Aim To study the Lie symmetries and conserved quantities of the dynamical equationsof relative motion for holonomic mechanical systems. Methods Lie's method of the invariance of ordinary differential equations u...Aim To study the Lie symmetries and conserved quantities of the dynamical equationsof relative motion for holonomic mechanical systems. Methods Lie's method of the invariance of ordinary differential equations under infinitesimal transformations was used. Results and Conclusion The determining equaiton of the Lie symmetries for the dynamical equationS of relative motion is established.The structure quation and the form conserved quantities are obtained. An example iD illustrate the application of the result is given.展开更多
This paper discusses in detail the conformal invariance by infinitesimal transformations of a dynamical system of relative motion. The necessary and sufficient conditions of conformal invariance and Lie symmetry are g...This paper discusses in detail the conformal invariance by infinitesimal transformations of a dynamical system of relative motion. The necessary and sufficient conditions of conformal invariance and Lie symmetry are given simultaneously by the action of infinitesimal transformations. Then it obtains the conserved quantities of conformal invariance by the infinitesimal transformations. Finally an example is given to illustrate the application of the results.展开更多
Lie symmetry and the generalized Hojman conserved quantity of Nielsen equations for a variable mass holonomic system of relative motion are studied. The determining equation of Lie symmetry of Nielsen equations for a ...Lie symmetry and the generalized Hojman conserved quantity of Nielsen equations for a variable mass holonomic system of relative motion are studied. The determining equation of Lie symmetry of Nielsen equations for a variable mass holonomic system of relative motion under the infinitesimal transformations of groups is given. The expression of generalized Hojman conserved quantity deduced directly from Lie symmetry for a variable mass holonomic system of relative motion is obtained. An example is given to illustrate the application of the results.展开更多
Mei symmetry and Mei conserved quantity of Appell equations for a variable mass holonomic system of relative motion are studied.The definition and criterion of the Mei symmetry of Appell equations for a variable mass ...Mei symmetry and Mei conserved quantity of Appell equations for a variable mass holonomic system of relative motion are studied.The definition and criterion of the Mei symmetry of Appell equations for a variable mass holonomic system of relative motion under the infinitesimal transformations of groups are given.The structural equation of Mei symmetry of Appell equations and the expression of Mei conserved quantity deduced directly from Mei symmetry for a variable mass holonomic system of relative motion are gained.Finally,an example is given to illustrate the application of the results.展开更多
The Lie symmetry and Hojman conserved quantity of Nielsen equations in a dynamical system of relative motion with nonholonomic constraint of the Chetaev type are studied. The differential equations of motion of the Ni...The Lie symmetry and Hojman conserved quantity of Nielsen equations in a dynamical system of relative motion with nonholonomic constraint of the Chetaev type are studied. The differential equations of motion of the Nielsen equation for the system, the definition and the criterion of Lie symmetry, and the expression of the Hojman conserved quantity deduced directly from the Lie symmetry for the system are obtained. An example is given to illustrate the application of the results.展开更多
Noether symmetry of Nielsen equation and Noether conserved quantity deduced directly from Noether symmetry for dynamical systems of the relative motion are studied. The definition and criteria of Noether symmetry of a...Noether symmetry of Nielsen equation and Noether conserved quantity deduced directly from Noether symmetry for dynamical systems of the relative motion are studied. The definition and criteria of Noether symmetry of a Nielsen equation under the infinitesimal transformations of groups are given. Expression of Noether conserved quantity deduced directly from Noether symmetry of Nielsen equation for the system are obtained. Finally, an example is given to illustrate the application of the results.展开更多
