Pub Date : 2022-01-01DOI: 10.21494/iste.op.2022.0809
A. Hafoud, A. Ghanmi
{"title":"Explicit formulas of the heat kernel on the quaternionic projective spaces","authors":"A. Hafoud, A. Ghanmi","doi":"10.21494/iste.op.2022.0809","DOIUrl":"https://doi.org/10.21494/iste.op.2022.0809","url":null,"abstract":"","PeriodicalId":43512,"journal":{"name":"Advances in Pure and Applied Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68702959","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 : 2022-01-01DOI: 10.21494/iste.op.2022.0887
P. Bansal, Ajay Mahaputra Kumar, A. Bansal
{"title":"Continuous Modulated Shearlet Transform","authors":"P. Bansal, Ajay Mahaputra Kumar, A. Bansal","doi":"10.21494/iste.op.2022.0887","DOIUrl":"https://doi.org/10.21494/iste.op.2022.0887","url":null,"abstract":"","PeriodicalId":43512,"journal":{"name":"Advances in Pure and Applied Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68703194","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 Orbital Graph of Primitive Group with Socle <i>A</i><sub>7</sub> × <i>A</i><sub>7</sub>","authors":"Jing Wu, Chang Wang, Jinlong Yang, Hong-Ku N Xu","doi":"10.4236/apm.2022.123012","DOIUrl":"https://doi.org/10.4236/apm.2022.123012","url":null,"abstract":"","PeriodicalId":43512,"journal":{"name":"Advances in Pure and Applied Mathematics","volume":"101 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73584995","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}
This paper is positioned as a sequel edition of [1]. First, as in [1], define "division sequence", "complete division sequence", "star conversion", and "extended star conversion". Next, we use Well-Founded Induction and Peirce's law to prove the Collatz conjecture. This proof uses the theorem proving system Idris.
{"title":"Proof of Collatz Conjecture Using Division Sequence","authors":"M. Furuta","doi":"10.4236/apm.2022.122009","DOIUrl":"https://doi.org/10.4236/apm.2022.122009","url":null,"abstract":"This paper is positioned as a sequel edition of [1]. First, as in [1], define \"division sequence\", \"complete division sequence\", \"star conversion\", and \"extended star conversion\". Next, we use Well-Founded Induction and Peirce's law to prove the Collatz conjecture. This proof uses the theorem proving system Idris.","PeriodicalId":43512,"journal":{"name":"Advances in Pure and Applied Mathematics","volume":"2 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84210355","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 Procedure for Trisecting an Acute Angle","authors":"Lyndon O. Barton","doi":"10.4236/apm.2022.122005","DOIUrl":"https://doi.org/10.4236/apm.2022.122005","url":null,"abstract":"","PeriodicalId":43512,"journal":{"name":"Advances in Pure and Applied Mathematics","volume":"44 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81106636","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 prime-number-formula at any distance from the origin has a systematic error, proportional to the square of the number of primes up to the square root of the distance. The proposed completion in the present paper eliminates by a quickly converging recursive formula the systematic error. The remaining error is reduced to a symmetric dispersion, with standard deviation proportional to the number of primes at the square root of the distance. 1: Evaluation of the number of primes The total number of the primes is the integral of the local logarithmic density of free positions, evaluated by Riemann. The first approximation of the integral is the sum of the logarithmic density over all integers, in the following used as sum over all integers: π c ( )= 2 c c 1 ln c ( ) d πln_appr c ( ) 2 c n 1 ln n ( ) (1.1) This above sum may be written as summing up first over all integers within the sections of the length ( c ) and then summing up over all the ( c ) sections of the length ( c ). Taking the average value over each section and summing up over the sections is an approximation, in the following used as sum over all sections.
