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Alzheimer's disease is a complex, multi-factorial, and multi-parametric neurodegenerative etiology. Mathematical models can help understand such a complex problem by providing a way to explore and conceptualize principles, merging biological knowledge with experimental data into a model amenable to simulation and external validation, all without the need for extensive clinical trials. We performed a scoping review of mathematical models describing the onset and evolution of Alzheimer's disease as a result of biophysical factors following the PRISMA standard. Our search strategy applied to the PubMed database yielded 846 entries. After using our exclusion criteria, only 17 studies remained from which we extracted data, which focused on three aspects of mathematical modeling: how authors addressed continuous time (since even when the measurements are punctual, the biological processes underlying Alzheimer's disease evolve continuously), howmodels were solved, and how the high dimensionality and non-linearity of models were managed. Most articles modeled Alzheimer's disease at the cellular level, operating on a short time scale (e.g., minutes or hours), i.e., the micro view (12/17); the rest considered regional or brain-level processes with longer timescales (e.g., years or decades) (the macro view). Most papers were concerned primarily with amyloid beta (n = 8), few described both amyloid beta and tau proteins (n = 3), while some considered more than these two factors (n = 6). Models used partial differential equations (n = 3), ordinary differential equations (n = 7), and both partial differential equations and ordinary differential equations (n = 3). Some did not specify their mathematical formalism (n = 4). Sensitivity analyses were performed in only a small number of papers (4/17). Overall, we found that only two studies could be considered valid in terms of parameters and conclusions, and two more were partially valid. This puts the majority (n = 13) as being either invalid or with insufficient information to ascertain their status. This was themain finding of our paper, in that serious shortcomings make their results invalid or non-reproducible. These shortcomings come from insufficient methodological description, poor calibration, or the impossibility of experimentally validating or calibrating the model. Those shortcomings should be addressed by future authors to unlock the usefulness of mathematicalmodels in Alzheimer's disease. [ABSTRACT FROM AUTHOR]

This paper studies the estimation of parameters estimation in a traffic flow model. The model is represented by a system of differential equations with a time delay. The main result of this paper is the calculation of the range of values for the parameters describing the intensity of acceleration and braking, as well as a coefficient that describes how smoothly the pursuing vehicle adjusts its speed to the one in front. The parameters of the model are estimated with analytical calculations and numerical experiments. A special computer program is developed for the numerical experiment. [ABSTRACT FROM AUTHOR]

This paper proposes an electric vehicle routing problem, considers the states of charging stations and suggests solution strategies. The charging of electric vehicles is a main issue in the field of electric vehicle routing. There are many studies that find the locations of charging stations, recharging functions for the batteries of vehicles, and so on. However, the state of charging stations significantly affects the routes of electric vehicles, which is not much explored. The states may include open or closed charging stations, occupied or empty charging slots, and so on. This paper investigates how the states of charging stations are estimated and how routing strategies are determined. We formulate a mixed integer programming model and suggest how to solve the problem with an exact method. Numerical examples provide the optimal routing strategies of electric vehicles for the changing environments regarding the states of charging stations. [ABSTRACT FROM AUTHOR]

The mechanical properties of porous concrete, such as strength and durability, are significantly influenced by moisture transport, particularly in the case of recycled aggregate concretes. The pore distribution and pore size of the concrete, as well as the ambient temperature in the surrounding environment, exert a significant influence on the moisture transport. This paper establishes the fractal Fick’s law, the fractal Darcy law, and the fractal Richards equation. In conclusion, a fractal model for the diffusion and permeability in porous concrete is established. This study examines the mechanisms of moisture diffusion and water permeability in concrete. The comparison of the theoretical prediction with the experimental data indicates a high degree of congruence, thereby suggesting that the concrete’s relative humidity response can be predicted by the established model. This provides a foundation for the optimal design of concrete with required mechanical properties in special applications. [ABSTRACT FROM AUTHOR]

In recent years, due to the rapid growth of the world's population, the demand for agricultural products and food is growing increasingly. Therefore, the agricultural supply chain optimization has been grabbed by researchers to reduce food security concerns. On the other hand, the production amount of farmers is affected by various factors, including environmental conditions. In this paper, a supply chain network is investigated by developing a Mixed-Integer Linear Programming (MILP) model to effectively improve economic objectives under uncertainty. Then, a scenario-based robust optimization approach is employed to deal with the uncertainty. One of the novelities of our paper is considering weather conditions and economic fluctuations in different scenarios. The effectiveness of the proposed mathematical model has been confirmed by a real case study of dates farms. Dates and its by-products have a significant role in GDP, job creation, export, and the creation of various packaging and processing. Moreover, three meta-heuristic algorithms including Whale Optimization Algorithm (WOA), Particle Swarm Optimization (PSO), and a hybrid algorithm based on them (WOA–PSO) are adapted to deal with the NP-hardness of the problems. Moreover, the parameters of the proposed algorithms are improved by the Taguchi method, and to achieve more exact measurements, sensitivity analysis is performed. Finally, the numerical results confirmed that the accuracy of the hybrid algorithm was between 1.9 and 2.8%. Therefore, this approach could be practical and efficient for solving large-sized problems. The obtained outcomes demonstrated that the planned model provides tactical considerations for the related managers. [ABSTRACT FROM AUTHOR]