The Mei symmetry and the Mei conserved quantity of Appell equations in a dynamical system of relative motion with non-Chetaev nonholonomic constraints are studied.The differential equations of motion of the Appell equ...The Mei symmetry and the Mei conserved quantity of Appell equations in a dynamical system of relative motion with non-Chetaev nonholonomic constraints are studied.The differential equations of motion of the Appell equation for the system,the definition and the criterion of the Mei symmetry,and the expression of the Mei conserved quantity deduced directly from the Mei symmetry for the system are obtained.An example is given to illustrate the application of the results.展开更多
In this paper, the Lie-form invariance of a nonholonomic system of relative motion in event space is studied. Firstly, the definition and the criterion of the Lie-form invariance of the nonholonomic system of relative...In this paper, the Lie-form invariance of a nonholonomic system of relative motion in event space is studied. Firstly, the definition and the criterion of the Lie-form invariance of the nonholonomic system of relative motion in event space is given. Secondly, the Hojman conserved quantity and a new type of conserved quantity deduced from the Lie-form invariance are obtained. An example is given to illustrate the application of the results.展开更多
A qualia role-based entity-dependency graph(EDG)is proposed to represent and extract quantity relations for solving algebra story problems stated in Chinese.Traditional neural solvers use end-to-end models to translat...A qualia role-based entity-dependency graph(EDG)is proposed to represent and extract quantity relations for solving algebra story problems stated in Chinese.Traditional neural solvers use end-to-end models to translate problem texts into math expressions,which lack quantity relation acquisition in sophisticated scenarios.To address the problem,the proposed method leverages EDG to represent quantity relations hidden in qualia roles of math objects.Algorithms were designed for EDG generation and quantity relation extraction for solving algebra story problems.Experimental result shows that the proposedmethod achieved an average accuracy of 82.2%on quantity relation extraction compared to 74.5%of baseline method.Another prompt learning result shows a 5%increase obtained in problem solving by injecting the extracted quantity relations into the baseline neural solvers.展开更多
This study aims to examine the usability of environmentally harmless vegetable oil in the minimum quantity of lubrication(MQL)system in face milling of AISI O2 steel and to optimize the cutting parameters by different...This study aims to examine the usability of environmentally harmless vegetable oil in the minimum quantity of lubrication(MQL)system in face milling of AISI O2 steel and to optimize the cutting parameters by different statistical methods.Vegetable oil was preferred as cutting fluid,and Taguchi method was used in the preparation of the test pattern.After testing with the prepared test pattern,cutting performance in all parameters has been improved according to dry conditions thanks to the MQL system.The highest tool life was obtained by using cutting parameters of 7.5 m cutting length,100 m/min cutting speed,100 mL/h MQL flow rate and 0.1 mm/tooth feed rate.Optimum cutting parameters were determined according to the Taguchi analysis,and the obtained parameters were confirmed with the verification tests.In addition,the optimum test parameter was determined by applying the gray relational analysis method.After using ANOVA analysis according to the measured surface roughness and cutting force values,the most effective cutting parameter was observed to be the feed rate.In addition,the models for surface roughness and cutting force values were obtained with precisions of 99.63%and 99.68%,respectively.Effective wear mechanisms were found to be abrasion and adhesion.展开更多
