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The application of additive manufacturing in the field of aviation hydraulics greatly improves the design freedom of hydraulic valve internal flow channels. Pressure loss in hydraulic valve internal flow channels is a primary factor that designers need to consider, and the rapid prediction of pressure loss is very helpful for flow channel design. At present, most studies only focus on how much the pressure loss in an additive manufacturing (AM) hydraulic channel is reduced compared with an original hydraulic channel, and a mathematical model of pressure loss in an AM curved channel is still lacking. In this paper, the pressure loss in a curved flow channel was firstly studied, and the main parameters affecting the pressure loss were determined using the dimensionless analysis method. Using computational fluid dynamics simulation, the relationships between the flow channel diameter, the flow channel length, the flow channel curvature radius, the fluid velocity and pressure loss were studied. According to the multiple regression analysis method, the mathematical model of pressure loss in aviation hydraulic channels was developed, and the model was solved based on the orthogonal experimental results. The pressure loss in the flow channel samples fabricated using selective laser melting was tested, and the results showed that the average error between the test results and the mathematical model calculation results was 7.72%. This model can be used to quickly predict the pressure loss in curved flow channels in the aviation hydraulic field. [ABSTRACT FROM AUTHOR]

This paper presents a comparison of Isolated (Flyback) and non-Isolated (Buck) multiple input-single output (MISO) DC-DC converters. The analysis of DC-DC converters is based on pulsed voltage source cells (PVSC). The modeling of both converter types is detailed through their mathematical models and electrical simulations using Matlab/Simulink and PSIM. The comparison focuses on the sizing parameters, non-ideal output characteristics and efficiency. Results show that the output voltage of the MISO Buck converter exhibits a linear dependence on the duty cycles control signal and has slightly higher efficiency than the Flyback converter. To validate the operation of both converters, a scenario with two inputs (low-power hydroelectric and photovoltaic voltage sources) is considered. The modeling and control of both source systems are detailed and the MISO converter performance response is evaluated under sources changes and efficiency point of view. [ABSTRACT FROM AUTHOR]

This paper proposes a partial differential equation model based on the model introduced by V. A. Kuznetsov and M. A. Taylor, which explains the dynamics of a tumor–immune interaction system, where the immune reactions are described by a Michaelis–Menten function. In this work, time delay and diffusion process are considered in order to make the studied model closer to reality. Firstly, we analyze the local stability of equilibria and the existence of Hopf bifurcation by using the delay as a bifurcation parameter. Secondly, we use the normal form theory and the center manifold reduction to determine the normal form of Hopf bifurcation for the studied model. Finally, some numerical simulations are provided to illustrate the analytic results. We show how diffusion has a significant effect on the dynamics of the delayed interaction tumor–immune system. [ABSTRACT FROM AUTHOR]

Chemical graph theory (CGT) is a field of mathematical science that applies classical graph theory to chemical structures and processes. Chemical graphs are the principal data format used in cheminformatics to illustrate chemical interactions. Several researchers have addressed boundary-value problems using star graphs. Star graphs were used since their method requires a central point linked to other vertices but not to itself. Our objective is to expand the mechanism by introducing the idea of an isobutane graph that has the chemical formula C 4 H 10 and CAS number 75-28-5. By using the appropriate fixed point theory findings, this paper investigates the existence of solutions to fractional boundary value problems of Caputo type on such graphs. Additionally, two examples are provided to strengthen our important conclusions. [ABSTRACT FROM AUTHOR]

Numerical methods have gained momentum among specific engineering problems that must be solved in such a manner that accuracy and speed are the two most important aspects to consider regarding the output. This paper presents a fast, semi-analytical method (SAM) and original mathematical algorithms to determine the pressure distribution and von Mises stress for spur gears' meshing teeth. The SAM begins with the Hartnett approach, based on Boussinesq's equation for the half-space theory of linear elasticity, which implicitly means an infinite width of the gear flank. To simulate more realistic quarter-space conditions, corrections based on virtual mirror pressure are introduced in the computational algorithm. Mathematical surfaces modeling is an important aspect for spur gears as an intermediate stage to determine the pressure distribution and von Mises stress. Shaft misalignment changes the contact problem from symmetric, in which the half- or quarter-space model can be used, to asymmetric. In the latter case, the model must determine the entire contact area. The obtained output is validated by comparisons between our original FEA results and results from the literature using SAMs and FEA. [ABSTRACT FROM AUTHOR]

P-sets (P stands for Packet), a set pair with dynamic and law characteristics, are made up of an internal and an outer P-set, which is obtained by introducing dynamic characteristics into the Cantor set and improving the Cantor set. The concepts of α F -sub-information, α F ¯ -sub-information, and (α F , α F ¯ ) -sub-information are presented in this paper based on P-sets, and it is then suggested that the relationship between the generation of sub-information and its attribute, the process of attribute reasoning, reasoning structure, and sub-information intelligent separation-acquisition be explored. These findings were used to design a sub-information intelligent separation-identification algorithm. By using these results, the application of intelligent separation and the identification of case information are given. [ABSTRACT FROM AUTHOR]

Cancer cell migration, as the principal element of tumor invasion, involves different cellular mechanisms. Various modes of cell migration including single and collective motions contribute to the invasion patterns. The competition between adhesive cell–cell and cell–matrix forces is a key factor that determines such patterns. In this paper, we study a distinct shell-type mode of tumor invasion observed in brain and breast tumors. In this mode, cells at the outer layer of the tumor collectively move away from the core and form a shell-type shape. Both the core and the shell sustain a sharp interface between cells and the surrounding matrix. To model the preserved interface, we adopted a Cahn–Hilliard-type free energy relation with the contribution of the interfacial stress. This nonconvex form of free energy allows for cells to remain together and preserve the tumor core via adhesive cell–cell forces while separating the core from the surrounding matrix across a continuous sharp interface. In addition, the motion of the shell was modeled using the chemotactic migration of cells in response to the gradient of nutrients. The associated fluxes of cells were implemented in a general form of balance law. A non-Michaelis–Menten kinetics model was adopted for the proliferation rate of cells. The flux of nutrients was also modeled using a simple diffusion equation. The comparison between the model predictions and experimental observations indicates the ability of the model to manifest the salient features of the invasion pattern. [ABSTRACT FROM AUTHOR]