Batteries play a crucial role in the domain of energy storage systems and electric vehicles by enabling energy resilience, promoting renewable integration, and driving the advancement of eco-friendly mobility. However, the degradation of batteries over time remains a significant challenge. This paper presents a comprehensive review aimed at investigating the intricate phenomenon of battery degradation within the realm of sustainable energy storage systems and electric vehicles (EVs). This review consolidates current knowledge on the diverse array of factors influencing battery degradation mechanisms, encompassing thermal stresses, cycling patterns, chemical reactions, and environmental conditions. The key degradation factors of lithium-ion batteries such as electrolyte breakdown, cycling, temperature, calendar aging, and depth of discharge are thoroughly discussed. Along with the key degradation factor, the impacts of these factors on lithium-ion batteries including capacity fade, reduction in energy density, increase in internal resistance, and reduction in overall efficiency have also been highlighted throughout the paper. Additionally, the data-driven approaches of battery degradation estimation have taken into consideration. Furthermore, this paper delves into the multifaceted impacts of battery degradation on the performance, longevity, and overall sustainability of energy storage systems and EVs. Finally, the main drawbacks, issues and challenges related to the lifespan of batteries are addressed. Recommendations, best practices, and future directions are also provided to overcome the battery degradation issues towards sustainable energy storage system. [ABSTRACT FROM AUTHOR]

The work in this paper is applied to the Zhangbei Power grid. In the flexible direct current (DC) power system, the fault current rises extremely fast when a DC fault occurs. The requirements for the peak of breaking current and fault energy absorption of DC circuit breakers (DCCBs) increase linearly, which significantly increases the cost of the equipment. Therefore, in order to reduce the design difficulty of DCCBs, this paper proposes a strategy to control energy after the fault occurs. Firstly, the energy dimension is added on the basis of the traditional vector control of MMC, which constitutes a three-dimensional energy direct control. Subsequently, the architectures of energy fluctuation control and feedforward control are proposed. The influencing mechanisms for the peak fault current, peak fault voltage and energy dissipation are analyzed. Finally, the simulation of energy fluctuation control and feedforward control is constructed on PSCAD/EMTDC. The simulation results show that the energy fluctuation control is obviously better than the conventional three-dimensional energy control, and the feedforward energy control is further improved on this basis. Compared with the conventional vector control, the peak energy is reduced by 45.43% and the peak current is reduced by 25.39%, which helps to simplify the equipment design and reduce the equipment cost. [ABSTRACT FROM AUTHOR]

The residual subsidence caused by underground mining in mountain area has a long subsidence duration time and great potential harm, which seriously threatens the safety of people's production and life in the mining area. Therefore, it is necessary to use appropriate monitoring methods and mathematical models to effectively monitor and predict the residual subsidence caused by underground mining. Compared with traditional level survey and InSAR (Interferometric Synthetic Aperture Radar) technology, GNSS (Global Navigation Satellite System) online monitoring technology has the advantages of long-term monitoring, high precision and more flexible monitoring methods. The empirical equation method of residual subsidence in mining subsidence is effectively combined with the rock creep equation, which can not only describe the residual subsidence process from the mechanism, but also predict the residual subsidence. Therefore, based on GNSS online monitoring technology, combined with the mining subsidence model of mountain area and adding the correlation coefficient of the compaction degree of caving broken rock and the Kelvin model of rock mechanics, this paper constructs the residual subsidence time series model of arbitrary point on the ground in mountain area. Through the example, the predicted results of the model in the inversion parameter phase and the dynamic prediction phase are compared with the measured data sequence. The results show that the model can carry out effective numerical calculation according to the GNSS monitoring data of any point on the ground, and the model prediction effect is good, which provides a new method for the prediction of residual subsidence in mountain mining. [ABSTRACT FROM AUTHOR]

Rolling mill bearings are prone to wear, erosion, and other damage characteristics due to prolonged exposure to rolling forces. Therefore, regular inspection of rolling mill bearings is necessary. Ultrasonic technology, due to its non-destructive nature, allows for measuring the oil film thickness distribution within the bearing during disassembly. However, during the process of using ultrasonic reflection coefficients to determine the oil film thickness and distribution state of rolling mill bearings, changes in bearing temperature due to prolonged operation can occur. Ultrasonic waves are susceptible to temperature variations, and different temperatures of the measured structure can lead to changes in measurement results, ultimately distorting the results. This paper proposes using density and sound speed compensation methods to address this issue. It simulates and analyzes the oil film reflection coefficients at different temperatures, ultimately confirming the feasibility and effectiveness of this approach. The paper establishes a functional relationship between bearing pressure and reflection coefficients, oil film thickness, and reflection coefficients. This allows for the compensation of reflection coefficients under any pressure conditions, enhancing the accuracy of oil film thickness detection. The proposed method provides technical support for the maintenance of plate rolling processes in the steel industry. [ABSTRACT FROM AUTHOR]

