In the present study, non-routine mathematical problem-solving skills of high school students and its relation with the achievement on a standardized university entrance exam (LYS) were searched. To measure non-rout...In the present study, non-routine mathematical problem-solving skills of high school students and its relation with the achievement on a standardized university entrance exam (LYS) were searched. To measure non-routine problem-solving skills of students, a PST (problem-solving test) that comprises nine non-routine open-ended problems was conducted to the 144 senior high school students. Besides, LYS scores of students were obtained from their schools. Quantitative and qualitative analyses of students' scripts on PST revealed that high school students could solve successfully non-routine problems and employ different problem-solving strategies without any intervention. More importantly, Pearson correlation coefficient which was computed using PST and LYS scores showed that there exists a strong link between high school students' success on university entrance exam and their abilities in non-routine problem-solving. Along with the qualitative evidences, this finding indicates that non-routine problem-solving requires higher thinking skills, and students who are successful at solving this kind of problems can adapt their critical and creative thinking to the other domains, such as science or language.展开更多
In view of the frequent deterioration of molten steel quality during the tundish filling process,the slag-steel-air interface behavior in a tundish,including liquid level fluctuation,slag eyes,slag entrapment and air ...In view of the frequent deterioration of molten steel quality during the tundish filling process,the slag-steel-air interface behavior in a tundish,including liquid level fluctuation,slag eyes,slag entrapment and air suction during the steady-state casting and filling process,was comparatively studied through physical modeling and mathematical simulation methods.During the filling process,the liquid surface forms a large-size slag eye under the impact of molten steel from a ladle shroud,which simultaneously results in a violent fluctuation of liquid level.Concurrently,the liquid flow entrains the air phase and the cover slag into the tundish impact zone,resulting in slag entrapment and air suction.At filling flow rates of 1.5Q,2.0Q,and 2.5Q(Q is the flow rate under steady-state casting),the amount of slag entrapped is 8.39×10-5,9.65×10-5,and 12.7×10-5m3,respectively,while the volume of air aspirated is 0.84×10-4,1.47×10-4,and 2.01×10-4m3,indicating that slag entrapment and air suction intensify with an increase in tundish filling flow rate.Flow field characterization identifies eddy currents in the impact zone as the primary driver of the above phenomena.Proper filling process parameters were proposed to improve the steel quality during the tundish filling.展开更多
Mathematical programming solvers are software tools designed to solve real‑world problems using mathematical programming algorithms.This survey explores the evolution of optimization technologies,from traditional meth...Mathematical programming solvers are software tools designed to solve real‑world problems using mathematical programming algorithms.This survey explores the evolution of optimization technologies,from traditional methods such as the simplex algorithm and branch‑and‑bound techniques to modern advancements that are facilitated by parallel computing,GPU acceleration,and AI algorithms.We also emphasize the recent emergence of mathematical programming solvers developed by research institutes and companies headquartered in China as major players,who have achieved remarkable success in benchmarks when compared to established solvers.This article provides a comprehensive overview of the theoretical foundations,historical progress,and emerging trends in mathematical programming solvers,offering valuable insights for both researchers and practitioners in the field.展开更多
In the cold-chamber high-pressure die casting(CC-HPDC)process for light alloys,strong shear stress generated by the fast-flowing melt through narrow runners breaks externally solidified crystals(ESCs).Two runner confi...In the cold-chamber high-pressure die casting(CC-HPDC)process for light alloys,strong shear stress generated by the fast-flowing melt through narrow runners breaks externally solidified crystals(ESCs).Two runner configurations were applied in the CC-HPDC process of aluminum alloy to address this problem.A comprehensive finite element model was established to calculate shear stress in the runner regions during die filling,and a novel mathematical model of grain breakup was proposed to quantitatively analyze ESCs fragmentation through different runners.Particles ranging in size from 12.2 to 16.1μm constitute a significant proportion of the ESCs and serve as the primary focus of subsequent shear fragmentation.Finally,HPDC test trials validate the mathematical model by characterizing grain morphology and size distribution in as-cast samples and the error of the model is less than 20%.The results demonstrate that the novel model is highly effective for the design of runner systems and the optimization of process parameters in the CC-HPDC process for light alloys.展开更多
