Journal overview:Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,one of the transactions of China Society for Industrial and Appli...Journal overview:Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,one of the transactions of China Society for Industrial and Applied Mathematics,is a home for original research papers of the highest quality in all areas of mathematics with applications.The target audience comprises:pure and applied mathematicians,graduate students in broad fields of sciences and technology,scientists and engineers interested in mathematics.展开更多
Journal overview:Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,one of the transactions of China Society for Industrial and Appli...Journal overview:Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,one of the transactions of China Society for Industrial and Applied Mathematics,is a home for original research papers of the highest quality in all areas of mathematics with applications.The target audience comprises:pure and applied mathematicians,graduate students in broad fields of sciences and technology,scientists and engineers interested in mathematics.展开更多
Journal overview:Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,one of the transactions of China Society for Industrial and Appli...Journal overview:Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,one of the transactions of China Society for Industrial and Applied Mathematics,is a home for original research papers of the highest quality in all areas of mathematics with applications.The target audience comprises:pure and applied mathematicians,graduate students in broad fields of sciences and technology,scientists and engineers interested in mathematics.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^(-5)m^(3),respectively,while the volume of air aspirated is 0.84×10^(-4),1.47×10^(-4),and 2.01×10^(-4)m^(3),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
Journal overview:Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,one of the transactions of China Society for Industrial and Appli...Journal overview:Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,one of the transactions of China Society for Industrial and Applied Mathematics,is a home for original research papers of the highest quality in all areas of mathematics with applications.The target audience comprises:pure and applied mathematicians,graduate students in broad felds of sciences and technology,scientists and engineers interested in mathematics.展开更多
Journal overview:Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,one of the transactions of China Society for Industrial and Appli...Journal overview:Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,one of the transactions of China Society for Industrial and Applied Mathematics,is a home for original research papers of the highest quality in all areas of mathematics with applications.The target audience comprises:pure and applied mathematicians,graduate students in broad fields of sciences and technology,scientists and engineers interested in mathematics.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
Journal overview:Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,one of the transactions of China Society for Industrial and Appli...Journal overview:Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,one of the transactions of China Society for Industrial and Applied Mathematics,is a home for original research papers of the highest quality in all areas of mathematics with applications.The target audience comprises:pure and applied mathematicians,graduate students in broad fields of sciences and technology,scientists and engineers interested in mathematics.展开更多
As a tool for quantifying individuals’visual attention and information processing,eye-tracking technology is gradually being applied in the reform of higher education.This paper focuses on issues in university mathem...As a tool for quantifying individuals’visual attention and information processing,eye-tracking technology is gradually being applied in the reform of higher education.This paper focuses on issues in university mathematics teaching,such as heavy cognitive load,delayed feedback,and insufficient adaptability.Based on theories of cognitive psychology,the study explores application pathways of this technology in cognitive diagnosis,instructional optimization,classroom regulation,personalized support,and teaching assessment.Research shows that eye-tracking data can reveal key cognitive features during the learning process,enhance the visualization of instructional feedback,and improve the scientific basis of decision-making.This provides both theoretical support and practical reference for data-driven and precise transformation in university mathematics education.展开更多
Under the background of information technology in education,there is insufficient integration of technological knowledge,pedagogical knowledge,and subject content knowledge in the teaching of propositions in high scho...Under the background of information technology in education,there is insufficient integration of technological knowledge,pedagogical knowledge,and subject content knowledge in the teaching of propositions in high school mathematics.Teachers mostly equate information technology with multimedia presentations,and students often memorize formulas mechanically,which leads to difficulties in the application of complex propositions.In this study,we take“the cosine formula of the difference between two angles”as an example.Based on the TPACK framework,we use contextual teaching and geometric drawing board demonstration to integrate subject content,pedagogical knowledge,and technological knowledge in teaching design and practice.It is found that by dynamically displaying the derivation process of the formula and guiding students to explore independently,it can help them understand the logic of the formula and improve their application ability.This study provides a paradigm for teaching propositions in high school mathematics and suggests that the TPACK framework can facilitate knowledge integration and cultivate students’mathematical literacy such as problem posing and creative inquiry,which is of great significance for teaching practice.展开更多