One of the modern, recently developed mathematical approaches for modeling various complex chaotic processes (the bacteria migration is apparently one of them), is the application of fractional differential equations. Introduction of fractional derivatives is also a very effective approach for investigation of the reactive processes (growth of bacteria in our case). Our recent advances in application of fractional differential equations for modeling the anomalous transport of reactive and non-reactive contaminants (see our recent publications in the References) allow us to expect that the anomalous transport of growing bacteria can also be effectively described by the models with fractional derivatives. Based on these modern approaches, utilizing fractional differential equations, in this paper we developed a reliable mathematical model that could be properly calibrated and, consequently, provide an adequate description of the growing bacteria transport. This model accounts for the memory effects in the bacteria transport due to the random character of bacteria trapping and release by the porous matrix. Two types of bacteria in the saturated porous medium are considered: mobile and immobile bacteria. Bacteria in the mobile phase are migrating in the fluid and have the velocity of the bulk flow, whereas bacteria in the immobile phase are the bacteria that are captured by the porous matrix. These bacteria have zero velocity and can cause clogging of some pores (therefore, porosity is possibly not constant). Examining different conventional models and comparing computations based on these models, we show that this extremely complex character of bacteria transport cannot be described by the traditional approach based on classical partial differential equations. In this paper we suggest fractional differential equations as a simple but very effective tool that can be used for constructing the proper model capable of simulating all the above-mentioned effects associated with migration of alive bacteria. Using this approach, a reliable model of the growing bacteria transport in the porous medium is developed and validated by comparison with experimental laboratory results. We proved that this novel model can be properly linearized and calibrated, so that an excellent agreement with available experimental results can be achieved. This simple model can be used in many applications, for example, as a part of more general mathematical models for predicting the outcomes of the bioremediation of contaminated soils. [ABSTRACT FROM AUTHOR]

The transient characteristics of pressure in the condenser under fault conditions have a crucial impact on the safe operation of the entire nuclear power plant. In order to ascertain whether the condenser pressure of a HPR1000 nuclear power unit meets the requirements of the steam generator, this paper establishes a mathematical model of the condenser, along with the connected steam turbine bypass steam system and circulating water system, based on Apros. The accuracy of the simulation model is verified by comparing the coasting curve of the circulating water pump with the flow change curve under the pump-tripping condition in Apros. Under the initial CCR condition and the half-side operating condition of the condenser, simulation analyses were conducted for two transient sequences involving the loss of normal external power and the simultaneous tripping of two circulating water pumps. The corresponding changes of pressure in the condenser under the transient sequence were obtained. The study reveals that, under different initial conditions and transient sequences, the condenser pressure of the unit can meet the requirements of a 12 s steam discharge to the condenser before the internal pressure of the condenser reaches the "unavailable" set value when the turbine bypass system is under the fault condition. The research findings of this paper can provide reference data for the design, commissioning, and operation of subsequent HPR1000 nuclear power plants. [ABSTRACT FROM AUTHOR]

This paper considers the comparative analysis of the physical and mathematical methods of the optimal operation of aviation objects' automatic control systems, which is an urgent scientific and technical task. The paper also represents the corresponding stability criteria, depending on the operating conditions, and the influence of external factors that allows ensuring the automatic control systems' reliable operation not only in normal circumstances, but also in the presence of probable disagreements. The scientific novelty of the research lies in developing new stability criteria by means of synthesising the influence of different factors and also the ability to ensure optimal functioning of the automatic control systems. Corresponding mathematical and computer models have been developed. The use of these models allows to determine the optimal stability criteria for control systems with parameters of a different physical nature and ensure reliable operation of electromechanical systems for general and special applications based on the current analysis. The research results are illustrated by corresponding mathematical models, engineering calculations and modelling of the optimal control limits depending on the influence of various factors. The simulation results coincide with the theoretical calculations, which indicates the consistency between the microprocessor-based and software of automatic control systems. [ABSTRACT FROM AUTHOR]