Cyclic steam stimulation(CSS)is a common method for heavy oil reservoir,but the current research on steam channeling in horizontal wells is limited.This study proposes a novel mathematical model based on steam overrid...Cyclic steam stimulation(CSS)is a common method for heavy oil reservoir,but the current research on steam channeling in horizontal wells is limited.This study proposes a novel mathematical model based on steam override to predict steam channeling during the CSS process in horizontal wells,focusing on the quantization of the heated region,steam front edge position,and steam channeling time.The model was validated through a 3D physical simulation experiment.The experimental results were broadly consistent with the theoretical predictions.The study finds that steam channel is an upward-curved wedge shape,making it difficult to mobilize the bottom reservoir.The steam channeling time was predicted to be 10.10 min,with an 11.16%error compared to the experimental value of 8.97 min.Furthermore,the introduction of foam increased the oil steam ratio from 1.52 to 1.92.Reducing appropriately the steam injection rate,increasing well spacing,and decreasing steam temperature,together with periodic foam injection,can delay steam channeling.In conclusion,the model offers practical insights for steam channel prediction,which can improve the effectiveness of steam injection strategies in heavy oil reservoirs.展开更多
It is generally believed that the productivity of oil/gas wells in shale reservoirs increases with the population of hydraulic fractures in the stimulated reservoir volume.The objective of this work is to identify the...It is generally believed that the productivity of oil/gas wells in shale reservoirs increases with the population of hydraulic fractures in the stimulated reservoir volume.The objective of this work is to identify the dominant factors affecting hydraulic fracture population in shale oil/gas reservoirs.A semi-analytical model was first developed to simulate the sequential initiation and simultaneous propagation of hydraulic fractures during fracturing shale gas/oil reservoirs.The semi-analytical model was then coded in the FracPropag computer program for model validation and quick analyses.The sequential initiation and simultaneous propagation of hydraulic fractures predicted by FracPropag were compared with those inferred from the bottom-hole pressure curve for a real-case operation.A sensitivity study was performed with FracProp using data from the Tuscaloosa Marine Shale to identify key factors affecting the growing population of hydraulic fractures during hydraulic fracturing.The sequential initiation and simultaneous propagation of hydraulic fractures predicted by FracPropag were found to be remarkably consistent with those interpreted from the bottom-hole pressure curve for a real-case operation.A sensitivity study using FracProp with data from the Tuscaloosa Marine Shale identified three key factors that affect the growing population of hydraulic fractures during hydraulic fracturing.They are rheological type of fracturing fluid,rheological properties of fracturing fluid,and flow rate of hydraulic-fracturing fluid.It was found that,compared with water,the use of plastic fluids(e.g.,slick water)should reduce the number of short hydraulic fractures and thus fracture network complicity,while the use of dilatant fracturing fluids(e.g.,CMC solution)should increase the number of short hydraulic fractures and thus fracture network complicity.Regardless of fluid type,increasing the viscosity of fracturing fluid and slurry pumping rate will increase the number of short hydraulic fractures and thus fracture network complexity.All these effects are attributed to the fluid friction and thus fluid flow in long fractures.This work provides a useful tool for maximizing fracture population and fracture network complexity to improve well productivity in shale reservoirs.展开更多
Diffusion bonding and additive manufacturing(AM)are suitable joining and manufacturing techniques for producing aluminium alloy components even with highly intricate geometries.However,the generation of aluminium oxid...Diffusion bonding and additive manufacturing(AM)are suitable joining and manufacturing techniques for producing aluminium alloy components even with highly intricate geometries.However,the generation of aluminium oxide(Al2O3)scaling occurring on the surfaces of successively deposited aluminium layers decreases the metal-to-metal contact in extrusion-based AM applications.Al2 O3 scaling leads to poor quality of final fabricated parts and thereby achieving low bonding(joint)strength from bonded layers.In this regard,accurately predicting the minimum holding time required is essential for effectively mitigating Al2O3scaling,and achieving high-quality aluminium parts.This consideration involves optimising the duration of the diffusion bonding process and the consolidation pressure applied by print heads or consecutive rollers in extrusion-based AM process.There is currently neither mathematical model nor machine learning model developed for predicting the bonding time for similar or dissimilar aluminium and its alloys.Therefore,the current paper proposes both mathematical and supervised machine learning models using regression-based approach to predict the minimum holding time required to achieve sound AA7075-T6 joints at 450℃,475℃and 500℃.The mathematical model explicitly incorporates the closure of micro-voids through plastic deformation coupled with power-law creep of both AA7075-T6 and Al2O3,as well as volume,grain boundary,and surface diffusion.Notably,the creep and plastic deformations of Al2O3scaling are included for the first time in any diffusion bonding model for more realistically modelling void closure.Then,the bonding time was predicted using a machine learning code in which several techniques were incorporated to robust the model i.e.feature scaling,polynomial feature expansion,regularisation and mean squared error technique.The proposed mathematical model exhibited an excellent agreement with experimental results,particularly at low pressure levels and all data points at 450℃,whereas the machine learning model predicted bonding time more accurately than the mathematical model particularly at 475℃.展开更多
