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
Mathematical models of tire-lateral mad adhesion for use in mad vehicle dynamics studies are set up to express the relations of adhesion coefficients with slip ratio in lateral direction.The models of tire-lateral mad...Mathematical models of tire-lateral mad adhesion for use in mad vehicle dynamics studies are set up to express the relations of adhesion coefficients with slip ratio in lateral direction.The models of tire-lateral mad adhesion revolutionize the Pacejka's model in concept and therefore make it possible for applications in vehicle dynamics studies by the expression of lateral adhesion coefficient as a function of wheel slip ratio,instead of the wheel slip angle,taking into account in the mean time the influences of mad surface condition, vehicle velocity,vertical load,tire slip angle,and wheel camber angle.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
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
To address the sensitive and uncertain limitations of single-energy computed tomography(CT)calibration methods in computing proton stopping power ratio during treatment planning,different methods have been proposed us...To address the sensitive and uncertain limitations of single-energy computed tomography(CT)calibration methods in computing proton stopping power ratio during treatment planning,different methods have been proposed using a dual energy CT approach.This paper reviews the most recent dual-energy CT approaches for computing proton stopping power ratio.These include image domain and projection domain methods.The advantages and uncertainties of these methods are analyzed based on existing studies.This paper highlights recent advances in dual energy CT,discussing their implementation,advantages,limitations,and potential for clinical adoption.展开更多
Quantization noise caused by analog-to-digital converter(ADC)gives rise to the reliability performance degradation of communication systems.In this paper,a quantized non-Hermitian symmetry(NHS)orthogonal frequency-div...Quantization noise caused by analog-to-digital converter(ADC)gives rise to the reliability performance degradation of communication systems.In this paper,a quantized non-Hermitian symmetry(NHS)orthogonal frequency-division multiplexing-based visible light communication(OFDM-VLC)system is presented.In order to analyze the effect of the resolution of ADC on NHS OFDM-VLC,a quantized mathematical model of NHS OFDM-VLC is established.Based on the proposed quantized model,a closed-form bit error rate(BER)expression is derived.The theoretical analysis and simulation results both confirm the effectiveness of the obtained BER formula in high-resolution ADC.In addition,channel coding is helpful in compensating for the BER performance loss due to the utilization of lower resolution ADC.展开更多
G protein coupled receptor kinase 2 (GRK2) is a kinase that regulates cardiac signaling activity. Inhibiting GRK2 is a promising mechanism for the treatment of heart failure (HF). Further development and optimization ...G protein coupled receptor kinase 2 (GRK2) is a kinase that regulates cardiac signaling activity. Inhibiting GRK2 is a promising mechanism for the treatment of heart failure (HF). Further development and optimization of inhibitors targeting GRK2 are highly meaningful. Therefore, in order to design GRK2 inhibitors with better performance, the most active molecule was selected as a reference compound from a data set containing 4-pyridylhydrazone derivatives and triazole derivatives, and its scaffold was extracted as the initial scaffold. Then, a powerful optimization-based framework for de novo drug design, guided by binding affinity, was used to generate a virtual molecular library targeting GRK2. The binding affinity of each virtual compound in this dataset was predicted by our developed deep learning model, and the designed potential compound with high binding affinity was selected for molecular docking and molecular dynamics simulation. It was found that the designed potential molecule binds to the ATP site of GRK2, which consists of key amino acids including Arg199, Gly200, Phe202, Val205, Lys220, Met274 and Asp335. The scaffold of the molecule is stabilized mainly by H-bonding and hydrophobic contacts. Concurrently, the reference compound in the dataset was also simulated by docking. It was found that this molecule also binds to the ATP site of GRK2. In addition, its scaffold is stabilized mainly by H-bonding and π-cation stacking interactions with Lys220, as well as hydrophobic contacts. The above results show that the designed potential molecule has similar binding modes to the reference compound, supporting the effectiveness of our framework for activity-focused molecular design. Finally, we summarized the interaction characteristics of general GRK2 inhibitors and gained insight into their molecule-target binding mechanisms, thereby facilitating the expansion of lead to hit compound.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
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
