, regardless of the order of the fractional derivative, the trajectories of the disease classes always converge toward infection-free steady states over time, no matter what initial conditions are assumed for the diseases. The model has been verified using real observations. [ABSTRACT FROM AUTHOR]

The objective of this paper is to present a novel design of intelligent neuro-supervised networks (INSNs) in order to study the dynamics of a mathematical model for Parkinson's disease illness (PDI), governed with three differential classes to represent the rhythms of brain electrical activity measurements at different locations in the cerebral cortex. The proposed INSNs are constructed by exploiting the knacks of multilayer structure neural networks back-propagated with the Levenberg–Marquardt (LM) and Bayesian regularization (BR) optimization approaches. The reference data for the grids of input and the target samples of INSNs were formulated with a reliable numerical solver via the Adams method for sundry scenarios of PDI models by way of variation of sensor locations in order to measure the impact of the rhythms of brain electrical activity. The designed INSNs for both backpropagation procedures were implemented on created datasets segmented arbitrarily into training, testing, and validation samples by optimization of mean squared error based fitness function. Comparison of outcomes on the basis of exhaustive simulations of proposed INSNs via both LM and BR methodologies was conducted with reference solutions of PDI models by means of learning curves on MSE, adaptive control parameters of algorithms, absolute error, histogram error plots, and regression index. The outcomes endorse the efficacy of both INSNs solvers for different scenarios in PDI models, but the accuracy of the BR-based method is relatively superior, albeit at the cost of slightly more computations. [ABSTRACT FROM AUTHOR]

This work focuses on the methods of creating in-fiber devices, such as sensors, filters, and scatterers, using the fiber fuse effect. The effect allows for the creation of structures in a fiber core. However, it is necessary to know exactly how this process works, when the plasma spark occurs, what size it reaches, and how it depends on external parameters such as power and wavelength of radiation. Thus, this present study aims to create the possibility of predicting the consequences of optical breakdown. This paper describes a mathematical model of the optical breakdown initiation in a fiber core based on the thermal conductivity equation. The breakdown generates a plasma spark, which subsequently moves along the fiber. The problem is solved in the axisymmetric formulation. The computational domain consists of four elements with different thermophysical properties at the boundaries of which conjugation conditions are fulfilled. The term describing the heat source in the model is determined by the wavelength of radiation and the refractive indices of the core and the shell and also includes the radiation absorption on the released electrons during the thermal ionization of the quartz glass. The temperature field distributions in the optical fiber are obtained. Based on the calculations, it is possible to estimate the occurrence times of various phase states inside the fiber, in particular, the plasma spark occurrence time. [ABSTRACT FROM AUTHOR]

This paper proposes a fractional-order chaotic system using a tri-stable locally active memristor. The characteristics of the memristor, dynamic mechanism of oscillation, and behaviors of the proposed system were analyzed, and then a visually meaningful image encryption scheme was designed based on the chaotic system, DNA encoding, and integer wavelet transform (IWT). Firstly, the mathematical model of the memristor was designed, which was nonvolatile, locally active, and tri-stable. Secondly, the stability, dynamic mechanism of oscillation, bifurcation behaviors, and complexity of the fractional-order memristive chaotic system were investigated and the conditions of stability were obtained. Thirdly, the largest Lyapunov exponent, bifurcation diagram, and complexity of the novel system were calculated and the coexisting bifurcation, coexisting attractors, spectral entropy, and so on are shown. Finally, a visually meaningful image encryption scheme based on the proposed system was designed, and its security was assessed by statistical analysis and different attacks. Numerical simulation demonstrated the effectiveness of the theoretical analysis and high security of the proposed image encryption scheme. [ABSTRACT FROM AUTHOR]

