Automatically answer math word problems is a challenging task in artificial intelligence.Previous solvers constructed mathematical expressions in sequence or binary tree.However,these approaches may suffer from the fo...Automatically answer math word problems is a challenging task in artificial intelligence.Previous solvers constructed mathematical expressions in sequence or binary tree.However,these approaches may suffer from the following issues:Models relying on such structures exhibit fixed-order reasoning(e.g.,left-to-right),limiting flexibility and increasing error susceptibility;prior models rely on autoregressive reasoning in a single pass,accumulating minor errors(e.g.,incorrect math symbols)during generation,resulting in reduced accuracy.To address the above issues,we emulate the human“check and modify”process in reasoning and propose a unified M-tree self-correction solver(UTSCSolver)by iterative inference with self-correction mechanism.First,we use an iterative,non-autoregressive process for generating mathematical expressions,free from fixed generation orders to handle complex and diverse problems.Additionally,we design a self-correction mechanism based on alternating execution between a generator and a discriminator.This module iteratively detects and rectifies errors in generated expressions,leveraging previous iteration information for subsequent generation guidance.Experimental results show that our UTSC-Solver outperforms traditional models in accuracy on two popular datasets,while it improves the interpretability of mathematical reasoning.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
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 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
主题语境:个人成长与教育,篇幅:357词,建议用时:7分钟,In a remarkable academic feat,10-year-old Alisa Perales from San Bernardino is set to receive two associate degrees,becoming the youngest graduate in her schools histo...主题语境:个人成长与教育,篇幅:357词,建议用时:7分钟,In a remarkable academic feat,10-year-old Alisa Perales from San Bernardino is set to receive two associate degrees,becoming the youngest graduate in her schools history.According to California Community Colleges,she achieved these degrees in multiple sciences and mathematics with a near-perfect GPA.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
In this work,we consider the collapse of a D-dimensional sphere in the framework of a higher-dimensional spherically symmetric space-time in which the gravitational action chosen is claimed to be somehow linked to the...In this work,we consider the collapse of a D-dimensional sphere in the framework of a higher-dimensional spherically symmetric space-time in which the gravitational action chosen is claimed to be somehow linked to the D-dimensional modified term.This work investigates the criteria for the dynamical instability of anisotropic relativistic sphere systems with D-dimensional modified gravity.The certain conditions are applied that lead to the collapse equation and their effects on adiabatic indexΓin both Newtonian(N)and Post-Newtonian(PN)regimes by using a perturbation scheme.The study explores that theΓplays a crucial role in determining the degree of dynamical instability.This index characterizes the fluid's stiffness and has a significant impact on defining the ranges of instability.This systematic investigation demonstrates the influence of various material properties such as anisotropic pressure,kinematic quantities,mass function,D-dimensional modified gravity parameters,and the radial profile of energy density on the instability of considered structures during their evolution.This work also displays the dynamical behavior of spherically symmetric fluid configuration via graphical approaches.展开更多
Howarth provides a deep view of the history of those geophysical sciences of the 19th and 20th centuries bordering most closely on geology,a task for which he is well qualified.He studied geology in the 1960s,he taugh...Howarth provides a deep view of the history of those geophysical sciences of the 19th and 20th centuries bordering most closely on geology,a task for which he is well qualified.He studied geology in the 1960s,he taught the application of statistics to geology for thirty years,and he has published broadly on mathematical geology.In a series of journal articles he has also used this expertise to examine the often unexplained quantitative methods used to map Earth’s magnetic declination in the 18^(th)century.He also applied his extensive background in graphical methods in the geosciences to the history of mineralogy and petrology.In short,Dr.Howarth is a geologist with historical sensibilities and an eye for the roles of mathematics and physics in geological development.This important book culminates decades of historical research.展开更多
In exploring hypersonic propulsion,precooler combined engines require the development of lightweight,efficient,and compact heat exchangers(HX).As additive manufacturing technology continues to progress,triply periodic...In exploring hypersonic propulsion,precooler combined engines require the development of lightweight,efficient,and compact heat exchangers(HX).As additive manufacturing technology continues to progress,triply periodic minimal surface(TPMS)structures,characterized by exceptionally high surface area to volume ratios and intricate geometric structures,have demonstrated superior heat transfer performance.This research examines the thermal-hydraulic(TH)behavior of FKS and Diamond as heat transfer structures under different Reynolds numbers through numerical simulations.The Nusselt number for FKS is 13.2%–17.6%higher than Diamond,while the friction factor for FKS is approximately 18.8%–29.3%higher.A detailed analysis of the internal flow mechanisms reveals that the flow pattern within TPMS can be summarized as cyclic convergence-separation-convergence.The fluid experiences constant disturbances from the structure in all spatial directions,generating strong turbulent mixing and large wall shear stresses,which significantly enhance heat transfer performance.展开更多