The primary purpose of this study is to present mathematical modeling methods inspired by graph theory operations and logic as a tool to structurally analyze the socio-economic composition of a city based on the geogr...The primary purpose of this study is to present mathematical modeling methods inspired by graph theory operations and logic as a tool to structurally analyze the socio-economic composition of a city based on the geographical lo-cation of the investigated areas.We’ve incorporated graph theory concepts like connectivity,subgraph,degree,tree,complete graph,and dual graph as our model’s main components.We applied these methods to study the geo-graphical distribution of food hardship in New York City,as well as housing prices in Boise,Idaho,and Miami,Florida.We conducted a structural analysis of our models and concluded several notable properties within the model results.We’ve also included the ocean’s current direction and location for the New York City model to speculate on the mechanism behind our results fur-ther.Graphs and quantitative data regarding each one of these factors are simulated and created through Gephi and R Studio,where the combination of these factors will be concluded and presented as the result of the study.In this way,the result of our model brings a step-by-step demonstration of how the graph theory and analysis techniques we’ve developed can be applied to any city with proper quantitative or qualitative data.The report in our pro-totype model focuses on population poverty and socio-economic conditions,emphasized and indicated through food hardship and the housing market within the area.We also discussed several plausible applications of our meth-ods,including topics like climate change and the real estate market.Consid-ering that our model is a skeletal position-based map exhibiting the func-tionality of the analysis techniques we’ve developed,the graph is a prototype for environmental science and mathematics researchers to examine,where they can further improve and optimize it for more accurate and informative results.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
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
1 Summary Mathematical modeling has become a cornerstone in understanding the complex dynamics of infectious diseases and chronic health conditions.With the advent of more refined computational techniques,researchers ...1 Summary Mathematical modeling has become a cornerstone in understanding the complex dynamics of infectious diseases and chronic health conditions.With the advent of more refined computational techniques,researchers are now able to incorporate intricate features such as delays,stochastic effects,fractional dynamics,variable-order systems,and uncertainty into epidemic models.These advancements not only improve predictive accuracy but also enable deeper insights into disease transmission,control,and policy-making.Tashfeen et al.展开更多
To ensure the dimensional accuracy of the final blade profile,it is necessary for precision Electrochemical Machining(ECM)of blade profile to come into an equilibrium state.However,after Electrochemical Trepanning(ECT...To ensure the dimensional accuracy of the final blade profile,it is necessary for precision Electrochemical Machining(ECM)of blade profile to come into an equilibrium state.However,after Electrochemical Trepanning(ECTr),the cascade channel of the blisk is narrow,and the blank allowance distribution is uneven,making it difficult for the precision ECM to become balanced.In blisk production,the two-step method cannot make precision ECM enter equilibrium for some blisk types.A three-step processing method is proposed to overcome this problem.The threestep method adds Electrochemical Homogenizing Machining(ECHM)between the ECTr and precision ECM steps so that the blank allowance can be homogenized quickly without unduly affecting the minimum allowance.Comparative machining experiments of the two-and three-step methods were performed to verify the improvement to blade machining accuracy.The processing results show that the contour parameters of the blade after the three-step method implementation are much better.The allowance difference of the concave(convex)side decreased by 70.5%(65%).In addition,the current in the three-step method is stable at 110 A at the end of precision ECM,verifying successfully entering the equilibrium state.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 addition of cold flow improvers(CFIs)is considered as the optimum strategy to improve the cold flow properties(CFPs)of diesel fuels,but this strategy is always limited by the required large dosage.To obtain low-do...The addition of cold flow improvers(CFIs)is considered as the optimum strategy to improve the cold flow properties(CFPs)of diesel fuels,but this strategy is always limited by the required large dosage.To obtain low-dosage and high-efficiency CFIs for diesel,1,2,3,6-tetrahydrophthalic anhydride(THPA)was introduced as a third and polar monomer to enhance the depressive effects of alkyl methacrylatetrans anethole copolymers(C_(14)MC-TA).The terpolymers of alkyl methacrylate-trans anethole-1,2,3,6-tetrahydrophthalic anhydride(C_(14)MC-TA-THPA)were synthesized and compared with the binary copolymers of C_(14)MC-TA and alkyl methacrylate-1,2,3,6-tetrahydrophthalic anhydride(C_(14)MC-THPA).Results showed that C_(14)MC-THPA achieved the best depressive effects on the cold filter plugging