Hands-on work in junior high school mathematics has instructional value when it draws students into mathematical questions rather than stopping at finished products.Taking the lesson“Geometric Relationships in Paper ...Hands-on work in junior high school mathematics has instructional value when it draws students into mathematical questions rather than stopping at finished products.Taking the lesson“Geometric Relationships in Paper Folding”as a case,this paper discusses how a sequence of folding tasks can be organized around creases.Students begin with familiar paper shapes,make and mark creases,compare the relationships they see,and then explain parallelism,symmetry,equal sides,and transfer under changed conditions.The chain is arranged as situational activation,operational generation,relationship discovery,mathematical explanation,and transfer application.The crease becomes the hinge between action and reasoning:It starts as a physical trace,is read as a geometric line,axis,bisector,or boundary relation,and finally serves as evidence in explanation.When students are required to record their folds,name relationships,and check their reasons,paper folding can remain open-ended while keeping a clear mathematical focus.展开更多
Current Problem-Solving teaching in primary school science suffers from some misconceptions,such as“insufficient cultivation of problem awareness,lacking drive”,“insufficient deliberation in problem setting,lacking...Current Problem-Solving teaching in primary school science suffers from some misconceptions,such as“insufficient cultivation of problem awareness,lacking drive”,“insufficient deliberation in problem setting,lacking design”,“insufficient emphasis on the solving process,lacking effectiveness”,and“insufficient evaluation of solving results,lacking feedback”.To address these,this paper explores the“Four Emphases and Four Transformations”strategy for Problem-Solving teaching:First,emphasize connecting with life phenomena,transforming subject knowledge into practice;second,emphasize flexibly using questioning forms,rationalizing difficulty settings;third,emphasize providing differentiated guidance,autonomizing the solving process;fourth,emphasize monitoring the learning process,routinizing reflection and evaluation.展开更多
The Unified Complex System Theory(UCST)takes the mind-ether dual ontology as its core foundation,constructing a global complex system framework encompassing matter,energy,and information.Based on the dual ontology and...The Unified Complex System Theory(UCST)takes the mind-ether dual ontology as its core foundation,constructing a global complex system framework encompassing matter,energy,and information.Based on the dual ontology and hierarchical coupling principle of UCST,this paper breaks the millennia-old dual opposition between the“pure discovery”and“pure invention”of mathematics in traditional philosophical discourse,and puts forward the core proposition that mathematics is the hierarchical isomorphic mapping of the objective structure of the real world by the cognitive subject mind.On this theoretical premise,this paper innovatively establishes the UCST mathematical fundamental axiom system containing six interlocking core axioms,systematically reinterprets key core frontier topics in the foundations of mathematics such as infinite essence classification,intrinsic logic of set theory,physical attribution of continuum,and practical boundary of computability theory,and effectively dissolves the long-standing inherent logical paradoxes and theoretical dilemmas within traditional mathematical philosophy and the classical foundations of mathematics.Meanwhile,taking the self-consistent UCST axiom system as the unified critical normative criterion,this paper systematically sorts out and reveals the universal cognitive deviation arising from the forced arbitrary transition of abstract high-dimensional mathematical formal models to concrete four-dimensional empirical physical reality in the theoretical construction process of modern mainstream physics.It further scientifically clarifies the essential ontological,epistemological,and methodological boundary between instrumental mathematics and empirical physics in the whole scientific research system.This research advocates that academic circles should return mathematics to its original instrumental essence of fitting and describing four-dimensional empirical natural laws,and theoretical physics should firmly adhere to the basic research boundary of observable,verifiable,and falsifiable real spacetime entities.Ultimately,the research realizes the self-consistent unity of the essence connotation of mathematics,the standardized reconstruction of the foundations of mathematics,the ontological logic of complex systems,and the core principles of physical empiricism,providing a novel,rigorous,and operable complex system comprehensive perspective for the innovative development of contemporary philosophy of mathematics and the normative rectification of philosophy of science.展开更多
In the intelligent era,mathematics teaching in vocational undergraduate colleges faces prominent problems,including disconnection between theory and practice,superficial integration of AI,and fragmented application of...In the intelligent era,mathematics teaching in vocational undergraduate colleges faces prominent problems,including disconnection between theory and practice,superficial integration of AI,and fragmented application of mathematical modeling teaching.Taking mathematical modeling as the core link,this paper constructs an integrated teaching mode of“mathematics-major-AI”.Supported by school-enterprise training platforms,the study designs matched classroom teaching and after-class training for TCM pharmacy majors to carry out mathematical modeling,AI data analysis and practical verification.This mode eliminates the barriers among mathematical theories,professional skills and intelligent technologies,enhances students’practical ability to solve practical industrial problems,and offers feasible references for mathematics teaching reform in vocational undergraduate education.展开更多