The prevention and control of the spread of Cystic Echinococcosis is an important public health issue. Health education has been supported by many governments because it can increase public awareness of echinococcosis, promote the development of personal hygiene habits, and subsequently reduce the transmission of echinococcosis. In this paper, a dynamic model of echinococcosis is used to integrate all aspects of health education. Theoretical analysis and numerical model fitting were used to quantitatively analysed by the impact of health education on the spread of echinococcosis. Theoretical findings indicate that the basic reproduction number is crucial in determining the prevalence of echinococcosis within a given geographical area. The parameters of the model were estimated and fitted by using data from the Ningxia Hui Autonomous Region in China, and the sensitivity of the basic reproduction number was analysed by using the partial rank correlation coefficient method. These findings illustrate that all aspects of health education demonstrate a negative correlation with the basic reproduction number, suggesting the effectiveness of health education in reducing the basic reproduction number and mitigating the transmission of echinococcosis, which is consistent with reality. Particularly, the basic reproduction number showed a strong negative correlation with the burial rate of infected livestock (b) and the incidence of infected livestock viscera that is not fed to dogs (q). This paper further analyzes the implementation plan for canine deworming rates and sheep immunity rates, as well as the transmission of infected hosts over time under different parameters b and q. According to the findings, emphasizing the management of infected livestock in health education has the potential to significantly reduce the risk of echinococcosis transmission. This study will provide scientific support for the creation of higher quality health education initiatives. [ABSTRACT FROM AUTHOR]

In this paper, we solved a model of a well-known infectious disease called dengue fever via fractional natural decomposition and modified Predictor–Corrector (PC) methods. A study of the dengue epidemic in the Cape Verde Islands off the coast of West Africa in 2009 has been resumed here for a better understanding of the results. The results are obtained using Liouville–Caputo and new generalized Caputo-type fractional derivatives. The numerical simulations are presented for various orders of given derivatives. Existence and uniqueness analysis of the given problem are also performed in the new generalized Caputo sense. The explored results are verified using figures. The main target of this paper is to explore the different dynamics of the given dengue fever model via two types of fractional numerical algorithms. [ABSTRACT FROM AUTHOR]

The paper proposes an equivalent optical scheme of an in-line digital holographic system for particle recording and a mathematical model that establishes a one-to-one correspondence between the dimensional and spatial parameters of a digital holographic image of a particle and the imaged particle itself. The values of the model coefficients used to determine the real size and longitudinal coordinate of a particle according to its holographic image are found by calibration. The model was tested in field and laboratory conditions to calibrate a submersible digital holographic camera designed to study plankton in its habitat. It was shown that four calibration measurements are sufficient enough to determine the model coefficients, and the developed design of the submersible digital holographic camera makes it possible to perform these measurements during the recording of each hologram. In addition, this neither requires data on the refractive index of the medium with particles nor on the parameters of the optical elements of the scheme. The paper presents the results of marine experiments in the Kara Sea and the Laptev Sea, as well as in fresh water in laboratory conditions and in Lake Baikal. The error in measuring the particle size in seawater without the use of the model is 53.8%, while the error in determining their longitudinal coordinates is 79.3%. In fresh water, the same errors were 59% and 54.5%, respectively. The error in determining the position of a particle with the use of the designed mathematical model does not exceed 1.5%, and the error in determining the size is 4.8%. The model is sensitive to changes in the optical properties of the medium, so it is necessary to perform calibration in each water area, and one calibration is quite sufficient within the same water area. At the same time, the developed design of the submersible holographic camera allows, if necessary, calibration at each holographing of the medium volume with particles. [ABSTRACT FROM AUTHOR]

The paper presents the results of model and empirical research on the influence of the thermal state of a diesel engine (oil temperature) on its indicated (thermal) efficiency. The paper contains a test plan, including a description of the test object, test equipment, and measurement points on a real object. In the following part, the results of tests carried out on a real object (laboratory single-cylinder engine) and the results of model tests obtained on the original engine model are presented. The results are presented both in tabular and graphical form. The obtained test results allowed to determine the relative value of the influence of the engine's thermal state on its efficiency for various operating conditions (load and rotational speed). [ABSTRACT FROM AUTHOR]

Drone logistics is a novel method of distribution that will become prevalent. The advantageous location of the logistics hub enables quicker customer deliveries and lower fuel consumption, resulting in cost savings for the company's transportation operations. Logistics firms must discern the ideal location for establishing a logistics hub, which is challenging due to the simplicity of existing models and the intricate delivery factors. To simulate the drone logistics environment, this study presents a new mathematical model. The model not only retains the aspects of the current models, but also considers the degree of transportation difficulty from the logistics hub to the village, the capacity of drones for transportation, and the distribution of logistics hub locations.Moreover, this paper proposes an improved particle swarm optimization (PSO) algorithm which is a diversity-based hybrid PSO (DHPSO) algorithm to solve this model. In DHPSO, the Gaussian random walk can enhance global search in the model space, while the bubble-net attacking strategy can speed convergence. Besides, Archimedes spiral strategy is employed to overcome the local optima trap in the model and improve the exploitation of the algorithm. DHPSO maintains a balance between exploration and exploitation while better defining the distribution of logistics hub locations Numerical experiments show that the newly proposed model always achieves better locations than the current model. Comparing DHPSO with other state-of-the-art intelligent algorithms, the efficiency of the scheme can be improved by 42.58%. This means that logistics companies can reduce distribution costs and consumers can enjoy a more enjoyable shopping experience by using DHPSO's location selection. All the results show the location of the drone logistics hub is solved by DHPSO effectively. [ABSTRACT FROM AUTHOR]