point(CFPP)and solid point(SP)by 11℃and 16℃at a dosage of 1250 mg/L and monomer ratio of 6:1,while 1500mg/L C_(14)MC-TA(1:1)reached the optimal depressive effects on the CFPP and SP by 12℃and 18℃.THPA introduction significantly improved the depressive effects of C_(14)MC-TA.Lower dosages of C_(14)MCTA-THPA in diesel exerted better improvement effects on the CFPP and SP than that of C_(14)MC-TA and C_(14)MC-THPA.When the monomer ratio and dosage were 6:0.6:0.4 and 1000 mg/L,the improvement effect of C_(14)MC-TA-THPA on diesel reached the optimum level,and the CFPP and SP were reduced by 13℃and 19℃,respectively.A 3D nonlinear surface diagram fitted by a mathematical model was also used for the first time to better understand the relationships of monomer ratios,dosages,and depressive effects of CFIs in diesel.Surface analysis results showed that C_(14)MC-TA-THPA achieved the optimum depressive effects at a monomer ratio of 6:0.66:0.34 and dosage of 1000 mg/L,and the CFPP and SP decreased by 14℃ and 19℃,respectively.The predicted results were consistent with the actual ones.Additionally,the improvement mechanism of these copolymers in diesel was also explored.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
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
In recent years,the world has seen an exponential increase in energy demand,prompting scientists to look for innovative ways to exploit the power sun’s power.Solar energy technologies use the sun’s energy and light ...In recent years,the world has seen an exponential increase in energy demand,prompting scientists to look for innovative ways to exploit the power sun’s power.Solar energy technologies use the sun’s energy and light to provide heating,lighting,hot water,electricity and even cooling for homes,businesses,and industries.Therefore,ground-level solar radiation data is important for these applications.Thus,our work aims to use a mathematical modeling tool to predict solar irradiation.For this purpose,we are interested in the application of the Adaptive Neuro Fuzzy Inference System.Through this type of artificial neural system,10 models were developed,based on meteorological data such as the Day number(Nj),Ambient temperature(T),Relative Humidity(Hr),Wind speed(WS),Wind direction(WD),Declination(δ),Irradiation outside the atmosphere(Goh),Maximum temperature(Tmax),Minimum temperature(Tmin).These models have been tested by different static indicators to choose the most suitable one for the estimation of the daily global solar radiation.This study led us to choose the M8 model,which takes Nj,T,Hr,δ,Ws,Wd,G0,and S0 as input variables because it presents the best performance either in the learning phase(R^(2)=0.981,RMSE=0.107 kW/m^(2),MAE=0.089 kW/m2)or in the validation phase(R^(2)=0.979,RMSE=0.117 kW/m^(2),MAE=0.101 kW/m^(2)).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.
文摘Mathematical models of tire-lateral mad adhesion for use in mad vehicle dynamics studies are set up to express the relations of adhesion coefficients with slip ratio in lateral direction.The models of tire-lateral mad adhesion revolutionize the Pacejka's model in concept and therefore make it possible for applications in vehicle dynamics studies by the expression of lateral adhesion coefficient as a function of wheel slip ratio,instead of the wheel slip angle,taking into account in the mean time the influences of mad surface condition, vehicle velocity,vertical load,tire slip angle,and wheel camber angle.
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.
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.
文摘To address the sensitive and uncertain limitations of single-energy computed tomography(CT)calibration methods in computing proton stopping power ratio during treatment planning,different methods have been proposed using a dual energy CT approach.This paper reviews the most recent dual-energy CT approaches for computing proton stopping power ratio.These include image domain and projection domain methods.The advantages and uncertainties of these methods are analyzed based on existing studies.This paper highlights recent advances in dual energy CT,discussing their implementation,advantages,limitations,and potential for clinical adoption.
基金supported by the National Natural Science Foundation of China(No.62201508)the Zhejiang Provincial Natural Science Foundation of China(Nos.LZ21F010001 and LQ23F010004)the State Key Laboratory of Millimeter Waves of Southeast University,China(No.K202212).
文摘Quantization noise caused by analog-to-digital converter(ADC)gives rise to the reliability performance degradation of communication systems.In this paper,a quantized non-Hermitian symmetry(NHS)orthogonal frequency-division multiplexing-based visible light communication(OFDM-VLC)system is presented.In order to analyze the effect of the resolution of ADC on NHS OFDM-VLC,a quantized mathematical model of NHS OFDM-VLC is established.Based on the proposed quantized model,a closed-form bit error rate(BER)expression is derived.The theoretical analysis and simulation results both confirm the effectiveness of the obtained BER formula in high-resolution ADC.In addition,channel coding is helpful in compensating for the BER performance loss due to the utilization of lower resolution ADC.
