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Explicit formulas of the heat kernel on the quaternionic projective spaces 四元数射影空间上热核的显式公式
IF 0.4
Advances in Pure and Applied Mathematics Pub Date : 2022-01-01 DOI: 10.21494/iste.op.2022.0809
A. Hafoud, A. Ghanmi
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引用次数: 0
Continuous Modulated Shearlet Transform 连续调制Shearlet变换
IF 0.4
Advances in Pure and Applied Mathematics Pub Date : 2022-01-01 DOI: 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}
引用次数: 0
The Orbital Graph of Primitive Group with Socle A7 × A7 社交圈为A7 × A7的原始群轨道图
IF 0.4
Advances in Pure and Applied Mathematics Pub Date : 2022-01-01 DOI: 10.4236/apm.2022.123012
Jing Wu, Chang Wang, Jinlong Yang, Hong-Ku N Xu
{"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}
引用次数: 0
Anisotropic Constitutive Modeling of Compressible Biological Tissue 可压缩生物组织的各向异性本构模型
IF 0.4
Advances in Pure and Applied Mathematics Pub Date : 2022-01-01 DOI: 10.4236/apm.2022.125027
F. Zhao
{"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}
引用次数: 0
Proof of Collatz Conjecture Using Division Sequence 用除法序列证明Collatz猜想
IF 0.4
Advances in Pure and Applied Mathematics Pub Date : 2022-01-01 DOI: 10.4236/apm.2022.122009
M. Furuta
{"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}
引用次数: 2
A Procedure for Trisecting an Acute Angle 锐角的三分法
IF 0.4
Advances in Pure and Applied Mathematics Pub Date : 2022-01-01 DOI: 10.4236/apm.2022.122005
Lyndon O. Barton
{"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}
引用次数: 4
The Number of Primes 质数的数目
IF 0.4
Advances in Pure and Applied Mathematics Pub Date : 2022-01-01 DOI: 10.4236/apm.2022.122008
P. Doroszlai, Horacio Keller
{"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}
引用次数: 4
Proof of Riemann Conjecture 黎曼猜想的证明
IF 0.4
Advances in Pure and Applied Mathematics Pub Date : 2022-01-01 DOI: 10.4236/apm.2022.125028
Chuanmiao Chen
{"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}
引用次数: 3
Erratum to “The Symmetric Series of Multiples of Primes” [Advances in Pure Mathematics, 12 (2022) 160-177] “素数的对称倍数级数”的勘误[纯数学进展，12 (2022)160-177]
IF 0.4
Advances in Pure and Applied Mathematics Pub Date : 2022-01-01 DOI: 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}
引用次数: 0
Endpoints of Multi-Valued Weak Contractions on the Metric Space of Partially Ordered Groups 部分序群度量空间上多值弱收缩的端点
IF 0.4
Advances in Pure and Applied Mathematics Pub Date : 2022-01-01 DOI: 10.4236/apm.2022.1211049
Cong-Dian Cheng
{"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}
引用次数: 0
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