In this letter,we discuss the article by Li et al published in the World Journal of Gastrointestinal Surgery.Gallbladder cancer is a rare but fatal cancer that is often detected unexpectedly and at an advanced stage f...In this letter,we discuss the article by Li et al published in the World Journal of Gastrointestinal Surgery.Gallbladder cancer is a rare but fatal cancer that is often detected unexpectedly and at an advanced stage following routine cholecystectomy.Although the prognosis is poor,curative resections often combined with postoperative chemotherapy and/or radiation therapy can improve survival.However,targeted patient selection for the appropriate therapeutic approach is critical to minimize unnecessary morbidity.Using advanced statistical techniques,the authors developed a nomogram with the potential to predict survival after gallbladder cancer resection,identifying factors associated with long-and shortterm survival.This tool could improve patient selection for surgery and postoperative treatment.In this letter,we provide background on survival nomograms including an in-depth discussion of statistical methods employed in this study,the use of nomograms in other forms of cancer,limitations to the model,and directions for future research.展开更多
This study introduces an innovative computational framework leveraging the transformer architecture to address a critical challenge in chemical process engineering:predicting and optimizing light olefin yields in indu...This study introduces an innovative computational framework leveraging the transformer architecture to address a critical challenge in chemical process engineering:predicting and optimizing light olefin yields in industrial methanol-to-olefins(MTO)processes.Our approach integrates advanced machine learning techniques with chemical engineering principles to tackle the complexities of non-stationary,highly volatile production data in large-scale chemical manufacturing.The framework employs the maximal information coefficient(MIC)algorithm to analyze and select the significant variables from MTO process parameters,forming a robust dataset for model development.We implement a transformer-based time series forecasting model,enhanced through positional encoding and hyperparameter optimization,significantly improving predictive accuracy for ethylene and propylene yields.The model's interpretability is augmented by applying SHapley additive exPlanations(SHAP)to quantify and visualize the impact of reaction control variables on olefin yields,providing valuable insights for process optimization.Experimental results demonstrate that our model outperforms traditional statistical and machine learning methods in accuracy and interpretability,effectively handling nonlinear,non-stationary,highvolatility,and long-sequence data challenges in olefin yield prediction.This research contributes to chemical engineering by providing a novel computerized methodology for solving complex production optimization problems in the chemical industry,offering significant potential for enhancing decisionmaking in MTO system production control and fostering the intelligent transformation of manufacturing processes.展开更多
To ameliorate the difficulties of on-site dynamic disaster control in the end-mining stage of traditional mining engineering,this paper introduces the mathematical research and engineering application of the end-minin...To ameliorate the difficulties of on-site dynamic disaster control in the end-mining stage of traditional mining engineering,this paper introduces the mathematical research and engineering application of the end-mining technology system with non-pillar in mines(ETSNM)in recent years.The petal warning criterion for the stability of the surrounding rock of the roadway at the end-mining stage was obtained by studying the inverse problem of the petal theorem.A conformal mathematical model of the end-mining stage was established using the conformal mapping method,and the limit theorem of the peak point of mine pressure(LTPPMP)in the end-mining stage was demonstrated.Based on the cross-fusion of the above basic mathematical theory and the LTPPMP,a new ETSNM model was proposed,which includes no coal pillar,no dedicated retracement roadways,and fast retracement equipment(NNF).The mathematical principles of engineering technology for height control,speed limit,and roof cutting in the end-mining stage with non-pillar were revealed.The scientific and application values of the ETSNM were confirmed through engineering applications.Based on this,a new non-pillar control technology for dynamic disasters in the end-mining stage was proposed.The above research will play an active role in promoting the engineering application of ETSNM driven by mathematical theory.展开更多
