Pub Date : 2021-04-07DOI: 10.25236/AJMS.2021.020101
Xiaoying Yang
In this paper, we study the existence of positive solutions for a class of fractional functional integro-differential equations with two fractional derivative terms. First, we transform the boundary value problem into an equivalent integral equation, establish the operator T and prove its full continuity, then the existence theorems of positive solutions of boundary value problems is established by using the fixed point theorems of cone extension and cone compression.
{"title":"Existence of positive solutions for boundary value problems of nonlinear fractional functional integro-differential equations","authors":"Xiaoying Yang","doi":"10.25236/AJMS.2021.020101","DOIUrl":"https://doi.org/10.25236/AJMS.2021.020101","url":null,"abstract":"In this paper, we study the existence of positive solutions for a class of fractional functional integro-differential equations with two fractional derivative terms. First, we transform the boundary value problem into an equivalent integral equation, establish the operator T and prove its full continuity, then the existence theorems of positive solutions of boundary value problems is established by using the fixed point theorems of cone extension and cone compression.","PeriodicalId":372277,"journal":{"name":"Academic Journal of Mathematical Sciences","volume":"52 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123826332","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 : 1900-01-01DOI: 10.25236/ajms.2023.040209
Zhirui Min
: Wordle, a popular word guessing game offered daily by The New York Times, has been widely loved and shared due to its straightforward rules and strong fun. This paper uses the ARIMA time series prediction model to predict future user number and then defines the word attribute by combining the word frequency and letter frequency through entropy weight method. To predict the percentage of tries in the future, we fit the percentage of tries with the word attribute from January 7, 2022 to December 31, 2022.This paper forecasts the number of Wordle users on March 1, 2023 and came up with a prediction of 16,458 users. Predicting the word “EERIE” on March 1, 2023 through fitting function and the corresponding percentage of tries is (0,13,35,33,14,2). This paper is instructive for setting the direction of future updates for Wordle as well as giving a forecast method for the future development of Wordle.
{"title":"A study of the number of Wordle users and experience predictions","authors":"Zhirui Min","doi":"10.25236/ajms.2023.040209","DOIUrl":"https://doi.org/10.25236/ajms.2023.040209","url":null,"abstract":": Wordle, a popular word guessing game offered daily by The New York Times, has been widely loved and shared due to its straightforward rules and strong fun. This paper uses the ARIMA time series prediction model to predict future user number and then defines the word attribute by combining the word frequency and letter frequency through entropy weight method. To predict the percentage of tries in the future, we fit the percentage of tries with the word attribute from January 7, 2022 to December 31, 2022.This paper forecasts the number of Wordle users on March 1, 2023 and came up with a prediction of 16,458 users. Predicting the word “EERIE” on March 1, 2023 through fitting function and the corresponding percentage of tries is (0,13,35,33,14,2). This paper is instructive for setting the direction of future updates for Wordle as well as giving a forecast method for the future development of Wordle.","PeriodicalId":372277,"journal":{"name":"Academic Journal of Mathematical Sciences","volume":"253 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123682780","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 : 1900-01-01DOI: 10.25236/ajms.2023.040208
Xuyi Shi, Jiachen Guang, Liang Shao
: Using LSTM time series analysis and forecasting is an important guide for Wordle's game development direction planning and economic revenue visualization. Accurate game report data prediction is of great significance for game development, economic investment, post-game planning, and improving player experience. As Wordle's game becomes more and more popular, it is essential to make predictions and projections about the future of the game as well as collate the data. In order to accurately predict the data reported by Wordle players in the future, based on the theory of time series analysis, combined with the extensive collection and screening of retrieval data, and the advantages of LSTM model and linear regression equation in the direction of prediction, a multi-dimensional prediction model for big data was established. With this prediction model, the development of Wordle games can be predicted according to a variety of prediction dimensions. After the accurate prediction of big data, the influential factors behind the data can be analyzed, which can simplify people's understanding of data to a certain extent, and successfully realize the transition from sophisticated technology to service-oriented demand.
{"title":"Wordle data analysis based on time series analysis model","authors":"Xuyi Shi, Jiachen Guang, Liang Shao","doi":"10.25236/ajms.2023.040208","DOIUrl":"https://doi.org/10.25236/ajms.2023.040208","url":null,"abstract":": Using LSTM time series analysis and forecasting is an important guide for Wordle's game development direction planning and economic revenue visualization. Accurate game report data prediction is of great significance for game development, economic investment, post-game planning, and improving player experience. As Wordle's game becomes more and more popular, it is essential to make predictions and projections about the future of the game as well as collate the data. In order to accurately predict the data reported by Wordle players in the future, based on the theory of time series analysis, combined with the extensive collection and screening of retrieval data, and the advantages of LSTM model and linear regression equation in the direction of prediction, a multi-dimensional prediction model for big data was established. With this prediction model, the development of Wordle games can be predicted according to a variety of prediction dimensions. After the accurate prediction of big data, the influential factors behind the data can be analyzed, which can simplify people's understanding of data to a certain extent, and successfully realize the transition from sophisticated technology to service-oriented demand.","PeriodicalId":372277,"journal":{"name":"Academic Journal of Mathematical Sciences","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126378025","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 : 1900-01-01DOI: 10.25236/ajms.2023.040308
Xiaokun Sun
: This article starts with the current development status of mathematics teaching and mathematical modeling in application-oriented undergraduate colleges, analyzes the existing problems, and considers and practices the integration perspective and methods of mathematical modeling and university mathematics teaching, as well as the objectives of mathematical modeling and university mathematics curriculum construction. Specific aspects and measures for the development of curriculum construction are proposed.
