{"title":"Duality between Bessel Functions and Chebyshev Polynomials in Expansions of Functions","authors":"A. Wünsche","doi":"10.4236/apm.2023.138034","DOIUrl":"https://doi.org/10.4236/apm.2023.138034","url":null,"abstract":"","PeriodicalId":43512,"journal":{"name":"Advances in Pure and Applied Mathematics","volume":"117 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81192736","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 Infinity Tree: Representing Infinities of Real Numbers with Countably Infinite Tree Structures","authors":"Philip C. Jackson","doi":"10.4236/apm.2023.134013","DOIUrl":"https://doi.org/10.4236/apm.2023.134013","url":null,"abstract":"","PeriodicalId":43512,"journal":{"name":"Advances in Pure and Applied Mathematics","volume":"11 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73255165","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":"Zipf’s Law, Benford’s Law, and Pareto Rule","authors":"O. Kafri","doi":"10.4236/apm.2023.133010","DOIUrl":"https://doi.org/10.4236/apm.2023.133010","url":null,"abstract":"","PeriodicalId":43512,"journal":{"name":"Advances in Pure and Applied Mathematics","volume":"108 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79549429","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":"All Zeros of the Riemann Zeta Function in the Critical Strip Are Located on the Critical Line and Are Simple","authors":"F. Stenger","doi":"10.4236/apm.2023.136025","DOIUrl":"https://doi.org/10.4236/apm.2023.136025","url":null,"abstract":"In this paper we study the function (","PeriodicalId":43512,"journal":{"name":"Advances in Pure and Applied Mathematics","volume":"14 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79774896","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 boundary value problems of the third-order ordinary differential equation have many practical application backgrounds and their some special cases have been studied by many authors. However, few scholars have studied the boundary value problems of the complete third-order differential equations
{"title":"Existence and Uniqueness Results for a Fully Third-Order Boundary Value Problem","authors":"Xiaoming Liu, Yongxiang Li","doi":"10.4236/apm.2023.138033","DOIUrl":"https://doi.org/10.4236/apm.2023.138033","url":null,"abstract":"The boundary value problems of the third-order ordinary differential equation have many practical application backgrounds and their some special cases have been studied by many authors. However, few scholars have studied the boundary value problems of the complete third-order differential equations","PeriodicalId":43512,"journal":{"name":"Advances in Pure and Applied Mathematics","volume":"21 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75401259","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 constrained motion of a particle on an elliptical path is studied using Hamiltonian mechanics through Poisson bracket and Lagrangian mechanics through Euler Lagrange equation using non-natural Lagrangian. We calculate the generalized momentum pθ and we find that this quantity is not conserved and the conjugate θ coordinate is not a cyclic coordinate.
{"title":"Canonical Treatment of Elliptical Motion","authors":"Ola A. Jarab’ah","doi":"10.4236/apm.2023.139041","DOIUrl":"https://doi.org/10.4236/apm.2023.139041","url":null,"abstract":"The constrained motion of a particle on an elliptical path is studied using Hamiltonian mechanics through Poisson bracket and Lagrangian mechanics through Euler Lagrange equation using non-natural Lagrangian. We calculate the generalized momentum pθ and we find that this quantity is not conserved and the conjugate θ coordinate is not a cyclic coordinate.","PeriodicalId":43512,"journal":{"name":"Advances in Pure and Applied Mathematics","volume":"278 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":"135699211","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 Note on the Inverse Connected <i>p</i>-Median Problem on Block Graphs","authors":"Chun-Hsiang Bai, Liqi Zhang, Jianjie Zhou","doi":"10.4236/apm.2023.134011","DOIUrl":"https://doi.org/10.4236/apm.2023.134011","url":null,"abstract":"","PeriodicalId":43512,"journal":{"name":"Advances in Pure and Applied Mathematics","volume":"35 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84012095","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: 10.4236/apm.2023.1310047
Carlos Antonio Marin-Mendoza, Rogelio Valdez-Delgado
A novel method of renormalization called Pacman renormalization allows us to study (unicritical) Siegel functions through Pacman-type functions. It has been used to investigate the Siegel parameters with combinatorially periodic rotation number in the main cardioid of the Mandelbrot set. It is already known that it can be defined a Pacman renormalization operator such that for Siegel pacmen, with combinatorially periodic rotation numbers, the operator is compact, analytic and has a unique fixed point, at which it is hyperbolic with one-dimensional unstable manifold. In this paper we observe that this Pacman renormalization operator is compact and analytic at any Siegel Pacman or Siegel map with combinatorially bounded rotation number. This allows us to define a renormalization operator on the hybrid classes of the standard Siegel pacmen to which we built its horseshoe where the operator is topologically semiconjugated to the left shift on the space of bi-infinite sequences of natural numbers bounded by some constant.
{"title":"Pacman Renormalization in Siegel Parameters of Bounded Type","authors":"Carlos Antonio Marin-Mendoza, Rogelio Valdez-Delgado","doi":"10.4236/apm.2023.1310047","DOIUrl":"https://doi.org/10.4236/apm.2023.1310047","url":null,"abstract":"A novel method of renormalization called Pacman renormalization allows us to study (unicritical) Siegel functions through Pacman-type functions. It has been used to investigate the Siegel parameters with combinatorially periodic rotation number in the main cardioid of the Mandelbrot set. It is already known that it can be defined a Pacman renormalization operator such that for Siegel pacmen, with combinatorially periodic rotation numbers, the operator is compact, analytic and has a unique fixed point, at which it is hyperbolic with one-dimensional unstable manifold. In this paper we observe that this Pacman renormalization operator is compact and analytic at any Siegel Pacman or Siegel map with combinatorially bounded rotation number. This allows us to define a renormalization operator on the hybrid classes of the standard Siegel pacmen to which we built its horseshoe where the operator is topologically semiconjugated to the left shift on the space of bi-infinite sequences of natural numbers bounded by some constant.","PeriodicalId":43512,"journal":{"name":"Advances in Pure and Applied Mathematics","volume":"28 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":"135156132","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: 10.21494/iste.op.2023.0905
A. Kawa, S. N. Hasan, B. Wani
{"title":"Multiplicative Jordan type higher derivations of unital rings with non trivial idempotents","authors":"A. Kawa, S. N. Hasan, B. Wani","doi":"10.21494/iste.op.2023.0905","DOIUrl":"https://doi.org/10.21494/iste.op.2023.0905","url":null,"abstract":"","PeriodicalId":43512,"journal":{"name":"Advances in Pure and Applied Mathematics","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44576398","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}
We prove the boundedness of the multilinear operators associated to the pseudo- differential operator for the extreme cases.
在极端情况下，证明了与伪微分算子相关的多线性算子的有界性。
{"title":"Boundedness for Multilinear Operators of Pseudo-Differential Operators","authors":"Lanzhe Liu","doi":"10.7153/JMI-04-20","DOIUrl":"https://doi.org/10.7153/JMI-04-20","url":null,"abstract":"We prove the boundedness of the multilinear operators associated to the pseudo- differential operator for the extreme cases.","PeriodicalId":43512,"journal":{"name":"Advances in Pure and Applied Mathematics","volume":"96 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76669178","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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