Pipeline Inspection Gauge(pig)is an important equipment for oil and gas pipelines during different stages of their operations to perform functions such as dewatering,cleaning,and inspection.Owing to the hyperelasticit...Pipeline Inspection Gauge(pig)is an important equipment for oil and gas pipelines during different stages of their operations to perform functions such as dewatering,cleaning,and inspection.Owing to the hyperelasticity,time and temperature-dependent material behaviour of the sealing disc attached on the pig,the contact between the pig and the pipeline expresses complex behaviour,leading to an uncertainty in the prediction of the pig's frictional force.Knowing the deformation of the sealing discs well is essential and can be highly meaningful for predicting the pig motion,as well as reducing the pigging risks.In this study,the geometrical deformation of the sealing discs with different sizes are investigated through experiments and numerical simulations.The effects of the four nondimensionalized parameters(interference,thickness per pipeline inner diameter,and clamping ratio)of the sealing discs on the deformation behaviour were observed and discussed,and an improved mathematical model for predicting the geometrical deformation of the sealing discs was proposed and verified.With the auxiliary angleαadded in the improved mathematical model,the relative error declines to 1.87%and 3.18%respectively for predicting deformation of the sealing discs in size of 2-inch and 40-inch pig.The results of this study can help better understand the frictional force of a pig with sealing discs,as well as its motion.展开更多
In 1955,a young woman named Annie Easley heard about jobs at a space center in Ohio.The space centre was looking for“human computers”.This was before most people used computer machines.The space centre wanted people...In 1955,a young woman named Annie Easley heard about jobs at a space center in Ohio.The space centre was looking for“human computers”.This was before most people used computer machines.The space centre wanted people with strong maths skills.Annie was only twenty-two,but she had always been good at maths.So she got the job.In time,the space centre Annie worked at became a part of NASA,which sends people into space.展开更多
To ensure the dimensional accuracy of the final blade profile,it is necessary for precision Electrochemical Machining(ECM)of blade profile to come into an equilibrium state.However,after Electrochemical Trepanning(ECT...To ensure the dimensional accuracy of the final blade profile,it is necessary for precision Electrochemical Machining(ECM)of blade profile to come into an equilibrium state.However,after Electrochemical Trepanning(ECTr),the cascade channel of the blisk is narrow,and the blank allowance distribution is uneven,making it difficult for the precision ECM to become balanced.In blisk production,the two-step method cannot make precision ECM enter equilibrium for some blisk types.A three-step processing method is proposed to overcome this problem.The threestep method adds Electrochemical Homogenizing Machining(ECHM)between the ECTr and precision ECM steps so that the blank allowance can be homogenized quickly without unduly affecting the minimum allowance.Comparative machining experiments of the two-and three-step methods were performed to verify the improvement to blade machining accuracy.The processing results show that the contour parameters of the blade after the three-step method implementation are much better.The allowance difference of the concave(convex)side decreased by 70.5%(65%).In addition,the current in the three-step method is stable at 110 A at the end of precision ECM,verifying successfully entering the equilibrium state.展开更多
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
This geo-historical case study analyses Vistelius’ingenious idea of conceptual stochastic models and their application as Markov chain analysis in the geosciences.Vistelius(1915–1995)is regarded as one of the founde...This geo-historical case study analyses Vistelius’ingenious idea of conceptual stochastic models and their application as Markov chain analysis in the geosciences.Vistelius(1915–1995)is regarded as one of the founders of mathematical geology.He was the fi rst to defi ne mathematical geology as“a scientifi c discipline concerned with the construction,analysis and use of conceptual mathematical models of geological events to solve concrete problems”(Vistelius in Principles of mathematical geology,Nauka,Leningrad,1980;Principles of mathematical geology,Kluwer Academic Publishers,Dordrecht,1992).Mathematical models in this context should be primarily probabilistic because of the large number of infl uencing natural factors.They must be conceptual to avoid fundamental errors in application.Vistelius devoted his seminal book to geological random sequences and their description and analysis using Markov models as stochastic tools.He applied this approach to grain sequences in granitic intrusive rocks and to sedimentary rock layers.Among other things,Vistelius has used Markov chain analysis in mineral resource exploration to distinguish between“ideal”granites,which are not subsequently mineralized,and mainly hydrothermally mineralized,sometimes ore-bearing granites which contain at least two generations of main minerals.The application of this special conceptual stochastic model is demonstrated on Lusatian granite(Saxony,Germany).展开更多
基金supported by the National Natural Science Foundation of China(62106244)the Fundamental Research Funds for the Central Universities(WK2150110021)the University Synergy Innovation Program of Anhui Province(GXXT-2022-042).
