It focuses on that students must be developed the ability to solve the practical problem by building the mathematics models and the ability to combine the theory with the practice. It also states that students must be...It focuses on that students must be developed the ability to solve the practical problem by building the mathematics models and the ability to combine the theory with the practice. It also states that students must be improved the learning interests and practical experience.展开更多
This study introduces an innovative computational framework leveraging the transformer architecture to address a critical challenge in chemical process engineering:predicting and optimizing light olefin yields in indu...This study introduces an innovative computational framework leveraging the transformer architecture to address a critical challenge in chemical process engineering:predicting and optimizing light olefin yields in industrial methanol-to-olefins(MTO)processes.Our approach integrates advanced machine learning techniques with chemical engineering principles to tackle the complexities of non-stationary,highly volatile production data in large-scale chemical manufacturing.The framework employs the maximal information coefficient(MIC)algorithm to analyze and select the significant variables from MTO process parameters,forming a robust dataset for model development.We implement a transformer-based time series forecasting model,enhanced through positional encoding and hyperparameter optimization,significantly improving predictive accuracy for ethylene and propylene yields.The model's interpretability is augmented by applying SHapley additive exPlanations(SHAP)to quantify and visualize the impact of reaction control variables on olefin yields,providing valuable insights for process optimization.Experimental results demonstrate that our model outperforms traditional statistical and machine learning methods in accuracy and interpretability,effectively handling nonlinear,non-stationary,highvolatility,and long-sequence data challenges in olefin yield prediction.This research contributes to chemical engineering by providing a novel computerized methodology for solving complex production optimization problems in the chemical industry,offering significant potential for enhancing decisionmaking in MTO system production control and fostering the intelligent transformation of manufacturing processes.展开更多
Improving the specific,technical,economic,and environmental characteristics of piston engines(ICE)operating on alternative gaseous fuels is a pressing task for the energy and mechanical engineering industries.The aim ...Improving the specific,technical,economic,and environmental characteristics of piston engines(ICE)operating on alternative gaseous fuels is a pressing task for the energy and mechanical engineering industries.The aim of the study was to optimize the parameters of the ICE working cycle after replacing the base fuel(propane-butane blend)with syngas from wood sawdust to improve its technical and economic performance based on mathematical modeling.The modeling results were verified through experimental studies(differences for key parameters did not exceed 4.0%).The object of the study was an electric generator based on a single-cylinder spark ignition engine with a power of 1 kW.The article describes the main approaches to creating a mathematical model of the engine working cycle,a test bench for modeling verification,physicochemical properties of the base fuel(propane-butane blend),and laboratory syngas.It was shown that replacing the fuel from a propane-butane blend to laboratory syngas caused a decrease in engine efficiency to 33%(the efficiency of the base ICE was 0.179 vs.the efficiency of 0.119 for the converted ICE for the 0.59 kW power mode).Engine efficiency was chosen as the key criterion for optimizing the working cycle.As a result of optimization,the efficiency of the converted syngas engine was 6.1%higher than that of the base engine running on the propane-butane blend,and the power drop did not exceed 8.0%.Thus,careful fine-tuning of the working cycle parameters allows increasing the technical and economic characteristics of the syngas engine to the level of ICEs running on traditional types of fuel.展开更多
The increasing demand due to development and advancement in every field of life has caused the depletion of fossil fuels.This depleting fossil fuel reserve throughout the world has enforced to get energy from alternat...The increasing demand due to development and advancement in every field of life has caused the depletion of fossil fuels.This depleting fossil fuel reserve throughout the world has enforced to get energy from alternative/renewable sources.One of the economicalways to get energy is through the utilization of solar ponds.In this study,a mathematical model of a salt gradient solar pond under the Islamabad climatic conditions has been analyzed for the first time.The model uses a one-dimensional finite difference explicit method for optimization of different zone thicknesses.The model depicts that NCZ(Non-Convective Zone)thickness has a significant effect on LCZ(Lower Convective Zone)temperature and should be kept less than 1.7mfor the optimal temperature.It is also observed that for long-termoperation of a solar pond,heat should be extracted by keeping the mass flowrate of 17.3 kg/m^(2)/day.Themodel also suggests that when the bottom reflectivity is about 0.3,then only 24%of the radiation is absorbed in the pond.展开更多
In this letter,we discuss the article by Li et al published in the World Journal of Gastrointestinal Surgery.Gallbladder cancer is a rare but fatal cancer that is often detected unexpectedly and at an advanced stage f...In this letter,we discuss the article by Li et al published in the World Journal of Gastrointestinal Surgery.Gallbladder cancer is a rare but fatal cancer that is often detected unexpectedly and at an advanced stage following routine cholecystectomy.Although the prognosis is poor,curative resections often combined with postoperative chemotherapy and/or radiation therapy can improve survival.However,targeted patient selection for the appropriate therapeutic approach is critical to minimize unnecessary morbidity.Using advanced statistical techniques,the authors developed a nomogram with the potential to predict survival after gallbladder cancer resection,identifying factors associated with long-and shortterm survival.This tool could improve patient selection for surgery and postoperative treatment.In this letter,we provide background on survival nomograms including an in-depth discussion of statistical methods employed in this study,the use of nomograms in other forms of cancer,limitations to the model,and directions for future research.展开更多
Malaria is a significant global health challenge.This devastating disease continues to affect millions,especially in tropical regions.It is caused by Plasmodium parasites transmitted by female Anopheles mosquitoes.Thi...Malaria is a significant global health challenge.This devastating disease continues to affect millions,especially in tropical regions.It is caused by Plasmodium parasites transmitted by female Anopheles mosquitoes.This study introduces a nonlinear mathematical model for examining the transmission dynamics of malaria,incorporating both human and mosquito populations.We aim to identify the key factors driving the endemic spread of malaria,determine feasible solutions,and provide insights that lead to the development of effective prevention and management strategies.We derive the basic reproductive number employing the next-generation matrix approach and identify the disease-free and endemic equilibrium points.Stability analyses indicate that the disease-free equilibrium is locally and globally stable when the reproductive number is below one,whereas an endemic equilibrium persists when this threshold is exceeded.Sensitivity analysis identifies the most influential mosquito-related parameters,particularly the bite rate and mosquito mortality,in controlling the spread of malaria.Furthermore,we extend our model to include a treatment compartment and three disease-preventive control variables such as antimalaria drug treatments,use of larvicides,and the use of insecticide-treated mosquito nets for optimal control analysis.The results show that optimal use of mosquito nets,use of larvicides for mosquito population control,and treatment can lower the basic reproduction number and control malaria transmission with minimal intervention costs.The analysis of disease control strategies and findings offers valuable information for policymakers in designing cost-effective strategies to combat malaria.展开更多
