Pub Date : 2022-10-01DOI: 10.1051/wujns/2022275424
Qinglong Wu, Zhan Yao, Tanhui Wu, H. Fang, Yangqing Hou
A new research perspective is proposed to optimize the topology of truss structure by force cone method, which involves force cone drawing rules and growth rules. Through the comparison with the mature variable density topology optimization method, the effectiveness of force cone method is verified. This kind of new method is simple and easy to understand (no need to master complex structural optimization design theory). Besides, it is time-saving in finite element calculations, and can obtain an optimized truss layout easily. By drawing the force cone, its application on a large radio telescope's back frame structure shows that, compared with the existing one in terms of structural stiffness, Root Mean Square (RMS) precision, and beam stress distribution, the optimized back frame using the force cone method has higher stiffness, better RMS, more uniform stress, and lighter weight.
{"title":"Back Frame Optimization of a Large Radio Telescope Based on Force Cone Method","authors":"Qinglong Wu, Zhan Yao, Tanhui Wu, H. Fang, Yangqing Hou","doi":"10.1051/wujns/2022275424","DOIUrl":"https://doi.org/10.1051/wujns/2022275424","url":null,"abstract":"A new research perspective is proposed to optimize the topology of truss structure by force cone method, which involves force cone drawing rules and growth rules. Through the comparison with the mature variable density topology optimization method, the effectiveness of force cone method is verified. This kind of new method is simple and easy to understand (no need to master complex structural optimization design theory). Besides, it is time-saving in finite element calculations, and can obtain an optimized truss layout easily. By drawing the force cone, its application on a large radio telescope's back frame structure shows that, compared with the existing one in terms of structural stiffness, Root Mean Square (RMS) precision, and beam stress distribution, the optimized back frame using the force cone method has higher stiffness, better RMS, more uniform stress, and lighter weight.","PeriodicalId":23976,"journal":{"name":"Wuhan University Journal of Natural Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42005642","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-10-01DOI: 10.1051/wujns/2022275367
P. Hou, HaiLin Jin
In this paper, we introduce the Minkowski measure of asymmetry for the spherical bodies of constant width. Then we prove that the spherical balls are the most symmetric bodies among all spherical bodies of constant width, and the completion of the spherical regular simplexes are the most asymmetric bodies.
{"title":"The Minkowski Measure of Asymmetry for Spherical Bodies of Constant Width","authors":"P. Hou, HaiLin Jin","doi":"10.1051/wujns/2022275367","DOIUrl":"https://doi.org/10.1051/wujns/2022275367","url":null,"abstract":"In this paper, we introduce the Minkowski measure of asymmetry for the spherical bodies of constant width. Then we prove that the spherical balls are the most symmetric bodies among all spherical bodies of constant width, and the completion of the spherical regular simplexes are the most asymmetric bodies.","PeriodicalId":23976,"journal":{"name":"Wuhan University Journal of Natural Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46734758","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-10-01DOI: 10.1051/wujns/2022275405
Z. Zuo, Ying Hu, Qing Huang, Yuan Wang, Changjing Wang
The automatic algorithm programming model can increase the dependability and efficiency of algorithm program development, including specification generation, program refinement, and formal verification. However, the existing model has two flaws: incompleteness of program refinement and inadequate automation of formal verification. This paper proposes an automatic algorithm programming model based on the improved Morgan's refinement calculus. It extends the Morgan's refinement calculus rules and designs the C++ generation system for realizing the complete process of refinement. Meanwhile, the automation tools VCG (Verification Condition Generator) and Isabelle are used to improve the automation of formal verification. An example of a stock's maximum income demonstrates the effectiveness of the proposed model. Furthermore, the proposed model has some relevance for automatic software generation.