In the context of the“Two New”initiatives,high school mathematics instruction still grapples with three interlocking problems:knowledge fragmentation,limited cultivation of higher-order thinking,and weak alignment a...In the context of the“Two New”initiatives,high school mathematics instruction still grapples with three interlocking problems:knowledge fragmentation,limited cultivation of higher-order thinking,and weak alignment among teaching,learning,and assessment.To counter these challenges,we propose an Inquiry-Construction Double-Helix model that uses a domain-specific knowledge graph as its cognitive spine.The model interweaves two mutually reinforcing strands-student-driven inquiry and systematic knowledge construction-into a double-helix trajectory analogous to DNA replication.The Inquiry Strand is launched by authentic,situation-based tasks that shepherd students through the complete cycle:question→hypothesis→verification→reflection.The Construction Strand simultaneously externalizes,restructures,and internalizes core disciplinary concepts via visual,hierarchical knowledge graphs.Within the flow of a lesson,the two strands alternately dominate and scaffold each other,securing the co-development of conceptual understanding,procedural fluency,and mathematical literacy.Empirical evidence demonstrates that this model significantly enhances students’systematic knowledge integration,problem-solving transfer ability,and core mathematical competencies,offering a replicable and operable teaching paradigm and practical pathway for deepening high school mathematics classroom reform.展开更多
With the development of educational digitalization,how to effectively apply digital animation technology to traditional classroom teaching has become an urgent problem to be solved.This study explores the application ...With the development of educational digitalization,how to effectively apply digital animation technology to traditional classroom teaching has become an urgent problem to be solved.This study explores the application of Manim in the course of Mathematical Methods for Physics.Taking the visualization of Fourier series,complex numbers,and other content as examples,it improves students’understanding of complex and abstract mathematical physics concepts through dynamic and visual teaching methods.The teaching effect shows that Manim helps to enhance students’learning experience,improve teaching efficiency and effectiveness,and has a positive impact on students’active learning ability.The research in this paper can provide references and inspiration for the educational digitalization of higher education.展开更多
To meet the demands of higher education reform and innovative talent cultivation,the teaching team of Tarim University,with ability cultivation as the core,has established a new“331”university mathematics teaching s...To meet the demands of higher education reform and innovative talent cultivation,the teaching team of Tarim University,with ability cultivation as the core,has established a new“331”university mathematics teaching system.Through the multi-dimensional linkage of master teachers’guidance,course optimization,stratified teaching,practical reinforcement,and competition-driven,it has significantly improved students’mathematical application ability and innovative quality.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
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
In the context of the new era of education,advanced mathematics not only undertakes the function of knowledge transmission but also plays a vital role in cultivating logical thinking,scientific spirit,and value orient...In the context of the new era of education,advanced mathematics not only undertakes the function of knowledge transmission but also plays a vital role in cultivating logical thinking,scientific spirit,and value orientation.However,traditional teaching has overemphasized knowledge instillation while neglecting value guidance,making it difficult to meet the demands of cultivating interdisciplinary talents.This study introduces the OBE concept and constructs a“knowledge–ability–value”teaching framework,integrating outcome orientation,backward design,and diversified evaluation to promote the systematic incorporation of ideological and political education into the curriculum.Taking limits,definite integrals,and series as representative knowledge points,the paper designs case-based pathways to foster dialectical thinking,patriotism,and scientific spirit.Practice has shown that this model effectively unifies knowledge education and value education,enhancing students’logical reasoning,sense of responsibility,and scientific literacy.The study provides an operational pathway for the reform of ideological and political education in advanced mathematics courses and carries practical significance for implementing the goal of“all-round education.”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
文摘Journal overview:Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,one of the transactions of China Society for Industrial and Applied Mathematics,is a home for original research papers of the highest quality in all areas of mathematics with applications.The target audience comprises:pure and applied mathematicians,graduate students in broad fields of sciences and technology,scientists and engineers interested in mathematics.
文摘Journal overview:Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,one of the transactions of China Society for Industrial and Applied Mathematics,is a home for original research papers of the highest quality in all areas of mathematics with applications.The target audience comprises:pure and applied mathematicians,graduate students in broad fields of sciences and technology,scientists and engineers interested in mathematics.