Symmetry is a key part of the study of basic forces and particles, as well as the creation of mathematical models that help scientists in various scientific disciplines understand complex events. Scientists can figure out what a system is made of and how it works by looking at its symmetry. They can then use this information to make predictions and create new materials and technologies. Humanity has conquered many once-fatal diseases due to medical research and technological advancements. Although this progress is encouraging, there are still a great many areas that require continual human efforts. An effort is made in this article to choose the best treatment strategy to completely manage the pandemic of COVID-19 under conjunctive complex fuzzy knowledge. In this paper, the concept of conjunctive complex fuzzy relations is presented and numerous set theoretical aspects of this phenomenon are established. The investigation of this ideology is further expanded to describe different sorts of essential structural conjunctive complex fuzzy relations. Matrix and graphical representations of the formation of these newly specified relations are also provided. Moreover, this concept has been successfully employed to provide a therapy strategy for a rapid recovery from COVID-19. Furthermore, a comparative analysis is conducted to demonstrate the validity and applicability of the suggested approaches compared to existing methods. [ABSTRACT FROM AUTHOR]

This paper explores the 3D printing of poly vinyl alcohol (PVA) using the fused deposition modeling (FDM) process by conducting statistical modeling and optimization. This study focuses on varying the infill percentage (10–50%) and patterns (Cubic, Gyroid, tri-hexagon and triangle, Grid) as input parameters for the response surface methodology (DOE) while measuring modulus, elongation at break, and weight as experimental responses. To determine the optimal parameters, a regression equation analysis was conducted to identify the most significant parameters. The results indicate that both input parameters significantly impact the output responses. The Design Expert software was utilized to create surface and residual plots, and the interaction between the two input parameters shows that increasing the infill percentage (IP) leads to printing heavier samples, while the patterns do not affect the weight of the parts due to close printing structures. On the contrary, the discrepancy between the predicted and actual responses for the optimal samples is below 15%. This level of error is deemed acceptable for the DOE experiments. [ABSTRACT FROM AUTHOR]

The electrical energy supply of industrial equipment is provided by electrical power stations with high- (HT), medium- (MV) and low-voltage (LV) busbars. Consumers are connected to either MV or LV busbars. In this paper, a real power station was considered, through which the gasoline extraction from the well gas installation is powered. Electric consumers (electric motors) supplied by a MV busbar have active power of 13.54 MW, and those fed by a LV busbar have active power of 6.4 MW. Since electrical consumers operate in explosive environments, the design and operating conditions are more severe than in the case of electrical installations operating in non-explosive environments. The case of a single phase-to-ground fault occurring on the HV transmission lines feeding the power station has been analysed. First, the mathematical models for the calculation of the phase voltages, the dissymmetry and asymmetry coefficients, the reduction coefficient of the plus sequence component, and the effective values of the phase voltages were established. The influence of the source impedance (the equivalent impedance of the HV transmission lines) and of the neutral point configuration of the HV/MV medium-voltage transformer on the calculated quantities was analysed. Then, the results obtained using the established mathematical models were compared with those obtained experimentally by provoking a single-phase-to-ground fault near the HV busbars of the real power station. This study has shown that the de-symmetrisation of the phase voltages of the MV and LV busbars is lower when using the Y/Δ connection for the HV/MV transformer. As a result, it is recommended the Y/Δ connection be used for this transformer, instead of the Y0/Δ connection. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of chaos control in an economic mathematical dynamical model. By regarding the control variables as the bifurcation parameters, the stability of equilibria and the existence of Hopf bifurcations of the relevance feedback system are investigated, and the criterion of controllability for the chaotic system is obtained based on a time-delayed feedback control technique. Furthermore, numerical simulations are provided to demonstrate the feasibility of our methods and results. [ABSTRACT FROM AUTHOR]

Leak 2D is a new two-dimensional dual permeability mathematical model for the simulation of the preferential flow in the vadose zone. In this model, water flow in the soil matrix domain is described by the two-dimensional h-based Richards' equation. Water flow in the fracture domain is estimated using the kinematic wave approach. Richards' equation is solved by a combination of the alternating direction implicit (A.D.I.) method and the Douglas and Jones predictor−corrector method. The kinematic wave equation is solved explicitly. In the present paper, Leak 2D is calibrated and validated with data obtained in a Hele–Shaw apparatus filled with sand. Preferential flow is achieved by inserting four artificial macropores of various sizes into the soil. Six irrigations of various intensities and durations were used for the calibration and validation process. The water content at various depths was recorded by five sensors that were inserted into the soil. A comparison of the simulated water content with the measured profiles shows that Leak 2D can sufficiently describe preferential flow into the unsaturated zone of the soil, even under extreme irrigation conditions. [ABSTRACT FROM AUTHOR]