{"title":"Automatic Algorithm Programming Model Based on the Improved Morgan's Refinement Calculus","authors":"Z. Zuo, Ying Hu, Qing Huang, Yuan Wang, Changjing Wang","doi":"10.1051/wujns/2022275405","DOIUrl":"https://doi.org/10.1051/wujns/2022275405","url":null,"abstract":"The automatic algorithm programming model can increase the dependability and efficiency of algorithm program development, including specification generation, program refinement, and formal verification. However, the existing model has two flaws: incompleteness of program refinement and inadequate automation of formal verification. This paper proposes an automatic algorithm programming model based on the improved Morgan's refinement calculus. It extends the Morgan's refinement calculus rules and designs the C++ generation system for realizing the complete process of refinement. Meanwhile, the automation tools VCG (Verification Condition Generator) and Isabelle are used to improve the automation of formal verification. An example of a stock's maximum income demonstrates the effectiveness of the proposed model. Furthermore, the proposed model has some relevance for automatic software generation.","PeriodicalId":23976,"journal":{"name":"Wuhan University Journal of Natural Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46454401","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-10-01DOI: 10.1051/wujns/2022275383
Z. Duan, Baojun Du, Jiangang Zhang
In this paper, on the basis of previous epidemic models, we considered the bidirectionality of a certain process of the model and established the Ignorant, Exposers, Resister of product, Supporter of product, Uninterested (IERSU) model, and applied it to a new field. Firstly, the next generation matrix method was used to obtain the threshold parameter which helps to distinguish the equilibrium point of the model. Secondly, the local and global stability of the equilibrium point of the model were proved by the judgment and properties of the negative definite matrix, Lyapunov's first method and LaSalle's invariance principle. Finally, according to the numerical simulation, the influence of different parameters of the model was analyzed and a series of strategies were discussed.
{"title":"Application of Promotion Process Based on Epidemic Models Considering Bidirectionality","authors":"Z. Duan, Baojun Du, Jiangang Zhang","doi":"10.1051/wujns/2022275383","DOIUrl":"https://doi.org/10.1051/wujns/2022275383","url":null,"abstract":"In this paper, on the basis of previous epidemic models, we considered the bidirectionality of a certain process of the model and established the Ignorant, Exposers, Resister of product, Supporter of product, Uninterested (IERSU) model, and applied it to a new field. Firstly, the next generation matrix method was used to obtain the threshold parameter which helps to distinguish the equilibrium point of the model. Secondly, the local and global stability of the equilibrium point of the model were proved by the judgment and properties of the negative definite matrix, Lyapunov's first method and LaSalle's invariance principle. Finally, according to the numerical simulation, the influence of different parameters of the model was analyzed and a series of strategies were discussed.","PeriodicalId":23976,"journal":{"name":"Wuhan University Journal of Natural Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47963187","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-10-01DOI: 10.1051/wujns/2022275439
Lan Jin, Lishuang Wu, Xuefeng Zhang, L. Xie
To improve surface accuracy of the work-piece and obtain potentially valuable information, a dynamic milling force prediction model was proposed based on data mining. In view of the current dynamic milling force obtained through finite element simulation and analytical calculation, in the finite element modeling, the model built is inevitably different from the actual working conditions, and the analytical calculation is slightly cumbersome and complex, and a dynamic milling force prediction model based on data mining is proposed. The model was established using a combination of regression analysis and Radial Basis Function (RBF) neural network. Using data mining as a means, the internal relationship between milling force, cutting parameters, temperature, vibration and surface quality is deeply analyzed, and the influence of dynamic milling force changes on different situations is extracted and summarized by the methods of cluster analysis and correlation analysis. The results show that the proposed dynamic milling force model has a good prediction effect, ensures the production quality, reduces the occurrence of flutter, improves the surface accuracy of the work-piece, and provides a more accurate basis for the selection of process parameters.
{"title":"Study on the Predictive of Dynamic Milling Force of Milling Process Based on Data Mining","authors":"Lan Jin, Lishuang Wu, Xuefeng Zhang, L. Xie","doi":"10.1051/wujns/2022275439","DOIUrl":"https://doi.org/10.1051/wujns/2022275439","url":null,"abstract":"To improve surface accuracy of the work-piece and obtain potentially valuable information, a dynamic milling force prediction model was proposed based on data mining. In view of the current dynamic milling force obtained through finite element simulation and analytical calculation, in the finite element modeling, the model built is inevitably different from the actual working conditions, and the analytical calculation is slightly cumbersome and complex, and a dynamic milling force prediction model based on data mining is proposed. The model was established using a combination of regression analysis and Radial Basis Function (RBF) neural network. Using data mining as a means, the internal relationship between milling force, cutting parameters, temperature, vibration and surface quality is deeply analyzed, and the influence of dynamic milling force changes on different situations is extracted and summarized by the methods of cluster analysis and correlation analysis. The results show that the proposed dynamic milling force model has a good prediction effect, ensures the production quality, reduces the occurrence of flutter, improves the surface accuracy of the work-piece, and provides a more accurate basis for the selection of process parameters.","PeriodicalId":23976,"journal":{"name":"Wuhan University Journal of Natural Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48387714","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-08-01DOI: 10.1051/wujns/2022274313
Zhiqiang Zhang, Fuzhang Wang, Juan Zhang
A simple direct space-time meshless scheme, based on the radial or non-radial basis function, is proposed for the one-dimensional Klein-Gordon equations. Since these equations are time-dependent, it is worthwhile to present two schemes for the basis functions from radial and non-radial aspects. The first scheme is fulfilled by considering time variable as normal space variable, to construct an "isotropic" space-time radial basis function. The other scheme considered a realistic relationship between space variable and time variable which is not radial. The time-dependent variable is treated regularly during the whole solution process and the Klein-Gordon equations can be solved in a direct way. Numerical results show that the proposed meshless schemes are simple, accurate, stable, easy-to-program and efficient for the Klein-Gordon equations.