The effects of rare earth on the growth of rice, rape and soybean in three kinds of soils were studied with the method supposed by Economic Co-operation and Development organization (OECD), and the EC50(median growth...The effects of rare earth on the growth of rice, rape and soybean in three kinds of soils were studied with the method supposed by Economic Co-operation and Development organization (OECD), and the EC50(median growth concentration)values were obtained. The inhibition of RE on the growth of rice and rape in red soil and on the growth of soybean in yellow fluvo-aquic soil is higher with stronger poison effects. Compared with other heavy metals such as Hg, Cd, Pb, As, the poison of RE on crops is weaker.展开更多
Solving arithmetic word problems that entail deep implicit relations is still a challenging problem.However,significant progress has been made in solving Arithmetic Word Problems(AWP)over the past six decades.This pap...Solving arithmetic word problems that entail deep implicit relations is still a challenging problem.However,significant progress has been made in solving Arithmetic Word Problems(AWP)over the past six decades.This paper proposes to discover deep implicit relations by qualia inference to solve Arithmetic Word Problems entailing Deep Implicit Relations(DIR-AWP),such as entailing commonsense or subject-domain knowledge involved in the problem-solving process.This paper proposes to take three steps to solve DIR-AWPs,in which the first three steps are used to conduct the qualia inference process.The first step uses the prepared set of qualia-quantity models to identify qualia scenes from the explicit relations extracted by the Syntax-Semantic(S2)method from the given problem.The second step adds missing entities and deep implicit relations in order using the identified qualia scenes and the qualia-quantity models,respectively.The third step distills the relations for solving the given problem by pruning the spare branches of the qualia dependency graph of all the acquired relations.The research contributes to the field by presenting a comprehensive approach combining explicit and implicit knowledge to enhance reasoning abilities.The experimental results on Math23K demonstrate hat the proposed algorithm is superior to the baseline algorithms in solving AWPs requiring deep implicit relations.展开更多
目的建立旋覆代赭汤(Xuanfu Daizhe Decoction,XDD)中9种酚酸类成分一测多评(quantitative analysis of multicomponents by single marker,QAMS)定量测定方法,研究酚酸类成分的传递规律,结合基准关联度,分析配伍的影响,并探究“去渣再...目的建立旋覆代赭汤(Xuanfu Daizhe Decoction,XDD)中9种酚酸类成分一测多评(quantitative analysis of multicomponents by single marker,QAMS)定量测定方法,研究酚酸类成分的传递规律,结合基准关联度,分析配伍的影响,并探究“去渣再煎”的影响。方法制备15批XDD基准样品,以绿原酸为内标物,确定其他8种成分的相对校正因子(fs/i)并计算含量,同时采用外标法测定,比较两者结果差异,计算饮片-水煎液-基准样品的转移率,分析传递规律;制备不同配伍样品,以9种酚酸类成分转移率和指纹图谱相似度为评价指标,计算基准关联度;制备不同煎煮条件样品,检测9种酚酸类成分的转移率。结果QAMS法定量测定结果与外标法无显著差异。新绿原酸、绿原酸、隐绿原酸、咖啡酸、1,3-二咖啡酰奎宁酸、异绿原酸B、异绿原酸A、1,5-二咖啡酰奎宁酸、异绿原酸C的平均转移率分别为147.34%、42.60%、321.53%、131.49%、419.76%、172.93%、18.47%、25.06%、74.68%,酚酸类成分发生降解与异构化可能是部分成分转移率大于100%的主要原因;配伍、煎煮时间、浓缩对9种酚酸类成分的传递均有影响,其中旋覆花与半夏配伍后各指标成分和指纹图谱相似度的基准关联度均大于90%,而“去渣再煎”可以进一步促进酚酸类成分的降解与异构化。结论建立的QAMS法方便、稳定,初步明确从饮片到XDD基准样品中酚酸类有效成分群之间的变化、量值传递规律和可能的影响因素,为XDD的质量控制和制剂开发提供科学依据。展开更多
文摘Aim To study the Lie symmetries and conserved quantities of the dynamical equationsof relative motion for holonomic mechanical systems. Methods Lie's method of the invariance of ordinary differential equations under infinitesimal transformations was used. Results and Conclusion The determining equaiton of the Lie symmetries for the dynamical equationS of relative motion is established.The structure quation and the form conserved quantities are obtained. An example iD illustrate the application of the result is given.
基金supported by the National Natural Science Foundation of China (Grant No 10372053)the Natural Science Foundation of Henan Province,China (Grant Nos 082300410330 and 082300410370)
文摘This paper discusses in detail the conformal invariance by infinitesimal transformations of a dynamical system of relative motion. The necessary and sufficient conditions of conformal invariance and Lie symmetry are given simultaneously by the action of infinitesimal transformations. Then it obtains the conserved quantities of conformal invariance by the infinitesimal transformations. Finally an example is given to illustrate the application of the results.
