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As the EU and the US successively proposed the carbon border adjustment mechanism (CBAM) and the Clean Competition Act (CCA), importers are now required to declare the carbon emissions of their products. Particularly, wheel companies face increasing time pressure with the gradual development of implementation paths for net-zero emissions and implementing carbon pricing policies in various countries. This research uses the production data of Taiwan wheel companies to establish a mathematical model for the activity-based cost optimisation decision-making process. It explores the impact of different carbon emission costs on a company's product mix with pricing decisions. Further, the research proposes five mathematical programmes for single-period cost optimisation decision-making under carbon pricing. These models provide some detailed view, such as changes in profits and product mix caused by high carbon taxes or other changes for each resource. Furthermore, the production cost optimal model proposed in this research can be used by enterprises to fulfill their social responsibilities while ensuring profitability and serve as a reference for making net-zero transformation decisions. [ABSTRACT FROM AUTHOR]

In secondary lymphoid tissues, human immunodeficiency virus (HIV) can replicate in both the follicular and extrafollicular compartments. Yet, virus is concentrated in the follicular compartment in the absence of antiretroviral therapy, in part due to the lack of cytotoxic T lymphocyte (CTL)-mediated activity there. CTLs home to the extrafollicular compartment, where they can suppress virus load to relatively low levels. We use mathematical models to show that this compartmentalization can explain seemingly counter-intuitive observations. First, it can explain the observed constancy of the viral decline slope during antiviral therapy in the peripheral blood, irrespective of the presence of CTL in Simian Immunodeficiency Virus (SIV)-infected macaques, under the assumption that CTL-mediated lysis significantly contributes to virus suppression. Second, it can account for the relatively long times it takes for CTL escape mutants to emerge during chronic infection even if CTL-mediated lysis is responsible for virus suppression. The reason is the heterogeneity in CTL activity and the consequent heterogeneity in selection pressure between the follicular and extrafollicular compartments. Hence, to understand HIV dynamics more thoroughly, this analysis highlights the importance of measuring virus populations separately in the extrafollicular and follicular compartments rather than using virus load in peripheral blood as an observable; this hides the heterogeneity between compartments that might be responsible for the particular patterns seen in the dynamics and evolution of the HIV in vivo.

IntroductionCancer combination treatments involving immunotherapies with targeted radiation therapy are at the forefront of treating cancers. However, dosing and scheduling of these therapies pose a challenge. Mathematical models provide a unique way of optimizing these therapies.MethodsUsing a preclinical model of multiple myeloma as an example, we demonstrate the capability of a mathematical model to combine these therapies to achieve maximum response, defined as delay in tumor growth. Data from mice studies with targeted radionuclide therapy (TRT) and chimeric antigen receptor (CAR)-T cell monotherapies and combinations with different intervals between them was used to calibrate mathematical model parameters. The dependence of progression-free survival (PFS), overall survival (OS), and the time to minimum tumor burden on dosing and scheduling was evaluated. Different dosing and scheduling schemes were evaluated to maximize the PFS and optimize timings of TRT and CAR-T cell therapies.ResultsTherapy intervals that were too close or too far apart are shown to be detrimental to the therapeutic efficacy, as TRT too close to CAR-T cell therapy results in radiation related CAR-T cell killing while the therapies being too far apart result in tumor regrowth, negatively impacting tumor control and survival. We show that splitting a dose of TRT or CAR-T cells when administered in combination is advantageous only if the first therapy delivered can produce a significant benefit as a monotherapy.DiscussionMathematical models are crucial tools for optimizing the delivery of cancer combination therapy regimens with application along the lines of achieving cure, maximizing survival or minimizing toxicity.

The aim of this paper is to examine the stability of a class of nonlinear stochastic operators on a finite‐dimensional simplex. We identify a number of properties of the set of the class of stochastic operators, including the stability of each operator. We then use these operators to define non‐homogeneous Markov measures that rely on initial data and carry out an investigation into the absolute continuity and singularity of these measures. [ABSTRACT FROM AUTHOR]

In the process of natural gas hydrate exploitation, the secondary hydrate formation may occur in both the reservoir and the completion layer. The secondary hydrate formed during the exploitation process and the sand particles falling from the reservoir will block the flow channel and reduce the gas production. In this paper, the permeability change of sand filling layer under the influence of sand and hydrate blockage is studied from a three-dimensional perspective, and the permeability change characteristics of sand mixing and secondary hydrate formation in filling layer caused by pore space blockage are summarized. A three-dimensional model for predicting the permeability of gravel layer is developed. In previous studies, the mathematical model parameters derived from the empirical formula are always not unique, which will cause inaccurate permeability prediction results. In this study, the simulated annealing algorithm is used to optimize the parameters such as boundary conditions and cooling tables. The undetermined parameters in the existing mathematical prediction model of gravel layer permeability are optimized into a determined maximum value to solve the optimization problem of the undetermined parameters of the permeability model. The algorithm in this paper takes the actual value of gravel layer permeability with different sand content and hydrate concentration in the experiment as the standard, and takes the mean square error of the predicted value and the experimental value of the prediction model as the objective function. The simulated annealing algorithm is used to estimate and optimize the undetermined parameters of the model. The algorithm results show that the mean square error between the predicted value and the experimental value is minimized with n = 22.7 and τ = 1.014(n and τ are the parameters to be optimized in the permeability model of this paper). The fitting degree between the optimized permeability prediction model and the experimental value is higher than that before optimization, which verifies the correctness and rationality of the algorithm in this paper. • Simulated annealing algorithm is used to optimize the permeability model. • The simulated annealing algorithm is optimized to have faster solution speed. • The NMSE error calculation method is used to make the predicted permeability model better fit the actual value. • The optimized model is combined with the capacity model. [ABSTRACT FROM AUTHOR]

The testing of relay protection devices is an extremely important task on which the stable and safe operation of the power systems depends. One of the most complex and responsible kinds of protection in networks with rotating generation, which includes hydrogen fuel generation, is protection against loss-of-synchronism. Integration of heterogeneous generating electrical devices based on renewable energy sources and based on a hydrogen fuel cell is associated with the need for reliable relay protection. It disconnects tie-lines between the systems in out-of-step conditions. And it is a challenging task to simulate input signals corresponding to the exact settings of the out-of-step protection to make sure it operates correctly. This is because one has to simulate exact parameters of impedance locus (its radius, coordinates of the center in the impedance plane, spin direction, speed, etc.) while available tools embedded in testing devices often don't support such parameters directly. To deal with the problem, the authors present the approach to simulate instantaneous values of line currents and phase-to-ground voltages during the out-of-step operation. These electrical signals form the locus of the impedance vector with the desired parameters to test the operation of the out-of-step protection devices. The software based on the proposed algorithm also provides a graphical representation of the simulation results. All the proposed solutions proved to reduce the time required for commissioning of out-of-step protection and thereby increase tests quality and speed. (provided to the authors on 29.08.2024 for printing in IJHE from the archive of Fermaltech Montenegro Limited, made by A.L. Gusev using Designer. On the DALL E 3 platform.). [Display omitted] [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]