Pipeline Inspection Gauge(pig)is an important equipment for oil and gas pipelines during different stages of their operations to perform functions such as dewatering,cleaning,and inspection.Owing to the hyperelasticit...Pipeline Inspection Gauge(pig)is an important equipment for oil and gas pipelines during different stages of their operations to perform functions such as dewatering,cleaning,and inspection.Owing to the hyperelasticity,time and temperature-dependent material behaviour of the sealing disc attached on the pig,the contact between the pig and the pipeline expresses complex behaviour,leading to an uncertainty in the prediction of the pig's frictional force.Knowing the deformation of the sealing discs well is essential and can be highly meaningful for predicting the pig motion,as well as reducing the pigging risks.In this study,the geometrical deformation of the sealing discs with different sizes are investigated through experiments and numerical simulations.The effects of the four nondimensionalized parameters(interference,thickness per pipeline inner diameter,and clamping ratio)of the sealing discs on the deformation behaviour were observed and discussed,and an improved mathematical model for predicting the geometrical deformation of the sealing discs was proposed and verified.With the auxiliary angleαadded in the improved mathematical model,the relative error declines to 1.87%and 3.18%respectively for predicting deformation of the sealing discs in size of 2-inch and 40-inch pig.The results of this study can help better understand the frictional force of a pig with sealing discs,as well as its motion.展开更多
Chikungunya is a mosquito-borne viral infection caused by the chikungunya virus(CHIKV).It is characterized by acute onset of high fever,severe polyarthralgia,myalgia,headache,and maculopapular rash.The virus is rapidl...Chikungunya is a mosquito-borne viral infection caused by the chikungunya virus(CHIKV).It is characterized by acute onset of high fever,severe polyarthralgia,myalgia,headache,and maculopapular rash.The virus is rapidly spreading and may establish in new regions where competent mosquito vectors are present.This research analyzes the regulatory dynamics of a stochastic differential equation(SDE)model describing the transmission of the CHIKV,incorporating seasonal variations,immunization efforts,and environmentalffuctuations modeled through Poisson random measure noise under demographic heterogeneity.The model guarantees the existence of a global positive solution and demonstrates periodic dynamics driven by environmental factors.A key contribution of this study is the formulation of a stochastic threshold parameter,R0L,which characterizes the conditions for disease persistence or extinction under random environmental inffuences.Although our analysis highlights age-speciffc heterogeneities to illustrate differential transmission risks,the framework is general and can incorporate other vulnerable demographic groups,ensuring broader applicability of the results.Using the Monte Carlo Markov Chain(MCMC)method,we estimate R0L=1.4978(95%C-I:1.4968–1.5823)based on CHIKV data from Florida,USA,spanning 2005 to 2017,suggesting that the outbreak remains active and requires targeted control strategies.The effectiveness of immunization,screening,and treatment strategies varies depending on the prioritized demographic groups,due to substantial differences in CHIKV incidence across age categories in the USA.Numerical simulations were conducted using the truncated Euler–Maruyama method to robustly capture the stochastic dynamics of CHIKV transmission with Poissondriven jumps.Employing an iterative approach and assuming mild convexity conditions,we formulated and solved a parameterized near-optimality problem using the Ekeland variational principle.Ourffndings indicate that vaccination campaigns are signiffcantly more effective when focused on vulnerable adults over the age of 66,as well as individuals aged 21 to 25.Furthermore,enhancements in vaccine effcacy,diagnostic screening,and treatment protocols all contribute substantially to minimizing infection rates compared to current standard approaches.These insights support the development of targeted,age-speciffc public health interventions that can signiffcantly improve the management and control of future CHIKV outbreaks.展开更多
A mathematical model of the decarburization reaction zone was established for the Ruhrstahl–Heraeus (RH) forced oxygen blowing decarburization process by Matlab R2022b software. For the problem of inaccurate predicti...A mathematical model of the decarburization reaction zone was established for the Ruhrstahl–Heraeus (RH) forced oxygen blowing decarburization process by Matlab R2022b software. For the problem of inaccurate prediction due to the large variation range of oxygen absorption rate under different process conditions, we statistically analyzed the main factors affecting the oxygen absorption rate. The backpropagation neural network was used to train and predict the oxygen absorption rate and was used to calculate the RH decarburization reaction zone model. We designed and developed a mathematical modeling software with process control of decarburization in RH degasser, which can realize the change of operating process parameters in the dynamic prediction process. The optimized mathematical model has more than 95% of the furnaces whose absolute error in calculation of carbon content is within ± 5 × 10^(−6), more than 90% of the heats whose relative error in calculation of oxygen content is within ± 15%, and the average absolute error of calculation of oxygen content is 26.4 × 10^(−6). Finally, we studied the influence of oxygen blowing timing, oxygen blowing volume and initial oxygen content on the forced decarburization process.展开更多
In order to help athletes optimize their performances in competitions while prevent overtraining and the risk of overuse injuries,it is important to develop science-based strategies for optimally designing training pr...In order to help athletes optimize their performances in competitions while prevent overtraining and the risk of overuse injuries,it is important to develop science-based strategies for optimally designing training programs.The purpose of the present study is to develop a novel method by the combined use of optimal control theory and a training-performance model for designing optimal training programs,with the hope of helping athletes achieve the best performance exactly on the competition day while properly manage training load during the training course for preventing overtraining.The training-performance model used in the proposed optimal control framework is a conceptual extension of the Banister impulse-response model that describes the dynamics of performance,training load(served as the control variable),fitness(the overall positive effects on performance),and fatigue(the overall negative effects on performance).The objective functional of the proposed optimal control framework is to maximize the fitness and minimize the fatigue on the competition day with the goal of maximizing the performance on the competition day while minimizing the cumulative training load during the training course.The Forward-Backward Sweep Method is used to solve the proposed optimal control framework to obtain the optimal solutions of performance,training load,fitness,and fatigue.The simulation results show that the performance on the competition day is higher while the cumulative training load during the training course is lower with using optimal control theory than those without,successfully showing the feasibility and benefits of using the proposed optimal control framework to design optimal training programs for helping athletes achieve the best performance exactly on the competition day while properly manage training load during the training course for preventing overtraining.The present feasibility study lays the foundation of the combined use of optimal control theory and training-performance models to design personalized optimal training programs in real applications in athletic training and sports science for helping athletes achieve the best performances in competitions while prevent overtraining and the risk of overuse injuries.展开更多