文摘Lie symmetry and the generalized Hojman conserved quantity of Nielsen equations for a variable mass holonomic system of relative motion are studied. The determining equation of Lie symmetry of Nielsen equations for a variable mass holonomic system of relative motion under the infinitesimal transformations of groups is given. The expression of generalized Hojman conserved quantity deduced directly from Lie symmetry for a variable mass holonomic system of relative motion is obtained. An example is given to illustrate the application of the results.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 11142014 and 61178032)
文摘Mei symmetry and Mei conserved quantity of Appell equations for a variable mass holonomic system of relative motion are studied.The definition and criterion of the Mei symmetry of Appell equations for a variable mass holonomic system of relative motion under the infinitesimal transformations of groups are given.The structural equation of Mei symmetry of Appell equations and the expression of Mei conserved quantity deduced directly from Mei symmetry for a variable mass holonomic system of relative motion are gained.Finally,an example is given to illustrate the application of the results.
文摘The Lie symmetry and Hojman conserved quantity of Nielsen equations in a dynamical system of relative motion with nonholonomic constraint of the Chetaev type are studied. The differential equations of motion of the Nielsen equation for the system, the definition and the criterion of Lie symmetry, and the expression of the Hojman conserved quantity deduced directly from the Lie symmetry for the system are obtained. An example is given to illustrate the application of the results.
基金Supported by the National Natural Science Foundation of China under Grant No.10572021the Preparatory Research Foundation of Jiangnan University under Grant No.2008LYY011
文摘Noether symmetry of Nielsen equation and Noether conserved quantity deduced directly from Noether symmetry for dynamical systems of the relative motion are studied. The definition and criteria of Noether symmetry of a Nielsen equation under the infinitesimal transformations of groups are given. Expression of Noether conserved quantity deduced directly from Noether symmetry of Nielsen equation for the system are obtained. Finally, an example is given to illustrate the application of the results.
基金Project supported by the National Natural Science Foundation of China (Grant No. 11142014 and 61178032)
文摘The Mei symmetry and the Mei conserved quantity of Appell equations in a dynamical system of relative motion with non-Chetaev nonholonomic constraints are studied.The differential equations of motion of the Appell equation for the system,the definition and the criterion of the Mei symmetry,and the expression of the Mei conserved quantity deduced directly from the Mei symmetry for the system are obtained.An example is given to illustrate the application of the results.
文摘In this paper, the Lie-form invariance of a nonholonomic system of relative motion in event space is studied. Firstly, the definition and the criterion of the Lie-form invariance of the nonholonomic system of relative motion in event space is given. Secondly, the Hojman conserved quantity and a new type of conserved quantity deduced from the Lie-form invariance are obtained. An example is given to illustrate the application of the results.
基金supported by the National Natural Science Foundation of China (Nos.62177024,62007014)the Humanities and Social Sciences Youth Fund of the Ministry of Education (No.20YJC880024)+1 种基金China Post Doctoral Science Foundation (No.2019M652678)the Fundamental Research Funds for the Central Universities (No.CCNU20ZT019).
文摘A qualia role-based entity-dependency graph(EDG)is proposed to represent and extract quantity relations for solving algebra story problems stated in Chinese.Traditional neural solvers use end-to-end models to translate problem texts into math expressions,which lack quantity relation acquisition in sophisticated scenarios.To address the problem,the proposed method leverages EDG to represent quantity relations hidden in qualia roles of math objects.Algorithms were designed for EDG generation and quantity relation extraction for solving algebra story problems.Experimental result shows that the proposedmethod achieved an average accuracy of 82.2%on quantity relation extraction compared to 74.5%of baseline method.Another prompt learning result shows a 5%increase obtained in problem solving by injecting the extracted quantity relations into the baseline neural solvers.
文摘This study aims to examine the usability of environmentally harmless vegetable oil in the minimum quantity of lubrication(MQL)system in face milling of AISI O2 steel and to optimize the cutting parameters by different statistical methods.Vegetable oil was preferred as cutting fluid,and Taguchi method was used in the preparation of the test pattern.After testing with the prepared test pattern,cutting performance in all parameters has been improved according to dry conditions thanks to the MQL system.The highest tool life was obtained by using cutting parameters of 7.5 m cutting length,100 m/min cutting speed,100 mL/h MQL flow rate and 0.1 mm/tooth feed rate.Optimum cutting parameters were determined according to the Taguchi analysis,and the obtained parameters were confirmed with the verification tests.In addition,the optimum test parameter was determined by applying the gray relational analysis method.After using ANOVA analysis according to the measured surface roughness and cutting force values,the most effective cutting parameter was observed to be the feed rate.In addition,the models for surface roughness and cutting force values were obtained with precisions of 99.63%and 99.68%,respectively.Effective wear mechanisms were found to be abrasion and adhesion.