{"title":"The Space-Time Meshless Methods for the Solution of One-Dimensional Klein-Gordon Equations","authors":"Zhiqiang Zhang, Fuzhang Wang, Juan Zhang","doi":"10.1051/wujns/2022274313","DOIUrl":"https://doi.org/10.1051/wujns/2022274313","url":null,"abstract":"A simple direct space-time meshless scheme, based on the radial or non-radial basis function, is proposed for the one-dimensional Klein-Gordon equations. Since these equations are time-dependent, it is worthwhile to present two schemes for the basis functions from radial and non-radial aspects. The first scheme is fulfilled by considering time variable as normal space variable, to construct an \"isotropic\" space-time radial basis function. The other scheme considered a realistic relationship between space variable and time variable which is not radial. The time-dependent variable is treated regularly during the whole solution process and the Klein-Gordon equations can be solved in a direct way. Numerical results show that the proposed meshless schemes are simple, accurate, stable, easy-to-program and efficient for the Klein-Gordon equations.","PeriodicalId":23976,"journal":{"name":"Wuhan University Journal of Natural Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47484679","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-08-01DOI: 10.1051/wujns/2022274303
Chong Wang, Suqian Zhao, Shuwen Cui
For given two digraphs, we can construct a larger digraph through join. The two digraphs that make up the join are called the factors of the join. In this paper, we give a necessary and sufficient condition that the function on the join determined by the discrete Morse functions on factors is a discrete Morse function. Moreover, we further prove the discrete Morse theory on join when the factors satisfy certain conditions.
{"title":"Discrete Morse Theory on Join of Digraphs","authors":"Chong Wang, Suqian Zhao, Shuwen Cui","doi":"10.1051/wujns/2022274303","DOIUrl":"https://doi.org/10.1051/wujns/2022274303","url":null,"abstract":"For given two digraphs, we can construct a larger digraph through join. The two digraphs that make up the join are called the factors of the join. In this paper, we give a necessary and sufficient condition that the function on the join determined by the discrete Morse functions on factors is a discrete Morse function. Moreover, we further prove the discrete Morse theory on join when the factors satisfy certain conditions.","PeriodicalId":23976,"journal":{"name":"Wuhan University Journal of Natural Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42966516","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-08-01DOI: 10.1051/wujns/2022274321
Juan Xue, C. Wang, Lan Wang
Under the S-shaped utility of loss aversion, this paper considers the bequest motivation of pension plan participants, random salary income before retirement and the substitution rate between receiving pension benefits after retirement and wages before retirement, and studies the optimal investment strategy of defined contribution (DC) pension. Assuming that pension funds can invest in a financial market consisting of three assets (risk-free asset cash, rolling bonds and stocks), inflation is considered by discount. Under the S-shaped utility, the Lagrange method is used to find the terminal optimal surplus of pensions in retirement, so as to find the terminal optimal wealth, and then the martingale method is used to find the optimal wealth process and investment strategy. Finally, a sensitivity analysis is carried out on the the influence of bequest motivation and loss aversion on the optimal investment strategy of DC pension.