In this paper, a mathematical simulation model of an electric vehicle traction battery has been developed, in which the battery was studied during the dynamic modes of its charge and discharge for heavy electric vehicles in various driving conditions—the conditions of the urban cycle and movement outside the city. The state of a lithium-ion battery is modeled based on operational factors, including changes in battery temperature. The simulation results will be useful for the implementation of real-time systems that take into account the processes of changing the characteristics of traction batteries. The developed mathematical model can be used in battery management systems to monitor the state of charge and battery degradation using the assessment of the state of charge (SOC) and the state of health (SOH). This is especially important when designing and operating a smart battery management system (BMS) in virtually any application of lithium-ion batteries, providing information on how long the device will run before it needs to be charged (SOC value) and when the battery should be replaced due to loss of battery capacity (SOH value). Based on the battery equivalent circuit and the system of equations, a simulation model was created to calculate the electrical and thermal characteristics. The equivalent circuit includes active and reactive elements, each of which imitates the physicochemical parameter of the battery under study or the structural element of the electrochemical battery. The input signals of the mathematical model are the current and ambient temperatures obtained during the tests of the electric vehicle, and the output signals are voltage, electrolyte temperature and degree of charge. The resulting equations make it possible to assign values of internal resistance to a certain temperature value and a certain value of the degree of charge. As a result of simulation modeling, the dependence of battery heating at various ambient temperatures was determined. [ABSTRACT FROM AUTHOR]

This paper proposes an impedance-accelerated inverse-time over-current protection optimization scheme based on the improved quantum genetic algorithm. First, the speed of remote backup protection is improved by increasing the optimization level of backup protection. Second, to ensure the coordination of protection when the distributed generation is connected to the distribution network, a mathematical model for the optimization of inverse time protection parameters is established. The mathematical model takes the minimum total action time of the optimized main and backup protection as the objective function, and the selectivity and sensitivity requirements of the protection as the constraints. In addition, the genetic algorithm is improved from four aspects: coding method, population initialization, quantum revolving gate, and variational evolution. The theoretical analysis and simulation results show that the proposed scheme can effectively improve the selectivity and operation speed of the protection. [ABSTRACT FROM AUTHOR]

The paper presents the identification process of the mathematical model parameters of a differential-drive two-wheeled mobile robot. The values of the unknown parameters of the dynamics model were determined by carrying out their identification offline with the Levenberg-Marguardt method and identification online with the Recursive least-squares method. The authors compared the parameters identified by offline and online methods and proposed to support the recursive least squares method with the results obtained by offline identification. The correctness of the identification process of the robot dynamics model parameters, and the operation of the control system was verified by comparing the desired trajectories and those obtained through simulation studies and laboratory tests. Then an analysis of errors defined as the difference between the values of reference position, orientation and velocity, and those obtained from simulations and laboratory tests was carried out. On itd basis, the quality of regulation in the proposed algorithm was determined. [ABSTRACT FROM AUTHOR]

Compared with the traditional lattice structure, the triply periodic minimal surface (TPMS) structure can avoid stress concentration effectively. Here, it is promising in the fields of lightweight and energy absorption. However, the number of structural parameters and mechanical properties of the TPMS structure is plentiful, and the relationship between them is unclassified. In this paper, for the first time, a unified mathematical model was proposed to establish the relationship between TPMS structural design parameters and mechanical properties. Fifteen primitive models were designed by changing the structural parameters (level-set value C and thickness T) and manufacturing by selective laser melting. The geometric defects and surface quality of the structures were explored by optical microscope and scanning electron microscopy (SEM). The mechanical properties were investigated by quasi-static compression test and finite element simulation. The influence of building direction on structural mechanical behavior (failure mode, stress-strain curve) was studied. The real mechanical properties (Young's modulus and plateau stress) of the structure could be predicted according to different C and T combinations. Finally, the energy absorption characteristics were explored. The results showed that when the C value is 0.6 in the range of 0–0.6, the energy absorption performance of the structure is at the maximum level. [ABSTRACT FROM AUTHOR]

The aim of this paper is to investigate the qualitative behavior of the COVID-19 pandemic under an initial vaccination program. We constructed a mathematical model based on a nonlinear system of delayed differential equations. The time delay represents the time that the vaccine takes to provide immune protection against SARS-CoV-2. We investigate the impact of transmission rates, vaccination, and time delay on the dynamics of the constructed system. The model was developed for the beginning of the implementation of vaccination programs to control the COVID-19 pandemic. We perform a stability analysis at the equilibrium points and show, using methods of stability analysis for delayed systems, that the system undergoes a Hopf bifurcation. The theoretical results reveal that under some conditions related to the values of the parameters and the basic reproduction number, the system approaches the disease-free equilibrium point, but if the basic reproduction number is larger than one, the system approaches endemic equilibrium and SARS-CoV-2 cannot be eradicated. Numerical examples corroborate the theoretical results and the methodology. Finally, conclusions and discussions about the results are presented. [ABSTRACT FROM AUTHOR]

LFM signals are widely applied in radar, communication, sonar and many other fields. LFM signals received by these systems contain a lot of noise and outliers. In order to suppress the interference of strong impulse noise on target signals and realize the accurate estimation of LFM signal parameters, the impulse noise of echo signals need to be filtered. In this paper, to solve the problem of poor performance of LFM signal parameter estimation based on fractional Fourier transform in impulse noise, alpha stable distribution is used to establish the mathematical model of impulse noise. The proposed fastest tracking differentiator with an adaptive tracking factor is used to suppress the strong impulse noise, and fractional Fourier transform is used to estimate the parameter of the LFM signals. The experimental results show that the proposed fastest tracking differentiator with an adaptive tracking factor has a good filtering performance. It can effectively filter the impulse noise in the echo signal and allows the FrFT method to accurate estimate the parameters of the LFM signals in strong impulse noise. [ABSTRACT FROM AUTHOR]