文摘Automatically answer math word problems is a challenging task in artificial intelligence.Previous solvers constructed mathematical expressions in sequence or binary tree.However,these approaches may suffer from the following issues:Models relying on such structures exhibit fixed-order reasoning(e.g.,left-to-right),limiting flexibility and increasing error susceptibility;prior models rely on autoregressive reasoning in a single pass,accumulating minor errors(e.g.,incorrect math symbols)during generation,resulting in reduced accuracy.To address the above issues,we emulate the human“check and modify”process in reasoning and propose a unified M-tree self-correction solver(UTSCSolver)by iterative inference with self-correction mechanism.First,we use an iterative,non-autoregressive process for generating mathematical expressions,free from fixed generation orders to handle complex and diverse problems.Additionally,we design a self-correction mechanism based on alternating execution between a generator and a discriminator.This module iteratively detects and rectifies errors in generated expressions,leveraging previous iteration information for subsequent generation guidance.Experimental results show that our UTSC-Solver outperforms traditional models in accuracy on two popular datasets,while it improves the interpretability of mathematical reasoning.
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.
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.
文摘主题语境:个人成长与教育,篇幅:357词,建议用时:7分钟,In a remarkable academic feat,10-year-old Alisa Perales from San Bernardino is set to receive two associate degrees,becoming the youngest graduate in her schools history.According to California Community Colleges,she achieved these degrees in multiple sciences and mathematics with a near-perfect GPA.
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supported by Researchers Supporting Project number:RSPD2024R650,King Saud University,Riyadh,Saudi Arabia(BA)。
文摘In this work,we consider the collapse of a D-dimensional sphere in the framework of a higher-dimensional spherically symmetric space-time in which the gravitational action chosen is claimed to be somehow linked to the D-dimensional modified term.This work investigates the criteria for the dynamical instability of anisotropic relativistic sphere systems with D-dimensional modified gravity.The certain conditions are applied that lead to the collapse equation and their effects on adiabatic indexΓin both Newtonian(N)and Post-Newtonian(PN)regimes by using a perturbation scheme.The study explores that theΓplays a crucial role in determining the degree of dynamical instability.This index characterizes the fluid's stiffness and has a significant impact on defining the ranges of instability.This systematic investigation demonstrates the influence of various material properties such as anisotropic pressure,kinematic quantities,mass function,D-dimensional modified gravity parameters,and the radial profile of energy density on the instability of considered structures during their evolution.This work also displays the dynamical behavior of spherically symmetric fluid configuration via graphical approaches.
文摘Howarth provides a deep view of the history of those geophysical sciences of the 19th and 20th centuries bordering most closely on geology,a task for which he is well qualified.He studied geology in the 1960s,he taught the application of statistics to geology for thirty years,and he has published broadly on mathematical geology.In a series of journal articles he has also used this expertise to examine the often unexplained quantitative methods used to map Earth’s magnetic declination in the 18^(th)century.He also applied his extensive background in graphical methods in the geosciences to the history of mineralogy and petrology.In short,Dr.Howarth is a geologist with historical sensibilities and an eye for the roles of mathematics and physics in geological development.This important book culminates decades of historical research.
基金supported by the Natural Science Basic Research Program of Shaanxi(Program No.2024JC-YBMS-449)Project ZR2022QE233 supported by Shandong Provincial Natural Science Foundation.
