Let G be a graph and A(G) the adjacency matrix of G. The spectrum of G is the eigenvalues together with their multiplicities of A(G). Chang et al. (2011) characterized the structures of all graphs with rank 4. Monsalve and Rada (2021) gave the bound of spectral radius of all graphs with rank 4. Based on these results as above, we further investigate the spectral properties of graphs with rank 4. And we give the expressions of the spectral radius and energy of all graphs with rank 4. In particular, we show that some graphs with rank 4 are determined by their spectra.
设G为图，a (G)为G的邻接矩阵，G的谱是a (G)的特征值及其复数。Chang et al.(2011)对所有4级图的结构进行了表征。Monsalve和Rada(2021)给出了所有4阶图的谱半径界。在上述结果的基础上，我们进一步研究了4阶图的谱性质。并给出了所有4阶图的谱半径和能量的表达式。特别地，我们证明了一些阶数为4的图是由它们的谱决定的。
{"title":"On the Spectral Properties of Graphs with Rank 4","authors":"Jianxuan Luo","doi":"10.4236/am.2023.1411045","DOIUrl":"https://doi.org/10.4236/am.2023.1411045","url":null,"abstract":"Let G be a graph and A(G) the adjacency matrix of G. The spectrum of G is the eigenvalues together with their multiplicities of A(G). Chang et al. (2011) characterized the structures of all graphs with rank 4. Monsalve and Rada (2021) gave the bound of spectral radius of all graphs with rank 4. Based on these results as above, we further investigate the spectral properties of graphs with rank 4. And we give the expressions of the spectral radius and energy of all graphs with rank 4. In particular, we show that some graphs with rank 4 are determined by their spectra.","PeriodicalId":64940,"journal":{"name":"应用数学(英文)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135712208","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}
{"title":"The Doubly Truncated Generalized Log-Lindley Distribution","authors":"Abd-Elmoneim A. M. Teamah, Hussin M. Elmenify","doi":"10.4236/am.2023.147030","DOIUrl":"https://doi.org/10.4236/am.2023.147030","url":null,"abstract":"","PeriodicalId":64940,"journal":{"name":"应用数学(英文)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80532555","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}
It is common for two teams or two players to play a game in which the first one to win a majority of the initially determined number of matches wins the championship. We will explore the probabilistic conditions under which a team (or player) that is considered weak may win the championship over a team (or player) that is considered strong, or a game may go all the way to the end, creating excitement among fans. It is unlikely to occur if the initially estimated probability remains constant when the weaker one wins each game against the stronger one. The purpose of this study is to identify probabilistically what conditions are necessary to increase the probability of such an outcome. We examine probabilistically by quantifying momentum gains to see if momentum gains by a weaker team (or player) winning a series of games would increase the likelihood of such an outcome occurring. If the weaker one gains momentum by winning a series of games and the probability of winning the next game is greater than the initial probability, we can see that such a result will occur in this study. Especially when the number of games is limited to seven, the initial probability that a weaker one will beat a stronger one in each game must be 0.35 or higher in order to win the championship and excite the fans by having the game go all the way to the end.
{"title":"Probability Theory Predicts That Winning Streak Is a Shortcut for the Underdog Team to Win the World Series","authors":"Motohisa Osaka","doi":"10.4236/am.2023.1410041","DOIUrl":"https://doi.org/10.4236/am.2023.1410041","url":null,"abstract":"It is common for two teams or two players to play a game in which the first one to win a majority of the initially determined number of matches wins the championship. We will explore the probabilistic conditions under which a team (or player) that is considered weak may win the championship over a team (or player) that is considered strong, or a game may go all the way to the end, creating excitement among fans. It is unlikely to occur if the initially estimated probability remains constant when the weaker one wins each game against the stronger one. The purpose of this study is to identify probabilistically what conditions are necessary to increase the probability of such an outcome. We examine probabilistically by quantifying momentum gains to see if momentum gains by a weaker team (or player) winning a series of games would increase the likelihood of such an outcome occurring. If the weaker one gains momentum by winning a series of games and the probability of winning the next game is greater than the initial probability, we can see that such a result will occur in this study. Especially when the number of games is limited to seven, the initial probability that a weaker one will beat a stronger one in each game must be 0.35 or higher in order to win the championship and excite the fans by having the game go all the way to the end.","PeriodicalId":64940,"journal":{"name":"应用数学(英文)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136302938","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}
Jorge Fujioka, Rosalío Fernando Rodríguez, Áurea Espinosa-Cerón
We study two generalized versions of a system of equations which describe the time evolution of the hydrodynamic fluctuations of density and velocity in a linear viscoelastic fluid. In the first of these versions, the time derivatives are replaced by conformable derivatives, and in the second version left-handed Caputo’s derivatives are used. We show that the solutions obtained with these two types of derivatives exhibit significant similarities, which is an interesting (and somewhat surprising) result, taking into account that the conformable derivatives are local operators, while Caputo’s derivatives are nonlocal operators. We also show that the solutions of the generalized systems are similar to the solutions of the original system, if the order α of the new derivatives (conformable or Caputo) is less than one. On the other hand, when α is greater than one, the solutions of the generalized systems are qualitatively different from the solutions of the original system.