The whole world has entered the era of the Vuca. Some traditional methods of problem analysis begin to fail. Complexity science is needed to study and solve problems from the perspective of complex systems. As a complex system full of volatility and uncertainty, price fluctuations have attracted wide attention from researchers. Therefore, through a literature review, this paper analyzes the research on complex theories on price prediction. The following conclusions are drawn: (1) The price forecast receives widespread attention year by year, and the number of published articles also shows a rapid rising trend. (2) The hybrid model can achieve higher prediction accuracy than the single model. (3) The complexity of models is increasing. In the future, the more complex methods will be applied to price forecast, including AI technologies such as LLM. (4) Crude-oil prices and stock prices will continue to be the focus of research, with carbon prices, gold prices, Bitcoin, and others becoming new research hotspots. The innovation of this research mainly includes the following three aspects: (1) The whole analysis of all the articles on price prediction using mathematical models in the past 10 years rather than the analysis of a single field such as oil price or stock price. (2) Classify the research methods of price forecasting in different fields, and found the common problems of price forecasting in different fields (including data processing methods and model selection, etc.), which provide references for different researchers to select price forecasting models. (3) Use VOSviewer to analyze the hot words appearing in recent years according to the timeline, find the research trend, and provide references for researchers to choose the future research direction. [ABSTRACT FROM AUTHOR]

When deblurring an image, ensuring that the restored intensities are strictly non-negative is crucial. However, current numerical techniques often fail to consistently produce favorable results, leading to negative intensities that contribute to significant dark regions in the restored images. To address this, our study proposes a mathematical model for non-blind image deblurring based on total fractional-order variational principles. Our proposed model not only guarantees strictly positive intensity values but also imposes limits on the intensities within a specified range. By removing negative intensities or constraining them within the prescribed range, we can significantly enhance the quality of deblurred images. The key concept in this paper involves converting the constrained total fractional-order variational-based image deblurring problem into an unconstrained one through the introduction of the augmented Lagrangian method. To facilitate this conversion and improve convergence, we describe new numerical algorithms and introduce a novel circulant preconditioned matrix. This matrix effectively overcomes the slow convergence typically encountered when using the conjugate gradient method within the augmented Lagrangian framework. Our proposed approach is validated through computational tests, demonstrating its effectiveness and viability in practical applications. [ABSTRACT FROM AUTHOR]

Mathematical modeling can help the medical community to more fully understand and explore the physiological and pathological processes within the human body and can provide more accurate and reliable medical predictions and diagnoses. Neural network models, machine learning models, and statistical models, among others, have become important tools. The paper details the applications of mathematical modeling in the medical field: by building differential equations to simulate the patient's cardiovascular system, physicians can gain a deeper understanding of the pathogenesis and treatment of heart disease. With machine learning algorithms, medical images can be better quantified and analyzed, thus improving the precision and accuracy of diagnosis and treatment. In the drug development process, network models can help researchers more quickly screen for potentially active compounds and optimize them for eventual drug launch and application. By mining and analyzing a large number of medical data, more accurate and comprehensive disease risk assessment and prediction results can be obtained, providing the medical community with a more scientific and accurate basis for decision-making. In conclusion, research on medical problems based on mathematical models has become an important part of modern medical research, and great progress has been made in different fields. [ABSTRACT FROM AUTHOR]