The work considers the problem of gas hydrate dissociation in a porous medium using the two-term Forchheimer law,corresponding to high flow rates of reservoir fluids.Such rates can arise during the decomposition of ga...The work considers the problem of gas hydrate dissociation in a porous medium using the two-term Forchheimer law,corresponding to high flow rates of reservoir fluids.Such rates can arise during the decomposition of gas hydrates,since a large amount of gas is released.Intensive emissions of gases from the earth’s interior are observed on the ocean floor.They are also associated with a large number of subvertical geological structures under the ocean floor,coming to the surface in the formof local ring funnels(pockmarks).Many similar objects have also been found on land.Particular interest in this problemis caused by climate threats associated with the release of greenhouse gases.The movement of gas released fromthe hydrate to the breakthrough channel is similar to the gas inflow to the well(without hydrate),which is usually described by a two-term filtration law.In this work,a mathematical model of gas hydrate dissociation with a nonlinear Forchheimer-type law ofmotion is developed.The systemis split in two blocks by physical processes,taking into account the quadratic correction to the velocity in the filtration law.The first block is responsible for the convective transfer of saturation parameters in the model,water,gas and hydrate saturations are taken into account.The second block corresponds to the equation of dissipative piezoconductivity with a different number of thermodynamic degrees of freedom,taking into account heat and mass transfer in a porous medium.The performed splitting allows using explicit-implicit difference schemes when solving problems and avoiding strong refinement of the step in time and space.For numerical modeling,the support operator method is used,which makes it possible to discretize partial differential equations on irregular grids,which allows taking into account the complex geometry and lithology of the reservoir.A difference scheme based on the support operator method is developed,which,due to the mutually consistent approximation of vector analysis operations(divergence and gradient),allows to take into account the various flux laws between adjacent grid cells,including quadratic corrections to the velocity.Based on the developed numerical algorithms and their program implementations,calculations of gas hydrate dissociation are performed both in a reservoir of simple geometric structure and in a heterogeneous reservoir of complex configuration.The results obtained correspond to the physics of the processes under consideration.展开更多
Spillover of trypanosomiasis parasites from wildlife to domestic livestock and humans remains a major challenge world over.With the disease targeted for elimination by 2030,assessing the impact of control strategies i...Spillover of trypanosomiasis parasites from wildlife to domestic livestock and humans remains a major challenge world over.With the disease targeted for elimination by 2030,assessing the impact of control strategies in communities where there are human-cattle-wildlife interactions is therefore essential.A compartmental framework incorporating tsetse flies,humans,cattle,wildlife and various disease control strategies is developed and analyzed.The reproduction is derived and its sensitivity to different model parameters is investigated.Meanwhile,the optimal control theory is used to identify a combination of control strategies capable of minimizing the infected human and cattle population over time at minimal costs of implementation.The results indicates that tsetse fly mortality rate is strongly and negatively correlated to the reproduction number.It is also established that tsetse fly feeding rate in strongly and positively correlated to the reproduction number.Simulation results indicates that time dependent control strategies can significantly reduce the infections.Overall,the study shows that screening and treatment of humans may not lead to disease elimination.Combining this strategy with other strategies such as screening and treatment of cattle and vector control strategies will result in maximum reduction of tsetse fly population and disease elimination.展开更多
Recent trends suggest that Chinese herbal medicine formulas(CHM formulas)are promising treatments for complex diseases.To characterize the precise syndromes,precise diseases and precise targets of the precise targets ...Recent trends suggest that Chinese herbal medicine formulas(CHM formulas)are promising treatments for complex diseases.To characterize the precise syndromes,precise diseases and precise targets of the precise targets between complex diseases and CHM formulas,we developed an artificial intelligence-based quantitative predictive algorithm(DeepTCM).DeepTCM has gone through multilevel model calibration and validation against a comprehensive set of herb and disease data so that it accurately captures the complex cellular signaling,molecular and theoretical levels of traditional Chinese medicine(TCM).As an example,our model simulated the optimal CHM formulas for the treatment of coronary heart disease(CHD)with depression,and through model sensitivity analysis,we calculated the balanced scoring of the formulas.Furthermore,we constructed a biological knowledge graph representing interactions by associating herb-target and gene-disease interactions.Finally,we experimentally confirmed the therapeutic effect and pharmacological mechanism of a novel model-predicted intervention in humans and mice.This novel multiscale model opened up a new avenue to combine“disease syndrome”and“macro micro”system modeling to facilitate translational research in CHM formulas.展开更多
The soil freezing characteristic curve(SFCC)plays a fundamental role in comprehending thermohydraulic behavior and numerical simulation of frozen soil.This study proposes a dynamic model to uniformly express SFCCs ami...The soil freezing characteristic curve(SFCC)plays a fundamental role in comprehending thermohydraulic behavior and numerical simulation of frozen soil.This study proposes a dynamic model to uniformly express SFCCs amidst varying total water contents throughout the freezing-thawing process.Firstly,a general model is proposed,wherein the unfrozen water content at arbitrary temperature is determined as the lesser of the current total water content and the reference value derived from saturated SFCC.The dynamic performance of this model is verified through test data.Subsequently,in accordance with electric double layer(EDL)theory,the theoretical residual and minimum temperatures in SFCC are calculated to be-14.5℃to-20℃for clay particles and-260℃,respectively.To ensure that the SFCC curve ends at minimum temperature,a correction function is introduced into the general model.Furthermore,a simplified dynamic model is proposed and investigated,necessitating only three parameters inherited from the general model.Additionally,both general and simplified models are evaluated based on a test database and proven to fit the test data exactly across the entire temperature range.Typical recommended parameter values for various types of soils are summarized.Overall,this study provides not only a theoretical basis for most empirical equations but also proposes a new and more general equation to describe the SFCC.展开更多
