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Method for calculating Dirichlet L-functions 狄利克雷l函数的计算方法
Mathematica Montisnigri Pub Date : 1900-01-01 DOI: 10.20948/mathmontis-2022-54-5
Brahim Mittou, Abdallah Derbal
{"title":"Method for calculating Dirichlet L-functions","authors":"Brahim Mittou, Abdallah Derbal","doi":"10.20948/mathmontis-2022-54-5","DOIUrl":"https://doi.org/10.20948/mathmontis-2022-54-5","url":null,"abstract":"Recently, the authors gave asymptotic formulas for L(s, χ), which associated with a primitive Dirichlet character χ, in terms of the generalized Bernoulli numbers. In this paper, based on the aforementioned asymptotic formulas we describe a method for calculating Dirichlet L-functions that can be used to validate the generalized Riemann hypothesis up to a height T > 0. Our method is a refinement of the one presented by Davies and Haselgrove.","PeriodicalId":170315,"journal":{"name":"Mathematica Montisnigri","volume":"60 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":"114078105","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}
引用次数: 0
On the LP boundedness of h-Fourier integral operators with rough symbols 粗糙符号h-Fourier积分算子的LP有界性
Mathematica Montisnigri Pub Date : 1900-01-01 DOI: 10.20948/mathmontis-2022-54-3
O. Elong
{"title":"On the LP boundedness of h-Fourier integral operators with rough symbols","authors":"O. Elong","doi":"10.20948/mathmontis-2022-54-3","DOIUrl":"https://doi.org/10.20948/mathmontis-2022-54-3","url":null,"abstract":"We prove LP boundedness of a class of semiclassical Fourier integral operators defined by smooth phase function and semiclassical rough symbols on the spatial variable 𝑥. We also consider a spacial case of ℎ -pseudodifferential operators.","PeriodicalId":170315,"journal":{"name":"Mathematica Montisnigri","volume":"46 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":"128165247","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}
引用次数: 0
On the average order of the gcd-sum function over the set of square integers gcd-sum函数在平方整数集合上的平均阶
Mathematica Montisnigri Pub Date : 1900-01-01 DOI: 10.20948/mathmontis-2023-56-4
M. Bouderbala
{"title":"On the average order of the gcd-sum function over the set of square integers","authors":"M. Bouderbala","doi":"10.20948/mathmontis-2023-56-4","DOIUrl":"https://doi.org/10.20948/mathmontis-2023-56-4","url":null,"abstract":"The gcd-sum function is one of the most important functions that has been studied by many researchers in recent years (Broughan, Bordellès, etc.). The gcd-sum function appears in a specific lattice point problem, where it can be used to estimate the number of integer coordinate points under the square root curve. In this paper, we give an average order of the gcd-sum function over the set of squares.","PeriodicalId":170315,"journal":{"name":"Mathematica Montisnigri","volume":"2012 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":"128896129","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}
引用次数: 0
Machine learning and neural networks based approach for deflection prediction of Euler-Bernoulli beam equations 基于机器学习和神经网络的欧拉-伯努利梁方程挠度预测方法
Mathematica Montisnigri Pub Date : 1900-01-01 DOI: 10.20948/mathmontis-2023-56-8
Zaur Rasulov, U. Yesil
{"title":"Machine learning and neural networks based approach for deflection prediction of Euler-Bernoulli beam equations","authors":"Zaur Rasulov, U. Yesil","doi":"10.20948/mathmontis-2023-56-8","DOIUrl":"https://doi.org/10.20948/mathmontis-2023-56-8","url":null,"abstract":"Beam-like structures are widespread but essential systems that have been extensively studied for centuries. Although several proposed solutions are effective, the time consumption and the difficulty of reconstructing the problem are the major disadvantages of these methods. This paper offers a new methodology for finding solutions to beam problems based on Machine Learning and Neural Networks with different optimization algorithms. Various regression models are compared on numerically stimulated Euler-Bernoulli beam modelling.","PeriodicalId":170315,"journal":{"name":"Mathematica Montisnigri","volume":"154 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":"115194942","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}
引用次数: 0
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