Through the use of a unique approach, we study the fractional Biswas–Milovic model with Kerr and parabolic law nonlinearities in this paper. The Caputo approach is used to take the fractional derivative. The method employed here is the homotopy perturbation transform method (HPTM), which combines the homotopy perturbation method (HPM) and Yang transform (YT). The HPTM combines the homotopy perturbation method, He's polynomials, and the Yang transform. He's polynomial is a wonderful tool for dealing with nonlinear terms. To confirm the validity of each result, the technique was substituted into the equation. The described techniques can be used to find the solutions to these kinds of equations as infinite series, and when these series are in closed form, they give a precise solution. Graphs are used to show the derived numerical results. The maple software package is used to carry out the numerical simulation work. The results of this research are highly positive and demonstrate how effective the suggested method is for mathematical modeling of natural occurrences. [ABSTRACT FROM AUTHOR]

Continuous earthmoving machines, such as bucket-wheel excavators (BWEs), are the largest mobile terrestrial machines exposed to the working loads of a periodic character. This paper aims to launch a new idea regarding the preservation of the load-carrying structures of these machines by the means of implementing a controllable frequency-controlled drive of the excavating device. Successful implementation of this idea requires a detailed analysis of the dynamic response of the load-carrying structure in order to determine the domains of frequency of revolutions of the bucket-wheel-drive electromotor (FREM) where the dynamic response of the structure is favorable. The main goal of the presented research was the development of a unique three-step method for the identification of the FREM ranges, where the vibroactivity of the load-carrying structure is within the allowed boundaries. A methodologically original study of the dynamic response was conducted on a unique dynamic model of the BWE slewing superstructure that allows for continuous variation of the FREM, i.e., of the frequency of excitation caused by the forces resisting the excavation. Validation of the spatial reduced dynamic model of the slewing superstructure and the corresponding mathematical model, as well as the overall approach to the determination of the dynamic response, were performed by the means of vibrodiagnostics under the real exploitation conditions. Application of the developed method has yielded: (1) the resonant-free FREM domains; (2) the FREM domains, where the structure is not exposed to the excessive dynamic impacts; and (3) the frequency ratio ranges defining the resonant areas. Additionally, the results of the research have pointed out that the resonant-free state represents a necessary but insufficient condition for the proper dynamic behavior of the BWE slewing superstructure. [ABSTRACT FROM AUTHOR]

The vision system provides an important way for construction robots to obtain the type and spatial location information of the object. The characteristics of the construction environment, construction object, and robot structure are jointly examined in this paper to propose an approach of object segmentation by spraying the robot based on multi-layer perceptron. Firstly, the hand-eye system experimental platform is built through establishing the mathematical model of the system and calibrating the parameters of the model. Secondly, effort is made to carry out research on image preprocessing algorithms and related experiments, and compare the effects of different binocular stereo-matching algorithms in the actual engineering environment. Finally, research and an experiment are conducted to identify the applicability and effect of the depth image object segmentation algorithm based on multi-layer perceptron. The experimental results prove that the application of multi-layer perceptron to object segmentation by spraying robots can meet the requirement on solution accuracy and is suitable for the object segmentation of complex projects in real life. This approach not only overcomes the shortcomings of the existing recognition methods that are poor in accuracy and difficult to be used widely, but also provides basic data for the subsequent three-dimensional reconstruction, thus making a significant contribution to the research of image processing by spraying robots. [ABSTRACT FROM AUTHOR]

A battery-swapping station (BSS) can serve as a flexible source in distribution systems, since electric vehicle (EV) batteries can be charged at different time periods prior to their swapping at a BSS. This paper presents an EV battery service transformation from charging to swapping batteries for EVs for the capacity enhancement of a distribution system. A novel mathematical model is proposed to optimally quantify and maximize the flexibility of BSS loads in providing demand response for the utility operator while considering technical operations in the distribution grid. Case studies and numerical findings that consider data from the National Household Travel Survey and a 32-bus distribution system are reported and discussed to demonstrate the effectiveness of the proposed model. Offering battery-swapping services helps reduce not only the peak load, but also the station operation cost. [ABSTRACT FROM AUTHOR]

Magnetorheological dampers (MRD) are increasingly used in smart structural damping systems due to their good damping properties. In practical applications, as a nonlinear device, the parameters of the internal excitation coil of the magnetorheological damper will change during operation under the influence of the temperature and external environment, deteriorating the dynamic performance of the output current of the driver and reducing the damping effect of the system. Therefore, the current driver needs to be optimized for this phenomenon in order to ensure accurate current output. In this paper, a mathematical model of the buck circuit combined with the MRD equivalent circuit is established, and after analyzing the model, the parameters of the PI controller are rectified to lay the foundation for the design of the adaptive law. Then, with the help of the fuzzy control method, a fuzzy PI control strategy for MRD current driver is established, which enables the current driving system to adjust the control parameters adaptively when the MRD parameters change and ensure the accurate driving current output. The experimental results demonstrate that the fuzzy PI control strategy has a stronger robustness in the face of parameter changes of the control object compared with the traditional PI control at a system parameter change rate of 40%. [ABSTRACT FROM AUTHOR]

This paper investigates a simple memristor emulator consisting of a diode bridge and a capacitor. It exhibits pinched hysteresis loops, and what is more striking is the higher frequency, as it operates up to greater than 5 MHz. Based on the proposed memristor, a higher-frequency Colpitts circuit was established. According to the mathematical model of the system, the system only possesses one unstable equilibrium point. Period doubling bifurcation, reverse periodic doubling bifurcation, different types of periodic and chaotic orbits, transient chaos, coexisting bifurcations and offset boosting are depicted. More interestingly, it has coexisting multiple attractors with different topologies, such as a chaotic attractor accompanied with periodic orbits, period-1 orbits with bicuspid structure and periodic-2 orbits with tridentate structure. Moreover, a hardware circuit using discrete components was fabricated and experimental measurements were consistent with the MATLAB numerical results, further confirming the real feasibility of the proposed circuit. [ABSTRACT FROM AUTHOR]