Background and Purpose: Endothelin‐1 (ET‐1) receptor A (ETA) antagonists reduce proteinuria and prevent renal outcomes in chronic kidney disease (CKD) patients, but their utility has been limited because of associated fluid retention, resulting in increased heart failure risk. Understanding the mechanisms responsible for fluid retention could result in solutions that preserve renoprotective effects while mitigating fluid retention, but the complexity of the endothelin system has made identification of the underlying mechanisms challenging. Approach: We utilized a previously developed mathematical model of ET‐1 kinetics, ETA receptor antagonism, kidney function, haemodynamics, and sodium and water homeostasis to evaluate hypotheses for mechanisms of fluid retention with ETA antagonism. To do this, we simulated the RADAR clinical trial of atrasentan in patients with type 2 diabetes and CKD and evaluated the ability of the model to predict the observed decreases in haematocrit, urine albumin creatinine ratio (UACR), mean arterial pressure (MAP), and estimated glomerular filtration rate (eGFR). Background and Key Results: An effect of ETA antagonism on venodilation and increased venous capacitance was found to be the critical mechanism necessary to reproduce the simultaneous decrease in both MAP and haematocrit observed in RADAR. Conclusions and Impact: These findings indicate that fluid retention with ETA antagonism may not be caused by a direct antidiuretic effect within the kidney but is instead be an adaptive response to venodilation and increased venous capacity, which acutely tends to reduce cardiac filling pressure and cardiac output, and that fluid retention occurs in an attempt to maintain cardiac filling and cardiac output. [ABSTRACT FROM AUTHOR]

This paper evaluates the nonlinear dynamics of a melanoma cancer model through the iterative technique of finding compact invariant sets (LMCIS). The objective is to discover equilibrium points, ascertain their stability qualities, and determine the presence of compact invariant sets within the model. For instance, this approach is assessed in a model demonstrating the interplay between four cellular populations and administrating interleukin-12 (IL-12) immunotherapy. Nevertheless, the mechanism by which this anti-cancer therapy operates has yet to be completely defined. The approach is evaluated using severe treatment situations to provide evidence for the presence of equilibrium points inside the iteratively confined zone and to assess its effectiveness. The outcomes derived from using this approach were then compared with a conventional iteration of Newton's method. Newton's approach extends to the resolution of the system of equations inside the model, facilitating the identification of the equilibrium points with a small tolerance error. While the iterations of the localization algorithm were set close to the results obtained by this method. Finally, the simulation outcomes are shown via the utilization of MATLAB R2020b. The findings demonstrate the temporal progression of the model under the effect of immunotherapy and without it. [ABSTRACT FROM AUTHOR]

Tight sandstone water-bearing gas reservoirs typically exhibit low porosity and low permeability, with reservoir rocks characterized by complex pore structures, often featuring micron-scale or smaller pore throats. This intricate reservoir structure significantly restricts fluid flow within the reservoir, necessitating a certain threshold pressure gradient (TPG) to be overcome before flow can commence. This study focuses on the Ordos Basin and explores the influence of high water content tight sandstone gas reservoirs on TPG under different water saturation and formation pressure conditions through experiments. A mathematical model of TPG is established using multiple linear regression method. The results show that TPG is primarily affected by water saturation, followed by formation pressure. As the water saturation increases, the TPG of the core decreases, and the change becomes more pronounced when the water saturation exceeds 50%. As formation pressure increases, the weakening of the slippage effect in gas molecules leads to TPG stabilization, especially when local pressure exceeds 25.0 MPa. The research also shows that low-permeability cores exhibit greater TPG variation with pressure changes, while high-permeability cores remain more stable. A mathematical model was developed and validated to predict TPG based on permeability, water saturation, and formation pressure. These findings highlight the need to monitor formation water content during tight sandstone gas reservoir development to optimize production strategies, providing valuable insights for improving reservoir management and guiding future research. [ABSTRACT FROM AUTHOR]

To reveal the velocity distribution law of a gas lift reverse circulation well washing flow field in drilling shaft sinking, a velocity mathematical model of well washing flow field is established. The theoretical analytical solutions and velocity distribution laws in the drill pipe and bottom hole were provided and validated through numerical simulations and similar model tests. Furthermore, this study explores the impacts of mud circulation, wind pressure, rock debris, and mud properties on the flow field distribution, presenting the sensitivity order of the factors. This study indicated the following findings. (1) The velocity theoretical model of well washing flow field was validated through numerical simulation and similar model tests, and the relative error ranged from 4.2 to 18.5%, demonstrating the high consistency. (2) The rock debris and mud experienced slight and consistent deceleration within the drill pipe. Upon reaching the gas input end, the axial upward return of the multiphase flow resulted in a "jumping" sharp increase. (3) The mud circulation, wind pressure, and void fraction positively correlated with the multiphase fluid velocity in the drill pipe, but negatively correlated with the mud density and slag content. The axial upward velocity of the rock debris decreased with increasing particle size and density. (4) The sensitivity of each factor to the discharge speed of rock debris was summarized as follows: air content > mud circulation > wind pressure > mud density > rock debris density > rock debris particle size > slag content. These findings could offer a theoretical basis for selecting well washing parameters and enhancing drilling and washing efficiency. [ABSTRACT FROM AUTHOR]