This paper introduces a novel stochastic inverse method that utilizes perturbation theory and advanced intelligence techniques to solve the multi‐parameter identification problem of concrete dams using displacement field monitoring data. The proposed method considers the uncertainties associated with the dam displacement monitoring data, which are comprised of two distinct sources: the first is related to stochastic mechanical properties of the dam, and the second is due to observation errors. The displacements at different measuring points generated by dam mechanical properties exhibit spatial correlation, while the observation errors at different points can be considered statistically random. In this context, the inversion formulas are derived for unknown stochastic parameters of the dam by combining perturbation equations and Taylor expansion methods. An improved meta‐heuristic optimization method is employed to identify the mean of stochastic parameters, while mathematical and statistical methods are used to determine the variance of stochastic parameters. The feasibility of the proposed method is verified through numerical examples of a typical dam section under different conditions. Additionally, the paper discusses and demonstrates the applicability of this method in a practical dam project. Results indicate that this method can effectively capture the uncertainty of dam's mechanical properties and separates them from observation errors. [ABSTRACT FROM AUTHOR]

This paper presents the results of an investigation of the possibility of the reliable determination of the residual stress–strain state in polymers and composites using a combination of bridge curvature, optical scanning, and finite element methods. A three-factor experiment was conducted to determine the strength of printed PLA plastic products. The effect of the residual stresses on the strength of the printed products was evaluated. By comparing the values of the same strength stresses, a relationship between the nature of the stresses and the strength of the samples was found. A tendency of the negative influence of tensile stresses and the opposite strengthening effect of compressive stresses was obvious, so at the same values of tensile strength, the value of residual stress of 42.9 MPa is lower than that of the fibre compression at the value of 88.9 MPa. The proposed new methods of the residual stress determination allow obtaining a complete picture of the stressed state of the material in the investigated areas of the products. This may be necessary in confirming the calculated models of the residual stress–strain state, clarifying the strength criteria and assessing the quality of the selected technological modes of manufacturing the products. [ABSTRACT FROM AUTHOR]

Copyright of Opuntia Brava is the property of Universidad de Ciencias Pedagogicas de Las Tunas, Centro de Documentacion e Informacion Pedagogica and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This paper investigates the behavior of a fluid queue driven by a non-truncated Erlangian service queue, focusing on the symmetrical properties within the system. This study determines the formulations of the steady-state distribution of both the buffer content and stationary state probabilities of a background queueing system. The efficient generating function technique is employed, utilizing a new generalization of the modified Bessel function of the second kind. Performance metrics such as mean buffer content and throughput are calculated, and server utilization is examined. The results contribute to the understanding of fluid queueing systems and offer insights into their performance in various applications, including telecommunications, manufacturing systems, healthcare operations, and ecological models, where symmetry plays a critical role in optimizing performance. [ABSTRACT FROM AUTHOR]

The effective operation of model-based control strategies in modern energy systems, characterized by significant complexity, is contingent upon highly accurate large-scale models. However, achieving such precision becomes challenging in complex energy systems rife with uncertainties and disturbances. Controlling different parts of the energy system poses a challenge to achieving optimal power system efficiency, particularly when employing model-based control strategies, thereby adding complexity to current systems. This paper proposes a novel model-independent control approach aimed at augmenting transient stability and voltage regulation performance in multi machine energy systems. The approach involves the introduction of an optimized model-free fractional-order-based excitation system stabilizer for synchronous generators in a multi machine energy system. To overcome the limitations associated with complex system model identification, which add degrees of simplification at defined operating conditions and assume the system model remains fixed despite high uncertainty and numerous disturbances, an optimal model-independent fractional-order-based excitation control strategy is introduced. The efficacy of the proposed approach is validated through comparative numerical analyses using the MATLAB/Simulink environment. These simulations were conducted on a two-area, 12-bus multi-machine power system. Simulation results demonstrate that the presented excitation system stabilizer outperforms conventional controllers in terms of transient and small-signal stability. It also suppresses the low-frequency electromechanical oscillations within the multimachine energy system. [ABSTRACT FROM AUTHOR]

Design of experiments is a statistical approach from which an optimized number of experiments is determined. Taguchi design of experiments, applied on Erichsen tests, is chosen to be considered in this paper. The most important parameters in this forming process, Erichsen index (IE), and maximum generated force (F max), are experimentally and theoretically determined. Three input factors are selected, at diverse levels, in order to study their influence on Erichsen output results. The considered input factors are sheet thickness, punch diameter, and friction coefficient. New mathematical models which take into account the effects of these factors and their interactions are developed. Moreover, the influence of Erichsen test on the S235 steel microstructural behavior is experimentally examined as function of the sheet thickness. A good agreement between experimental and theoretical findings proves that the proposed models provide a precise prediction and an exact estimation of the Erichsen output parameters (IE and F max). The efficiency of the adopted design of experiments via Taguchi method is well confirmed. [ABSTRACT FROM AUTHOR]

