Let G be a finite directed graph with no loop and no heavy edges, or an undirected graph with no loops and no edges. 𝑁 is a given natural number. This paper proves that the existence problem of two paths with length 𝑁 in G (referred to as 𝑁-path) is completely equivalent to the solutions of a multivariate of polynomial 𝑁 the range of {0,1} or {0,1, −1}. Therefore, the Gröbner bases method can be used to give an effective discrimination of the existence of the solution. This result can be applied to solve the problems of cutting edge judgment, tree and forest judgment in G.
{"title":"Gröbner bases method for solving N-path in finite graph and its application","authors":"Zhiqin Zhao, Xuewei Xiong","doi":"10.1117/12.2679167","DOIUrl":"https://doi.org/10.1117/12.2679167","url":null,"abstract":"Let G be a finite directed graph with no loop and no heavy edges, or an undirected graph with no loops and no edges. 𝑁 is a given natural number. This paper proves that the existence problem of two paths with length 𝑁 in G (referred to as 𝑁-path) is completely equivalent to the solutions of a multivariate of polynomial 𝑁 the range of {0,1} or {0,1, −1}. Therefore, the Gröbner bases method can be used to give an effective discrimination of the existence of the solution. This result can be applied to solve the problems of cutting edge judgment, tree and forest judgment in G.","PeriodicalId":301595,"journal":{"name":"Conference on Pure, Applied, and Computational Mathematics","volume":"290 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117306074","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}
With the development of technology, internet technology is becoming more and more mature, so that users can choose different categories of information according to their needs and suitable for their own characteristics and preferences when surfing the internet, instead of having to passively obtain it. Therefore, when browsing information, users will choose websites that interest them or suit their characteristics and interests according to their own needs, and search engines will calculate the corresponding ranking according to the user's browsing information, and finally recommend the website to the target user. The application of recommendation technology in the field of information retrieval not only helps users to obtain useful content from the huge amount of data, but also improves the effect of search engine optimization. This paper introduces a recommendation model based on mathematical expressions and focuses on its role in modelling user behaviour, while the algorithmic process is also described in this paper.
{"title":"Application of mathematical expression-based recommendation models in user behaviour modelling","authors":"Chun-cheong. Pang","doi":"10.1117/12.2678980","DOIUrl":"https://doi.org/10.1117/12.2678980","url":null,"abstract":"With the development of technology, internet technology is becoming more and more mature, so that users can choose different categories of information according to their needs and suitable for their own characteristics and preferences when surfing the internet, instead of having to passively obtain it. Therefore, when browsing information, users will choose websites that interest them or suit their characteristics and interests according to their own needs, and search engines will calculate the corresponding ranking according to the user's browsing information, and finally recommend the website to the target user. The application of recommendation technology in the field of information retrieval not only helps users to obtain useful content from the huge amount of data, but also improves the effect of search engine optimization. This paper introduces a recommendation model based on mathematical expressions and focuses on its role in modelling user behaviour, while the algorithmic process is also described in this paper.","PeriodicalId":301595,"journal":{"name":"Conference on Pure, Applied, and Computational Mathematics","volume":"56 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127995733","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 this study, the chemical composition data of ancient glass were sorted out and analyzed. Based on the training principle of BP neural network, BP neural network was established to solve the problem. After several iterations, 14 input layers, 5 neurons and the training method of radial basis function were finally determined. The data before weathering of weathered relics were finally obtained, so as to predict and restore the missing value of ancient glass chemical elements. In order to verify the rationality and sensitivity of the results, certain parameters were determined to process the data, and cluster analysis was performed again. By comparing the two results, we found that the difference between the two results was small, which verified the rationality and stability of the classification results. Then, through k-means algorithm, the types of glass were subclassified based on the different chemical composition content. For example, high-potassium glass was divided into high-potassium high-calcium glass and high-potassium low-calcium glass, and lead-barium glass was divided into lead-barium high-calcium glass and lead-barium low-calcium glass.
{"title":"Prediction of missing values of chemical elements in glass relics and subclassification based on neural network","authors":"Tingting Yan, Dongyang Xi, Xiaodan Wang, Long Ma","doi":"10.1117/12.2678968","DOIUrl":"https://doi.org/10.1117/12.2678968","url":null,"abstract":"In this study, the chemical composition data of ancient glass were sorted out and analyzed. Based on the training principle of BP neural network, BP neural network was established to solve the problem. After several iterations, 14 input layers, 5 neurons and the training method of radial basis function were finally determined. The data before weathering of weathered relics were finally obtained, so as to predict and restore the missing value of ancient glass chemical elements. In order to verify the rationality and sensitivity of the results, certain parameters were determined to process the data, and cluster analysis was performed again. By comparing the two results, we found that the difference between the two results was small, which verified the rationality and stability of the classification results. Then, through k-means algorithm, the types of glass were subclassified based on the different chemical composition content. For example, high-potassium glass was divided into high-potassium high-calcium glass and high-potassium low-calcium glass, and lead-barium glass was divided into lead-barium high-calcium glass and lead-barium low-calcium glass.","PeriodicalId":301595,"journal":{"name":"Conference on Pure, Applied, and Computational Mathematics","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127859926","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 recent years, epidemics, earthquakes, forest fires, floods, and other public health emergencies and natural disasters have occurred frequently, and the role of emergency logistics has become more and more prominent. In this paper, on the basis of sorting out the current situation of emergency logistics guarantee in China, we use hierarchical analysis and fuzzy evaluation methods to calculate the weight of each index factor and guarantee the effectiveness of emergency logistics, respectively. The study gives examples to analyze and calculate the guarantee effectiveness of emergency logistics so as to draw the influence of emergency logistics. The key factors of emergency logistics can provide decision guidance for strengthening the construction of the emergency logistics system and improving the level of emergency logistics guarantee.
{"title":"Research on the influence factors of emergency logistics guarantee effectiveness based on hierarchical analysis method and fuzzy comprehensive judgment method","authors":"Jiawei He, Qixiang Li, Zichao Song, Lu Li","doi":"10.1117/12.2678932","DOIUrl":"https://doi.org/10.1117/12.2678932","url":null,"abstract":"In recent years, epidemics, earthquakes, forest fires, floods, and other public health emergencies and natural disasters have occurred frequently, and the role of emergency logistics has become more and more prominent. In this paper, on the basis of sorting out the current situation of emergency logistics guarantee in China, we use hierarchical analysis and fuzzy evaluation methods to calculate the weight of each index factor and guarantee the effectiveness of emergency logistics, respectively. The study gives examples to analyze and calculate the guarantee effectiveness of emergency logistics so as to draw the influence of emergency logistics. The key factors of emergency logistics can provide decision guidance for strengthening the construction of the emergency logistics system and improving the level of emergency logistics guarantee.","PeriodicalId":301595,"journal":{"name":"Conference on Pure, Applied, and Computational Mathematics","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127914206","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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