Background: In Taiwan, the human immunodeficiency virus (HIV) is primarily transmitted among men who have sex with men (MSM). We believe that the primary source of heterogeneity influencing transmission is from whether the infected individuals engage in behaviors that promote transmission. Therefore, we differentiated and modeled the statuses of infected individuals, estimated parameters, and predicted future infection trends to better understand HIV transmission dynamics among MSM. Methods: We devised a computational approach to accurately estimate the number of infectious individuals during early surveillance years in Taiwan using monthly data of newly diagnosed patients with HIV from January 2005 to December 2006. Subsequently, using annual incident cases from 2005 to 2019, we estimated the susceptibility rate, transmission rates, and duration of risk and conducted short-term forecasts of HIV infection among MSM through mathematical modeling based on the susceptible-infected-removed model. Parameters and their values, such as HIV and acquired immunodeficiency syndrome (AIDS) transmission rates and removal rates, were also estimated. Results: A total of 850 infectious individuals with HIV were identified in 2005. From 2005 to 2019, approximately 0.68% (95% confidence interval: 0.64–0.71%) of Taiwan's male population were estimated to be susceptible to HIV infection via MSM. The transmission rate did not significantly differ between individuals with HIV and AIDS (0.0110 and 0.107 per 10,000 individuals, respectively). The average infection duration between infection and AIDS onset was 4.5 years and between AIDS onset and death was 2.1 years. In 2019, the proportion of infectious infected individuals continuously decreased. By 2026, only 11.85% and 10.21% of individuals with HIV and AIDS, respectively, will be infectious. Conclusions: Our study presents a new dynamic mathematical model for estimating infectious HIV cases among MSM in Taiwan. By accounting for the heterogeneity of infectious HIV/AIDS within the MSM population, we effectively estimated the number of infections during early surveillance years and implement concentrated measures, thereby reducing infectious HIV/AIDS cases, which contributes to the overall reduction in HIV/AIDS cases. With these estimations, identifying target populations and implementing effective intervention measures at appropriate times can be improved. [ABSTRACT FROM AUTHOR]

Cancer is a systemic heterogeneous disease involving complex molecular networks. Tumor formation involves an epithelial‐mesenchymal transition (EMT), which promotes both metastasis and plasticity of cancer cells. Recent experiments have proposed that cancer cells can be transformed into adipocytes via a combination of drugs. However, the underlying mechanisms for how these drugs work, from a molecular network perspective, remain elusive. To reveal the mechanism of cancer‐adipose conversion (CAC), this study adopts a systems biology approach by combing mathematical modeling and molecular experiments, based on underlying molecular regulatory networks. Four types of attractors are identified, corresponding to epithelial (E), mesenchymal (M), adipose (A) and partial/intermediate EMT (P) cell states on the CAC landscape. Landscape and transition path results illustrate that intermediate states play critical roles in the cancer to adipose transition. Through a landscape control approach, two new therapeutic strategies for drug combinations are identified, that promote CAC. These predictions are verified by molecular experiments in different cell lines. The combined computational and experimental approach provides a powerful tool to explore molecular mechanisms for cell fate transitions in cancer networks. The results reveal underlying mechanisms of intermediate cell states that govern the CAC, and identified new potential drug combinations to induce cancer adipogenesis. [ABSTRACT FROM AUTHOR]

In a fast-changing world, understanding how organisms adapt to their environment is a pressing necessity. Research has focused on genetic adaptation, while our understanding of non-genetic modes is still in its infancy. The host-associated microbiome can be considered a non-genetic mode of adaptation, which can strongly influence an organism's ability to cope with its environment. However, the role of the microbiome in host ecological dynamics is largely unexplored, particularly in animal communities. Here, we discuss the following hypothesis: invasive species may rapidly adapt to local conditions by adopting beneficial microbes from similar co-occurring native species. This occurs when the invader's fitness is influenced by adaptation to local conditions that is facilitated by microbes acquired from native microbiomes. We present a minimal mathematical model to explore this hypothesis and show that a delayed acquisition of native microbes may explain the occurrence of an invasion lag. Overall, our results contribute to broadening the conceptualization of rapid adaptation via microbiome transfer and offer insights towards designing early intervention strategies for invasive species management. [ABSTRACT FROM AUTHOR]

Introduction: Treating extensive burn injury requires an individually tailored resuscitation protocol that includes hourly-titrated intravenous fluid infusion to avert both hypovolemic shock and edema. Due to the complexity of burn pathophysiology and significant variability in treatment protocols, there is an ongoing effort to optimize burn resuscitation. The goal of this work is to contribute to this effort by developing a mathematical model of burn pathophysiology and resuscitation for in silico testing of burn resuscitation protocols and decision-support systems. Methods: In our previous work, we developed and validated a mathematical model consisting of volume kinetics, burn-induced perturbations, and kidney function. In this work, we expanded our previous mathematical model to incorporate novel mathematical models of cardiovascular system and hormonal system (renin-angiotensin-aldosterone (RAAS) system and antidiuretic hormone) which affect blood volume and pressure regulation. We also developed a detailed mathematical model of kidney function to regulate blood volume, pressure, and sodium levels, including components for glomerular filtration rate, reabsorption rates in nephron tubules, Tubuglomerular feedback, and myogenic mechanisms. We trained and validated the expanded mathematical model using experimental data from 15 pigs and 9 sheep with extensive burns to quantitatively evaluate its prediction accuracy for hematocrit, cardiac output, mean arterial pressure, central venous pressure, serum sodium levels, and urinary output. We then trained and tested the mathematical model using a clinical dataset of 233 human burn patients with demographic data and urinary output measurements. Results: The mathematical model could predict all tested variables very well, while internal variables and estimated parameters were consistent with the literature. Discussion: To the best of our knowledge, this is the first mathematical model of burn injury and resuscitation which is extensively validated to replicate actual burn patients. Hence, this in silico platform may complement large animal pre-clinical testing of burn resuscitation protocols. Beyond its primary purpose, the mathematical model can be used as a training tool for healthcare providers delivering insight into the pathophysiology of burn shock, and offering novel mathematical models of human physiology which can be independently used for other purposes and contexts. [ABSTRACT FROM AUTHOR]

This article discusses the option of upgrading an ore-thermal furnace to produce technical silicon by installing strain gage sensors with signal converters and a rangefinder in the electrode lifting system. This upgrade will enable the reception of real-time data on changes in mass (carbon monoxide) or electrode breakage and the position of the working end of the electrode. The latter parameter is associated with the position of the reaction zone in the furnace, which directly affects the specific amount of electricity consumption, the temperature and volume of silicon leaving the furnace, and heat losses and dust removal with exhaust gases. The upgrade will increase the observability of the control object, which will improve the quality of control of the technological process of carbothermic silicon reduction. [ABSTRACT FROM AUTHOR]