Multistage fracturing in horizontal well has become one of the important techniques for the efficient development of low-permeability sandstone reservoirs. In multistage hydraulic fractured horizontal wells (MHFHWs), the depth of fracturing fluid invasion into the formation is a key parameter evaluating the imbibition enhancement after fracturing. However, few studies have been conducted on the invasion depth of fracturing fluids combining experiments and mathematical models under high-pressure differences in MHFHWs. Therefore, in this work, a mathematical model with experimental validation is proposed for evaluating the fracturing fluids invasion under high pressure. We first conducted a series of displacement experiments under different pressure differences to obtain the breakthrough time and invasion velocity. All core samples are taken from the block X of Xinjiang oilfield. A mathematical model of fracturing fluid injection was then established, considering the two-dimensional filtration of fracturing fluid. Then, the calculated invasion velocity was validated against the experimental data. Afterward, the invasion depth and invasion volume were determined for this typical horizontal well. Results show that at the end of 72 min, the invasion depth reaches 1.516 m when measured by core experiments and 1.434 m when calculated by the proposed model. The total invasion volume of all fracturing stages is estimated as 21,560.05 m3 and the actual total fluid volume injected is 24,019.6 m3. The paper formed a scientific and reasonable evaluation method of fracturing fluid invasion depth during the fracturing of horizontal wells, which provides solid theoretical support for the effective evaluation of fracturing to improve oil recovery. [ABSTRACT FROM AUTHOR]

Nowadays, high-speed permanent magnet synchronous machines (HSPMSMs) are widely used in high-speed direct-drive applications. Moreover, modular multilevel converters (MMCs) have attracted a lot of attention. In this paper, the mathematical model of the MMC for the HSPMSM was built on high- and low-speed regions, respectively, and the control of each model is completely decoupled. Moreover, energy balance control schemes based on the common mode current injection of the MMC with HSPMSM drive applications have been proposed for high- and low-speed cases, respectively. Based on this model, the controller is proposed for high- and low-speed cases, respectively. Simulation and experiment results indicate that the proposed energy balance control method for an MMC in the high-speed PMSM drive application exhibits significant performance, which can ensure the energy balance of the MMC and eliminate the circulating current of the MMC directly. [ABSTRACT FROM AUTHOR]

Dynamic reconfiguration, the monitoring of power production, and the fault diagnosis of photovoltaic arrays, among other applications, require fast and accurate models of photovoltaic arrays. In the literature, some models use the Lambert-W function to represent each module of the array, which increases the calculation time. Other models that use implicit equations to avoid the Lambert-W function do not use the inflection voltages to simplify the system of nonlinear equations that represent the array, increasing the computational burden. Therefore, this paper proposes mathematical models for series-parallel (SP) and total-cross-tied (TCT) photovoltaic arrays based on the implicit equations of the single-diode model and the inflection points of the current–voltage curves. These models decrease the calculation time by reducing the complexity of the nonlinear equation systems that represent each string of SP arrays and the whole TCT. Consequently, the calculation process that solves the model speeds up in comparison with processes that solve traditional explicit models based on the Lambert-W function. The results of several simulation scenarios using the proposed SP model with different array sizes show a reduction in the computation time by 82.97 % in contrast with the traditional solution. Additionally, when the proposed TCT model for arrays larger than 2 × 2 is used, the reduction in the computation time is between 47.71 % and 92.28 % . In dynamic reconfiguration, the results demonstrate that the proposed SP model provides the same optimal configuration but 7 times faster than traditional solutions, and the TCT model is solved at least 4 times faster than classical solutions. [ABSTRACT FROM AUTHOR]

In this paper, an atmospheric structure constant C n 2 model is proposed for evaluating the channel turbulence degree of atmospheric laser communication. First, we derive a mathematical model for the correlation between the atmospheric coherence length r 0 , the isoplanatic angle θ 0 and C n 2 using the Hufnagel–Valley (HV) turbulence model. Then, we calculate the seven parameters of the HV model with the actual measured r 0 and θ 0 data as input quantities, so as to draw the C n 2 profile and the θ 0 profile. The experimental results show that the fitted average C n 2 contours and single-day C n 2 contours have superior fitting performance compared with our historical data, and the daily correlation coefficient between the single-day computed θ 0 contours and the measured θ 0 contours is up to 87%. This result verifies the feasibility of the proposed method. The results validate the feasibility of the proposed method and provide a new technical tool for the inversion of turbulence C n 2 profiles. [ABSTRACT FROM AUTHOR]