Diffusion processes in operations involving polymeric materials are of significant interest. Determining experimental values for diffusion coefficients is often challenging. Estimating these coefficients in concentrated polymer solution, polymer films, and membranes relies on experimental tests where the polymer is brought into contact with certain components/solvents. The diffusion coefficient values depend on the diffusion type, which is affected mainly by the nature of the polymer, concentration, and temperature. The literature presents an extensive amount of information regarding the diffusion phenomenon. This paper makes a particular contribution by showing how experimental data obtained from different applications can be processed to determine diffusion coefficients. The manuscript addresses some aspects regarding solvent diffusion in polymers, and illustrates how to determine the diffusion coefficients from experimental data. For specific cases of diffusion, several models for the predictive estimation of diffusion coefficients are also presented. Polymer–solvent systems such as polyvinyl alcohol (PVA)–water, cellulose acetate (CA)–tetrahydrofuran (THF) and cellulose triacetate (CTA)–dichloromethane (DCM) are investigated, with their diffusion mechanisms influenced by changes in structure caused by variations in concentration and temperature. The experimental data obtained through a gravitational technique allow for the highlighting of the diffusion mechanism and the selection of an appropriate mathematical model. A change in the structure of the polymer during the experiment leads to diffusion anomalies. Modeling the experimental data yielded diffusion coefficient values that vary based on the type of system investigated, composition and temperature. Thus, in the case of the CTA-DCM system, the diffusion coefficient at 303 K, at various concentration values, is in the range of 4.5 and 8·10−11 m2/s; for the PVA-H2O system, D = 4.1·10−12 m2/s at 303 K, and D = 6.5·10−12 m2/s at 333 K; while for the CA-THF system, the solvent–polymer diffusion coefficient has a value of 2.5∙10−12 m2/s at 303 K, and D = 1.75∙10−11 m2/s at 323 K. Mathematical models can be useful in studies regarding the drying of polymer films with complex structures, providing knowledge for designing or selecting suitable equipment. [ABSTRACT FROM AUTHOR]

Preventive treatment for people with latent Tuberculosis infection (LTBI) has aroused our great interest. In this paper, we propose and analyze a novel mathematical model of TB considering preventive treatment with media impact. The basic reproduction number R0 is defined by the next generation matrix method. In the case without media impact, we prove that the disease-free equilibrium is globally asymptotically stable (unstable) if R0 <1 (R0 >1). Furthermore, we obtain that a unique endemic equilibrium exists when R0 > 1, which is globally asymptotically stable in the case of permanent immunity and no media impact. We fit the model to the newly reported TB cases data from 2009 to 2019 of four regions in China and estimate the parameters. And we estimated R0 = 0:5013 < 1 in Hubei indicating that TB in Hubei will be eliminated in the future. However, the estimated R0 = 1:015> 1 in Henan, R0 = 1:282 >1 in Jiangxi and R0 = 1:930 >1 in Xinjiang imply that TB will continue to persist in these three regions without further prevention and control measures. Besides, sensitivity analysis is carried out to illustrate the role of model parameters for TB control. Our finding reveals that appropriately improving the rate of timely treatment for actively infected people and increasing the rate of individuals with LTBI seeking preventive treatment could achieve the goal of TB elimination. In addition, another interesting finding shows that media impact can only reduce the number of active infections to a limited extent, but cannot change the prevalence of TB. [ABSTRACT FROM AUTHOR]

The threat posed by the COVID-19 pandemic has been accompanied by an epidemic of misinformation, causing confusion and mistrust among the public. Misinformation about COVID-19 whether intentional or unintentional takes many forms, including conspiracy theories, false treatments, and inaccurate information about the origins and spread of the virus. Though the pandemic has brought to light the significant impact of misinformation on public health, mathematical modeling emerged as a valuable tool for understanding the spread of COVID-19 and the impact of public health interventions. However, there has been limited research on the mathematical modeling of the spread of misinformation related to COVID-19. In this paper, we present a mathematical model of the spread of misinformation related to COVID-19. The model highlights the challenges posed by misinformation, in that rather than focusing only on the reproduction number that drives new infections, there is an additional threshold parameter that drives the spread of misinformation. The equilibria of the model are analyzed for both local and global stability, and numerical simulations are presented. We also discuss the model's potential to develop effective strategies for combating misinformation related to COVID-19. [ABSTRACT FROM AUTHOR]

The corrosion problem of the tank floor of the oil depot tank area becomes more and more serious with the extension of the operation time. At present, how to determine the potential distribution of the storage tank floor and how to judge the cathodic protection effect of the storage tank floor is the bottleneck of technological development. In this paper, by constructing a mathematical model of cathodic protection in the tank area, influence of deep well anode on potential distribution of tank bottom is calculated by boundary element method (BEM) with computer programming, to study the potential distribution of the tank floor under different anode parameters. The results show that the calculated results are in good agreement with the field measured results, which verifies the accuracy and reliability of the calculation. [ABSTRACT FROM AUTHOR]