This study investigated the effect of hot water blanching (HWB), high‐humidity air‐impingement blanching (HHAIB), different HHAIB blanching times (2, 4, 6, 8, and 10 min), and different HHAIB blanching temperatures (80, 85, 90, and 95°C) on texture quality, lignin content, weight loss, color, microstructure, and drying kinetics of bamboo shoots. After HWB treatment, the lignin content of bamboo shoots was apparently lower than that of HHAIB and the samples obtained the highest weight loss value of 6.13%. Both the texture values (brittleness and chewiness) and lignin content of bamboo shoots exhibited an overall downward trend as the HHAIB blanching time and blanching temperature increased. Specifically, the lignin content of bamboo shoots decreased from 5.59% to 4.58% with an increase in HHAIB blanching time from 2 to 10 min and dropped from 5.48% to 4.63% as HHAIB blanching temperature increased from 80 to 85°C, respectively. The lignin content was proved to be positively correlated (p < 0.05) with texture attributes (brittleness and chewiness). A second polynomial model was obtained for fitting the variation kinetics of lignin content during thermal processing. Reducing the HHAIB blanching time and blanching temperature would obtain a lower weight loss and a better color performance (ΔE and L*). Additionally, microstructure observation revealed that the distribution density of microchannels initially increased and then decreased with the extension of blanching time, while it continuously became firmer as HHAIB blanching temperature increased. Overall, the optimal processing parameters were achieved under the HHAIB blanching temperature of 85°C for 6 min, ensuring a high‐quality performance of bamboo shoot products. [ABSTRACT FROM AUTHOR]

Sowing depth is a critical factor in crop growth and is determined by both the soil conditions and the force of the opener. The trend for the future is to control sowing depth based on soil dynamic parameters. Therefore, this paper developed a downforce measurement and control system based on the 'T'-shaped furrow opener and investigated the influence of soil dynamic parameters and opener downforce on sowing depth. A test-rig was constructed and the accuracy of the system in measuring downforce and controlling downforce and sowing depth was verified. The study shows that at different sowing depths, soil moisture, bulk density and their interaction have a significant effect on downforce (P < 0.01). As the moisture content decreases and the bulk density increases, the required downforce increases for the same sowing depth. A mathematical model of downforce-sowing depth-soil bulk density-soil moisture content was established using experimental data, with an R2 of 0.916, VIF <5 and a Durbin-Watson value of 1.628. Field experiments show that, at an operating speed of 6 km h−1, the control strategy based on the soil dynamic parameters predicted by downforce theory significantly outperformed the strategy of adjusting the downforce in response to perceived changes in downforce. This indicates that after dynamic and rapid measurement of soil bulk density and moisture content during field operations, sowing depth can be accurately controlled based on the directed downforce of the opener. The mathematical model provides a theoretical basis for sowing depth control based on soil dynamic parameters. • Proposing a sowing depth control strategy based on soil dynamic parameters. • System developed under static conditions and validated through dynamic experiments. • A mathematical model for the precise control of sowing depth was established. [ABSTRACT FROM AUTHOR]

This paper aims to investigate appropriate mathematical models devoted to the optimization of some cleaning processes related to pharmaceutical contaminant removal. In our recent works, we found the rehabilitation of the existing cleaning plants as a viable solution for the removal of this type of micropollutants from waters by introducing efficient techniques such as adsorption on granulated active carbon filters and micro-, nano-, or ultrafiltration. To have these processes under better control and to assure the transfer from small- to large-scale treatment stations, specific mathematical models are necessary. Starting from Navier–Stokes equations and imposing proper boundary conditions, some mathematical physics problems are obtained for which adequate solving methods via variational methods and surjectivity results are proposed. The importance of these solution characterizations consists in their continuation in adequate numerical methods and the possibility to visualize the result by using a CFD program. [ABSTRACT FROM AUTHOR]

Optimal disturbances of the periodic solution of the hepatitis B dynamics model corresponding to the chronic recurrent form of the disease are found. The dependence of the optimal disturbance on the phase of periodic solution is analyzed. Four phases of the solution are considered, they correspond to clinically different periods of development of the immune response and severity of the disease, namely, activation of antiviral immune reactions, attenuation of reactions, peak and minimum viral load. The possibility of using optimal disturbances to exit the domain of attraction of the considered periodic solution using minimal impact is studied. The components of disturbances that may underlie the phenomenon of spontaneous recovery from chronic hepatitis B observed in clinical practice are identified. [ABSTRACT FROM AUTHOR]

In this work, we obtained a general formulation for the mating probability and fertile egg production in helminth parasites, focusing on the reproductive behavior of polygamous parasites and its implications for transmission dynamics. By exploring various reproductive variables in parasites with density-dependent fecundity, such as helminth parasites, we departed from the traditional assumptions of Poisson and negative binomial distributions to adopt an arbitrary distribution model. Our analysis considered critical factors such as mating probability, fertile egg production, and the distribution of female and male parasites among hosts, whether they are distributed together or separately. We show that the distribution of parasites within hosts significantly influences transmission dynamics, with implications for parasite persistence and, therefore, with implications in parasite control. Using statistical models and empirical data from Monte Carlo simulations, we provide insights into the complex interplay of reproductive variables in helminth parasites, enhancing our understanding of parasite dynamics and the transmission of parasitic diseases. [ABSTRACT FROM AUTHOR]

The monitoring and diagnostic system has been suggested as a non-destructive diagnostic method. The structure and operation of the suggested system can be described by the concept of digital shadow (DS). One of the main DS subsystems is a set of sensors properly placed on the monitored object and coupled with a discrete data processing model created in Matlab/Simulink. The discrete model, as another important DS subsystem of the monitored facility, transfers information about its technical condition to the operator based on data recorded by the sensor system. The digital monitoring model processes the recorded data in the form of the object's response to actions caused by its operating conditions. This work formalized a mathematical model determining the coupling of the digital model with the sensors placed on the monitored object. The formulated method using DS, due to its sensitivity, enables the detection of the damage in the object at an early stage. The tests allowed for detecting the regularities enabling the determination of the area of damage to the shaft and its size. [ABSTRACT FROM AUTHOR]

In recent years, due to the diversity of fire scenes in ports and ships, the problem of fire command is complicated. In the case of power failure, the original command platform and fire extinguishing system will not be able to be used normally, or the fire extinguishing resources carried by the ship when it is on fire cannot be used. In the traditional firefighting ability research, there is no clear measure of firefighting ability, resulting in inaccurate calculation results. By corresponding to the quantity and composition of resources for the study of fire extinguishing capability, the combination of the fire dynamics simulation software PyroSim2020 and a calculation model that converts its resources into the total amount and flow of fire extinguishing agent can be provided. Based on the analytic hierarchy process (AHP), a firefighting demand grade calculation and judgment model was established, which included five factors: fire scale, combustion material characteristics, foam extinguishing agent performance, firefighting object characteristics, and external factors. It concluded that the demand assignment values of each index element were 2, 5, 6, 9, and 10, and further proposed the grade judgment criteria for the calculation results of comprehensive fire demand. Through the quantitative simulation of firefighting demand based on the fire scenario and calculation model test of the consumption prediction of cooperative firefighting equipment, it can also provide a strategic reference for related cooperative fire rescue. [ABSTRACT FROM AUTHOR]