Although primary school mathematics is presented in intuitive and concrete forms, it contains complex mathematical principles and structures. If teachers master only the concepts, formulas, and algorithms presented in...Although primary school mathematics is presented in intuitive and concrete forms, it contains complex mathematical principles and structures. If teachers master only the concepts, formulas, and algorithms presented in textbooks, they will find it difficult to explain in depth why the relevant rules are valid and will likewise be unable to reveal the intrinsic connections among different bodies of knowledge. This paper constructs a three-level hierarchical structure comprising the curriculum knowledge layer, the direct explanatory layer, and the structural unification layer. It then traces the corresponding superordinate knowledge in the domains of Numbers and Algebra, Geometry, and Statistics and Probability, and further proposes a relational knowledge graph composed of four types of relationships—explanation, dependency, unification, and generalization—thereby forming a multilevel and multipath framework for the relational knowledge graph.展开更多
In recent years,with the rapid development of artificial intelligence and big data technologies,knowledge graphs have gained widespread attention and application.As a fundamental course in mathematics and statistics,P...In recent years,with the rapid development of artificial intelligence and big data technologies,knowledge graphs have gained widespread attention and application.As a fundamental course in mathematics and statistics,Probability Theory and Mathematical Statistics contains complex and highly interconnected knowledge points,making traditional learning methods less effective for understanding its internal logic.Therefore,constructing a knowledge graph and developing a corresponding question-answering system for this subject is of great significance.This project uses the Probability Theory and Mathematical Statistics Tutorial(3rd Edition)as the data source to construct a knowledge graph based on Neo4j.Cypher language and APOC tools were used for data import and graph construction,while Neo4j Bloom was employed for visualization.In addition,a question-answering system was developed using natural language processing techniques and the Flask framework to provide intelligent query services.The system can help students better understand and learn probability theory and mathematical statistics while reducing dependence on traditional textbooks.展开更多
0 INTRODUCTION As a high-risk construction project,underground engineering is characterized by large investment,long construction period,complexconstruction techniques,numerous unforeseeable risk factors,and significa...0 INTRODUCTION As a high-risk construction project,underground engineering is characterized by large investment,long construction period,complexconstruction techniques,numerous unforeseeable risk factors,and significantenvironmental impacts.Identifying potentialdisaster risks from the intricate web of influencing factors plays a critical role in ensuring project safety.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
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
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
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
This study constructs a reflective feedback model based on a pedagogical agent(PA)and explores its impact on students’problem-solving ability and cognitive load.A quasi-experimental design was used in the study,with ...This study constructs a reflective feedback model based on a pedagogical agent(PA)and explores its impact on students’problem-solving ability and cognitive load.A quasi-experimental design was used in the study,with 84 students from a middle school selected as the research subjects(44 in the experimental group and 40 in the control group).The experimental group used the reflective feedback model,while the control group used the factual feedback model.The results show that,compared with factual feedback,the reflective feedback model based on the pedagogical agent significantly improves students’problem-solving ability,especially at the action and thinking levels.In addition,this model effectively reduces students’cognitive load,especially in terms of internal and external load.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
摘要In the present study, non-routine mathematical problem-solving skills of high school students and its relation with the achievement on a standardized university entrance exam (LYS) were searched. To measure non-routine problem-solving skills of students, a PST (problem-solving test) that comprises nine non-routine open-ended problems was conducted to the 144 senior high school students. Besides, LYS scores of students were obtained from their schools. Quantitative and qualitative analyses of students' scripts on PST revealed that high school students could solve successfully non-routine problems and employ different problem-solving strategies without any intervention. More importantly, Pearson correlation coefficient which was computed using PST and LYS scores showed that there exists a strong link between high school students' success on university entrance exam and their abilities in non-routine problem-solving. Along with the qualitative evidences, this finding indicates that non-routine problem-solving requires higher thinking skills, and students who are successful at solving this kind of problems can adapt their critical and creative thinking to the other domains, such as science or language.