As society continues to age, people are becoming more concerned about their health care. This has led to an increase in the demand for medical products in urban areas, emphasizing the need for regular and prompt deliveries. However, the existing logistics centers are located in the suburbs of Seoul, a metropolitan city, which makes it challenging to ensure timely delivery. To address this issue, this study aims to establish new logistics centers in urban areas, particularly in Seoul, while minimizing CO2 emissions from delivery vehicles in alignment with sustainability efforts. The scientific gap addressed in and the novelty of this paper is that the input parameters are prepared based on actual data from a medical company in Korea to reflect reality, and the mathematical model-based optimization technique is applied to determine the optimal location of a new logistics center. The genetic algorithm is developed to solve the proposed mathematical model by deriving optimal or near-optimal solutions. Furthermore, the numerical experiment examined the impact of establishing a new logistics center in one of the candidate areas of local governments in Seoul by considering environmental impact. As a result, the new logistics network can reduce CO2 emissions by approximately 66.74% compared to the existing logistics network. [ABSTRACT FROM AUTHOR]

Gumboro disease is a viral poultry disease that causes immune suppression on the infected birds leading to poor production, mortality, and exposure to secondary infections, hence a major threat in the poultry industry worldwide. A mathematical model of the transmission dynamics of Gumboro disease is developed in this paper having four compartments of chicken population and one compartment of Gumboro pathogen population. The basic reproduction number R og is derived, and the dynamical behaviors of both the disease-free equilibrium (DFE) and endemic equilibrium are analyzed using the ordinary differential equation theory. From the analysis, we found that the system exhibits an asymptotic stable DFE whenever R og < 1 and an asymptotic stable EE whenever R og > 1. The numerical simulation to verify the theoretical results was carried out using MATLAB ode45 solver, and the results were found to be consistent with the theoretical findings. [ABSTRACT FROM AUTHOR]

Copyright of Iron Steel Vanadium Titanium is the property of Iron Steel Vanadium Titanium Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Controlling the distribution of water and wastewater between industrial processes is vital to rationalize water usage and preserve the environment. In this paper, a mathematical technique is proposed to optimize water–wastewater networks, and a nonlinear program is introduced to minimize the consumption of freshwater and, consequently, the flowrate of wastewater discharge. A general mathematical model, able to handle industrial plants containing up to eight sources and eight sinks, is developed using LINGO optimization software to facilitate dealing with complex case studies. The introduced model can handle single-contaminant networks as well as multiple-contaminant ones. The optimal water network is synthesized through two steps; the first step involves the introduction of the case study data into the developed mathematical model. The second step considers using the optimal solution produced after running the developed LINGO model as feed data for a pre-designed Excel sheet able to deal with these results and simultaneously draw the optimal water–wastewater network. The proposed mathematical model is applied to two case studies. The first case study includes actual data from four fertilizer plants located in Egypt; the water resources and requirements are simultaneously integrated to obtain a sensible cutting in both freshwater consumption (lowered by 52.2%) and wastewater discharge (zero wastewater discharge). The second case study regards a Brazilian petrochemical plant; the obtained results show noticeable reductions in freshwater consumption by 12.3%, while the reduction percentage of wastewater discharge is 4.5%. [ABSTRACT FROM AUTHOR]

The numerical method for modeling the behavior of nanofluid within the closed container in the presence of Lorentz force was dissected in this paper. The working fluid contains water and two shapes of nanoparticles. The porous geometry has one sinusoidal inner surface which faces constant heat flux. Influences of gravity and vertical Lorentz was complicated in modeling and momentum equations have been edited with adding related source terms. The precision of code was tested and respectable agreement has been obtained. The influences of loading nanomaterial and strength of two important forces (gravity and buoyancy) have been analyzed in the result section. Loading nanoparticles leads to a growth of Nu around 26.99% and 41.04% when Ha = 0 and 15. Increasing buoyancy leads to augment of Nu about 44.34% and 1.46% in the absence and existence of Ha. Applying Lorentz force makes Nu to decrease about 40.39% when Ra = 7 0 0. [ABSTRACT FROM AUTHOR]

The principal economic sector devoted to the breeding, raising, and production of farm animals is known as the livestock industry. There are precise standards for making high-quality feed in animal husbandry. Precision livestock feeding is a crucial component, with the potential to significantly impact the profitability of livestock; it permits the provision of diets to animals that are precisely tailored to their specific daily nutritional needs. Through simulation modeling, a single model can be created for automated systems to determine daily rations for farm animals. For the purposes of this document, precision livestock feeding refers to the practice of tailoring feed to individual animals or groups of animals, taking into account their changing nutritional needs over time and individual differences in terms of nutritional requirements. The practice aims to optimize animal health and performance while reducing feed waste. This paper presents a formal model for determining the quantities of components needed to achieve a minimum cost mixture that satisfies compositional and quantitative criteria. The present research calculates the amount of hay and silage required to feed an animal per day at the most economical cost by applying an optimization approach that involves defining and solving an optimization problem. The problem is solved using a well-known software package, which is necessary for the practical application of the resulting model. Real data from livestock production in Bulgaria are used to numerically test the model. [ABSTRACT FROM AUTHOR]