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The mathematical modeling of a combination of non-thermal technologies for E. coli inactivation is of great interest for describing the dynamic behavior of microorganisms in food, with the goal of process control, optimization, and prediction. This research focused on the design and implementation of a mathematical model to predict the effect of power ultrasound (US), high-pressure processing (HPP), and the combination of both non-thermal technologies on the inactivation kinetics of E. coli (DSM682) inoculated in orange juice. Samples were processed by US, HPP, and a combination of both technologies at varying process parameters, and a mathematical model for microbial inactivation was developed using a System Dynamics approach. The results showed that the combination of these technologies exhibited a synergistic effect, resulting in no detectable colony-forming units per mL of juice. The developed model accurately predicted the inactivation of E. coli following the combination of these technologies (R2 = 0.82) and can be used to predict microbial load reduction or optimize it based on process parameters. Additionally, combining both techniques offers a promising approach for extending the shelf life of fresh juices using non-thermal stabilization technology. [ABSTRACT FROM AUTHOR]

A universal mathematical model of an autonomous asynchronous generator with capacitor self-excitation in retarded phase coordinates is proposed, taking into account the electromagnetic connections between the windings of the stator and rotor phases, saturation of the main magnetic circuit, and active power losses in the magnetic circuit elements. The model provides an opportunity to analyze stable periodic modes and transient electromagnetic and electromechanical processes in autonomous power supply systems with arbitrary switching schemes of its elements and asynchronous generators. The model provides the possibility of taking into account the residual magnetization of the magnetic circuit of an asynchronous generator and the change in rotor speed during the course of the self-excitation process of an asynchronous generator with a grounded neutral of the stator winding and an asymmetric load. References 10, figures 2. [ABSTRACT FROM AUTHOR]

Background: Understanding how infectious disease transmission varies from person to person, including associations with age and contact behavior, can help design effective control strategies. Within households, transmission may be highly variable because of differing transmission risks by age, household size, and individual contagiousness. Our aim was to disentangle those factors by fitting mathematical models to SARS-CoV-2 household survey and serologic data. Methods: We surveyed members of 3,381 Utah households from January-April 2021 and performed SARS-CoV-2 antibody testing on all available members. We paired these data with a probabilistic model of household importation and transmission composed of a novel combination of transmission variability and age- and size-structured heterogeneity. We calculated maximum likelihood estimates of mean and variability of household transmission probability between household members in different age groups and different household sizes, simultaneously with importation probability and probabilities of false negative and false positive test results. Results: 12.8% of individual participants, residing in 17.4% of the participating households, showed serologic evidence of prior infection or reported a prior positive test on the survey. Serologically positive individuals in younger age groups were less likely than older adults to have tested positive during their infection according to our survey results. Our model results suggested that adolescents and young adults (ages 13–24) acquired SARS-CoV-2 infection outside the household at a rate substantially higher than younger children and older adults. Our estimate of the household secondary attack rate (HSAR) among adults aged 45 and older exceeded HSARs to and/or from younger age groups at a given household size. We found lower HSAR in households with more members, independent of age differences. The age-specific HSAR patterns we found could not be explained by age-dependent biological susceptibility and transmissibility alone, suggesting that age groups contacted each other at different rates within households. Conclusions: We disentangled several factors contributing to age-specific infection risk, including non-household exposure, within-household exposure to specific age groups, and household size. Within-household contact rate differences played a significant role in driving household transmission epidemiology. These findings provide nuanced insights for understanding community outbreak patterns and mechanisms of differential infection risk. [ABSTRACT FROM AUTHOR]

Summary Societal impact statement The European spruce bark‐beetle, Ips typographus, is a major pest of Norway spruce across mainland Europe; however, until 2018, it was considered absent from the United Kingdom (UK). The finding of a breeding population of I. typographus in Kent, England, in 2018 and subsequent findings in pheromone traps across the southeast of England, has led to an urgent need to improve understanding of environmental suitability across the UK. Two distinct published phenological models for I. typographus, developed in Sweden and Austria, were adapted for use in the UK and validated against pheromone trap data collected at the original site of infestation and in the surrounding area from 2019 to 2022. Both models captured some, but not all, of the within‐season variation in trap catches. One, the PHENIPS model, more accurately captured early season flight patterns. The climate in the southeast of England is mild enough to facilitate two generations of the beetle, while further north the pest is expected to be univoltine. At high altitude in Scotland, there is insufficient thermal warming within a season for the completion of one annual generation. Phenological modelling does not explain why the pest failed to establish in England prior to 2018 including when a large amount of infested material was imported to sawmills in the 1940s. Under 2 and 3°C global warming scenarios, we might expect to see an increase in potential voltinism across the UK in the next few decades, increasing the risk of large outbreaks of I. typographus were it allowed to establish. In 2018, a breeding population of the European spruce bark‐beetle, Ips typographus, was discovered in woodland in southeast England. Ips typographus is a major forest pest in continental Europe; however, despite previous findings at ports and sawmills, this was the first recorded infestation in the UK. The number of generations per year (voltinism) varies with latitude and altitude. Applying a phenological model, we find that the current climate in southern UK could support two generations, while temperature accumulation in parts of Scotland may be insufficient to support one generation. Global warming will increase voltinism and hence the risk of establishment. [ABSTRACT FROM AUTHOR]

Background: Heart rate is one of the most crucial vital signs and can be measured remotely using microwave Doppler radar. As the distance between the body and the Doppler radar sensor increases, the output signal weakens, making it difficult to extract heartbeat waveforms. In this study, we propose a new template-matching method that addresses this issue by simulating Doppler radar signals. This method extracts the heartbeat waveform with higher accuracy while the participant is naturally sitting in a chair. Methods: An extended triangular wave model was created as a mathematical representation of cardiac physiology, taking into account heart movements. The Doppler radar output signal was then simulated based on this model to automatically obtain a template for one cycle. The validity of the proposed method was confirmed by calculating the PPIs using the template and comparing their accuracy to the R-R intervals (RRIs) of the electrocardiogram for five participants and by analyzing the signals of eight participants in their natural state using the mathematical model of heart movements. All measurements were conducted from a distance of 500 mm. Results: The correlation coefficients between the RRIs of the electrocardiogram and the PPIs using the proposed method were examined for five participants. The correlation coefficients were 0.93 without breathing and 0.70 with breathing. This demonstrates a higher correlation considering the long distance of 500 mm, and the fact that body movements were not specifically restricted, suggesting that the proposed method can successfully estimate RRI. The average correlation coefficients, calculated between the Doppler output signals and the templates for each of the eight participants, exceeded 0.95. Overall, the proposed method showed higher correlation coefficients than those reported in previous studies, indicating that our method performed well in extracting heartbeat waveforms. Conclusions: Our results indicate that the proposed method of remote heart monitoring using microwave Doppler radar demonstrates higher accuracy in estimating the RRI of the electrocardiogram while at rest sitting in a chair, and the ability to extract the heartbeat waveforms from the measured Doppler output signal, eliminating the need to create templates in advance as required by conventional template matching methods. This approach offers more flexibility in the measurement environment than conventional methods. [ABSTRACT FROM AUTHOR]