基金support from National Natural Science Foundation of China(Grant No.51874033)to Prof.Hai-Yan Tang.
摘要In view of the frequent deterioration of molten steel quality during the tundish filling process,the slag-steel-air interface behavior in a tundish,including liquid level fluctuation,slag eyes,slag entrapment and air suction during the steady-state casting and filling process,was comparatively studied through physical modeling and mathematical simulation methods.During the filling process,the liquid surface forms a large-size slag eye under the impact of molten steel from a ladle shroud,which simultaneously results in a violent fluctuation of liquid level.Concurrently,the liquid flow entrains the air phase and the cover slag into the tundish impact zone,resulting in slag entrapment and air suction.At filling flow rates of 1.5Q,2.0Q,and 2.5Q(Q is the flow rate under steady-state casting),the amount of slag entrapped is 8.39×10-5,9.65×10-5,and 12.7×10-5m3,respectively,while the volume of air aspirated is 0.84×10-4,1.47×10-4,and 2.01×10-4m3,indicating that slag entrapment and air suction intensify with an increase in tundish filling flow rate.Flow field characterization identifies eddy currents in the impact zone as the primary driver of the above phenomena.Proper filling process parameters were proposed to improve the steel quality during the tundish filling.
基金supported by the National Natural Science Foundation of China(Grant Nos.72425001,72401219,72231006,and 72301165).
摘要Mathematical programming solvers are software tools designed to solve real‑world problems using mathematical programming algorithms.This survey explores the evolution of optimization technologies,from traditional methods such as the simplex algorithm and branch‑and‑bound techniques to modern advancements that are facilitated by parallel computing,GPU acceleration,and AI algorithms.We also emphasize the recent emergence of mathematical programming solvers developed by research institutes and companies headquartered in China as major players,who have achieved remarkable success in benchmarks when compared to established solvers.This article provides a comprehensive overview of the theoretical foundations,historical progress,and emerging trends in mathematical programming solvers,offering valuable insights for both researchers and practitioners in the field.
基金The financial supports from the National Natural Science Foundation of China(No.52304360)the Open Foundation of the State Key Laboratory of Advanced Metallurgy,University of Science and Technology Beijing,China(No.K22-07)+1 种基金the Key Research and Development Program of Xiangjiang Laboratory,China(NO.22XJ01002)the EPSRC Centre for Innovative Manufacturing in Liquid Metal Engineering,China(The EPSRC Centre-LiME,No.RRR1025R33390)are greatly acknowledged.
摘要In the cold-chamber high-pressure die casting(CC-HPDC)process for light alloys,strong shear stress generated by the fast-flowing melt through narrow runners breaks externally solidified crystals(ESCs).Two runner configurations were applied in the CC-HPDC process of aluminum alloy to address this problem.A comprehensive finite element model was established to calculate shear stress in the runner regions during die filling,and a novel mathematical model of grain breakup was proposed to quantitatively analyze ESCs fragmentation through different runners.Particles ranging in size from 12.2 to 16.1μm constitute a significant proportion of the ESCs and serve as the primary focus of subsequent shear fragmentation.Finally,HPDC test trials validate the mathematical model by characterizing grain morphology and size distribution in as-cast samples and the error of the model is less than 20%.The results demonstrate that the novel model is highly effective for the design of runner systems and the optimization of process parameters in the CC-HPDC process for light alloys.