基金supported by the National Natural Science Foundation of China Excellent Young Scientist Fund(22422801)the National Natural Science Foundation of China General Project(22278053)+1 种基金the National Natural Science Foundation of China General Project(22078041)Dalian High-level Talents Innovation Support Program(2023RQ059).
文摘G protein coupled receptor kinase 2 (GRK2) is a kinase that regulates cardiac signaling activity. Inhibiting GRK2 is a promising mechanism for the treatment of heart failure (HF). Further development and optimization of inhibitors targeting GRK2 are highly meaningful. Therefore, in order to design GRK2 inhibitors with better performance, the most active molecule was selected as a reference compound from a data set containing 4-pyridylhydrazone derivatives and triazole derivatives, and its scaffold was extracted as the initial scaffold. Then, a powerful optimization-based framework for de novo drug design, guided by binding affinity, was used to generate a virtual molecular library targeting GRK2. The binding affinity of each virtual compound in this dataset was predicted by our developed deep learning model, and the designed potential compound with high binding affinity was selected for molecular docking and molecular dynamics simulation. It was found that the designed potential molecule binds to the ATP site of GRK2, which consists of key amino acids including Arg199, Gly200, Phe202, Val205, Lys220, Met274 and Asp335. The scaffold of the molecule is stabilized mainly by H-bonding and hydrophobic contacts. Concurrently, the reference compound in the dataset was also simulated by docking. It was found that this molecule also binds to the ATP site of GRK2. In addition, its scaffold is stabilized mainly by H-bonding and π-cation stacking interactions with Lys220, as well as hydrophobic contacts. The above results show that the designed potential molecule has similar binding modes to the reference compound, supporting the effectiveness of our framework for activity-focused molecular design. Finally, we summarized the interaction characteristics of general GRK2 inhibitors and gained insight into their molecule-target binding mechanisms, thereby facilitating the expansion of lead to hit compound.
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 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.
文摘The primary purpose of this study is to present mathematical modeling methods inspired by graph theory operations and logic as a tool to structurally analyze the socio-economic composition of a city based on the geographical lo-cation of the investigated areas.We’ve incorporated graph theory concepts like connectivity,subgraph,degree,tree,complete graph,and dual graph as our model’s main components.We applied these methods to study the geo-graphical distribution of food hardship in New York City,as well as housing prices in Boise,Idaho,and Miami,Florida.We conducted a structural analysis of our models and concluded several notable properties within the model results.We’ve also included the ocean’s current direction and location for the New York City model to speculate on the mechanism behind our results fur-ther.Graphs and quantitative data regarding each one of these factors are simulated and created through Gephi and R Studio,where the combination of these factors will be concluded and presented as the result of the study.In this way,the result of our model brings a step-by-step demonstration of how the graph theory and analysis techniques we’ve developed can be applied to any city with proper quantitative or qualitative data.The report in our pro-totype model focuses on population poverty and socio-economic conditions,emphasized and indicated through food hardship and the housing market within the area.We also discussed several plausible applications of our meth-ods,including topics like climate change and the real estate market.Consid-ering that our model is a skeletal position-based map exhibiting the func-tionality of the analysis techniques we’ve developed,the graph is a prototype for environmental science and mathematics researchers to examine,where they can further improve and optimize it for more accurate and informative results.
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 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.
文摘1 Summary Mathematical modeling has become a cornerstone in understanding the complex dynamics of infectious diseases and chronic health conditions.With the advent of more refined computational techniques,researchers are now able to incorporate intricate features such as delays,stochastic effects,fractional dynamics,variable-order systems,and uncertainty into epidemic models.These advancements not only improve predictive accuracy but also enable deeper insights into disease transmission,control,and policy-making.Tashfeen et al.