This paper presents new software (Concrelife) capable of reliably simulating chloride ions penetration in reinforced concrete from different environments in the most common 1-D rectangular geometry scenarios. Its numerical solution is obtained from the simulation of models whose structure is based on Network Simulation Method. These models are generated by the program itself and run in the powerful free code NgSpice. The mathematical model of the problem includes the formation of bound chloride, precipitated chloride, reduction of porosity, saturated and unsaturated conditions, etc. All this allows tackling all kinds of scenarios, such as successive changes in concentration and temperature at the boundary, wet-drying cycles, washing of structures, etc. Concrelife has been developed with a pleasant window environment, intuitive and easy for a user not expert in numerical techniques, both for the introduction of data and for the graphic representation of the results, which include the spatial and temporal concentration of all species of chloride, porosity, water content in pores etc. To test and verify the results of the software, applications are presented to real scenarios. [ABSTRACT FROM AUTHOR]

In this paper, we construct a highly simplified mathematical model for studying the problem of conjugate heat transfer in gas turbine blades and their cooling ducts. Our simple model focuses on the relevant coupling structures and aims to reduce the unrelated complexity as much as possible. Then, we apply the port-Hamiltonian formalism to this model and its subsystems and investigate the interconnections. Finally, we apply a simple spatial discretization to the system to investigate the properties of the resulting finite-dimensional port-Hamiltonian system and to determine whether the order of coupling and discretization affect the resulting semi-discrete system. [ABSTRACT FROM AUTHOR]

The precision modelling of intrinsic camera geometry is a common issue in the fields of photogrammetry (PH) and computer vision (CV). However, in both fields, intrinsic camera geometry has been modelled differently, which has led researchers to adopt different definitions of intrinsic camera parameters (ICPs), including focal length, principal point, radial distortion, decentring distortion, affinity and shear. These ICPs are indispensable for vision-based measurements. These differences can confuse researchers from one field when using ICPs obtained from a camera calibration software package developed in another field. This paper clarifies the ICP definitions used in each field and proposes an ICP transformation algorithm. The originality of this study lies in its use of least-squares adjustment, applying the image points involving ICPs defined in PH and CV image frames to convert a complete set of ICPs. This ICP transformation method is more rigorous than the simplified formulas used in conventional methods. Selecting suitable image points can increase the accuracy of the generated adjustment model. In addition, the proposed ICP transformation method enables users to apply mixed software in the fields of PH and CV. To validate the transformation algorithm, two cameras with different view angles were calibrated using typical camera calibration software packages applied in each field to obtain ICPs. Experimental results demonstrate that our proposed transformation algorithm can be used to convert ICPs derived from different software packages. Both the PH-to-CV and CV-to-PH transformation processes were executed using complete mathematical camera models. We also compared the rectified images and distortion plots generated using different ICPs. Furthermore, by comparing our method with the state of art method, we confirm the performance improvement of ICP conversions between PH and CV models. [ABSTRACT FROM AUTHOR]

In this paper, we present a new way to assess the concentration of estradiol (E2) and Insulin Growth Factor-1 (IGF) based on the results from ultrasound scans combined with mathematical models. The IGF1 model is based on the progesterone (P4) concentration, which can be estimated with models calculating P4 level based on the size/volume of corpus luteum (CL) measured during ultrasound scans. At this moment little is known about the underlying reasons for double ovulation and silent heat occurrences. Both of these are linked to the level of IGF1: double ovulations are linked to higher IGF1 levels and and silent heat is linked to lower E2 to P4 ratio. These models can help to improve understanding of the related concentrations of E2 and IGF1. Currently, it is known that diet and genetic factors have an impact on ovulation rates and silent heat. In this study, we also examine the decline of the production of E2 in vivo by atretic follicles throughout the process of atresia. This is the first recorded quantitative description of this decline. [ABSTRACT FROM AUTHOR]

In this paper, the procedure of finding the coefficients of an equation to describe the thermal conductivity of refrigerants low in global warming potential (GWP) is transformed into a multi-objective optimization problem by constructing a multi-objective mathematical model based on the Pareto approach. For the first time, the NSGAII algorithm was used to describe a thermophysical property such as thermal conductivity. The algorithm was applied to improve the performance of existing equations. Two objective functions were optimized by using the NSGAII algorithm. The average absolute relative deviation was minimized, while the coefficient of determination was maximized. After the minimization process, the optimal solution located on the Pareto frontier was chosen through a comparative analysis between ten selection methods available in the literature. The procedure generated a new set of coefficients of the studied equation that decreased its average absolute relative deviation by 0.24%, resulting in better performance over the entire database and for fluids with a high number of points. Finally, the system model was compared with existing literature models to evaluate its suitability for predicting the thermal conductivity of low-GWP refrigerants. [ABSTRACT FROM AUTHOR]

Fuzzy topological topographic mapping ( F T T M ) is a mathematical model that consists of a set of homeomorphic topological spaces designed to solve the neuro magnetic inverse problem. The key to the model is its topological structure that can accommodate electrical or magnetic recorded brain signal. A sequence of FTTM, F T T M n , is an extension of FTTM whereby its form can be arranged in a symmetrical form, i.e., polygon. The special characteristic of F T T M , namely, the homeomorphisms between its components, allows the generation of new F T T M . The generated F T T M s can be represented as pseudo graphs. A pseudo-graph consists of vertices that signify the generated F T T M and edges that connect their incidence components. A graph of pseudo degree zero, G 0 (F T T M n k  ) , however, is a special type of graph where each of the F T T M components differs from its adjacent. A researcher posted a conjecture on G 0 3 (F T T M n 3) in 2014, and it was finally proven in 2021 by researchers who used their novel grid-based method. In this paper, the extended G 0 3 (F T T M n 3) , namely, the conjecture on G 0 4 (F T T M n 4) that was posed in 2018, is narrated and proven using simple mathematical induction. [ABSTRACT FROM AUTHOR]