{"title":"Optimal Investment Strategy of Defined Contribution Pension Based on Bequest Motivation and Loss Aversion","authors":"Juan Xue, C. Wang, Lan Wang","doi":"10.1051/wujns/2022274321","DOIUrl":"https://doi.org/10.1051/wujns/2022274321","url":null,"abstract":"Under the S-shaped utility of loss aversion, this paper considers the bequest motivation of pension plan participants, random salary income before retirement and the substitution rate between receiving pension benefits after retirement and wages before retirement, and studies the optimal investment strategy of defined contribution (DC) pension. Assuming that pension funds can invest in a financial market consisting of three assets (risk-free asset cash, rolling bonds and stocks), inflation is considered by discount. Under the S-shaped utility, the Lagrange method is used to find the terminal optimal surplus of pensions in retirement, so as to find the terminal optimal wealth, and then the martingale method is used to find the optimal wealth process and investment strategy. Finally, a sensitivity analysis is carried out on the the influence of bequest motivation and loss aversion on the optimal investment strategy of DC pension.","PeriodicalId":23976,"journal":{"name":"Wuhan University Journal of Natural Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44335784","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-08-01DOI: 10.1051/wujns/2022274273
Tingting Chen, Qi Guo
Some basic concepts for functions defined on subsets of the unit sphere, such as the s-directional derivative, s-gradient and s-Gateaux and s-Frechet differentiability etc, are introduced and investigated. These concepts are different from the usual ones for functions defined on subsets of Euclidean spaces, however, the results obtained here are very similar. Then, as applications, we provide some criterions of s-convexity for functions defined on unit spheres which are improvements or refinements of some known results.
{"title":"Differentiability of Functions on Spheres and Criterions of Convexity","authors":"Tingting Chen, Qi Guo","doi":"10.1051/wujns/2022274273","DOIUrl":"https://doi.org/10.1051/wujns/2022274273","url":null,"abstract":"Some basic concepts for functions defined on subsets of the unit sphere, such as the s-directional derivative, s-gradient and s-Gateaux and s-Frechet differentiability etc, are introduced and investigated. These concepts are different from the usual ones for functions defined on subsets of Euclidean spaces, however, the results obtained here are very similar. Then, as applications, we provide some criterions of s-convexity for functions defined on unit spheres which are improvements or refinements of some known results.","PeriodicalId":23976,"journal":{"name":"Wuhan University Journal of Natural Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44320371","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In order to optimize the solid phase extraction (SPE) conditions of perfluorooctanoic acid (PFOA) in the raw leachate and treated leachate, the effects of activator properties, SPE cartridge, pH value, ionic strength, and eluent properties were studied through single factor experiments. The optimal results of each single factor were obtained. Considering that the concentration of PFOA in the treated leachate is lower than that of the raw leachate, the SPE conditions of the treated leachate have been further optimized. Based on the above single-factor experiment, the main influencing factors were screened out as the volume of activator, ionic strength, and volume of eluent, and the three-factor three-level response surface methodology (RSM) was optimized. The optimum SPE conditions of PFOA from treated landfill leachate were as follows: Activation of weak anion exchange(WAX) cartridge with 10 mL methanol, dosage of 600 mg KCl, 6 mL 1% ammonia methanol eluted PFOA, the theory recovery rate is over 95.67%. It has been verified that the error between the predicted value and the actual extraction recovery is small and has good repeatability.
{"title":"Optimization of Solid-Phase Extraction Conditions for Perfluorooctanoic Acid in Leachate","authors":"Ying Wang, Xiaolan Zeng, Zhipeng Yu, Jiyuan Jin, Ruidong Mi, Yuan Sun","doi":"10.1051/wujns/2022274341","DOIUrl":"https://doi.org/10.1051/wujns/2022274341","url":null,"abstract":"In order to optimize the solid phase extraction (SPE) conditions of perfluorooctanoic acid (PFOA) in the raw leachate and treated leachate, the effects of activator properties, SPE cartridge, pH value, ionic strength, and eluent properties were studied through single factor experiments. The optimal results of each single factor were obtained. Considering that the concentration of PFOA in the treated leachate is lower than that of the raw leachate, the SPE conditions of the treated leachate have been further optimized. Based on the above single-factor experiment, the main influencing factors were screened out as the volume of activator, ionic strength, and volume of eluent, and the three-factor three-level response surface methodology (RSM) was optimized. The optimum SPE conditions of PFOA from treated landfill leachate were as follows: Activation of weak anion exchange(WAX) cartridge with 10 mL methanol, dosage of 600 mg KCl, 6 mL 1% ammonia methanol eluted PFOA, the theory recovery rate is over 95.67%. It has been verified that the error between the predicted value and the actual extraction recovery is small and has good repeatability.","PeriodicalId":23976,"journal":{"name":"Wuhan University Journal of Natural Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44138013","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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