基金supported by the National Natural Science Foundation of China(No.52075253)the Innovation Research Team of the National Natural Science Foundation of China(No.51921003)。
文摘To ensure the dimensional accuracy of the final blade profile,it is necessary for precision Electrochemical Machining(ECM)of blade profile to come into an equilibrium state.However,after Electrochemical Trepanning(ECTr),the cascade channel of the blisk is narrow,and the blank allowance distribution is uneven,making it difficult for the precision ECM to become balanced.In blisk production,the two-step method cannot make precision ECM enter equilibrium for some blisk types.A three-step processing method is proposed to overcome this problem.The threestep method adds Electrochemical Homogenizing Machining(ECHM)between the ECTr and precision ECM steps so that the blank allowance can be homogenized quickly without unduly affecting the minimum allowance.Comparative machining experiments of the two-and three-step methods were performed to verify the improvement to blade machining accuracy.The processing results show that the contour parameters of the blade after the three-step method implementation are much better.The allowance difference of the concave(convex)side decreased by 70.5%(65%).In addition,the current in the three-step method is stable at 110 A at the end of precision ECM,verifying successfully entering the equilibrium state.
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supported from the Natural Science Foundation Project of Shanghai(Nos.23ZR1425300 and 22ZR1426100)Experimental Technical Team Construction Project of Shanghai Education Commission(No.10110N230080)+1 种基金National Natural Science Foundation of China(No.22075183)Research and Innovation Project of Shanghai Municipal Education Commission(No.2023ZKZD54).
文摘The addition of cold flow improvers(CFIs)is considered as the optimum strategy to improve the cold flow properties(CFPs)of diesel fuels,but this strategy is always limited by the required large dosage.To obtain low-dosage and high-efficiency CFIs for diesel,1,2,3,6-tetrahydrophthalic anhydride(THPA)was introduced as a third and polar monomer to enhance the depressive effects of alkyl methacrylatetrans anethole copolymers(C_(14)MC-TA).The terpolymers of alkyl methacrylate-trans anethole-1,2,3,6-tetrahydrophthalic anhydride(C_(14)MC-TA-THPA)were synthesized and compared with the binary copolymers of C_(14)MC-TA and alkyl methacrylate-1,2,3,6-tetrahydrophthalic anhydride(C_(14)MC-THPA).Results showed that C_(14)MC-THPA achieved the best depressive effects on the cold filter plugging point(CFPP)and solid point(SP)by 11℃and 16℃at a dosage of 1250 mg/L and monomer ratio of 6:1,while 1500mg/L C_(14)MC-TA(1:1)reached the optimal depressive effects on the CFPP and SP by 12℃and 18℃.THPA introduction significantly improved the depressive effects of C_(14)MC-TA.Lower dosages of C_(14)MCTA-THPA in diesel exerted better improvement effects on the CFPP and SP than that of C_(14)MC-TA and C_(14)MC-THPA.When the monomer ratio and dosage were 6:0.6:0.4 and 1000 mg/L,the improvement effect of C_(14)MC-TA-THPA on diesel reached the optimum level,and the CFPP and SP were reduced by 13℃and 19℃,respectively.A 3D nonlinear surface diagram fitted by a mathematical model was also used for the first time to better understand the relationships of monomer ratios,dosages,and depressive effects of CFIs in diesel.Surface analysis results showed that C_(14)MC-TA-THPA achieved the optimum depressive effects at a monomer ratio of 6:0.66:0.34 and dosage of 1000 mg/L,and the CFPP and SP decreased by 14℃ and 19℃,respectively.The predicted results were consistent with the actual ones.Additionally,the improvement mechanism of these copolymers in diesel was also explored.
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In recent years,the world has seen an exponential increase in energy demand,prompting scientists to look for innovative ways to exploit the power sun’s power.Solar energy technologies use the sun’s energy and light to provide heating,lighting,hot water,electricity and even cooling for homes,businesses,and industries.Therefore,ground-level solar radiation data is important for these applications.Thus,our work aims to use a mathematical modeling tool to predict solar irradiation.For this purpose,we are interested in the application of the Adaptive Neuro Fuzzy Inference System.Through this type of artificial neural system,10 models were developed,based on meteorological data such as the Day number(Nj),Ambient temperature(T),Relative Humidity(Hr),Wind speed(WS),Wind direction(WD),Declination(δ),Irradiation outside the atmosphere(Goh),Maximum temperature(Tmax),Minimum temperature(Tmin).These models have been tested by different static indicators to choose the most suitable one for the estimation of the daily global solar radiation.This study led us to choose the M8 model,which takes Nj,T,Hr,δ,Ws,Wd,G0,and S0 as input variables because it presents the best performance either in the learning phase(R^(2)=0.981,RMSE=0.107 kW/m^(2),MAE=0.089 kW/m2)or in the validation phase(R^(2)=0.979,RMSE=0.117 kW/m^(2),MAE=0.101 kW/m^(2)).
