Muhammad Shoaib Sardar, Hamna Choudhry, Jia-Bao Liu
Let be a simple graph with vertex set and edge set . In a graph , a subset of edges denoted by is referred to as an edge-dominating set of if every edge that is not in
In this article, a modified version of frame called frame associated with a sequence of scalars (FASS) is defined. This modified version of frame is used to study quantum measurements. Also, using FASS, some Naimark-type results are obtained. Finally, a formula to give the average probability of an incorrect measurement using FASS is obtained.
{"title":"Naimark-Type Results Using Frames","authors":"Raksha Sharma, Nikhil Khanna","doi":"10.1155/2024/8588361","DOIUrl":"https://doi.org/10.1155/2024/8588361","url":null,"abstract":"In this article, a modified version of frame called frame associated with a sequence of scalars (FASS) is defined. This modified version of frame is used to study quantum measurements. Also, using FASS, some Naimark-type results are obtained. Finally, a formula to give the average probability of an incorrect measurement using FASS is obtained.","PeriodicalId":15840,"journal":{"name":"Journal of Function Spaces","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139920474","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Oqlah Al-Refai, Ala Amourah, Tariq Al-Hawary, Basem Aref Frasin
This study establishes a new method to investigate bounds of ;, for certain general classes of bi-univalent functions. The results include a number of improvements and generalizations for well-known estimations. We also discuss bounds of and consider several corollaries, remarks, and consequences of the results presented in this paper.
{"title":"A New Method for Estimating General Coefficients to Classes of Bi-univalent Functions","authors":"Oqlah Al-Refai, Ala Amourah, Tariq Al-Hawary, Basem Aref Frasin","doi":"10.1155/2024/9889253","DOIUrl":"https://doi.org/10.1155/2024/9889253","url":null,"abstract":"This study establishes a new method to investigate bounds of <span><svg height=\"12.5794pt\" style=\"vertical-align:-3.29107pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 18.1261 12.5794\" width=\"18.1261pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,3.419,0)\"></path></g><g transform=\"matrix(.0091,0,0,-0.0091,9.412,3.132)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,14.559,0)\"><use xlink:href=\"#g113-9\"></use></g></svg>;</span> <span><svg height=\"11.5564pt\" style=\"vertical-align:-2.26807pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 22.3 11.5564\" width=\"22.3pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,4.498,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,14.669,0)\"></path></g></svg><span></span><span><svg height=\"11.5564pt\" style=\"vertical-align:-2.26807pt\" version=\"1.1\" viewbox=\"25.8821838 -9.28833 11.235 11.5564\" width=\"11.235pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,25.932,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,32.458,0)\"></path></g></svg>,</span></span> for certain general classes of bi-univalent functions. The results include a number of improvements and generalizations for well-known estimations. We also discuss bounds of <svg height=\"15.535pt\" style=\"vertical-align:-3.9436pt\" version=\"1.1\" viewbox=\"-0.0498162 -11.5914 64.2012 15.535\" width=\"64.2012pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"><use xlink:href=\"#g113-9\"></use></g><g transform=\"matrix(.013,0,0,-0.013,3.419,0)\"><use xlink:href=\"#g113-111\"></use></g><g transform=\"matrix(.013,0,0,-0.013,9.945,0)\"><use xlink:href=\"#g113-98\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,16.525,-5.741)\"></path></g><g transform=\"matrix(.0091,0,0,-0.0091,15.938,3.784)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,24.377,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,34.914,0)\"><use xlink:href=\"#g113-98\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,40.907,3.132)\"><use xlink:href=\"#g50-51\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,45.339,3.132)\"><use xlink:href=\"#g50-111\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,49.998,3.132)\"></path></g><g transform=\"matrix(.0091,0,0,-0.0091,55.558,3.132)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,60.559,0)\"><use xlink:href=\"#g113-9\"></use></g></svg> and consider several corollaries, remarks, and consequences of the results presented in this paper.","PeriodicalId":15840,"journal":{"name":"Journal of Function Spaces","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139764124","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Retracted: Roughness in Hypervector Spaces","authors":"Journal of Function Spaces","doi":"10.1155/2024/9768105","DOIUrl":"https://doi.org/10.1155/2024/9768105","url":null,"abstract":"<jats:p />","PeriodicalId":15840,"journal":{"name":"Journal of Function Spaces","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139599681","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Retracted: On Stackelberg Leader with Min-Max Followers to Solve Fuzzy Continuous Static Games","authors":"Journal of Function Spaces","doi":"10.1155/2024/9871806","DOIUrl":"https://doi.org/10.1155/2024/9871806","url":null,"abstract":"<jats:p />","PeriodicalId":15840,"journal":{"name":"Journal of Function Spaces","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139602097","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Retracted: Notion of Complex Spherical Fuzzy Graph with Application","authors":"Journal of Function Spaces","doi":"10.1155/2024/9858016","DOIUrl":"https://doi.org/10.1155/2024/9858016","url":null,"abstract":"<jats:p />","PeriodicalId":15840,"journal":{"name":"Journal of Function Spaces","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139602439","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Retracted: Intuitionistic Fuzzy Fixed Point Theorems in Complex-Valued b-Metric Spaces with Applications to Fractional Differential Equations","authors":"Journal of Function Spaces","doi":"10.1155/2024/9879263","DOIUrl":"https://doi.org/10.1155/2024/9879263","url":null,"abstract":"<jats:p />","PeriodicalId":15840,"journal":{"name":"Journal of Function Spaces","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139599205","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Retracted: On Development of Neutrosophic Cubic Graphs with Applications in Decision Sciences","authors":"Journal of Function Spaces","doi":"10.1155/2024/9813527","DOIUrl":"https://doi.org/10.1155/2024/9813527","url":null,"abstract":"<jats:p />","PeriodicalId":15840,"journal":{"name":"Journal of Function Spaces","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139600001","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Retracted: On Neutrosophic Extension of the Maxwell Model: Properties and Applications","authors":"Journal of Function Spaces","doi":"10.1155/2024/9890259","DOIUrl":"https://doi.org/10.1155/2024/9890259","url":null,"abstract":"<jats:p />","PeriodicalId":15840,"journal":{"name":"Journal of Function Spaces","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139601971","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Retracted: On Adjacency Metric Dimension of Some Families of Graph","authors":"Journal of Function Spaces","doi":"10.1155/2024/9753495","DOIUrl":"https://doi.org/10.1155/2024/9753495","url":null,"abstract":"<jats:p />","PeriodicalId":15840,"journal":{"name":"Journal of Function Spaces","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139598807","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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