The selection of different landslide susceptibility evaluation models will result in differentiated spatial prediction results, and selecting the optimal model is an effective method to improve the accuracy of landslide spatial prediction. Taking the Chaya County landslide in Tibet as the research object, 8 evaluation factors from 3 categories were selected. Based on the single model evaluation using certainty factor (CF), frequency ratio (FR), information value (I), and weight-of-evidence (WoE), the evaluation results of the four single models were fused using normalization fusion and principal component analysis (PCA) fusion methods to obtain 6 landslide susceptibility zoning maps in the study area. The research results show that the frequency ratio values of the 6 models show a significant increasing trend from low susceptibility areas to extremely high susceptibility areas. The sum of frequency ratio values in extremely high and high susceptibility level zones exceeds 97% of the total frequency ratio value, effectively evaluating the susceptibility of landslides in the study area. By constructing receiver operating characteristics (ROC) curves to analyze the effectiveness of the evaluation models, it is shown that the PCA fusion model, evidence weight model, and information value model have high area under curve (AUC). Over-all, the PCA fusion model performs better when considering the results of frequency ratio in high and extremely high susceptibility zones. The study fills a gap in the comparative study of multiple models in the Tibetan Plateau mountainous area and provides a scientific basis for landslide prediction and prevention in the region. [ABSTRACT FROM AUTHOR]

It is important to examine and comprehend how HIV interacts with the immune system in order to manage the infection, enhance patient outcomes, advance medical research, and support global health and socioeconomic stability. In this study, we formulate the dynamics of HIV infection to investigate the intricate interactions between HIV and T-cells. The Atangana-Baleanu and Caputo-Fabrizio derivative frameworks are applied to comprehensively examine the phenomenon of HIV viral transmission. The basic concepts and results of fractional calculus are presented for the analysis of the model. In our work, we focus on the dynamical behavior of HIV and immune system. We introduce numerical schemes to elucidate the solution pathways of the recommended system of HIV. We have shown the influence of various input factors on the solution pathways of the recommended fractional system and highlighted the oscillatory behavior and chaotic nature of the dynamics. Our findings demonstrate the complexity of the system under study by revealing the existence of the chaotic and oscillatory nature in the dynamics of HIV. In order to quantitatively characterize HIV dynamics, a number of simulations are carried out, providing a visual representation of the effects of different input variables. It has been observed that the chaos and the oscillatory behaviour is strongly related to the nonlinearity of the system. The present study provides a basis for further initiatives that try to enhance interventions and policies to lessen the worldwide burden of infection. [ABSTRACT FROM AUTHOR]

Phenological mismatch has been highlighted as a reason why climate change is causing declines of migratory populations. The likelihood of declines due to phenological mismatch might depend on what cues trigger migration. Migrants that use environmental cues (e.g. temperature, resource availability) to trigger migration are often considered to be less vulnerable than migrants that use temporal information (e.g. photoperiod). We developed a proof‐of‐concept model that demonstrates that which cue type performs better in the context of phenological change can depend on differences in seasonal amplitude between the habitats used by a migrant. Environmental cues perform better than temporal cues when the habitat that undergoes a phenological change has a larger seasonal amplitude. This result aligns with observations that populations of short‐distance migrants that use environmental cues are less likely to decline as a consequence of phenological mismatch than long‐distance avian migrants that use temporal cues. Temporal cues perform better than environmental cues when the habitat that undergoes a phenological change has a smaller seasonal amplitude. This result may correspond to empirical scenarios where the more seasonal habitat is associated with variation in precipitation patterns or human actions that are not changing in phenology. In addition to these results, we offer distinctions that will help clarify future work on phenological mismatch. First, we highlight the difference between the cue accuracy (difference between the timing of migration using the cue and optimal migration timing) and the cue efficacy (the difference between the fitness using the cue and the fitness using optimal migration). Second, we recommend considering both how the benefits available from migrating and the benefits that are captured by migrants change with phenological change. [ABSTRACT FROM AUTHOR]

The article provides a theoretical investigation of the laminar film-condensation of shear-thinning fluids onto an isothermal, vertical plate in the presence of gravity, interfacial shear, wall friction, and inertia. The liquid motion occurs toward gravity, overcoming the resistances of interfacial shear, wall friction, and inertia. The liquid motion induces momentum to the adjacent stagnant saturated vapor by interfacial shear. The vapor motion, in turn, influences the liquid film's heat transfer and fluid dynamics. For film condensation, it is well-known that the film, along the length of the plate, can be grouped in two separate heat transfer regimes, viz. conduction-dominated regime and convection-dominated regime. For the first time, we have identified three distinct fluid dynamic regions across the film (viz. R1, R2, and R3) unique to power-law fluids. R1 is bounded between the condensing surface and the locus of Newtonian shear stress. R2 is bounded between the locus of Newtonian shear stress and the locus of zero shear stress. Beyond R2, R3 is stretched up to the liquid-vapor interface. The transverse temperature gradient is subtly different in these three fluid dynamic regions. We examine flow physics on a non-dimensional platform. The critical role of the power-law index in determining wall-friction and condensate's mass flow rate and the impact of liquid Prandtl number in achieving the degree of subcooling has been nicely illustrated. We expose various limiting conditions for simplifying the robust mathematical theory. An analytical expression for the liquid's longitudinal velocity has been derived, neglecting inertia and interfacial shear. [ABSTRACT FROM AUTHOR]