In this paper, we conduct research on the applications of advanced mathematics on the mathematical modeling and the inner connections with linear algebra and the probability statistics. Aiming at model in mathematical...In this paper, we conduct research on the applications of advanced mathematics on the mathematical modeling and the inner connections with linear algebra and the probability statistics. Aiming at model in mathematical modeling and solving and model of evaluation and promotion of the two links, put forward the ＂bystander＂ and ＂the authorities＂ this two characters, and points out that excellent mathematical modeling participants should have ＂from a bystander to the authorities＂ and ＂from the authorities to return to bystanders＂ two-way role transformation ability. Great situation in mathematics teaching, by means of the mathematical modeling formed in the development of the teachers, as well as the teaching thought, teaching experience and achievements, the onward march of mathematical experiment should be faster than mathematical modeling. Our research provides the new paradigm for the math development which will be meaningful.展开更多
The mathematical analysis enters the higher mathematics as the mathematics specialized student from the general elementary mathematics the initiation curriculum, its content and middle school mathematics still exist r...The mathematical analysis enters the higher mathematics as the mathematics specialized student from the general elementary mathematics the initiation curriculum, its content and middle school mathematics still exist relate very much, while it during the expansion knowledge as also has many transformations. Under this basis, this paper proposes the analysis of the mathematical modeling thought in college mathematics teaching. Mathematics modelling teaching uses the open style teaching method also to wait for consummates regards the concrete course content the main point, the function as carries on each kind of variant to the open style mathematics educational model enable this kind of pattern to have pointed. We propose the novel paradigm for the education that will then be essential for the further development of the systems, in the future, we will then apply more of the methodologies to enhance the current proposed model.展开更多
In the last forty years,the rise of HIV has undoubtedly become a major concern in the field of public health,imposing significant economic burdens on affected regions.Consequently,it becomes imperative to undertake co...In the last forty years,the rise of HIV has undoubtedly become a major concern in the field of public health,imposing significant economic burdens on affected regions.Consequently,it becomes imperative to undertake comprehensive investigations into the mechanisms governing the dissemination of HIV within the human body.In this work,we have devised a mathematical model that elucidates the intricate interplay between CD4^(+)T-cells and viruses of HIV,employing the principles of fractional calculus.The production rate of CD4^(+)T-cells,like other immune cells depends on certain factors such as age,health status,and the presence of infections or diseases.Therefore,we incorporate a variable source term in the dynamics of HIV infection with a saturated incidence rate to enhance the precision of our findings.We introduce the fundamental concepts of fractional operators as a means of scrutinizing the proposed HIV model.To facilitate a deeper understanding of our system,we present an iterative scheme that elucidates the trajectories of the solution pathways of the system.We show the time series analysis of our model through numerical findings to conceptualize and understand the key factors of the system.In addition to this,we present the phase portrait and the oscillatory behavior of the system with the variation of different input parameters.This information can be utilized to predict the long-term behavior of the system,including whether it will converge to a steady state or exhibit periodic or chaotic oscillations.展开更多
Drug resistance is one of the most intractable issues in targeted therapy for cancer diseases.It has also been demonstrated to be related to cancer heterogeneity,which promotes the emergence of treatment-refractory ca...Drug resistance is one of the most intractable issues in targeted therapy for cancer diseases.It has also been demonstrated to be related to cancer heterogeneity,which promotes the emergence of treatment-refractory cancer cell populations.Focusing on how cancer cells develop resistance during the encounter with targeted drugs and the immune system,we propose a mathematical model for studying the dynamics of drug resistance in a conjoint heterogeneous tumor-immune setting.We analyze the local geometric properties of the equilibria of the model.Numerical simulations show that the selectively targeted removal of sensitive cancer cells may cause the initially heterogeneous population to become a more resistant population.Moreover,the decline of immune recruitment is a stronger determinant of cancer escape from immune surveillance or targeted therapy than the decay in immune predation strength.Sensitivity analysis of model parameters provides insight into the roles of the immune system combined with targeted therapy in determining treatment outcomes.展开更多
The understanding of the gas-liquid flow characteristics in a micro-packed bed reactor is still immature,especially for many gas-organic working systems commonly used in industry.Accordingly,this study proposes a plat...The understanding of the gas-liquid flow characteristics in a micro-packed bed reactor is still immature,especially for many gas-organic working systems commonly used in industry.Accordingly,this study proposes a platform to investigate the gas-eliquid flow characteristics in a micro-packed bed reactor and presents a unified expression for these characteristics of both organic and aqueous liquid phase.The influence of two-phase flow rate,working solution viscosity,and packing particle size on the liquid holdup and pressure drop were studied.The gas-organic working systems results show that the liquid holdup ranges between 0.5 and 0.8 and pressure drop ranges from 50 to 350 kPa·m^(-1).In particular,a strong correlation between the two flow characteristics parameters(liquid holdup and pressure drop)was proposed for the first time.Finally,a general pressure drop mathematical prediction model in micropacked bed were developed.展开更多
The global populationhas beenandwill continue to be severely impacted by theCOVID-19 epidemic.The primary objective of this research is to demonstrate the future impact of COVID-19 on those who suffer from other fatal...The global populationhas beenandwill continue to be severely impacted by theCOVID-19 epidemic.The primary objective of this research is to demonstrate the future impact of COVID-19 on those who suffer from other fatal conditions such as cancer,heart disease,and diabetes.Here,using ordinary differential equations(ODEs),two mathematical models are developed to explain the association between COVID-19 and cancer and between COVID-19 and diabetes and heart disease.After that,we highlight the stability assessments that can be applied to these models.Sensitivity analysis is used to examine how changes in certain factors impact different aspects of disease.The sensitivity analysis showed that many people are still nervous about seeing a doctor due to COVID-19,which could result in a dramatic increase in the diagnosis of various ailments in the years to come.The correlation between diabetes and cardiovascular illness is also illustrated graphically.The effects of smoking and obesity are also found to be significant in disease compartments.Model fitting is also provided for interpreting the relationship between real data and the results of thiswork.Diabetic people,in particular,need tomonitor their health conditions closely and practice heart health maintenance.People with heart diseases should undergo regular checks so that they can protect themselves from diabetes and take some precautions including suitable diets.The main purpose of this study is to emphasize the importance of regular checks,to warn people about the effects of COVID-19(including avoiding healthcare centers and doctors because of the spread of infectious diseases)and to indicate the importance of family history of cancer,heart diseases and diabetes.The provision of the recommendations requires an increase in public consciousness.展开更多
文摘It focuses on that students must be developed the ability to solve the practical problem by building the mathematics models and the ability to combine the theory with the practice. It also states that students must be improved the learning interests and practical experience.