基金supported by National Natural Science Foundation of China(52574063)National Natural Science Foundation of China(52074321)。
摘要Cyclic steam stimulation(CSS)is a common method for heavy oil reservoir,but the current research on steam channeling in horizontal wells is limited.This study proposes a novel mathematical model based on steam override to predict steam channeling during the CSS process in horizontal wells,focusing on the quantization of the heated region,steam front edge position,and steam channeling time.The model was validated through a 3D physical simulation experiment.The experimental results were broadly consistent with the theoretical predictions.The study finds that steam channel is an upward-curved wedge shape,making it difficult to mobilize the bottom reservoir.The steam channeling time was predicted to be 10.10 min,with an 11.16%error compared to the experimental value of 8.97 min.Furthermore,the introduction of foam increased the oil steam ratio from 1.52 to 1.92.Reducing appropriately the steam injection rate,increasing well spacing,and decreasing steam temperature,together with periodic foam injection,can delay steam channeling.In conclusion,the model offers practical insights for steam channel prediction,which can improve the effectiveness of steam injection strategies in heavy oil reservoirs.
基金supported by the Louisiana Board of Regents Support Fund(BoRSF),Grant No.LEQSF(2024–27)-RD-B-04.
摘要It is generally believed that the productivity of oil/gas wells in shale reservoirs increases with the population of hydraulic fractures in the stimulated reservoir volume.The objective of this work is to identify the dominant factors affecting hydraulic fracture population in shale oil/gas reservoirs.A semi-analytical model was first developed to simulate the sequential initiation and simultaneous propagation of hydraulic fractures during fracturing shale gas/oil reservoirs.The semi-analytical model was then coded in the FracPropag computer program for model validation and quick analyses.The sequential initiation and simultaneous propagation of hydraulic fractures predicted by FracPropag were compared with those inferred from the bottom-hole pressure curve for a real-case operation.A sensitivity study was performed with FracProp using data from the Tuscaloosa Marine Shale to identify key factors affecting the growing population of hydraulic fractures during hydraulic fracturing.The sequential initiation and simultaneous propagation of hydraulic fractures predicted by FracPropag were found to be remarkably consistent with those interpreted from the bottom-hole pressure curve for a real-case operation.A sensitivity study using FracProp with data from the Tuscaloosa Marine Shale identified three key factors that affect the growing population of hydraulic fractures during hydraulic fracturing.They are rheological type of fracturing fluid,rheological properties of fracturing fluid,and flow rate of hydraulic-fracturing fluid.It was found that,compared with water,the use of plastic fluids(e.g.,slick water)should reduce the number of short hydraulic fractures and thus fracture network complicity,while the use of dilatant fracturing fluids(e.g.,CMC solution)should increase the number of short hydraulic fractures and thus fracture network complicity.Regardless of fluid type,increasing the viscosity of fracturing fluid and slurry pumping rate will increase the number of short hydraulic fractures and thus fracture network complexity.All these effects are attributed to the fluid friction and thus fluid flow in long fractures.This work provides a useful tool for maximizing fracture population and fracture network complexity to improve well productivity in shale reservoirs.
摘要Diffusion bonding and additive manufacturing(AM)are suitable joining and manufacturing techniques for producing aluminium alloy components even with highly intricate geometries.However,the generation of aluminium oxide(Al2O3)scaling occurring on the surfaces of successively deposited aluminium layers decreases the metal-to-metal contact in extrusion-based AM applications.Al2 O3 scaling leads to poor quality of final fabricated parts and thereby achieving low bonding(joint)strength from bonded layers.In this regard,accurately predicting the minimum holding time required is essential for effectively mitigating Al2O3scaling,and achieving high-quality aluminium parts.This consideration involves optimising the duration of the diffusion bonding process and the consolidation pressure applied by print heads or consecutive rollers in extrusion-based AM process.There is currently neither mathematical model nor machine learning model developed for predicting the bonding time for similar or dissimilar aluminium and its alloys.Therefore,the current paper proposes both mathematical and supervised machine learning models using regression-based approach to predict the minimum holding time required to achieve sound AA7075-T6 joints at 450℃,475℃and 500℃.The mathematical model explicitly incorporates the closure of micro-voids through plastic deformation coupled with power-law creep of both AA7075-T6 and Al2O3,as well as volume,grain boundary,and surface diffusion.Notably,the creep and plastic deformations of Al2O3scaling are included for the first time in any diffusion bonding model for more realistically modelling void closure.Then,the bonding time was predicted using a machine learning code in which several techniques were incorporated to robust the model i.e.feature scaling,polynomial feature expansion,regularisation and mean squared error technique.The proposed mathematical model exhibited an excellent agreement with experimental results,particularly at low pressure levels and all data points at 450℃,whereas the machine learning model predicted bonding time more accurately than the mathematical model particularly at 475℃.