To accurately characterize the geometric features in the repair of Ti-6Al-4 V alloy, a laser cladding mathematical model was developed and experimentally validated. The model employed a quartic polynomial function to analyze the geometric features of the clad layer, investigating correlations among deposition angle, clad layer width, melt pool depth, and clad layer area. Additionally, it utilized a quadratic polynomial function to characterize the geometric profile of the melt pool, establishing relationships involving clad layer width, melt pool depth, and melt pool area simultaneously. By means of the areas of the cladding layer and the melt pool, the value of the dilution rate can be obtained. Subsequently, the measured and predicted values of the clad layer, melt pool, and dilution rate were compared. The results demonstrated the mathematical model's capability to accurately forecast geometric features in laser cladding. Furthermore, an orthogonal experiment was conducted to investigate how process parameters—laser power, scanning speed, and powder feeding rate—affect the geometric dimensions (height, width, and melt pool depth) of single-pass, single-layer cladding, and to elucidate the underlying reasons. These investigations offered theoretical insights and practical guidelines for controlling the clad layer, melt pool, and dilution rate. [ABSTRACT FROM AUTHOR]

In this paper, the accelerated creep under uniaxial tension of hot fine-grained dense asphalt concrete at temperatures of 22–24 °C and stresses from 0.084 MPa to 0.596 MPa is experimentally investigated. The names and brief descriptions of the creep curve and accelerated creep characteristics are given. A mathematical model is proposed that has physical meaning and satisfactorily approximates the asphalt concrete accelerated creep. The model parameters are determined by the Levenberg–Marquardt method. The deformation and time characteristics of the accelerated creep of asphalt concrete are established and analyzed. [ABSTRACT FROM AUTHOR]

In rotating machinery, the condition of rolling bearings is paramount, directly influencing operational integrity. However, the literature on the fault evolution of rolling bearings in their nascent stages is notably limited. Addressing this gap, our study establishes an innovative nonlinear dynamic model for early fault evolution of rolling bearings based on collision impact. Firstly, considering the fault evolution characteristics, the influence of the rolling element and fault structure, the dynamic model of early fault evolution between the rolling element and the local fault is established. Secondly, according to the Hertzian contact deformation theory, a nonlinear dynamic model of rolling bearings expressed as mass-spring is established. Thirdly, the energy contribution method is used to integrate the fault evolution model and the nonlinear dynamic model of the rolling bearing. A nonlinear dynamic model of early fault evolution of the rolling bearing is proposed by using the Lagrangian equation. Comparing the simulation results of the nonlinear dynamic with the experimental results, it can be seen that the numerical model can effectively predict the evolution process and vibration characteristics of the fault evolution of rolling bearings in the early stage. [ABSTRACT FROM AUTHOR]

AbstractThis study focuses on developing an innovative device for isolating and managing exhaust gases from diesel locomotive engines, specifically aiming to reduce environmental impact and enhance operational safety. The study used experimental analysis, validated results using Cochrane and Fisher criteria, and conducted empirical data analysis. Study utilized an experimental stand with a 1.9-liter Volkswagen diesel engine, ZIL-130 compressor, custom exhaust gas storage system with tanks, thermometers, pressure gauges, and control valves. The study developed a mathematical model analysing input parameters and system outputs, achieving 95% accuracy, proving its reliability in representing exhaust gas dynamics of TEM2 diesel locomotives. [ABSTRACT FROM AUTHOR]

Background: Airway pressure release ventilation (APRV) has been shown to be protective against atelectrauma if expirations are brief. We hypothesize that this is protective because epithelial surfaces are not given enough time to come together and adhere during expiration, thereby avoiding their highly damaging forced separation during inspiration. Methods: We investigated this hypothesis in a porcine model of ARDS induced by Tween lavage. Animals were ventilated with APRV in 4 groups based on whether inspiratory pressure was 28 or 40 cmH2O, and whether expiration was terminated when end-expiratory flow reached either 75% (a shorter expiration) or 25% (a longer expiration) of its initial peak value. A mathematical model of respiratory system mechanics that included a volume-dependent elastance term characterized by the parameter E 2 was fit to airway pressure-flow data obtained each hour for 6 h post-Tween injury during both expiration and inspiration. We also measured respiratory system impedance between 5 and 19 Hz continuously through inspiration at the same time points from which we derived a time-course for respiratory system resistance ( R rs ). Results: E 2 during both expiration and inspiration was significantly different between the two longer expiration versus the two shorter expiration groups (ANOVA, p < 0.001). We found that E 2 was most depressed during inspiration in the higher-pressure group receiving the longer expiration, suggesting that E 2 reflects a balance between strain stiffening of the lung parenchyma and ongoing recruitment as lung volume increases. We also found in this group that R rs increased progressively during the first 0.5 s of inspiration and then began to decrease again as inspiration continued, which we interpret as corresponding to the point when continuing derecruitment was reversed by progressive lung inflation. Conclusions: These findings support the hypothesis that sufficiently short expiratory durations protect against atelectrauma because they do not give derecruitment enough time to manifest. This suggests a means for the personalized adjustment of mechanical ventilation. [ABSTRACT FROM AUTHOR]

Background: The pharmacodynamics of propofol in children have previously been described with the proprietary bispectral index (BIS) as an effect‐site marker, and it has been suggested that the rate of onset of propofol might be age dependent, that is, a shorter time to peak effect in younger children. However, these analyses were potentially confounded by co‐administered drugs, in particular opioids and benzodiazepines. Thus, the goal of this prospective study was to characterize the influence of age and weight on the onset of hypnotic effects from propofol, reflected by the time to peak of propofol effect‐site concentration in the absence of additional drugs. Methods: A total of 46 healthy children aged 2–12 years presenting for elective surgery were included in our observational cohort study. Solely propofol was administered via a target‐controlled infusion pump programmed with the Paedfusor pharmacokinetic model. The BIS and infusion pump data were recorded. The effect of an induction "bolus" was recorded having stopped the pump once a propofol plasma target concentration of 7 μg.mL−1 was achieved. A direct‐response and an indirect‐response model in the context of nonlinear mixed‐effects modeling was used to characterize and compare BIS data in children aged 2–6 years and older children aged 8–12 years. Results: Time to peak of propofol effect‐site concentration had a difference (p‐value <.01) for age and weight, that is 84 [74, 96] (median [IQR] secs for children aged 2–6 years vs. 99 [91, 113] secs for children aged 8–12 years and 82 [71, 95] secs for weight 11–25 kg vs. 99 [91, 114] secs for weight 30–63 kg). The plasma effect‐site equilibration rate constant for propofol had a heterogeneous distribution with a median of 2.36 (IQR: 2.05–2.93; range: 0.83–7.31) per minute but showed a weight‐dependent effect in patients with weight below 45 kg. Conclusions: In children, the age and weight have an influence on time to peak effect of propofol. In the absence of opioids and benzodiazepines, time to peak effect was approximately 20% longer in children aged 8–12 years as compared to younger children. Such clinically relevant age and weight effects are an important consideration in the individualized titration of propofol dosing. [ABSTRACT FROM AUTHOR]