基金supported by the Humanities and Social Sciences Foundation of the Ministry of Education(22YJC910011)the China Postdoctoral Science Foundation(2023M733444)the Key Research and Development Program in Artificial Intelligence of Liaoning Province(2023JH26/10200012).
文摘This study introduces an innovative computational framework leveraging the transformer architecture to address a critical challenge in chemical process engineering:predicting and optimizing light olefin yields in industrial methanol-to-olefins(MTO)processes.Our approach integrates advanced machine learning techniques with chemical engineering principles to tackle the complexities of non-stationary,highly volatile production data in large-scale chemical manufacturing.The framework employs the maximal information coefficient(MIC)algorithm to analyze and select the significant variables from MTO process parameters,forming a robust dataset for model development.We implement a transformer-based time series forecasting model,enhanced through positional encoding and hyperparameter optimization,significantly improving predictive accuracy for ethylene and propylene yields.The model's interpretability is augmented by applying SHapley additive exPlanations(SHAP)to quantify and visualize the impact of reaction control variables on olefin yields,providing valuable insights for process optimization.Experimental results demonstrate that our model outperforms traditional statistical and machine learning methods in accuracy and interpretability,effectively handling nonlinear,non-stationary,highvolatility,and long-sequence data challenges in olefin yield prediction.This research contributes to chemical engineering by providing a novel computerized methodology for solving complex production optimization problems in the chemical industry,offering significant potential for enhancing decisionmaking in MTO system production control and fostering the intelligent transformation of manufacturing processes.
基金the Ministry of Science and Higher Education of the Russian Federation(Ural Federal University Program of Development within the Priority-2030 Program)is gratefully acknowledged.
文摘Improving the specific,technical,economic,and environmental characteristics of piston engines(ICE)operating on alternative gaseous fuels is a pressing task for the energy and mechanical engineering industries.The aim of the study was to optimize the parameters of the ICE working cycle after replacing the base fuel(propane-butane blend)with syngas from wood sawdust to improve its technical and economic performance based on mathematical modeling.The modeling results were verified through experimental studies(differences for key parameters did not exceed 4.0%).The object of the study was an electric generator based on a single-cylinder spark ignition engine with a power of 1 kW.The article describes the main approaches to creating a mathematical model of the engine working cycle,a test bench for modeling verification,physicochemical properties of the base fuel(propane-butane blend),and laboratory syngas.It was shown that replacing the fuel from a propane-butane blend to laboratory syngas caused a decrease in engine efficiency to 33%(the efficiency of the base ICE was 0.179 vs.the efficiency of 0.119 for the converted ICE for the 0.59 kW power mode).Engine efficiency was chosen as the key criterion for optimizing the working cycle.As a result of optimization,the efficiency of the converted syngas engine was 6.1%higher than that of the base engine running on the propane-butane blend,and the power drop did not exceed 8.0%.Thus,careful fine-tuning of the working cycle parameters allows increasing the technical and economic characteristics of the syngas engine to the level of ICEs running on traditional types of fuel.
文摘The increasing demand due to development and advancement in every field of life has caused the depletion of fossil fuels.This depleting fossil fuel reserve throughout the world has enforced to get energy from alternative/renewable sources.One of the economicalways to get energy is through the utilization of solar ponds.In this study,a mathematical model of a salt gradient solar pond under the Islamabad climatic conditions has been analyzed for the first time.The model uses a one-dimensional finite difference explicit method for optimization of different zone thicknesses.The model depicts that NCZ(Non-Convective Zone)thickness has a significant effect on LCZ(Lower Convective Zone)temperature and should be kept less than 1.7mfor the optimal temperature.It is also observed that for long-termoperation of a solar pond,heat should be extracted by keeping the mass flowrate of 17.3 kg/m^(2)/day.Themodel also suggests that when the bottom reflectivity is about 0.3,then only 24%of the radiation is absorbed in the pond.
文摘In this letter,we discuss the article by Li et al published in the World Journal of Gastrointestinal Surgery.Gallbladder cancer is a rare but fatal cancer that is often detected unexpectedly and at an advanced stage following routine cholecystectomy.Although the prognosis is poor,curative resections often combined with postoperative chemotherapy and/or radiation therapy can improve survival.However,targeted patient selection for the appropriate therapeutic approach is critical to minimize unnecessary morbidity.Using advanced statistical techniques,the authors developed a nomogram with the potential to predict survival after gallbladder cancer resection,identifying factors associated with long-and shortterm survival.This tool could improve patient selection for surgery and postoperative treatment.In this letter,we provide background on survival nomograms including an in-depth discussion of statistical methods employed in this study,the use of nomograms in other forms of cancer,limitations to the model,and directions for future research.
基金supported by the Deanship of Scientific Research,Vice Presidency for Graduate Studies and Scientific Research,King Faisal University,Saudi Arabia[Grant No.KFU252959].