In this paper, the new generalized Radhakrishnan–Kundu–Lakshmanan equations with powers of nonlinearity are studied, which is one of the important mathematical models in nonlinear optics. Using the complex envelope traveling wave solution, the new generalized Radhakrishnan–Kundu–Lakshmanan equations are transformed into the nonlinear systems of ordinary differential equations. Under certain constraint conditions, the obtained equations are transformed into a special nonlinear equation. With the help of the solution of this nonlinear equation, some new optical solutions of the new generalized Radhakrishnan–Kundu–Lakshmanan equations with powers of nonlinearity are obtained, which include the solitary wave, singular soliton, periodic soliton, singular-periodic soliton, and exponential-type soliton. By numerical simulation, the corresponding graphs of the optical soliton solution of the new generalized Radhakrishnan–Kundu–Lakshmanan equations are given under the given fixed parameter values, which include the 3D graphics of the module and the 3D graphics of the imaginary part. By analyzing the 2D graphics of the module changing with n, the amplitude of the wave is symmetrical or asymmetrical. [ABSTRACT FROM AUTHOR]

The paper under discussion has some shortcomings in regard to mathematical formulation of the problem related to acoustics, its justification, some references analyses and the text, and we feel that this study has not been finished to its full extent. From the point of view of acoustic jet formation, the mathematical model used by the authors has a number of significant limitations which are not taken into account. Moreover, the formal analogy between the parameters of electromagnetic waves and acoustic waves should be used with caution in the conditions of localized beams (acoustic jet), and the limits of their application should be justified. [ABSTRACT FROM AUTHOR]

The EHA is a highly integrated closed hydraulic system which is widely used in aerospace, vehicles, and robotics because of its high power and lightweight size. Due to the high non-linearity of the control system, it is difficult to reach a high robustness, leading to instability of the EHA system. In this paper, the fuzzy PID control strategy is proposed for overall control of the whole EHA system. Firstly, the structure and operating principle of EHA are analyzed. Secondly, the mathematical model and simulation model of the EHA-FPVM were established. Specially, to solve the problem of difficult calculation of non-linear factors such as friction and external forces, a co-simulation model was built in Matlab/Simulink AMESim, and a fuzzy PID controller was designed to control the EHA-FPVM. Finally, the PID and fuzzy PID controller were used to conduct simulation experiments, the simulation results are compared, and a servo-hydraulic system evaluation method is introduced to assess the simulation results. The results show that the EHA fuzzy PID control system has better output performance, lower overshoot percentages and steady-state errors, and the obtained evaluation scores are higher and more suitable for controlling EHA. [ABSTRACT FROM AUTHOR]

In this study, the authors explored the issues of the Soderbergh electrolysis cell's increase in economic efficiency. This result was achieved by analyzing the temperature fields of the electrolysis cell in order to determine the overheating points. As a result, it led to the determination of the points of the hearth bottom's subsequent breakdown, causing the failure of the electrolysis cell. In this paper, the mathematical modeling of the temperature fields using a spatially distributed mathematical model and conducted experimental studies were carried out. The mathematical model also provides the opportunity to measure the temperature field in the hearth bottom (at the bottom) of the OA-300M electrolysis cell. The results of the given research can be used to solve the experimental determination of the hearth bottom internal defect problem. [ABSTRACT FROM AUTHOR]

A key challenge in further improving infrared (IR) sensor capabilities is the development of efficient data pre-processing algorithms. This paper addresses this challenge by providing a mathematical model and synthetic data generation framework for an uncooled IR sensor. The developed model is capable of generating synthetic data for the design of data pre-processing algorithms of uncooled IR sensors. The mathematical model accounts for the physical characteristics of the focal plane array, bolometer readout, optics and the environment. The framework permits the sensor simulation with a range of sensor configurations, pixel defectiveness, non-uniformity and noise parameters. [ABSTRACT FROM AUTHOR]

This paper presents a proposal for the use of energy indicators to evaluate the load modelling methods on the dynamics of a mobile crane. Three different variants of mathematical models of a load carried were examined and compared: as a lumped mass on one hook-sling, as a sphere on one hook-sling, and as a box on four hook-slings. The formalism of joint coordinates and homogeneous transformation matrices were applied to define the kinematics of the system. The equations of motion were derived using the Lagrange equations of the second kind. These equations were supplemented by the Lagrange multipliers and constraint equations formulated for the cut-joints and drives. The energy indicators were proposed to evaluate the behavior of the crane and the carried load. The authors proved that modeling a load in the form of a lumped mass is a great simplification in the analysis of crane dynamics. [ABSTRACT FROM AUTHOR]

Seventeen sustainable development goals were formulated to create a harmonious world order for the benefit of different nations and peoples. At the same time, economic practice provides a lot of examples of conflicts of an economic nature between individual sustainable development goals. One of these conflicts is the need for environmental imperatives and economic growth when a massive assessment of land used for crop production and green energy projects is needed. The present paper considers a non-traditional approach to the mass evaluation of land plots on the condition that geographic information systems provide the main source of information, such as the case of land allocation for green energy facilities and evaluation of agricultural plots. The novelty of the proposed approach firstly means the development of a comparative approach, which receives much less attention in the valuation literature than cost and income approaches, as it can give an adequate picture of the current state of the market. The model includes the study of the entire dataset, the selection of model distributions and the construction of estimates based on model distributions. The methodology of multivariate lognormal distribution of factors and prices of analogues is used. The peculiarity of the market evaluation of land plots in such cases is, as a rule, the absence of rank predictors and sufficient number of continuous predictors, which provides a base for the application of a novel approach. The method of express testing of hypotheses about joint normality of logarithms of values of pricing factors and prices is proposed. The market value is estimated as an estimate of the modal value of conditional lognormal price distribution. Secondly, the problem of market valuation is solved in case of the almost complete absence of information about price-forming factors in the areas being assessed, and thirdly, the factors are determined based on geoinformation databases (distance to the nearest large city, regional center, federal highway, large rivers, lakes, and solid waste landfills), which allow for market assessment in the absence of information on pricing factors for land plots, except for the offer price and the plot area. The research was necessitated by the claim to determine on a specific date the cadastral value of agricultural land for the purposes of taxation, corresponding to the market value, in the almost complete absence of information on pricing factors in the assessed areas. The value of land reflects a complex combination of factors, so the use of the proposed mathematical toolkit allows for building a consistent model for the evaluation of land where improvements are absent or have no value in terms of land acquisition purposes. [ABSTRACT FROM AUTHOR]

