Pub Date : 2024-02-14DOI: 10.34198/ejms.14324.379389
Bedaa Alawi Abd, A. Wanas
In this work, we define and study some families of multivalent analytic functions defined by the fuzzy subordination and Borel distribution. We discuss some interesting inclusion results and various other useful properties involving integral of these families.
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Pub Date : 2024-02-08DOI: 10.34198/ejms.14224.349378
Busayo Adeyege Okediji, A. Oladipo
Persistent homology is an important tool in non-linear data reduction. Its sister theory, persistent cohomology, has attracted less attention in the past years eventhough it has many advantages. Several literatures dealing with theory and computations of persistent homology and cohomology were surveyed. Reasons why cohomology has been neglected over time are identified and, few possible solutions to the identified problems are made available. Furthermore, using Ripserer, the computation of persistent homology and cohomology using 2-sphere both manually and computationally are carried out. In both cases, same result was obtained, particularly in the computation of their barcodes which visibly revealed the point where the two coincides. Conclusively, it is observed that persistent cohomology is not only faster in computation than persistent homology, but also uses less memory in a little time.
{"title":"Persistent Homology and Persistent Cohomology: A Review","authors":"Busayo Adeyege Okediji, A. Oladipo","doi":"10.34198/ejms.14224.349378","DOIUrl":"https://doi.org/10.34198/ejms.14224.349378","url":null,"abstract":"Persistent homology is an important tool in non-linear data reduction. Its sister theory, persistent cohomology, has attracted less attention in the past years eventhough it has many advantages. Several literatures dealing with theory and computations of persistent homology and cohomology were surveyed. Reasons why cohomology has been neglected over time are identified and, few possible solutions to the identified problems are made available. Furthermore, using Ripserer, the computation of persistent homology and cohomology using 2-sphere both manually and computationally are carried out. In both cases, same result was obtained, particularly in the computation of their barcodes which visibly revealed the point where the two coincides. Conclusively, it is observed that persistent cohomology is not only faster in computation than persistent homology, but also uses less memory in a little time.","PeriodicalId":507233,"journal":{"name":"Earthline Journal of Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139793928","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 : 2024-02-08DOI: 10.34198/ejms.14224.349378
Busayo Adeyege Okediji, A. Oladipo
Persistent homology is an important tool in non-linear data reduction. Its sister theory, persistent cohomology, has attracted less attention in the past years eventhough it has many advantages. Several literatures dealing with theory and computations of persistent homology and cohomology were surveyed. Reasons why cohomology has been neglected over time are identified and, few possible solutions to the identified problems are made available. Furthermore, using Ripserer, the computation of persistent homology and cohomology using 2-sphere both manually and computationally are carried out. In both cases, same result was obtained, particularly in the computation of their barcodes which visibly revealed the point where the two coincides. Conclusively, it is observed that persistent cohomology is not only faster in computation than persistent homology, but also uses less memory in a little time.
{"title":"Persistent Homology and Persistent Cohomology: A Review","authors":"Busayo Adeyege Okediji, A. Oladipo","doi":"10.34198/ejms.14224.349378","DOIUrl":"https://doi.org/10.34198/ejms.14224.349378","url":null,"abstract":"Persistent homology is an important tool in non-linear data reduction. Its sister theory, persistent cohomology, has attracted less attention in the past years eventhough it has many advantages. Several literatures dealing with theory and computations of persistent homology and cohomology were surveyed. Reasons why cohomology has been neglected over time are identified and, few possible solutions to the identified problems are made available. Furthermore, using Ripserer, the computation of persistent homology and cohomology using 2-sphere both manually and computationally are carried out. In both cases, same result was obtained, particularly in the computation of their barcodes which visibly revealed the point where the two coincides. Conclusively, it is observed that persistent cohomology is not only faster in computation than persistent homology, but also uses less memory in a little time.","PeriodicalId":507233,"journal":{"name":"Earthline Journal of Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139853810","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 : 2024-02-05DOI: 10.34198/ejms.14224.333347
N. P. Akpan, O. R. Uwaeme
The Remkan distribution is a two-parameter lifetime distribution that has been introduced into the literature to meet the ever-growing demand for the development of new lifetime distributions to meet the goodness of fit demand of complex datasets. The mathematical properties of the Remkan distribution have been derived in the literature. This study therefore aims to derive important statistical properties including the mode, quantile function, order statistics, entropy, stochastic ordering, average absolute deviation, and mid-point and Reliability indices such as the survivorship or existence measurement function, risk measurement function, and average residual measurement lifetime function.
{"title":"On the Statistical Properties of the Remkan Distribution","authors":"N. P. Akpan, O. R. Uwaeme","doi":"10.34198/ejms.14224.333347","DOIUrl":"https://doi.org/10.34198/ejms.14224.333347","url":null,"abstract":"The Remkan distribution is a two-parameter lifetime distribution that has been introduced into the literature to meet the ever-growing demand for the development of new lifetime distributions to meet the goodness of fit demand of complex datasets. The mathematical properties of the Remkan distribution have been derived in the literature. This study therefore aims to derive important statistical properties including the mode, quantile function, order statistics, entropy, stochastic ordering, average absolute deviation, and mid-point and Reliability indices such as the survivorship or existence measurement function, risk measurement function, and average residual measurement lifetime function.","PeriodicalId":507233,"journal":{"name":"Earthline Journal of Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139803266","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 : 2024-02-05DOI: 10.34198/ejms.14224.333347
N. P. Akpan, O. R. Uwaeme
The Remkan distribution is a two-parameter lifetime distribution that has been introduced into the literature to meet the ever-growing demand for the development of new lifetime distributions to meet the goodness of fit demand of complex datasets. The mathematical properties of the Remkan distribution have been derived in the literature. This study therefore aims to derive important statistical properties including the mode, quantile function, order statistics, entropy, stochastic ordering, average absolute deviation, and mid-point and Reliability indices such as the survivorship or existence measurement function, risk measurement function, and average residual measurement lifetime function.
{"title":"On the Statistical Properties of the Remkan Distribution","authors":"N. P. Akpan, O. R. Uwaeme","doi":"10.34198/ejms.14224.333347","DOIUrl":"https://doi.org/10.34198/ejms.14224.333347","url":null,"abstract":"The Remkan distribution is a two-parameter lifetime distribution that has been introduced into the literature to meet the ever-growing demand for the development of new lifetime distributions to meet the goodness of fit demand of complex datasets. The mathematical properties of the Remkan distribution have been derived in the literature. This study therefore aims to derive important statistical properties including the mode, quantile function, order statistics, entropy, stochastic ordering, average absolute deviation, and mid-point and Reliability indices such as the survivorship or existence measurement function, risk measurement function, and average residual measurement lifetime function.","PeriodicalId":507233,"journal":{"name":"Earthline Journal of Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139863074","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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