文摘Malaria is a significant global health challenge.This devastating disease continues to affect millions,especially in tropical regions.It is caused by Plasmodium parasites transmitted by female Anopheles mosquitoes.This study introduces a nonlinear mathematical model for examining the transmission dynamics of malaria,incorporating both human and mosquito populations.We aim to identify the key factors driving the endemic spread of malaria,determine feasible solutions,and provide insights that lead to the development of effective prevention and management strategies.We derive the basic reproductive number employing the next-generation matrix approach and identify the disease-free and endemic equilibrium points.Stability analyses indicate that the disease-free equilibrium is locally and globally stable when the reproductive number is below one,whereas an endemic equilibrium persists when this threshold is exceeded.Sensitivity analysis identifies the most influential mosquito-related parameters,particularly the bite rate and mosquito mortality,in controlling the spread of malaria.Furthermore,we extend our model to include a treatment compartment and three disease-preventive control variables such as antimalaria drug treatments,use of larvicides,and the use of insecticide-treated mosquito nets for optimal control analysis.The results show that optimal use of mosquito nets,use of larvicides for mosquito population control,and treatment can lower the basic reproduction number and control malaria transmission with minimal intervention costs.The analysis of disease control strategies and findings offers valuable information for policymakers in designing cost-effective strategies to combat malaria.
基金supported by Key Technologies Research and Development Program(Grant No.SQ2022YFC2806103)and the National Natural Science Foundation of China(Grant No.51509259).
文摘Pipeline Inspection Gauge(pig)is an important equipment for oil and gas pipelines during different stages of their operations to perform functions such as dewatering,cleaning,and inspection.Owing to the hyperelasticity,time and temperature-dependent material behaviour of the sealing disc attached on the pig,the contact between the pig and the pipeline expresses complex behaviour,leading to an uncertainty in the prediction of the pig's frictional force.Knowing the deformation of the sealing discs well is essential and can be highly meaningful for predicting the pig motion,as well as reducing the pigging risks.In this study,the geometrical deformation of the sealing discs with different sizes are investigated through experiments and numerical simulations.The effects of the four nondimensionalized parameters(interference,thickness per pipeline inner diameter,and clamping ratio)of the sealing discs on the deformation behaviour were observed and discussed,and an improved mathematical model for predicting the geometrical deformation of the sealing discs was proposed and verified.With the auxiliary angleαadded in the improved mathematical model,the relative error declines to 1.87%and 3.18%respectively for predicting deformation of the sealing discs in size of 2-inch and 40-inch pig.The results of this study can help better understand the frictional force of a pig with sealing discs,as well as its motion.
基金Ongoing Research Funding program(ORF-2025-1404),King Saud University,Riyadh,Saudi Arabia。
文摘Chikungunya is a mosquito-borne viral infection caused by the chikungunya virus(CHIKV).It is characterized by acute onset of high fever,severe polyarthralgia,myalgia,headache,and maculopapular rash.The virus is rapidly spreading and may establish in new regions where competent mosquito vectors are present.This research analyzes the regulatory dynamics of a stochastic differential equation(SDE)model describing the transmission of the CHIKV,incorporating seasonal variations,immunization efforts,and environmentalffuctuations modeled through Poisson random measure noise under demographic heterogeneity.The model guarantees the existence of a global positive solution and demonstrates periodic dynamics driven by environmental factors.A key contribution of this study is the formulation of a stochastic threshold parameter,R0L,which characterizes the conditions for disease persistence or extinction under random environmental inffuences.Although our analysis highlights age-speciffc heterogeneities to illustrate differential transmission risks,the framework is general and can incorporate other vulnerable demographic groups,ensuring broader applicability of the results.Using the Monte Carlo Markov Chain(MCMC)method,we estimate R0L=1.4978(95%C-I:1.4968–1.5823)based on CHIKV data from Florida,USA,spanning 2005 to 2017,suggesting that the outbreak remains active and requires targeted control strategies.The effectiveness of immunization,screening,and treatment strategies varies depending on the prioritized demographic groups,due to substantial differences in CHIKV incidence across age categories in the USA.Numerical simulations were conducted using the truncated Euler–Maruyama method to robustly capture the stochastic dynamics of CHIKV transmission with Poissondriven jumps.Employing an iterative approach and assuming mild convexity conditions,we formulated and solved a parameterized near-optimality problem using the Ekeland variational principle.Ourffndings indicate that vaccination campaigns are signiffcantly more effective when focused on vulnerable adults over the age of 66,as well as individuals aged 21 to 25.Furthermore,enhancements in vaccine effcacy,diagnostic screening,and treatment protocols all contribute substantially to minimizing infection rates compared to current standard approaches.These insights support the development of targeted,age-speciffc public health interventions that can signiffcantly improve the management and control of future CHIKV outbreaks.
基金supported by the Central Government Guides Local Science and Technology Development Foundation(No.2023JH6/100100046)the Project funded by China Postdoctoral Science Foundation(No.2023M730230).
文摘A mathematical model of the decarburization reaction zone was established for the Ruhrstahl–Heraeus (RH) forced oxygen blowing decarburization process by Matlab R2022b software. For the problem of inaccurate prediction due to the large variation range of oxygen absorption rate under different process conditions, we statistically analyzed the main factors affecting the oxygen absorption rate. The backpropagation neural network was used to train and predict the oxygen absorption rate and was used to calculate the RH decarburization reaction zone model. We designed and developed a mathematical modeling software with process control of decarburization in RH degasser, which can realize the change of operating process parameters in the dynamic prediction process. The optimized mathematical model has more than 95% of the furnaces whose absolute error in calculation of carbon content is within ± 5 × 10^(−6), more than 90% of the heats whose relative error in calculation of oxygen content is within ± 15%, and the average absolute error of calculation of oxygen content is 26.4 × 10^(−6). Finally, we studied the influence of oxygen blowing timing, oxygen blowing volume and initial oxygen content on the forced decarburization process.
基金funded by the National Science and Technology Council,grant number NSTC 113-2221-E-002-136-.