A huge amount of construction waste is generated in construction sites every day that needs to be transported by vehicle to disposal facilities for processing. Unlike in most typical transportation problems, once these vehicles are loaded with construction waste, they must travel directly to the disposal facility. Moreover, there are different types of construction waste that may require handling by different disposal facilities. In this paper, we develop a model and algorithm for identifying the optimal transportation routes specific to construction waste transportation. Our results can not only minimize the overall costs for both the logistics company and the contractor but also minimize the distance traveled, thus reducing urban traffic emissions. [ABSTRACT FROM AUTHOR]

In industrial applications, many systems present serious productivity problems due to limited resources. Generally, the dynamics of resource allocation are inherently discrete-event driven, such as the buffer allocation in production line systems. In this paper, we develop a discrete-event mathematical model for resource allocation optimization. In this work, we consider two crucial optimization objectives, e.g., deadlock-free and efficiency, that originate from the customer's actual requirements. The main aim is to develop a resource allocation scheme for fulfilling the production process (without deadlock) while ensuring that the cost of the process is minimized. As a case study, we consider the vehicle scheduling problem in a signal-free intersection. The intersection is divided into several disjoint spatial traffic resources, and vehicles need to occupy different traffic resources for passing through the intersection. Thus, the traffic control problem at the signal-free intersection is transformed into a scheduling problem with limited resource constraints. An online control approach is developed to schedule vehicles to go through the intersection safely and efficiently by optimizing the resource allocation order. Simulation results demonstrate the efficiency and robustness of the proposed model and optimization approach. [ABSTRACT FROM AUTHOR]

The Riemannian manifold optimization algorithms have been widely used in machine learning, computer vision, data mining, and other technical fields. Most of these algorithms are based on the geodesic or the retracement operator and use the classical methods (i.e., the steepest descent method, the conjugate gradient method, the Newton method, etc.) to solve engineering optimization problems. However, they lack the ability to solve non-differentiable mathematical models and ensure global convergence for non-convex manifolds. Considering this issue, this paper proposes a quantum-behaved particle swarm optimization (QPSO) algorithm on Riemannian manifolds named RQPSO. In this algorithm, the quantum-behaved particles are randomly distributed on the manifold surface and iteratively updated during the whole search process. Then, the vector transfer operator is used to translate the guiding vectors, which are not in the same Euclidean space, to the tangent space of the particles. Through the searching of these guiding vectors, we can achieve the retracement and update of points and finally obtain the optimized result. The proposed RQPSO algorithm does not depend on the expression form of a problem and could deal with various engineering technical problems, including both differentiable and non-differentiable ones. To verify the performance of RQPSO experimentally, we compare it with some traditional algorithms on three common matrix manifold optimization problems. The experimental results show that RQPSO has better performance than its competitors in terms of calculation speed and optimization efficiency. [ABSTRACT FROM AUTHOR]

Simple Summary: The reported global incidences of skin cancer led to the development of automated clinical aids for making proper clinical decision models. Correctly classifying the skin lesions during the early stage may increase the chances of being cured before cancer. However, the skin lesion dataset images pose many critical challenges related to available features to develop classification models with cross-domain adaptability and robustness. This paper made an attempt to select important features from skin lesion datasets for proper skin cancer classification by proposing some feature fusion strategies. Three pre-trained models were utilized to select the important features and then an adaptive weighted mechanism of choosing important features was explored to propose model-based and feature-based optimized feature fusion strategies by optimally and adaptively choosing the weights using a meta-heuristic artificial jellyfish algorithm. The empirical evidence shows that choosing the weights of the pre-trained networks adaptively in an optimized way gives a good starting point for initialization to mitigate the chances of exploding or vanishing gradients. This study mainly focuses on pre-processing the HAM10000 and BCN20000 skin lesion datasets to select important features that will drive for proper skin cancer classification. In this work, three feature fusion strategies have been proposed by utilizing three pre-trained Convolutional Neural Network (CNN) models, namely VGG16, EfficientNet B0, and ResNet50 to select the important features based on the weights of the features and are coined as Adaptive Weighted Feature Set (AWFS). Then, two other strategies, Model-based Optimized Weighted Feature Set (MOWFS) and Feature-based Optimized Weighted Feature Set (FOWFS), are proposed by optimally and adaptively choosing the weights using a meta-heuristic artificial jellyfish (AJS) algorithm. The MOWFS-AJS is a model-specific approach whereas the FOWFS-AJS is a feature-specific approach for optimizing the weights chosen for obtaining optimal feature sets. The performances of those three proposed feature selection strategies are evaluated using Decision Tree (DT), Naïve Bayesian (NB), Multi-Layer Perceptron (MLP), and Support Vector Machine (SVM) classifiers and the performance are measured through accuracy, precision, sensitivity, and F1-score. Additionally, the area under the receiver operating characteristics curves (AUC-ROC) is plotted and it is observed that FOWFS-AJS shows the best accuracy performance based on the SVM with 94.05% and 94.90%, respectively, for HAM 10000 and BCN 20000 datasets. Finally, the experimental results are also analyzed using a non-parametric Friedman statistical test and the computational times are recorded; the results show that, out of those three proposed feature selection strategies, the FOWFS-AJS performs very well because its quick converging nature is inculcated with the help of AJS. [ABSTRACT FROM AUTHOR]