{"title":"Reflections and Practice on the Integration of Applied Undergraduate Mathematical Modeling Thought and Mathematics Teaching","authors":"Xiaokun Sun","doi":"10.25236/ajms.2023.040308","DOIUrl":"https://doi.org/10.25236/ajms.2023.040308","url":null,"abstract":": This article starts with the current development status of mathematics teaching and mathematical modeling in application-oriented undergraduate colleges, analyzes the existing problems, and considers and practices the integration perspective and methods of mathematical modeling and university mathematics teaching, as well as the objectives of mathematical modeling and university mathematics curriculum construction. Specific aspects and measures for the development of curriculum construction are proposed.","PeriodicalId":372277,"journal":{"name":"Academic Journal of Mathematical Sciences","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128918074","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}
: The research on ordering and transportation strategy optimization of raw materials has a profound impact on the development of enterprises. Based on factor analysis and dynamic programming method, this paper reasonably formulates raw material ordering and transshipment optimization strategy. Due to the uneven quality of each supplier, transporters transport loss rate is not the same. For enterprises, how to formulate the most economical raw material ordering plan and the least loss transshipment plan has become a key issue to be solved. In this paper, a dynamic programming model and a 0-1 programming model are established to solve the problem of enterprise transshipment ordering scheme under different needs.
{"title":"Research on Enterprise Order and Transshipment Strategy Based on Factor Analysis and Dynamic Programming","authors":"Pengbo Wang, Jingping Cao, Xingyu Liu, Zhengyue Wang, Yuxin Wei","doi":"10.25236/ajms.2022.030203","DOIUrl":"https://doi.org/10.25236/ajms.2022.030203","url":null,"abstract":": The research on ordering and transportation strategy optimization of raw materials has a profound impact on the development of enterprises. Based on factor analysis and dynamic programming method, this paper reasonably formulates raw material ordering and transshipment optimization strategy. Due to the uneven quality of each supplier, transporters transport loss rate is not the same. For enterprises, how to formulate the most economical raw material ordering plan and the least loss transshipment plan has become a key issue to be solved. In this paper, a dynamic programming model and a 0-1 programming model are established to solve the problem of enterprise transshipment ordering scheme under different needs.","PeriodicalId":372277,"journal":{"name":"Academic Journal of Mathematical Sciences","volume":"250 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115842293","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 : 1900-01-01DOI: 10.25236/ajms.2022.030108
{"title":"Analysis of the U.S. economy using mathematical modeling","authors":"","doi":"10.25236/ajms.2022.030108","DOIUrl":"https://doi.org/10.25236/ajms.2022.030108","url":null,"abstract":"","PeriodicalId":372277,"journal":{"name":"Academic Journal of Mathematical Sciences","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125539480","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 : 1900-01-01DOI: 10.25236/ajms.2023.040310
Mingzhe Li
: Natural language processing (NLP) has greatly advanced in machine learning, but math education software lacks AI integration for solving math word problems in English. We propose using the BertGen pre-trained Transformer model, along with the MAWPS dataset augmented by our dataset augmenter. The Transformer model, with its multi-head attention mechanisms, excels at capturing long-range dependencies and referential relationships, crucial for math word problems at the primary school level. Our accuracy tests and performance on different datasets validate the effectiveness and generalizability of our approach. Moreover, our augmented dataset outperforms smaller unaugmented datasets, while maintaining diversity. The math word problem augmenter can be adapted for other math problem sets, supporting future research in the field.