文摘In order to help athletes optimize their performances in competitions while prevent overtraining and the risk of overuse injuries,it is important to develop science-based strategies for optimally designing training programs.The purpose of the present study is to develop a novel method by the combined use of optimal control theory and a training-performance model for designing optimal training programs,with the hope of helping athletes achieve the best performance exactly on the competition day while properly manage training load during the training course for preventing overtraining.The training-performance model used in the proposed optimal control framework is a conceptual extension of the Banister impulse-response model that describes the dynamics of performance,training load(served as the control variable),fitness(the overall positive effects on performance),and fatigue(the overall negative effects on performance).The objective functional of the proposed optimal control framework is to maximize the fitness and minimize the fatigue on the competition day with the goal of maximizing the performance on the competition day while minimizing the cumulative training load during the training course.The Forward-Backward Sweep Method is used to solve the proposed optimal control framework to obtain the optimal solutions of performance,training load,fitness,and fatigue.The simulation results show that the performance on the competition day is higher while the cumulative training load during the training course is lower with using optimal control theory than those without,successfully showing the feasibility and benefits of using the proposed optimal control framework to design optimal training programs for helping athletes achieve the best performance exactly on the competition day while properly manage training load during the training course for preventing overtraining.The present feasibility study lays the foundation of the combined use of optimal control theory and training-performance models to design personalized optimal training programs in real applications in athletic training and sports science for helping athletes achieve the best performances in competitions while prevent overtraining and the risk of overuse injuries.
基金the framework of the state assignment of Keldysh Institute of Applied Mathematics of RAS(Project No.125020701776-0)the Ministry of Education and Science of Russia for IO RAS(Project No.FMWE-2024-0018).
文摘The work considers the problem of gas hydrate dissociation in a porous medium using the two-term Forchheimer law,corresponding to high flow rates of reservoir fluids.Such rates can arise during the decomposition of gas hydrates,since a large amount of gas is released.Intensive emissions of gases from the earth’s interior are observed on the ocean floor.They are also associated with a large number of subvertical geological structures under the ocean floor,coming to the surface in the formof local ring funnels(pockmarks).Many similar objects have also been found on land.Particular interest in this problemis caused by climate threats associated with the release of greenhouse gases.The movement of gas released fromthe hydrate to the breakthrough channel is similar to the gas inflow to the well(without hydrate),which is usually described by a two-term filtration law.In this work,a mathematical model of gas hydrate dissociation with a nonlinear Forchheimer-type law ofmotion is developed.The systemis split in two blocks by physical processes,taking into account the quadratic correction to the velocity in the filtration law.The first block is responsible for the convective transfer of saturation parameters in the model,water,gas and hydrate saturations are taken into account.The second block corresponds to the equation of dissipative piezoconductivity with a different number of thermodynamic degrees of freedom,taking into account heat and mass transfer in a porous medium.The performed splitting allows using explicit-implicit difference schemes when solving problems and avoiding strong refinement of the step in time and space.For numerical modeling,the support operator method is used,which makes it possible to discretize partial differential equations on irregular grids,which allows taking into account the complex geometry and lithology of the reservoir.A difference scheme based on the support operator method is developed,which,due to the mutually consistent approximation of vector analysis operations(divergence and gradient),allows to take into account the various flux laws between adjacent grid cells,including quadratic corrections to the velocity.Based on the developed numerical algorithms and their program implementations,calculations of gas hydrate dissociation are performed both in a reservoir of simple geometric structure and in a heterogeneous reservoir of complex configuration.The results obtained correspond to the physics of the processes under consideration.
文摘Spillover of trypanosomiasis parasites from wildlife to domestic livestock and humans remains a major challenge world over.With the disease targeted for elimination by 2030,assessing the impact of control strategies in communities where there are human-cattle-wildlife interactions is therefore essential.A compartmental framework incorporating tsetse flies,humans,cattle,wildlife and various disease control strategies is developed and analyzed.The reproduction is derived and its sensitivity to different model parameters is investigated.Meanwhile,the optimal control theory is used to identify a combination of control strategies capable of minimizing the infected human and cattle population over time at minimal costs of implementation.The results indicates that tsetse fly mortality rate is strongly and negatively correlated to the reproduction number.It is also established that tsetse fly feeding rate in strongly and positively correlated to the reproduction number.Simulation results indicates that time dependent control strategies can significantly reduce the infections.Overall,the study shows that screening and treatment of humans may not lead to disease elimination.Combining this strategy with other strategies such as screening and treatment of cattle and vector control strategies will result in maximum reduction of tsetse fly population and disease elimination.
基金supported by the National Natural Science Foundation of China(Grant No.:82174246)the National Key R&D Program of China(Grant No.:2019YFC1708701)the Postdoctoral Innovation Talent Support Program(Grant No.:BX20220329).
文摘Recent trends suggest that Chinese herbal medicine formulas(CHM formulas)are promising treatments for complex diseases.To characterize the precise syndromes,precise diseases and precise targets of the precise targets between complex diseases and CHM formulas,we developed an artificial intelligence-based quantitative predictive algorithm(DeepTCM).DeepTCM has gone through multilevel model calibration and validation against a comprehensive set of herb and disease data so that it accurately captures the complex cellular signaling,molecular and theoretical levels of traditional Chinese medicine(TCM).As an example,our model simulated the optimal CHM formulas for the treatment of coronary heart disease(CHD)with depression,and through model sensitivity analysis,we calculated the balanced scoring of the formulas.Furthermore,we constructed a biological knowledge graph representing interactions by associating herb-target and gene-disease interactions.Finally,we experimentally confirmed the therapeutic effect and pharmacological mechanism of a novel model-predicted intervention in humans and mice.This novel multiscale model opened up a new avenue to combine“disease syndrome”and“macro micro”system modeling to facilitate translational research in CHM formulas.
基金supported by the National Natural Science Foundation of China(Grant No.51979002)the Fundamental Research Funds for the Central Universities(Grant No.2022YJS080).
文摘The soil freezing characteristic curve(SFCC)plays a fundamental role in comprehending thermohydraulic behavior and numerical simulation of frozen soil.This study proposes a dynamic model to uniformly express SFCCs amidst varying total water contents throughout the freezing-thawing process.Firstly,a general model is proposed,wherein the unfrozen water content at arbitrary temperature is determined as the lesser of the current total water content and the reference value derived from saturated SFCC.The dynamic performance of this model is verified through test data.Subsequently,in accordance with electric double layer(EDL)theory,the theoretical residual and minimum temperatures in SFCC are calculated to be-14.5℃to-20℃for clay particles and-260℃,respectively.To ensure that the SFCC curve ends at minimum temperature,a correction function is introduced into the general model.Furthermore,a simplified dynamic model is proposed and investigated,necessitating only three parameters inherited from the general model.Additionally,both general and simplified models are evaluated based on a test database and proven to fit the test data exactly across the entire temperature range.Typical recommended parameter values for various types of soils are summarized.Overall,this study provides not only a theoretical basis for most empirical equations but also proposes a new and more general equation to describe the SFCC.