{"title":"Conformable and Caputo’s Derivatives in Generalized Viscoelastic Models","authors":"Jorge Fujioka, Rosalío Fernando Rodríguez, Áurea Espinosa-Cerón","doi":"10.4236/am.2023.149035","DOIUrl":"https://doi.org/10.4236/am.2023.149035","url":null,"abstract":"We study two generalized versions of a system of equations which describe the time evolution of the hydrodynamic fluctuations of density and velocity in a linear viscoelastic fluid. In the first of these versions, the time derivatives are replaced by conformable derivatives, and in the second version left-handed Caputo’s derivatives are used. We show that the solutions obtained with these two types of derivatives exhibit significant similarities, which is an interesting (and somewhat surprising) result, taking into account that the conformable derivatives are local operators, while Caputo’s derivatives are nonlocal operators. We also show that the solutions of the generalized systems are similar to the solutions of the original system, if the order α of the new derivatives (conformable or Caputo) is less than one. On the other hand, when α is greater than one, the solutions of the generalized systems are qualitatively different from the solutions of the original system.","PeriodicalId":64940,"journal":{"name":"应用数学(英文)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135441942","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}
Predictive Emission Monitoring Systems (PEMS) offer a cost-effective and environmentally friendly alternative to Continuous Emission Monitoring Systems (CEMS) for monitoring pollution from industrial sources. Multiple regression is one of the fundamental statistical techniques to describe the relationship between dependent and independent variables. This model can be effectively used to develop a PEMS, to estimate the amount of pollution emitted by industrial sources, where the fuel composition and other process-related parameters are available. It often makes them sufficient to predict the emission discharge with acceptable accuracy. In cases where PEMS are accepted as an alternative me-thod to CEMS, which use gas analyzers, they can provide cost savings and sub-stantial benefits for ongoing system support and maintenance. The described mathematical concept is based on the matrix algebra representation in multiple regression involving multiple precision arithmetic techniques. Challenging numerical examples for statistical big data analysis, are investigated. Numerical examples illustrate computational accuracy and efficiency of statistical analysis due to increasing the precision level. The programming language C++ is used for mathematical model implementation. The data for research and development, including the dependent fuel and independent NOx emissions data, were obtained from CEMS software installed on a petrochemical plant.
{"title":"Multiple Regression and Big Data Analysis for Predictive Emission Monitoring Systems","authors":"Z. Krougly, Vladimir Krougly, Serge Bays","doi":"10.4236/am.2023.145023","DOIUrl":"https://doi.org/10.4236/am.2023.145023","url":null,"abstract":"Predictive Emission Monitoring Systems (PEMS) offer a cost-effective and environmentally friendly alternative to Continuous Emission Monitoring Systems (CEMS) for monitoring pollution from industrial sources. Multiple regression is one of the fundamental statistical techniques to describe the relationship between dependent and independent variables. This model can be effectively used to develop a PEMS, to estimate the amount of pollution emitted by industrial sources, where the fuel composition and other process-related parameters are available. It often makes them sufficient to predict the emission discharge with acceptable accuracy. In cases where PEMS are accepted as an alternative me-thod to CEMS, which use gas analyzers, they can provide cost savings and sub-stantial benefits for ongoing system support and maintenance. The described mathematical concept is based on the matrix algebra representation in multiple regression involving multiple precision arithmetic techniques. Challenging numerical examples for statistical big data analysis, are investigated. Numerical examples illustrate computational accuracy and efficiency of statistical analysis due to increasing the precision level. The programming language C++ is used for mathematical model implementation. The data for research and development, including the dependent fuel and independent NOx emissions data, were obtained from CEMS software installed on a petrochemical plant.","PeriodicalId":64940,"journal":{"name":"应用数学(英文)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81248826","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}
{"title":"The Stochastic Asymptotic Stability Analysis in Two Species Lotka-Volterra Model","authors":"Yuqiang Li, Yuehua He","doi":"10.4236/am.2023.147028","DOIUrl":"https://doi.org/10.4236/am.2023.147028","url":null,"abstract":"","PeriodicalId":64940,"journal":{"name":"应用数学(英文)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79899119","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}
{"title":"Like a Sum Is Generalized into an Integral, a Product May Be Generalized into an Inteduct","authors":"M. Grabinski, G. Klinkova","doi":"10.4236/am.2023.145017","DOIUrl":"https://doi.org/10.4236/am.2023.145017","url":null,"abstract":"","PeriodicalId":64940,"journal":{"name":"应用数学(英文)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88717637","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}
{"title":"A Comparative Survey of an Approximate Solution Method for Stochastic Delay Differential Equations","authors":"E. C. Emenonye, Donatus Anonwa","doi":"10.4236/am.2023.143012","DOIUrl":"https://doi.org/10.4236/am.2023.143012","url":null,"abstract":"","PeriodicalId":64940,"journal":{"name":"应用数学(英文)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84705834","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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