文摘The effects of rare earth on the growth of rice, rape and soybean in three kinds of soils were studied with the method supposed by Economic Co-operation and Development organization (OECD), and the EC50(median growth concentration)values were obtained. The inhibition of RE on the growth of rice and rape in red soil and on the growth of soybean in yellow fluvo-aquic soil is higher with stronger poison effects. Compared with other heavy metals such as Hg, Cd, Pb, As, the poison of RE on crops is weaker.
基金The National Natural Science Foundation of China(No.61977029)supported the worksupported partly by Nurturing Program for Doctoral Dissertations at Central China Normal University(No.2022YBZZ028).
文摘Solving arithmetic word problems that entail deep implicit relations is still a challenging problem.However,significant progress has been made in solving Arithmetic Word Problems(AWP)over the past six decades.This paper proposes to discover deep implicit relations by qualia inference to solve Arithmetic Word Problems entailing Deep Implicit Relations(DIR-AWP),such as entailing commonsense or subject-domain knowledge involved in the problem-solving process.This paper proposes to take three steps to solve DIR-AWPs,in which the first three steps are used to conduct the qualia inference process.The first step uses the prepared set of qualia-quantity models to identify qualia scenes from the explicit relations extracted by the Syntax-Semantic(S2)method from the given problem.The second step adds missing entities and deep implicit relations in order using the identified qualia scenes and the qualia-quantity models,respectively.The third step distills the relations for solving the given problem by pruning the spare branches of the qualia dependency graph of all the acquired relations.The research contributes to the field by presenting a comprehensive approach combining explicit and implicit knowledge to enhance reasoning abilities.The experimental results on Math23K demonstrate hat the proposed algorithm is superior to the baseline algorithms in solving AWPs requiring deep implicit relations.
文摘目的建立旋覆代赭汤(Xuanfu Daizhe Decoction,XDD)中9种酚酸类成分一测多评(quantitative analysis of multicomponents by single marker,QAMS)定量测定方法,研究酚酸类成分的传递规律,结合基准关联度,分析配伍的影响,并探究“去渣再煎”的影响。方法制备15批XDD基准样品,以绿原酸为内标物,确定其他8种成分的相对校正因子(fs/i)并计算含量,同时采用外标法测定,比较两者结果差异,计算饮片-水煎液-基准样品的转移率,分析传递规律;制备不同配伍样品,以9种酚酸类成分转移率和指纹图谱相似度为评价指标,计算基准关联度;制备不同煎煮条件样品,检测9种酚酸类成分的转移率。结果QAMS法定量测定结果与外标法无显著差异。新绿原酸、绿原酸、隐绿原酸、咖啡酸、1,3-二咖啡酰奎宁酸、异绿原酸B、异绿原酸A、1,5-二咖啡酰奎宁酸、异绿原酸C的平均转移率分别为147.34%、42.60%、321.53%、131.49%、419.76%、172.93%、18.47%、25.06%、74.68%,酚酸类成分发生降解与异构化可能是部分成分转移率大于100%的主要原因;配伍、煎煮时间、浓缩对9种酚酸类成分的传递均有影响,其中旋覆花与半夏配伍后各指标成分和指纹图谱相似度的基准关联度均大于90%,而“去渣再煎”可以进一步促进酚酸类成分的降解与异构化。结论建立的QAMS法方便、稳定,初步明确从饮片到XDD基准样品中酚酸类有效成分群之间的变化、量值传递规律和可能的影响因素,为XDD的质量控制和制剂开发提供科学依据。