文摘In exploring hypersonic propulsion,precooler combined engines require the development of lightweight,efficient,and compact heat exchangers(HX).As additive manufacturing technology continues to progress,triply periodic minimal surface(TPMS)structures,characterized by exceptionally high surface area to volume ratios and intricate geometric structures,have demonstrated superior heat transfer performance.This research examines the thermal-hydraulic(TH)behavior of FKS and Diamond as heat transfer structures under different Reynolds numbers through numerical simulations.The Nusselt number for FKS is 13.2%–17.6%higher than Diamond,while the friction factor for FKS is approximately 18.8%–29.3%higher.A detailed analysis of the internal flow mechanisms reveals that the flow pattern within TPMS can be summarized as cyclic convergence-separation-convergence.The fluid experiences constant disturbances from the structure in all spatial directions,generating strong turbulent mixing and large wall shear stresses,which significantly enhance heat transfer performance.
文摘In this letter,we discuss the article by Li et al published in the World Journal of Gastrointestinal Surgery.Gallbladder cancer is a rare but fatal cancer that is often detected unexpectedly and at an advanced stage following routine cholecystectomy.Although the prognosis is poor,curative resections often combined with postoperative chemotherapy and/or radiation therapy can improve survival.However,targeted patient selection for the appropriate therapeutic approach is critical to minimize unnecessary morbidity.Using advanced statistical techniques,the authors developed a nomogram with the potential to predict survival after gallbladder cancer resection,identifying factors associated with long-and shortterm survival.This tool could improve patient selection for surgery and postoperative treatment.In this letter,we provide background on survival nomograms including an in-depth discussion of statistical methods employed in this study,the use of nomograms in other forms of cancer,limitations to the model,and directions for future research.
基金supported by the Humanities and Social Sciences Foundation of the Ministry of Education(22YJC910011)the China Postdoctoral Science Foundation(2023M733444)the Key Research and Development Program in Artificial Intelligence of Liaoning Province(2023JH26/10200012).
文摘This study introduces an innovative computational framework leveraging the transformer architecture to address a critical challenge in chemical process engineering:predicting and optimizing light olefin yields in industrial methanol-to-olefins(MTO)processes.Our approach integrates advanced machine learning techniques with chemical engineering principles to tackle the complexities of non-stationary,highly volatile production data in large-scale chemical manufacturing.The framework employs the maximal information coefficient(MIC)algorithm to analyze and select the significant variables from MTO process parameters,forming a robust dataset for model development.We implement a transformer-based time series forecasting model,enhanced through positional encoding and hyperparameter optimization,significantly improving predictive accuracy for ethylene and propylene yields.The model's interpretability is augmented by applying SHapley additive exPlanations(SHAP)to quantify and visualize the impact of reaction control variables on olefin yields,providing valuable insights for process optimization.Experimental results demonstrate that our model outperforms traditional statistical and machine learning methods in accuracy and interpretability,effectively handling nonlinear,non-stationary,highvolatility,and long-sequence data challenges in olefin yield prediction.This research contributes to chemical engineering by providing a novel computerized methodology for solving complex production optimization problems in the chemical industry,offering significant potential for enhancing decisionmaking in MTO system production control and fostering the intelligent transformation of manufacturing processes.
基金supported by the National Natural Science Foundation of China(No.12071047,51774289,52074291).
文摘To ameliorate the difficulties of on-site dynamic disaster control in the end-mining stage of traditional mining engineering,this paper introduces the mathematical research and engineering application of the end-mining technology system with non-pillar in mines(ETSNM)in recent years.The petal warning criterion for the stability of the surrounding rock of the roadway at the end-mining stage was obtained by studying the inverse problem of the petal theorem.A conformal mathematical model of the end-mining stage was established using the conformal mapping method,and the limit theorem of the peak point of mine pressure(LTPPMP)in the end-mining stage was demonstrated.Based on the cross-fusion of the above basic mathematical theory and the LTPPMP,a new ETSNM model was proposed,which includes no coal pillar,no dedicated retracement roadways,and fast retracement equipment(NNF).The mathematical principles of engineering technology for height control,speed limit,and roof cutting in the end-mining stage with non-pillar were revealed.The scientific and application values of the ETSNM were confirmed through engineering applications.Based on this,a new non-pillar control technology for dynamic disasters in the end-mining stage was proposed.The above research will play an active role in promoting the engineering application of ETSNM driven by mathematical theory.
