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.2022.030110
Xiayi Zhang
: In order to study the changes of China's fund market, this paper carries out time series modeling and fitting prediction on the series based on the monthly series data of Shanghai Securities Fund Index from January 2010 to December 2019. EGARCH (1,1) model has a good fitting effect on Shanghai Securities Fund Index series, all parameters are not 0, and the residual series of the model is tested to obey the standard normal distribution. Finally, the fitted model is used to predict the Shanghai Securities Fund Index from January to May 2020, and compare it with the real value to test the accuracy of the model. The results show that the actual values are within the prediction interval of 95% confidence coefficient, and the fitting effect of the model is superior.
{"title":"Empirical Analysis of Fund Index Volatility Based on Conditional Heteroscedasticity Model","authors":"Xiayi Zhang","doi":"10.25236/ajms.2022.030110","DOIUrl":"https://doi.org/10.25236/ajms.2022.030110","url":null,"abstract":": In order to study the changes of China's fund market, this paper carries out time series modeling and fitting prediction on the series based on the monthly series data of Shanghai Securities Fund Index from January 2010 to December 2019. EGARCH (1,1) model has a good fitting effect on Shanghai Securities Fund Index series, all parameters are not 0, and the residual series of the model is tested to obey the standard normal distribution. Finally, the fitted model is used to predict the Shanghai Securities Fund Index from January to May 2020, and compare it with the real value to test the accuracy of the model. The results show that the actual values are within the prediction interval of 95% confidence coefficient, and the fitting effect of the model is superior.","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":"134613156","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.2023.040210
Jingzu Xia, Leyang Yu, Yuli Wang
: The spread of hot topics on the internet can easily attract public attention and discussion. However, the spread of rumours can cause social instability, while positive media guidance can generate economic value. Therefore, developing a model that can understand the propagation of popular topics on the internet is a worthwhile pursuit. In this study, a hybrid model is developed by combining the SEIRS (Susceptible-Exposed-Infected-Recovered-Susceptible) infectious disease model to simulate the overall trend and the ARIMA (Autoregressive Integrated Moving Average) model to simulate noise, to explain internet hot topic propagation. Using the wordle game as a case study, the model exhibits a notable capability in conforming to the general pattern and the majority of the minor variations, while demonstrating a high degree of interpretability.
{"title":"A Method for Simulating the Propagation of Network Hot Topics Based on Combined SEIRS-ARIMA Model","authors":"Jingzu Xia, Leyang Yu, Yuli Wang","doi":"10.25236/ajms.2023.040210","DOIUrl":"https://doi.org/10.25236/ajms.2023.040210","url":null,"abstract":": The spread of hot topics on the internet can easily attract public attention and discussion. However, the spread of rumours can cause social instability, while positive media guidance can generate economic value. Therefore, developing a model that can understand the propagation of popular topics on the internet is a worthwhile pursuit. In this study, a hybrid model is developed by combining the SEIRS (Susceptible-Exposed-Infected-Recovered-Susceptible) infectious disease model to simulate the overall trend and the ARIMA (Autoregressive Integrated Moving Average) model to simulate noise, to explain internet hot topic propagation. Using the wordle game as a case study, the model exhibits a notable capability in conforming to the general pattern and the majority of the minor variations, while demonstrating a high degree of interpretability.","PeriodicalId":372277,"journal":{"name":"Academic Journal of Mathematical Sciences","volume":"26 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":"132618939","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}
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