Most plant viral infections are vector-borne. There is a latent period of disease inside the vector after obtaining the virus from the infected plant. Thus, after interacting with an infected vector, the plant demonstrates an incubation time before becoming diseased. This paper analyzes a mathematical model for persistent vector-borne viral plant disease dynamics. The backpropagated neural network based on the Levenberg—Marquardt algorithm (NN-BLMA) is used to study approximate solutions for fluctuations in natural plant mortality and vector mortality rates. A state-of-the-art numerical technique is utilized to generate reference data for obtaining surrogate solutions for multiple cases through NN-BLMA. Curve fitting, regression analysis, error histograms, and convergence analysis are used to assess accuracy of the calculated solutions. It is evident from our simulations that NN-BLMA is accurate and reliable. [ABSTRACT FROM AUTHOR]

Agent-based modeling (ABM) is a flexible and simulation-friendly modeling approach. Ambient-oriented modeling is effective for systems containing ambient and spatial representations. In this paper we propose a framework for the integrated use of agent-based modeling and ambient-oriented modeling. We analyze both agents and ambient in detail. We also compare both modeling approaches as well and analyze their similarities and differences. The integrated implementation provides a new link between mathematical modeling and simulations. The model developed using this framework has four parts. The first part constitutes the identification, definition, and relations of agents. In this part, we use agent-based modeling along with the concepts of discrete-event simulations and system dynamics. The second part of the model is the mathematical representation of the relations of agents, i.e., the parent and child relation of agents. The third part of the model is the representation of the messages along with relational symbols where we utilize the concepts and symbols of relations and messages from ambient-oriented modeling. The fourth and final part of the model is the simulation, where we describe the rules that govern the processes represented in first two parts. The framework is helpful in overcoming certain limitations of both approaches. Moreover, we provide a scenario of a bus rapid transit system (BRTS) as a proof of concept, and we examine the generic concept of BRTSs using the proposed framework. [ABSTRACT FROM AUTHOR]

The degree of informatization of coal mine safety management is becoming higher and higher, and a large amount of information is generated in this process. How to convert the existing information into useful data for risk control has become a challenge. To solve this challenge, this paper studies the mathematical model of coal mine risk early warning in China based on data mining. Firstly, the coal mine risk data was comprehensively analyzed to provide basic data for the risk prediction model of data mining. Then, the adaptive neuro-fuzzy inference system (ANFIS) was optimized twice to build the coal mine risk prediction model. By optimizing the calculation method of the control chart, the coal mine risk early warning system was proposed. Finally, based on the coal mine risk early warning model, the software platform was developed and applied to coal mines in China to control the risks at all levels. The results show that the error of the optimized ANFIS was reduced by 66%, and the early warning error was reduced by 57%. This study aimed to provide implementation methods and tools for coal mine risk management and control, and data collected has reference significance for other enterprises. [ABSTRACT FROM AUTHOR]

The generalized Logistic function that solves a first-order nonlinear ODE with an arbitrary positive power term of the dependent variable is introduced in this paper, by means of which the traveling wave solutions of a class of nonlinear evolution equations, including the generalized Fisher equation, the generalized Nagumo equation, the generalized Burgers-Fisher equation, the generalized Gardner equation, the generalized KdV-Burgers equation, and the generalized Benney equation, are obtained successfully. In these particular cases, traveling wave solutions of several important model PDEs in mathematical physics are also discovered. [ABSTRACT FROM AUTHOR]

A. Montisci, S. Cargangiu, G. Sias, B. Cannas and A. Fanni, in [[16]], present a real time bolometer tomographic reconstruction algorithm in nuclear fusion reactors based on the combination of highly correlated grid elements to yield a square coefficient matrix with sufficiently low condition number. The procedure was derived from the polynomial reproduction properties satisfied by the Hermite splines without requiring the explicit construction/evaluation of the basic functions. The paper authored by Y.E. Shao and S.C. Lin [[1]] presents an innovative time-delay neural network-based classifier to diagnose the quality variables that cause out-of-control signals for a normal multivariate process with variance shifts. It is now clear that cooperation between academia and industries is crucial for social, cultural, technological and economic progress and innovation. [Extracted from the article]

In response to the key engineering problems of photovoltaic grid-connected inverter cluster resonance suppression affected by grid-connected inverter impedance, in this paper, a control strategy based on a disturbance observer is proposed to dynamically compensate for the damping coefficient of the controlled system and improve the robustness of the system. First, an engineering mathematical model of a 200 MW photovoltaic inverter cluster is established, and the mechanism of the active damping of the cluster inverter influenced by the disturbance is analyzed. Secondly, the capacitor current feedback is utilized to constitute the virtual damping, and the inverter output impedance is reshaped to suppress the resonance peak. Then, a Kalman filter is used to improve the traditional disturbance observer to accurately detect disturbance of the system during the dynamic process of the cluster inverter so as to better adapt to changes in grid impedance and dynamically compensate for the virtual damping of the cluster resonant system. Finally, the proposed control strategy is verified with respect to a practical PV power station. The experimental results demonstrate the feasibility of the proposed control method. [ABSTRACT FROM AUTHOR]

This article deals with the random sequential adsorption (RSA) of 2D disks of the same size on fractal surfaces with a Hausdorff dimension 1 < d < 2. According to the literature and confirmed by numerical simulations in the paper, the high coverage regime exhibits fractional dynamics, i.e., dynamics in t1/d where d is the fractal dimension of the surface. The main contribution this paper is that it proposes to capture this behavior with a particular class of nonlinear model: a driftless control affine model. [ABSTRACT FROM AUTHOR]

Logical dynamical systems (LDSs) have wide applications in gene regulation, game theory, digital circuits, and so on. In LDSs, phenomena such as impulsive effect, time delays, and asynchronous behavior are not negligible, which generate complex LDSs. This paper presents a detailed survey on models and methods of investigating LDSs. Firstly, some preliminary results on LDSs and semi-tensor product (STP) method are presented. Secondly, some new developments on modeling complex LDSs are summarized, including switched LDSs, probabilistic LDSs, delayed LDSs, LDSs with impulsive effects, asynchronous LDSs, constrained LDSs, and implicit LDSs. Finally, the control design techniques of LDSs are reviewed, including reachable set approach, sampled-data control, event-triggered control, and control Lyapunov function method. [ABSTRACT FROM AUTHOR]