质数公式在离原点任意距离处都有系统误差，与质数个数的平方和距离的平方根成正比。本文提出的补全方法用一个快速收敛的递推公式消除了系统误差。剩余的误差减小为对称色散，标准差与距离平方根处的素数成正比。1:素数的计算素数的总数是自由位置的局部对数密度的积分，由黎曼计算。第一个近似积分的对数密度在所有整数之和,在以下用作所有整数求和:πc () = 2 c c 1 ln c()dπln_appr c()2 c n 1 ln n()(1.1)以上的金额可能写成总结前对所有整数部分内的长度(c),然后总结所有的(c)部分长度(c)。取每个部分的平均值，并将其相加是一个近似值，在下面用作对所有部分求和。
{"title":"The Number of Primes","authors":"P. Doroszlai, Horacio Keller","doi":"10.4236/apm.2022.122008","DOIUrl":"https://doi.org/10.4236/apm.2022.122008","url":null,"abstract":"The prime-number-formula at any distance from the origin has a systematic error, proportional to the square of the number of primes up to the square root of the distance. The proposed completion in the present paper eliminates by a quickly converging recursive formula the systematic error. The remaining error is reduced to a symmetric dispersion, with standard deviation proportional to the number of primes at the square root of the distance. 1: Evaluation of the number of primes The total number of the primes is the integral of the local logarithmic density of free positions, evaluated by Riemann. The first approximation of the integral is the sum of the logarithmic density over all integers, in the following used as sum over all integers: π c ( )= 2 c c 1 ln c ( ) d πln_appr c ( ) 2 c n 1 ln n ( ) (1.1) This above sum may be written as summing up first over all integers within the sections of the length ( c ) and then summing up over all the ( c ) sections of the length ( c ). Taking the average value over each section and summing up over the sections is an approximation, in the following used as sum over all sections.","PeriodicalId":43512,"journal":{"name":"Advances in Pure and Applied Mathematics","volume":"6 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81698982","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":"Proof of Riemann Conjecture","authors":"Chuanmiao Chen","doi":"10.4236/apm.2022.125028","DOIUrl":"https://doi.org/10.4236/apm.2022.125028","url":null,"abstract":"","PeriodicalId":43512,"journal":{"name":"Advances in Pure and Applied Mathematics","volume":"114 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87643770","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 anisotropic continuum stored energy density (ACSED) functional is applied for accurate constitutive modeling of biological tissues and finite element implementation without the isochoric—volumetric split, the anisotropic—isotropic split, or the anisotropic invariant split. Related stress and elasticity tensors in the reference and current configurations are worked out. A new kinematic model is derived based on the tangent Poisson’s ratio as a cubic polynomial function of stretch. The ACSED model, along with the kinematic model, accurately fits uniaxial extension test data for compressible human skin, bovine articular cartilage, and human aorta samples.
{"title":"Anisotropic Constitutive Modeling of Compressible Biological Tissue","authors":"F. Zhao","doi":"10.4236/apm.2022.125027","DOIUrl":"https://doi.org/10.4236/apm.2022.125027","url":null,"abstract":"The anisotropic continuum stored energy density (ACSED) functional is applied for accurate constitutive modeling of biological tissues and finite element implementation without the isochoric—volumetric split, the anisotropic—isotropic split, or the anisotropic invariant split. Related stress and elasticity tensors in the reference and current configurations are worked out. A new kinematic model is derived based on the tangent Poisson’s ratio as a cubic polynomial function of stretch. The ACSED model, along with the kinematic model, accurately fits uniaxial extension test data for compressible human skin, bovine articular cartilage, and human aorta samples.","PeriodicalId":43512,"journal":{"name":"Advances in Pure and Applied Mathematics","volume":"26 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81669208","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 : 2022-01-01DOI: 10.4236/apm.2022.1212056
P. Doroszlai, Horacio Keller
{"title":"Erratum to “The Symmetric Series of Multiples of Primes” [Advances in Pure Mathematics, 12 (2022) 160-177]","authors":"P. Doroszlai, Horacio Keller","doi":"10.4236/apm.2022.1212056","DOIUrl":"https://doi.org/10.4236/apm.2022.1212056","url":null,"abstract":"","PeriodicalId":43512,"journal":{"name":"Advances in Pure and Applied Mathematics","volume":"33 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77600502","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 : 2022-01-01DOI: 10.4236/apm.2022.1211049
Cong-Dian Cheng
The present work considers the endpoint in the abstract metric space. It firstly introduces the metric space of partially ordered groups and the metric space of partially ordered modules, respectively; and defines the convergence of sequences and the multi-valued weak contractions, etc., on the introduced space. And then, with the methods of functional analysis and abstract algebra, it successively establishes an endpoint theorem for the metric space of partially ordered groups and an endpoint theorem for the metric space of partially ordered modules. The contributions of this article extend the theory of cone metric space constructed by Huang and Zhang (2007) and some recent results on the fixed point and endpoint theory, such as the endpoint theorem given by Amini-Harandi (2010).
{"title":"Endpoints of Multi-Valued Weak Contractions on the Metric Space of Partially Ordered Groups","authors":"Cong-Dian Cheng","doi":"10.4236/apm.2022.1211049","DOIUrl":"https://doi.org/10.4236/apm.2022.1211049","url":null,"abstract":"The present work considers the endpoint in the abstract metric space. It firstly introduces the metric space of partially ordered groups and the metric space of partially ordered modules, respectively; and defines the convergence of sequences and the multi-valued weak contractions, etc., on the introduced space. And then, with the methods of functional analysis and abstract algebra, it successively establishes an endpoint theorem for the metric space of partially ordered groups and an endpoint theorem for the metric space of partially ordered modules. The contributions of this article extend the theory of cone metric space constructed by Huang and Zhang (2007) and some recent results on the fixed point and endpoint theory, such as the endpoint theorem given by Amini-Harandi (2010).","PeriodicalId":43512,"journal":{"name":"Advances in Pure and Applied Mathematics","volume":"45 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78564474","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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