Aiming at the problem that the time varying unbalanced centrifugal force due to the time varying chip mass caused the regenerated chatter on the machined surface during the milling of magnetic levitation electric spindle, the stability of the milling system was predicted by constructing the stability lobe diagram. Firstly, by analyzing and establishing the mathematical models of dynamic milling force, time varying unbalanced centrifugal force and active magnetic bearing electromagnetic force, the dynamic model of magnetic levitation electric spindle milling system was established. Then, the stability profile of milling system was obtained by full discretization method. Finally, the cutting stability of the system was analyzed using MATLAB numerical calculation platform, and the influence of time varying mass characteristics and magnetic bearing electromagnetic force on the cutting stability of the system was obtained. The research results indicate that the limit axial cutting depth of the time varying system is respectively decreased by 0. 005 mm, 0. 010 mm, 0. 022 mm and 0. 033 mm, comparing with the constant system at lobe 1, lobe 2, lobe 3 and lobe 4, indicating that the time varying unbalanced centrifugal force can reduce the cutting stability of the system, and the higher the spindle speed, the greater the effect. When the force displacement stiffness of the magnetic levitation bearings is kq = - 2 × 10 5 N/ m, kq = - 2 × 10 6 N/ m, kq = - 2 × 10 7 N/ m, the ultimate axial cutting depth of the system is respectively 0. 37 mm, 0. 55 mm, 1. 45 mm, indicating that increasing the force displacement stiffness of the magnetic bearing can enhance the cutting stability of the system [ABSTRACT FROM AUTHOR]

Contemporary customers have increasingly heightened demands regarding their dietary preferences, favoring readily available and healthful ready-to-consume food and beverage alternatives. In order to fulfill this demand, the beverage industry has been exploring innovative products. Red beetroot juice (RBJ) is easily consumed and offers a beneficial advantage due to its betalain content. Both the traditional/spontaneous method and the industrial method are viable options for producing RBJ. The aim of this study was to examine the stability of betalains, the primary bioactive component in RBJ, throughout the fermentation process and during storage. The RBJ samples contained betalain pigments, as indicated by the infrared spectra. No decrease in betalain content was observed in either RBJ juice fermented by two different methods. The total betalain content of the RBJ samples was 594.068 and 535.152 mg/L at the beginning of fermentation through the spontaneous method and the method with the addition of Lacticaseibacillus paracasei 431 (Lc. paracasei), respectively, and 580.151 mg/L and 667.382 mg/L at the conclusion of fermentation, respectively. Mathematical models were employed to represent the degradation of betalains over time during storage. It was found that the sigmoidal model (R2 = 0.974) and other models (R2 = 0.957–0.969) demonstrated a greater potential to describe the degradation of betalains in RBJ samples produced by the spontaneous method compared to the first-order kinetics model (R2 = 0.932). The models used in the study were successful, with R2 values ranging between 0.927 and 0.932 in the RBJ samples produced with the addition of the probiotic Lc. paracasei for predicting betalain degradation. [ABSTRACT FROM AUTHOR]

Algal blooms pose a significant threat to the ecological integrity and biodiversity in aquatic ecosystems. In lakes, enriched with nutrients, these blooms result in overgrowth of periphyton, leading to biological clogging, oxygen depletion, and ultimately a decline in ecosystem's health and water quality. In this article, we presented a mathematical model centered around the role of aquatic species (specifically fish population) to alleviate algal blooms. The model analysis revealed significant shifts in dynamics, shedding light on the effectiveness of fish-mediated sustainability strategies to control algal proliferation. Notably, our study identified critical thresholds and regime transitions through the observation of saddle-node bifurcation within the proposed mathematical model. To validate our analytical findings, we have conducted numerical simulations, which provided robust evidence for the resilience of the ecosystem under different scenarios. [ABSTRACT FROM AUTHOR]

Energy-related carbon dioxide ( CO 2 ) emissions have significantly contributed to the increase in atmospheric CO 2 concentrations. Curbing the carbon dioxide emissions associated with energy generation is crucial for reducing the radiative forcing of carbon dioxide and tackling the climate change issue. The use of renewable energy technologies is one of the most advocated avenues to reduce the carbon footprint of the energy sector. This study presents a mathematical model designed to analyze the influence of renewable energy technologies on the control of atmospheric CO 2 concentrations. The proposed model consists of a set of nonlinear differential equations that describe the dynamic interplay among the human population, carbon dioxide level, energy use, and renewable energy technologies. An extensive mathematical analysis of the model is presented to delve into the long-term impact of renewable energy technologies on the control of atmospheric CO 2 levels. The model's analysis reveals that increasing the adoption rate of renewable energy technologies and improving their efficiency in reducing carbon dioxide emissions contribute to a reduction in the equilibrium CO 2 levels in Earth's atmosphere. One of the primary challenges to the widespread implementation of renewable energy technologies is the associated implementation costs. This study identifies optimal control strategies for lowering CO 2 levels while simultaneously minimizing the expenses linked to the deployment of renewable energy technologies by employing optimal control theory. Furthermore, sensitivity analysis is conducted to illustrate how changes in key parameters affect the system's dynamics. Numerical simulations confirm the validity of the theoretical conclusions. [ABSTRACT FROM AUTHOR]

To facilitate a direct comparison of the differences in network resources among countries worldwide, this paper proposes a method for quantifying the relationship between autonomous systems and territorial networks from the perspective of network topology. Using global router-level network topology data as the foundational data for the network resources of various countries, we abstract the dual mapping information of router geographic distribution and operational ownership into a matrix-form mathematical model. By employing relevant indicators from both network scale and border connectivity, we compare matrix model data from different periods to quantitatively assess changes in the network structures of countries globally. The study results show that internet resources are concentrated in the United States, which owns 38.04% of the global routers, distributed across 87.88% of the countries, significantly impacting the global network. Compared to the average quantitative indicators of each country, 67.00% of the countries exhibit higher deployment consistency, 37.30% show higher border connection consistency, 23.81% perform prominently in terms of impact, and 46.20% have outstanding border node degrees. From a continental perspective, the analysis indicates that Asian and African countries have a closer relationship between AS and territorial networks, while Europe's connections are relatively sparse. Over time, we observe a slight decline in deployment consistency in Asia, Africa, and Europe, a slight increase in border connection consistency in Asia, Africa, and North America, and enhanced impact in Asia, Africa, Europe, and South America. These trends suggest that the integration between AS and territorial networks is intensifying in most countries. [ABSTRACT FROM AUTHOR]