基金supported by Key Technologies Research and Development Program(Grant No.SQ2022YFC2806103)and the National Natural Science Foundation of China(Grant No.51509259).
文摘Pipeline Inspection Gauge(pig)is an important equipment for oil and gas pipelines during different stages of their operations to perform functions such as dewatering,cleaning,and inspection.Owing to the hyperelasticity,time and temperature-dependent material behaviour of the sealing disc attached on the pig,the contact between the pig and the pipeline expresses complex behaviour,leading to an uncertainty in the prediction of the pig's frictional force.Knowing the deformation of the sealing discs well is essential and can be highly meaningful for predicting the pig motion,as well as reducing the pigging risks.In this study,the geometrical deformation of the sealing discs with different sizes are investigated through experiments and numerical simulations.The effects of the four nondimensionalized parameters(interference,thickness per pipeline inner diameter,and clamping ratio)of the sealing discs on the deformation behaviour were observed and discussed,and an improved mathematical model for predicting the geometrical deformation of the sealing discs was proposed and verified.With the auxiliary angleαadded in the improved mathematical model,the relative error declines to 1.87%and 3.18%respectively for predicting deformation of the sealing discs in size of 2-inch and 40-inch pig.The results of this study can help better understand the frictional force of a pig with sealing discs,as well as its motion.
文摘In 1955,a young woman named Annie Easley heard about jobs at a space center in Ohio.The space centre was looking for“human computers”.This was before most people used computer machines.The space centre wanted people with strong maths skills.Annie was only twenty-two,but she had always been good at maths.So she got the job.In time,the space centre Annie worked at became a part of NASA,which sends people into space.
基金supported by the National Natural Science Foundation of China(No.52075253)the Innovation Research Team of the National Natural Science Foundation of China(No.51921003)。
文摘To ensure the dimensional accuracy of the final blade profile,it is necessary for precision Electrochemical Machining(ECM)of blade profile to come into an equilibrium state.However,after Electrochemical Trepanning(ECTr),the cascade channel of the blisk is narrow,and the blank allowance distribution is uneven,making it difficult for the precision ECM to become balanced.In blisk production,the two-step method cannot make precision ECM enter equilibrium for some blisk types.A three-step processing method is proposed to overcome this problem.The threestep method adds Electrochemical Homogenizing Machining(ECHM)between the ECTr and precision ECM steps so that the blank allowance can be homogenized quickly without unduly affecting the minimum allowance.Comparative machining experiments of the two-and three-step methods were performed to verify the improvement to blade machining accuracy.The processing results show that the contour parameters of the blade after the three-step method implementation are much better.The allowance difference of the concave(convex)side decreased by 70.5%(65%).In addition,the current in the three-step method is stable at 110 A at the end of precision ECM,verifying successfully entering the equilibrium state.
基金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.
基金Open Access funding enabled and organized by Projekt DEAL.
文摘This geo-historical case study analyses Vistelius’ingenious idea of conceptual stochastic models and their application as Markov chain analysis in the geosciences.Vistelius(1915–1995)is regarded as one of the founders of mathematical geology.He was the fi rst to defi ne mathematical geology as“a scientifi c discipline concerned with the construction,analysis and use of conceptual mathematical models of geological events to solve concrete problems”(Vistelius in Principles of mathematical geology,Nauka,Leningrad,1980;Principles of mathematical geology,Kluwer Academic Publishers,Dordrecht,1992).Mathematical models in this context should be primarily probabilistic because of the large number of infl uencing natural factors.They must be conceptual to avoid fundamental errors in application.Vistelius devoted his seminal book to geological random sequences and their description and analysis using Markov models as stochastic tools.He applied this approach to grain sequences in granitic intrusive rocks and to sedimentary rock layers.Among other things,Vistelius has used Markov chain analysis in mineral resource exploration to distinguish between“ideal”granites,which are not subsequently mineralized,and mainly hydrothermally mineralized,sometimes ore-bearing granites which contain at least two generations of main minerals.The application of this special conceptual stochastic model is demonstrated on Lusatian granite(Saxony,Germany).