{"title":"Analysis of Elementary Math Word Problems Based on AI Deep Learning","authors":"Mingzhe Li","doi":"10.25236/ajms.2023.040310","DOIUrl":"https://doi.org/10.25236/ajms.2023.040310","url":null,"abstract":": Natural language processing (NLP) has greatly advanced in machine learning, but math education software lacks AI integration for solving math word problems in English. We propose using the BertGen pre-trained Transformer model, along with the MAWPS dataset augmented by our dataset augmenter. The Transformer model, with its multi-head attention mechanisms, excels at capturing long-range dependencies and referential relationships, crucial for math word problems at the primary school level. Our accuracy tests and performance on different datasets validate the effectiveness and generalizability of our approach. Moreover, our augmented dataset outperforms smaller unaugmented datasets, while maintaining diversity. The math word problem augmenter can be adapted for other math problem sets, supporting future research in the field.","PeriodicalId":372277,"journal":{"name":"Academic Journal of Mathematical Sciences","volume":"81 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126224791","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 : 1900-01-01DOI: 10.25236/ajms.2023.040206
Xiting Wang, Keying Yan, Jiarui Qu
: High-intensity lighting has become an inevitable phenomenon in cities, so it is very important to establish an index system to measure the degree of light pollution risk. We selected the entropy weight method to determine the weight of each indicator that affects the risk of light pollution, and then used the TOPSIS model to quantitatively analyze the degree of light pollution risk and calculate the score. Finally, it was concluded that among the seven cities of Shanghai, Guangzhou, Kunming, Lhasa, Ningbo, Hohhot and Yinchuan, Shanghai had the highest light pollution risk score of 0.77, while Yinchuan had the lowest light pollution risk score of 0.23. This paper constructs a light pollution risk measurement system, which is of great significance to the measurement and prevention of light pollution.
{"title":"Study of light pollution risk level based on TOPSIS and integer programming summary","authors":"Xiting Wang, Keying Yan, Jiarui Qu","doi":"10.25236/ajms.2023.040206","DOIUrl":"https://doi.org/10.25236/ajms.2023.040206","url":null,"abstract":": High-intensity lighting has become an inevitable phenomenon in cities, so it is very important to establish an index system to measure the degree of light pollution risk. We selected the entropy weight method to determine the weight of each indicator that affects the risk of light pollution, and then used the TOPSIS model to quantitatively analyze the degree of light pollution risk and calculate the score. Finally, it was concluded that among the seven cities of Shanghai, Guangzhou, Kunming, Lhasa, Ningbo, Hohhot and Yinchuan, Shanghai had the highest light pollution risk score of 0.77, while Yinchuan had the lowest light pollution risk score of 0.23. This paper constructs a light pollution risk measurement system, which is of great significance to the measurement and prevention of light pollution.","PeriodicalId":372277,"journal":{"name":"Academic Journal of Mathematical Sciences","volume":"62 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124735159","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 : 1900-01-01DOI: 10.25236/ajms.2023.040304
Hongyu Zhou, Fengtong Wen
: With the rapid development of the information age, the emergence of information technology software such as the geometric sketchpad provides a powerful tool for teachers' teaching. Junior high school mathematics teachers can help junior high school students explore mathematical theorems, function concepts, geometric properties and other contents through the geometric sketchpad to assist classroom teaching, and promote the development of junior high school students' mathematical thinking. This paper combines the junior high school teaching cases, integrates the Geometer's Sketchpad into the specific teaching content, and deeply discusses the advantages and effects of Geometer's Sketchpad in junior high school mathematics teaching.
{"title":"The Application of Geometer's Sketchpad in Mathematics Teaching in Junior Middle School","authors":"Hongyu Zhou, Fengtong Wen","doi":"10.25236/ajms.2023.040304","DOIUrl":"https://doi.org/10.25236/ajms.2023.040304","url":null,"abstract":": With the rapid development of the information age, the emergence of information technology software such as the geometric sketchpad provides a powerful tool for teachers' teaching. Junior high school mathematics teachers can help junior high school students explore mathematical theorems, function concepts, geometric properties and other contents through the geometric sketchpad to assist classroom teaching, and promote the development of junior high school students' mathematical thinking. This paper combines the junior high school teaching cases, integrates the Geometer's Sketchpad into the specific teaching content, and deeply discusses the advantages and effects of Geometer's Sketchpad in junior high school mathematics teaching.","PeriodicalId":372277,"journal":{"name":"Academic Journal of Mathematical Sciences","volume":"88 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122768463","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 : 1900-01-01DOI: 10.25236/ajms.2023.040203
Weiqiang Liang, Shengjie Guo
: Based on graph theory and complex network theory, this paper conducts an empirical study on Penrose floor tile network. In this paper, the complex network characteristics of Penrose floor tile network is analyzed by calculating the parameters of different static indexes. By formulating a random attack strategy, the influence of different node and edge failures of the characteristics of Penrose floors tile network is studied.
{"title":"Analysis of Penrose Tile Network Based on Complex Network Theory","authors":"Weiqiang Liang, Shengjie Guo","doi":"10.25236/ajms.2023.040203","DOIUrl":"https://doi.org/10.25236/ajms.2023.040203","url":null,"abstract":": Based on graph theory and complex network theory, this paper conducts an empirical study on Penrose floor tile network. In this paper, the complex network characteristics of Penrose floor tile network is analyzed by calculating the parameters of different static indexes. By formulating a random attack strategy, the influence of different node and edge failures of the characteristics of Penrose floors tile network is studied.","PeriodicalId":372277,"journal":{"name":"Academic Journal of Mathematical Sciences","volume":"48 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128034541","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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