文摘In this paper, we conduct research on the applications of advanced mathematics on the mathematical modeling and the inner connections with linear algebra and the probability statistics. Aiming at model in mathematical modeling and solving and model of evaluation and promotion of the two links, put forward the ＂bystander＂ and ＂the authorities＂ this two characters, and points out that excellent mathematical modeling participants should have ＂from a bystander to the authorities＂ and ＂from the authorities to return to bystanders＂ two-way role transformation ability. Great situation in mathematics teaching, by means of the mathematical modeling formed in the development of the teachers, as well as the teaching thought, teaching experience and achievements, the onward march of mathematical experiment should be faster than mathematical modeling. Our research provides the new paradigm for the math development which will be meaningful.
文摘The mathematical analysis enters the higher mathematics as the mathematics specialized student from the general elementary mathematics the initiation curriculum, its content and middle school mathematics still exist relate very much, while it during the expansion knowledge as also has many transformations. Under this basis, this paper proposes the analysis of the mathematical modeling thought in college mathematics teaching. Mathematics modelling teaching uses the open style teaching method also to wait for consummates regards the concrete course content the main point, the function as carries on each kind of variant to the open style mathematics educational model enable this kind of pattern to have pointed. We propose the novel paradigm for the education that will then be essential for the further development of the systems, in the future, we will then apply more of the methodologies to enhance the current proposed model.
文摘In the last forty years,the rise of HIV has undoubtedly become a major concern in the field of public health,imposing significant economic burdens on affected regions.Consequently,it becomes imperative to undertake comprehensive investigations into the mechanisms governing the dissemination of HIV within the human body.In this work,we have devised a mathematical model that elucidates the intricate interplay between CD4^(+)T-cells and viruses of HIV,employing the principles of fractional calculus.The production rate of CD4^(+)T-cells,like other immune cells depends on certain factors such as age,health status,and the presence of infections or diseases.Therefore,we incorporate a variable source term in the dynamics of HIV infection with a saturated incidence rate to enhance the precision of our findings.We introduce the fundamental concepts of fractional operators as a means of scrutinizing the proposed HIV model.To facilitate a deeper understanding of our system,we present an iterative scheme that elucidates the trajectories of the solution pathways of the system.We show the time series analysis of our model through numerical findings to conceptualize and understand the key factors of the system.In addition to this,we present the phase portrait and the oscillatory behavior of the system with the variation of different input parameters.This information can be utilized to predict the long-term behavior of the system,including whether it will converge to a steady state or exhibit periodic or chaotic oscillations.
基金supported by the National Natural Science Foundation of China(11871238,11931019,12371486)。
文摘Drug resistance is one of the most intractable issues in targeted therapy for cancer diseases.It has also been demonstrated to be related to cancer heterogeneity,which promotes the emergence of treatment-refractory cancer cell populations.Focusing on how cancer cells develop resistance during the encounter with targeted drugs and the immune system,we propose a mathematical model for studying the dynamics of drug resistance in a conjoint heterogeneous tumor-immune setting.We analyze the local geometric properties of the equilibria of the model.Numerical simulations show that the selectively targeted removal of sensitive cancer cells may cause the initially heterogeneous population to become a more resistant population.Moreover,the decline of immune recruitment is a stronger determinant of cancer escape from immune surveillance or targeted therapy than the decay in immune predation strength.Sensitivity analysis of model parameters provides insight into the roles of the immune system combined with targeted therapy in determining treatment outcomes.
基金financial support from the National Natural Science Foundation of China(21991104).
文摘The understanding of the gas-liquid flow characteristics in a micro-packed bed reactor is still immature,especially for many gas-organic working systems commonly used in industry.Accordingly,this study proposes a platform to investigate the gas-eliquid flow characteristics in a micro-packed bed reactor and presents a unified expression for these characteristics of both organic and aqueous liquid phase.The influence of two-phase flow rate,working solution viscosity,and packing particle size on the liquid holdup and pressure drop were studied.The gas-organic working systems results show that the liquid holdup ranges between 0.5 and 0.8 and pressure drop ranges from 50 to 350 kPa·m^(-1).In particular,a strong correlation between the two flow characteristics parameters(liquid holdup and pressure drop)was proposed for the first time.Finally,a general pressure drop mathematical prediction model in micropacked bed were developed.
文摘The global populationhas beenandwill continue to be severely impacted by theCOVID-19 epidemic.The primary objective of this research is to demonstrate the future impact of COVID-19 on those who suffer from other fatal conditions such as cancer,heart disease,and diabetes.Here,using ordinary differential equations(ODEs),two mathematical models are developed to explain the association between COVID-19 and cancer and between COVID-19 and diabetes and heart disease.After that,we highlight the stability assessments that can be applied to these models.Sensitivity analysis is used to examine how changes in certain factors impact different aspects of disease.The sensitivity analysis showed that many people are still nervous about seeing a doctor due to COVID-19,which could result in a dramatic increase in the diagnosis of various ailments in the years to come.The correlation between diabetes and cardiovascular illness is also illustrated graphically.The effects of smoking and obesity are also found to be significant in disease compartments.Model fitting is also provided for interpreting the relationship between real data and the results of thiswork.Diabetic people,in particular,need tomonitor their health conditions closely and practice heart health maintenance.People with heart diseases should undergo regular checks so that they can protect themselves from diabetes and take some precautions including suitable diets.The main purpose of this study is to emphasize the importance of regular checks,to warn people about the effects of COVID-19(including avoiding healthcare centers and doctors because of the spread of infectious diseases)and to indicate the importance of family history of cancer,heart diseases and diabetes.The provision of the recommendations requires an increase in public consciousness.