文摘Journal overview:Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,one of the transactions of China Society for Industrial and Applied Mathematics,is a home for original research papers of the highest quality in all areas of mathematics with applications.The target audience comprises:pure and applied mathematicians,graduate students in broad fields of sciences and technology,scientists and engineers interested in mathematics.
基金support from National Natural Science Foundation of China(Grant No.51874033)to Prof.Hai-Yan Tang.
文摘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^(-5)m^(3),respectively,while the volume of air aspirated is 0.84×10^(-4),1.47×10^(-4),and 2.01×10^(-4)m^(3),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.
文摘Journal overview:Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,one of the transactions of China Society for Industrial and Applied Mathematics,is a home for original research papers of the highest quality in all areas of mathematics with applications.The target audience comprises:pure and applied mathematicians,graduate students in broad felds of sciences and technology,scientists and engineers interested in mathematics.
文摘Journal overview:Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,one of the transactions of China Society for Industrial and Applied Mathematics,is a home for original research papers of the highest quality in all areas of mathematics with applications.The target audience comprises:pure and applied mathematicians,graduate students in broad fields of sciences and technology,scientists and engineers interested in mathematics.
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.
文摘Journal overview:Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,one of the transactions of China Society for Industrial and Applied Mathematics,is a home for original research papers of the highest quality in all areas of mathematics with applications.The target audience comprises:pure and applied mathematicians,graduate students in broad fields of sciences and technology,scientists and engineers interested in mathematics.
基金The 2024 Education and Teaching Reform Project,“Exploration and Practice of University Mathematics Teaching Reform Driven by Eye-Tracking Technology”(Project No.:JG2024047)。
文摘As a tool for quantifying individuals’visual attention and information processing,eye-tracking technology is gradually being applied in the reform of higher education.This paper focuses on issues in university mathematics teaching,such as heavy cognitive load,delayed feedback,and insufficient adaptability.Based on theories of cognitive psychology,the study explores application pathways of this technology in cognitive diagnosis,instructional optimization,classroom regulation,personalized support,and teaching assessment.Research shows that eye-tracking data can reveal key cognitive features during the learning process,enhance the visualization of instructional feedback,and improve the scientific basis of decision-making.This provides both theoretical support and practical reference for data-driven and precise transformation in university mathematics education.
文摘Under the background of information technology in education,there is insufficient integration of technological knowledge,pedagogical knowledge,and subject content knowledge in the teaching of propositions in high school mathematics.Teachers mostly equate information technology with multimedia presentations,and students often memorize formulas mechanically,which leads to difficulties in the application of complex propositions.In this study,we take“the cosine formula of the difference between two angles”as an example.Based on the TPACK framework,we use contextual teaching and geometric drawing board demonstration to integrate subject content,pedagogical knowledge,and technological knowledge in teaching design and practice.It is found that by dynamically displaying the derivation process of the formula and guiding students to explore independently,it can help them understand the logic of the formula and improve their application ability.This study provides a paradigm for teaching propositions in high school mathematics and suggests that the TPACK framework can facilitate knowledge integration and cultivate students’mathematical literacy such as problem posing and creative inquiry,which is of great significance for teaching practice.
文摘In the context of the“Two New”initiatives,high school mathematics instruction still grapples with three interlocking problems:knowledge fragmentation,limited cultivation of higher-order thinking,and weak alignment among teaching,learning,and assessment.To counter these challenges,we propose an Inquiry-Construction Double-Helix model that uses a domain-specific knowledge graph as its cognitive spine.The model interweaves two mutually reinforcing strands-student-driven inquiry and systematic knowledge construction-into a double-helix trajectory analogous to DNA replication.The Inquiry Strand is launched by authentic,situation-based tasks that shepherd students through the complete cycle:question→hypothesis→verification→reflection.The Construction Strand simultaneously externalizes,restructures,and internalizes core disciplinary concepts via visual,hierarchical knowledge graphs.Within the flow of a lesson,the two strands alternately dominate and scaffold each other,securing the co-development of conceptual understanding,procedural fluency,and mathematical literacy.Empirical evidence demonstrates that this model significantly enhances students’systematic knowledge integration,problem-solving transfer ability,and core mathematical competencies,offering a replicable and operable teaching paradigm and practical pathway for deepening high school mathematics classroom reform.