This work presents a new standard in the model, identification, and control of monitoring purposes over anaerobic reactors. One requirement that guarantees a normal controller operation is for the faculty to measure the data needed periodically. Due to its inability to easily obtain the concentrations of acidogenic bacteria and methanogenic archaea periodically using reliable and commercial sensors, this paper presents an algorithm composed of an asymptotic observer (considering the reaction rates are unknown), aiming to estimate these concentrations. This method represents a significant advantage because it is possible to perform a resource-saving strategy using standard measurements, such as pH or alkalinity, to calculate them analytically in natural environments. Additionally, two yield parameters were included in the original anaerobic model two (AM2) to unlock implementations for a wide range of organic substrates. The static parameter identification was improved using a new method called step-ahead optimization. It demonstrates significant improvements fitting the mathematical model to data until a 78.7 % increase in efficiency (compared with the traditional optimization method genetic algorithm). After the period of convergence, the state observer evidences a small error with a maximum 2 % deviation. Finally, numerical simulations demonstrate the structure's strengths, which constitutes a significant step in paving the way further to implement feasible, cost-effective controls and monitoring systems in the industry. [ABSTRACT FROM AUTHOR]

This review paper is devoted to a brief overview of results and models concerning flows in networks and channels of networks. First of all, we conduct a survey of the literature in several areas of research connected to these flows. Then, we mention certain basic mathematical models of flows in networks that are based on differential equations. We give special attention to several models for flows of substances in channels of networks. For stationary cases of these flows, we present probability distributions connected to the substance in the nodes of the channel for two basic models: the model of a channel with many arms modeled by differential equations and the model of a simple channel with flows of substances modeled by difference equations. The probability distributions obtained contain as specific cases any probability distribution of a discrete random variable that takes values of 0 , 1 , ... . We also mention applications of the considered models, such as applications for modeling migration flows. Special attention is given to the connection of the theory of stationary flows in channels of networks and the theory of the growth of random networks. [ABSTRACT FROM AUTHOR]

The finite-time synchronization (FNTS) problem for a class of delayed fractional-order fully complex-valued dynamic networks (FFCDNs) with internal delay and non-delayed and delayed couplings is studied by directly constructing Lyapunov functions instead of decomposing the original complex-valued networks into two real-valued networks. Firstly, a mixed delay fractional-order mathematical model is established for the first time as fully complex-valued, where the outer coupling matrices of the model are not restricted to be identical, symmetric, or irreducible. Secondly, to overcome the limitation of the use range of a single controller, two delay-dependent controllers are designed based on the complex-valued quadratic norm and the norm composed of its real and imaginary parts' absolute values, respectively, to improve the synchronization control efficiency. Besides, the relationships between the fractional order of the system, the fractional-order power law, and the settling time (ST) are analyzed. Finally, the feasibility and effectiveness of the control method designed in this paper are verified by numerical simulation. [ABSTRACT FROM AUTHOR]

This paper presents a novel discrete-time (DT) chaotic map-based random-number generator (RNG), namely the Siponi map, which is a modification of the Logistic map. The Logistic map is usually applied to cryptosystems, mainly for the purposes of generating random numbers. In addition to being easy to implement, it has a better security level than other nonlinear functions. However, it can only process positive real-number inputs. Our proposed map is a deterministic function that can process positive and negative real values. We explored the map comprehensively and investigated its characteristics and parameters. We calculated the optimum parameter values using empirical and theoretical mathematical models to yield the maximum randomness of a sequence of bits. The limit variation of the maximum parameter value was determined based on a practical information measure. Empirical verification was performed for the Siponi map to generate bit sequences unrelated to the previous bit with high entropy values, and we found the extractor function threshold value to be 0.5, while the parameter control was −2 or 2. Using our proposed map, a simple RNG without post-processing passed DieHard statistical tests and all the tests on the NIST SP 800-22. Finally, we have implemented a Siponi map-based RNG on the FPGA board and demonstrated that the sources used are LUT = 4086, DSP = 62, and register = 2206. [ABSTRACT FROM AUTHOR]

Modeling complex hydrodynamic processes in coastal systems is an important problem of mathematical modeling that cannot be solved analytically. The approximation of convective terms is difficult from the point of view of error reduction. This paper proposes a difference scheme based on a linear combination of the Upwind Leapfrog scheme with 2/3 weight coefficient, and the Standard Leapfrog scheme with 1/3 weight coefficient. The weight coefficients are obtained as a result of solving the problem of minimizing the approximation error. Numerical experiments show the advantage of the developed scheme in comparison with other modifications of the Upwind Leapfrog scheme in the case when the convective transport prevails over the diffusion one. The proposed difference scheme solves transport problems more effectively than classical difference schemes in the case when the Péclet number falls in the range from 2 to 20. It follows that the considered difference scheme allows hydrodynamic problems to be solved in regions of complex shape effectively. [ABSTRACT FROM AUTHOR]

The analytic hierarchy process (AHP) is one of the most popular multi-criteria decision-making (MCDM) methods, and so is its extension fuzzy analytic hierarchy process (FAHP). However, the FAHP, unlike the AHP, easily handles the trusted weights by the consistency index (CI) or consistency ratio (CR). We need to first derive the consistent fuzzy pairwise comparison matrix (FPCM) by the transitivity axiom and then drive fuzzy weights. We also need a flexible mechanism for users to control the spread of fuzzy weights under tolerable consistency. In this paper, we propose a novel model based on mathematical programming to derive rational fuzzy weights of the FAHP and provide a parameter for decision-makers to control the spread of fuzzy weights. Three examples are used to demonstrate the proposed method and compared with others to validate and justify the proposed method. [ABSTRACT FROM AUTHOR]