基金Wuxi Educational Science“14th Five-Year Plan”Project,“Exploration of Junior High School Mathematics Comprehensive Practice Curriculum Oriented to the Basic Cultivation of Innovative Talents”(E/D/2023/04)Jiangsu Provincial“14th Five-Year Plan”Project,“Practical Research on Unit-Based Holistic Teaching of Junior High School Mathematics From the Perspective of Contextual Continuity”(C/2023/03/36).
摘要Hands-on work in junior high school mathematics has instructional value when it draws students into mathematical questions rather than stopping at finished products.Taking the lesson“Geometric Relationships in Paper Folding”as a case,this paper discusses how a sequence of folding tasks can be organized around creases.Students begin with familiar paper shapes,make and mark creases,compare the relationships they see,and then explain parallelism,symmetry,equal sides,and transfer under changed conditions.The chain is arranged as situational activation,operational generation,relationship discovery,mathematical explanation,and transfer application.The crease becomes the hinge between action and reasoning:It starts as a physical trace,is read as a geometric line,axis,bisector,or boundary relation,and finally serves as evidence in explanation.When students are required to record their folds,name relationships,and check their reasons,paper folding can remain open-ended while keeping a clear mathematical focus.
基金funded by Humanities and Social Sciences Research Youth Fund of the Ministry of Education in China:Research on the Assessment of Middle School Students’Scientific Inquiry Ability Based on Multimodal Data[25YJC880074].
摘要Current Problem-Solving teaching in primary school science suffers from some misconceptions,such as“insufficient cultivation of problem awareness,lacking drive”,“insufficient deliberation in problem setting,lacking design”,“insufficient emphasis on the solving process,lacking effectiveness”,and“insufficient evaluation of solving results,lacking feedback”.To address these,this paper explores the“Four Emphases and Four Transformations”strategy for Problem-Solving teaching:First,emphasize connecting with life phenomena,transforming subject knowledge into practice;second,emphasize flexibly using questioning forms,rationalizing difficulty settings;third,emphasize providing differentiated guidance,autonomizing the solving process;fourth,emphasize monitoring the learning process,routinizing reflection and evaluation.
基金supported by the scientific research project of Westlake University“Theoretical Research and Demonstration Application of Complex Systems and Deep-Sea Technology(Phase I)”under Grant Number WU2025A006.
摘要The Unified Complex System Theory(UCST)takes the mind-ether dual ontology as its core foundation,constructing a global complex system framework encompassing matter,energy,and information.Based on the dual ontology and hierarchical coupling principle of UCST,this paper breaks the millennia-old dual opposition between the“pure discovery”and“pure invention”of mathematics in traditional philosophical discourse,and puts forward the core proposition that mathematics is the hierarchical isomorphic mapping of the objective structure of the real world by the cognitive subject mind.On this theoretical premise,this paper innovatively establishes the UCST mathematical fundamental axiom system containing six interlocking core axioms,systematically reinterprets key core frontier topics in the foundations of mathematics such as infinite essence classification,intrinsic logic of set theory,physical attribution of continuum,and practical boundary of computability theory,and effectively dissolves the long-standing inherent logical paradoxes and theoretical dilemmas within traditional mathematical philosophy and the classical foundations of mathematics.Meanwhile,taking the self-consistent UCST axiom system as the unified critical normative criterion,this paper systematically sorts out and reveals the universal cognitive deviation arising from the forced arbitrary transition of abstract high-dimensional mathematical formal models to concrete four-dimensional empirical physical reality in the theoretical construction process of modern mainstream physics.It further scientifically clarifies the essential ontological,epistemological,and methodological boundary between instrumental mathematics and empirical physics in the whole scientific research system.This research advocates that academic circles should return mathematics to its original instrumental essence of fitting and describing four-dimensional empirical natural laws,and theoretical physics should firmly adhere to the basic research boundary of observable,verifiable,and falsifiable real spacetime entities.Ultimately,the research realizes the self-consistent unity of the essence connotation of mathematics,the standardized reconstruction of the foundations of mathematics,the ontological logic of complex systems,and the core principles of physical empiricism,providing a novel,rigorous,and operable complex system comprehensive perspective for the innovative development of contemporary philosophy of mathematics and the normative rectification of philosophy of science.
