Pub Date : 2023-01-01DOI: 10.23977/tracam.2023.030104
Triangular prism is a common geometric shape. From the perspective of algebraic topology, it is a familiar simple convex polyhedron in algebraic topology. In this paper, we mainly calculate that there are only two kinds of characteristic functions on a triangular prism, and the homology groups of triangular prism is obtained by different characteristic functions are different. Firstly, according to the Morse function on the convex polytope Pn, We can give the cell decoposition of the corresponding small cover Mn over Pn, and the cellular chain complex {Di(Mn(λ)),∂i} of Mn. Secondly, considering the relationship between the boundary homomorphism {∂i} and the characteristic function λ, we can give the principle of how to determine the boundary homomorphism is given. Finally, the homology groups are computed by defination {Hi= ker∂i / Im∂i+1}, we can give the corresponding results.
{"title":"The homology groups of small cover on a triangular prism and its number of characteristic functions","authors":"","doi":"10.23977/tracam.2023.030104","DOIUrl":"https://doi.org/10.23977/tracam.2023.030104","url":null,"abstract":"Triangular prism is a common geometric shape. From the perspective of algebraic topology, it is a familiar simple convex polyhedron in algebraic topology. In this paper, we mainly calculate that there are only two kinds of characteristic functions on a triangular prism, and the homology groups of triangular prism is obtained by different characteristic functions are different. Firstly, according to the Morse function on the convex polytope P<sup>n</sup>, We can give the cell decoposition of the corresponding small cover M<sup>n</sup> over P<sup>n</sup>, and the cellular chain complex {D<sub>i</sub>(M<sup>n</sup>(λ)),∂<sub>i</sub>} of M<sup>n</sup>. Secondly, considering the relationship between the boundary homomorphism {∂<sub>i</sub>} and the characteristic function λ, we can give the principle of how to determine the boundary homomorphism is given. Finally, the homology groups are computed by defination {H<sub>i</sub>= ker∂<sub>i</sub> / Im∂<sub>i+1</sub>}, we can give the corresponding results.","PeriodicalId":484637,"journal":{"name":"Transactions on Computational and Applied Mathematics","volume":"130 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135500750","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 : 2023-01-01DOI: 10.23977/tracam.2023.030105
Mathematics plays a significant role in geophysical exploration and exhibits multiple development trends. Machine learning and artificial intelligence are applied to the processing of geophysical data, extracting features, establishing models, and making predictions and interpretations through the analysis of extensive data sets. Big data analysis methods are widely employed in geophysical exploration to manage the growing volume of data and extract valuable information from it. Collaboration between mathematics, computer science, geology, and other disciplines is becoming increasingly intertwined to enhance the accuracy and efficiency of geophysical data processing and interpretation. The development of integrated approaches becomes a trend in geophysical exploration, enhancing accuracy and reliability by merging data and interpretations from various exploration methods. These developmental trends will drive innovation and advancement in the field of geophysical exploration, offering robust support for resource prospecting, environmental monitoring, and other domains.
{"title":"The Influence and Development Trends of Mathematics in Geophysical Exploration on Earth","authors":"","doi":"10.23977/tracam.2023.030105","DOIUrl":"https://doi.org/10.23977/tracam.2023.030105","url":null,"abstract":"Mathematics plays a significant role in geophysical exploration and exhibits multiple development trends. Machine learning and artificial intelligence are applied to the processing of geophysical data, extracting features, establishing models, and making predictions and interpretations through the analysis of extensive data sets. Big data analysis methods are widely employed in geophysical exploration to manage the growing volume of data and extract valuable information from it. Collaboration between mathematics, computer science, geology, and other disciplines is becoming increasingly intertwined to enhance the accuracy and efficiency of geophysical data processing and interpretation. The development of integrated approaches becomes a trend in geophysical exploration, enhancing accuracy and reliability by merging data and interpretations from various exploration methods. These developmental trends will drive innovation and advancement in the field of geophysical exploration, offering robust support for resource prospecting, environmental monitoring, and other domains.","PeriodicalId":484637,"journal":{"name":"Transactions on Computational and Applied Mathematics","volume":"69 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136366263","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 : 2023-01-01DOI: 10.23977/tracam.2023.030102
Online shopping reviews have become an important data source for merchants to make smarter decisions in product development, operations, and marketing. In this paper, we propose a modeling strategy to optimize data analysis and processing of online shopping review data. We address four main problems: identifying commonly used words in positive, negative, and helpful reviews, predicting the products to which the comments refer using semantic analysis, predicting the product rating based on the comments using sentiment analysis, and proposing ways to distinguish human comments from machine-generated ones. Additionally, we provide a recommendation letter to customers on how to read product reviews.
{"title":"Methods of Analysis of Amazon Product Reviews and Rating Prediction","authors":"","doi":"10.23977/tracam.2023.030102","DOIUrl":"https://doi.org/10.23977/tracam.2023.030102","url":null,"abstract":"Online shopping reviews have become an important data source for merchants to make smarter decisions in product development, operations, and marketing. In this paper, we propose a modeling strategy to optimize data analysis and processing of online shopping review data. We address four main problems: identifying commonly used words in positive, negative, and helpful reviews, predicting the products to which the comments refer using semantic analysis, predicting the product rating based on the comments using sentiment analysis, and proposing ways to distinguish human comments from machine-generated ones. Additionally, we provide a recommendation letter to customers on how to read product reviews.","PeriodicalId":484637,"journal":{"name":"Transactions on Computational and Applied Mathematics","volume":"103 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135500754","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 : 2023-01-01DOI: 10.23977/tracam.2023.030103
This article uses multiple regression analysis methods and canonical correlation analysis, combined with the college entrance examination scores and partial discipline scores in the first three years of university for students majoring in Information and Computing Science in a certain university. We separately analyze the connection between the college entrance examination and university discipline scores, and compare the advantages and disadvantages of the two methods. We hope to quantitatively analyze the transmission and extension of subject knowledge at different stages from a mathematical perspective, and also promote the practical application value of mathematics, providing more people with inspiration and thought on mathematics.
{"title":"Mathematical Analysis of the Relationship between College Entrance Exam Scores and Information and Computing Science Discipline Performance in a Chinese University","authors":"","doi":"10.23977/tracam.2023.030103","DOIUrl":"https://doi.org/10.23977/tracam.2023.030103","url":null,"abstract":"This article uses multiple regression analysis methods and canonical correlation analysis, combined with the college entrance examination scores and partial discipline scores in the first three years of university for students majoring in Information and Computing Science in a certain university. We separately analyze the connection between the college entrance examination and university discipline scores, and compare the advantages and disadvantages of the two methods. We hope to quantitatively analyze the transmission and extension of subject knowledge at different stages from a mathematical perspective, and also promote the practical application value of mathematics, providing more people with inspiration and thought on mathematics.","PeriodicalId":484637,"journal":{"name":"Transactions on Computational and Applied Mathematics","volume":"88 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135500755","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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