基金supported by the Teaching Reform Research Project of Shaanxi University of Science&Technology(23Y083)the Project of National University Association for Mathematical Methods in Physics(JZW-23-SL-02)+3 种基金the Graduate Course Construction Project of Shaanxi University of Science&Technology(KC2024Y03)the 2024 National Higher Education University Physics Reform Research Project(2024PR064)the Teaching Reform Research Project of the International Office of Shaanxi University of Science&Technology(YB202410)Graduate Education and Teaching Reform Research Project of Shaanxi University of Science&Technology(JG2025Y18).
文摘With the development of educational digitalization,how to effectively apply digital animation technology to traditional classroom teaching has become an urgent problem to be solved.This study explores the application of Manim in the course of Mathematical Methods for Physics.Taking the visualization of Fourier series,complex numbers,and other content as examples,it improves students’understanding of complex and abstract mathematical physics concepts through dynamic and visual teaching methods.The teaching effect shows that Manim helps to enhance students’learning experience,improve teaching efficiency and effectiveness,and has a positive impact on students’active learning ability.The research in this paper can provide references and inspiration for the educational digitalization of higher education.
基金Advanced Mathematics A1 First-Class Course of Tarim University(TDYLKC202428)Educational Reform Project of Xinjiang Production and Construction Corps(BTBKXM-2024-Y41)。
文摘To meet the demands of higher education reform and innovative talent cultivation,the teaching team of Tarim University,with ability cultivation as the core,has established a new“331”university mathematics teaching system.Through the multi-dimensional linkage of master teachers’guidance,course optimization,stratified teaching,practical reinforcement,and competition-driven,it has significantly improved students’mathematical application ability and innovative quality.
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 Deanship of Scientific Research,Vice Presidency for Graduate Studies and Scientific Research,King Faisal University,Saudi Arabia[Grant No.KFU252959].
文摘Malaria is a significant global health challenge.This devastating disease continues to affect millions,especially in tropical regions.It is caused by Plasmodium parasites transmitted by female Anopheles mosquitoes.This study introduces a nonlinear mathematical model for examining the transmission dynamics of malaria,incorporating both human and mosquito populations.We aim to identify the key factors driving the endemic spread of malaria,determine feasible solutions,and provide insights that lead to the development of effective prevention and management strategies.We derive the basic reproductive number employing the next-generation matrix approach and identify the disease-free and endemic equilibrium points.Stability analyses indicate that the disease-free equilibrium is locally and globally stable when the reproductive number is below one,whereas an endemic equilibrium persists when this threshold is exceeded.Sensitivity analysis identifies the most influential mosquito-related parameters,particularly the bite rate and mosquito mortality,in controlling the spread of malaria.Furthermore,we extend our model to include a treatment compartment and three disease-preventive control variables such as antimalaria drug treatments,use of larvicides,and the use of insecticide-treated mosquito nets for optimal control analysis.The results show that optimal use of mosquito nets,use of larvicides for mosquito population control,and treatment can lower the basic reproduction number and control malaria transmission with minimal intervention costs.The analysis of disease control strategies and findings offers valuable information for policymakers in designing cost-effective strategies to combat malaria.
基金2024 Education and Teaching Reform Project(Project No.:JG2024047)Basic Scientific Research Funding of the Xinjiang Uygur Autonomous Region(Project No.:XQZX20250005)。
文摘In the context of the new era of education,advanced mathematics not only undertakes the function of knowledge transmission but also plays a vital role in cultivating logical thinking,scientific spirit,and value orientation.However,traditional teaching has overemphasized knowledge instillation while neglecting value guidance,making it difficult to meet the demands of cultivating interdisciplinary talents.This study introduces the OBE concept and constructs a“knowledge–ability–value”teaching framework,integrating outcome orientation,backward design,and diversified evaluation to promote the systematic incorporation of ideological and political education into the curriculum.Taking limits,definite integrals,and series as representative knowledge points,the paper designs case-based pathways to foster dialectical thinking,patriotism,and scientific spirit.Practice has shown that this model effectively unifies knowledge education and value education,enhancing students’logical reasoning,sense of responsibility,and scientific literacy.The study provides an operational pathway for the reform of ideological and political education in advanced mathematics courses and carries practical significance for implementing the goal of“all-round education.”
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.