Context. One of the methods of solving the actual scientific and technical problem of reducing the maximum level of side lobes of autocorrelation functions of radar signals is the use of nonlinear-frequency modulated signals. This rounds the signal spectrum, which is equivalent to the weight (window) processing of the signal in the time do-main and can be used in conjunction with it. A number of studies of signals with non-linear frequency modulation, which include linearly-frequency modulated fragments, indicate that distortions of their frequency-phase structure occur at the junction of the fragments. These distortions, depending on the type of mathematical model of the signal – the current or shifted time, cause in the generated signal, respectively, a jump in the instantaneous frequency and the instantaneous phase or only the phase. The paper shows that jumps occur at the moments when the value of the derivative of the instantaneous phase changes at the end of the linearly-frequency modulated fragment. The instantaneous signal frequency, which is the first derivative of the instantaneous phase, has an interpretation of the rotation speed of the signal vector on the complex plane. The second derivative of the instantaneous phase of the signal is understood as the frequency modulation rate. Distortion of these components leads to the appearance of an additional component in the linear term of the instantaneous phase, starting with the second fragment. Disregarding these frequency-phase (or only phase) distortions causes distortion of the spectrum of the resulting signal and, as a rule, leads to an increase in the maxi-mum level of the side lobes of its autocorrelation function. The features of using fragments with frequency modulation laws in complex signals, which have different numbers of derivatives of the instantaneous phase of the signal, were not considered in the known works, therefore this article is devoted to this issue. Objective. The aim of the work is to develop a mathematical model of the current time of two-fragment nonlinear-frequency modulated signals with a sequential combination of linear-frequency and quadratically modulated fragments, which provides rounding of the signal spectrum in the region of high frequencies and reducing the maximum level of side lobes of the autocorrelation function and increasing the speed of its descent. Method. Nonlinear-frequency modulated signals consisting of linearly-frequency and quadratically modulated fragments were studied in the work. Using differential analysis, the degree of influence of the highest derivative of the instantaneous phase on the frequency-phase structure of the signal was determined. Its changes were evaluated using time and spectral correlation analysis methods. The parameters of the resulting signal evaluated are phase and frequency jumps at the junction of fragments, the shape of the spectrum, the maximum level of the side lobes of the autocorrelation function and the speed of their descent. Results. The article has further developed the theory of synthesis of nonlinear-frequency modulated signals. The theoretical contribution is to determine a new mechanism for the manifestation of frequency-phase distortion at the junction of fragments and its mathematical description. It was found that when switching from a linearly-frequency modulated fragment to a quadratically modulated frequency-phase distortion of the resulting signal, the third derivative of the instantaneous phase becomes, which, by analogy with the theory of motion of physical bodies, is an acceleration of frequency modulation. The presence of this derivative leads to the appearance of new components in the expression of the instantaneous frequency and phase of the signal. The compensation of these distortions provides a decrease in the maximum level of the side lobes by 5 dB and an increase in its descent rate by 8 dB/deck for the considered version of the non-linear-frequency modulated signal. Conclusions. A new mathematical model of the current time has been developed for calculating the values of the instantaneous phase of a nonlinear-frequency modulated signal, the first fragment of which has linear, and the second – quadratic frequency modulation. The difference between this model and the known ones is the introduction of new components that provide compensation for frequency-phase distortions at the junction of fragments and in a fragment with quadratic frequency modulation. The obtained oscillogram, spectrum and autocorrelation function of one of the synthesized two-fragment signals correspond to the theoretical form, which indicates the adequacy and reliability of the proposed mathematical model. [ABSTRACT FROM AUTHOR]

The infection caused by Rift Valley fever (RVF) virus is a dangerous vector-borne disease found in humans, domestic, and wild animals. It is transferred through insect vectors to ruminant host and then spread through direct contact of infected animals with their body fluid or organs. In this paper, a fractal-fractional model for the transmission of RVF in the Caputo's sense was presented. We analyzed the model and determined the basic reproduction number through the next-generation matrix technique, indicated by R0. The global sensitivity technique is used for the sensitivity test of R0 to find out the most sensitive input-factors to the reproduction parameter R0. The existence and uniqueness results of the proposed fractal-fractional model were established. Then, we presented the fractal-fractional dynamics of the proposed RVF model through a novel numerical scheme under the fractal-fractional Caputo operator. In the end, the recommended model of RVF was highlighted numerically with the variation of different input parameters of the system. The key factors of the system were highlighted to the policymakers for the control and prevention of the infection. [ABSTRACT FROM AUTHOR]