摘要In the intelligent era,mathematics teaching in vocational undergraduate colleges faces prominent problems,including disconnection between theory and practice,superficial integration of AI,and fragmented application of mathematical modeling teaching.Taking mathematical modeling as the core link,this paper constructs an integrated teaching mode of“mathematics-major-AI”.Supported by school-enterprise training platforms,the study designs matched classroom teaching and after-class training for TCM pharmacy majors to carry out mathematical modeling,AI data analysis and practical verification.This mode eliminates the barriers among mathematical theories,professional skills and intelligent technologies,enhances students’practical ability to solve practical industrial problems,and offers feasible references for mathematics teaching reform in vocational undergraduate education.
摘要Although primary school mathematics is presented in intuitive and concrete forms, it contains complex mathematical principles and structures. If teachers master only the concepts, formulas, and algorithms presented in textbooks, they will find it difficult to explain in depth why the relevant rules are valid and will likewise be unable to reveal the intrinsic connections among different bodies of knowledge. This paper constructs a three-level hierarchical structure comprising the curriculum knowledge layer, the direct explanatory layer, and the structural unification layer. It then traces the corresponding superordinate knowledge in the domains of Numbers and Algebra, Geometry, and Statistics and Probability, and further proposes a relational knowledge graph composed of four types of relationships—explanation, dependency, unification, and generalization—thereby forming a multilevel and multipath framework for the relational knowledge graph.
摘要In recent years,with the rapid development of artificial intelligence and big data technologies,knowledge graphs have gained widespread attention and application.As a fundamental course in mathematics and statistics,Probability Theory and Mathematical Statistics contains complex and highly interconnected knowledge points,making traditional learning methods less effective for understanding its internal logic.Therefore,constructing a knowledge graph and developing a corresponding question-answering system for this subject is of great significance.This project uses the Probability Theory and Mathematical Statistics Tutorial(3rd Edition)as the data source to construct a knowledge graph based on Neo4j.Cypher language and APOC tools were used for data import and graph construction,while Neo4j Bloom was employed for visualization.In addition,a question-answering system was developed using natural language processing techniques and the Flask framework to provide intelligent query services.The system can help students better understand and learn probability theory and mathematical statistics while reducing dependence on traditional textbooks.
基金supported by the National Natural Science Foundation of China(Nos.42107211 and 42130719)the Natural Science Foundation of Sichuan Province(No.2025ZNSFSC0097)the open project of State Key Laboratory of Performance Monitoring and Protecting of Rail Transit Infrastructure,East China Jiaotong University(No.HJGZ2022104).
摘要0 INTRODUCTION As a high-risk construction project,underground engineering is characterized by large investment,long construction period,complexconstruction techniques,numerous unforeseeable risk factors,and significantenvironmental impacts.Identifying potentialdisaster risks from the intricate web of influencing factors plays a critical role in ensuring project safety.
摘要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.
摘要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.
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).
摘要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supported by the Deanship of Scientific Research,Vice Presidency for Graduate Studies and Scientific Research,King Faisal University,Saudi Arabia[Grant No.KFU252959].
摘要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023 Zhejiang Provincial Department of Education General Project:Research on an interdisciplinary teaching model to promote the development of computational thinking in the context of the new curriculum standards[Grant NO:Y202351596]Key Project of Zhejiang Provincial Education Science Planning:Research on an interdisciplinary teaching model to promote students’computational thinking from multiple analytical perspectives[Grant NO:2025SB103].
摘要This study constructs a reflective feedback model based on a pedagogical agent(PA)and explores its impact on students’problem-solving ability and cognitive load.A quasi-experimental design was used in the study,with 84 students from a middle school selected as the research subjects(44 in the experimental group and 40 in the control group).The experimental group used the reflective feedback model,while the control group used the factual feedback model.The results show that,compared with factual feedback,the reflective feedback model based on the pedagogical agent significantly improves students’problem-solving ability,especially at the action and thinking levels.In addition,this model effectively reduces students’cognitive load,especially in terms of internal and external load.
摘要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.