Journal of Mathematics最新文献

{"title":"Characterization of Fractional Mixed Domination Number of Paths and Cycles","authors":"P. Shanthi, S. Amutha, N. Anbazhagan, G. Uma, Gyanendra Prasad Joshi, Woong Cho","doi":"10.1155/2024/6619654","DOIUrl":"https://doi.org/10.1155/2024/6619654","url":null,"abstract":"Let <i>G</i>′ be a simple, connected, and undirected (UD) graph with the vertex set <i>M</i>(<i>G</i>′) and an edge set <i>N</i>(<i>G</i>′). In this article, we define a function <span><svg height=\"12.7178pt\" style=\"vertical-align:-3.42947pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 13.643 12.7178\" width=\"13.643pt\" 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,-0.013,10.679,0)\"></path></g></svg><span></span><svg height=\"12.7178pt\" style=\"vertical-align:-3.42947pt\" version=\"1.1\" viewbox=\"17.2251838 -9.28833 23.344 12.7178\" width=\"23.344pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,17.275,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,32.988,0)\"></path></g></svg><span></span><svg height=\"12.7178pt\" style=\"vertical-align:-3.42947pt\" version=\"1.1\" viewbox=\"43.4741838 -9.28833 32.72 12.7178\" width=\"32.72pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,43.524,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,58.066,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,63.842,0)\"></path></g></svg><span></span><svg height=\"12.7178pt\" style=\"vertical-align:-3.42947pt\" version=\"1.1\" viewbox=\"79.90318380000001 -9.28833 13.689 12.7178\" width=\"13.689pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,79.953,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,84.438,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,90.678,0)\"></path></g></svg><span></span><svg height=\"12.7178pt\" style=\"vertical-align:-3.42947pt\" version=\"1.1\" viewbox=\"95.7711838 -9.28833 11.065 12.7178\" width=\"11.065pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,95.821,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,102.061,0)\"></path></g></svg></span> as a fractional mixed dominating function (FMXDF) if it satisfies <span><svg height=\"15.5493pt\" style=\"vertical-align:-5.86298pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.68632 60.785 15.5493\" width=\"60.785pt\" 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=\"#g113-103\"></use></g><g transform=\"matrix(.013,0,0,-0.013,8.352,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,12.85,0)\"></path></g><g transform=\"matrix(.0091,0,0,-0.0091,20.936,3.132)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,28.787,0)\"><use xlink:href=\"#g113-92\"></use></g><g transform=\"matrix(.013,0,0,-0.013,33.272,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,40.539,0)\"><use xlink:href=\"#g113-94\"></use></g><g transform=\"matrix(.013,0,0,-0.013,45.024,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,53.154,0)\"></path></g></svg><span></span><svg height=\"15.5493pt\" style=\"vertical-alig","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139587007","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"MDS and MHDR Cyclic Codes over Finite Chain Rings","authors":"Monika Dalal, Sucheta Dutt, Ranjeet Sehmi","doi":"10.1155/2024/4540992","DOIUrl":"https://doi.org/10.1155/2024/4540992","url":null,"abstract":"This work establishes a unique set of generators for a cyclic code over a finite chain ring. Towards this, we first determine the minimal spanning set and rank of the code. Furthermore, sufficient as well as necessary conditions for a cyclic code to be an MDS code and for a cyclic code to be an MHDR code are obtained. Finally, to support our results, some examples of optimal cyclic codes are presented.","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":"12 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139561640","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Numerical and Scientific Investigation of Some Molecular Structures Based on the Criterion of Super Classical Average Assignments","authors":"A. Rajesh Kannan, Nazek Alessa, K. Loganathan, Balachandra Pattanaik","doi":"10.1155/2024/9360076","DOIUrl":"https://doi.org/10.1155/2024/9360076","url":null,"abstract":"Numbering a graph is a very practical and effective technique in science and engineering. Numerous graph assignment techniques, including distance-based labeling, topological indices, and spectral graph theory, can be used to investigate molecule structures. Consider the graph <span><svg height=\"8.8423pt\" style=\"vertical-align:-0.2064009pt\" version=\"1.1\" viewbox=\"-0.0498162 -8.6359 9.02496 8.8423\" width=\"9.02496pt\" 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></svg>,</span> with the injection <svg height=\"8.68572pt\" style=\"vertical-align:-0.0498209pt\" version=\"1.1\" viewbox=\"-0.0498162 -8.6359 9.97754 8.68572\" width=\"9.97754pt\" 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></svg> from the node set to <span><svg height=\"11.5564pt\" style=\"vertical-align:-2.26807pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 13.715 11.5564\" width=\"13.715pt\" 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,-0.013,4.511,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,10.751,0)\"></path></g></svg><span></span><svg height=\"11.5564pt\" style=\"vertical-align:-2.26807pt\" version=\"1.1\" viewbox=\"15.8441838 -9.28833 9.204 11.5564\" width=\"9.204pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,15.894,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,22.134,0)\"><use xlink:href=\"#g113-45\"></use></g></svg><span></span><svg height=\"11.5564pt\" style=\"vertical-align:-2.26807pt\" version=\"1.1\" viewbox=\"27.227183800000002 -9.28833 18.427 11.5564\" width=\"18.427pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,27.277,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,32.42,0)\"><use xlink:href=\"#g113-47\"></use></g><g transform=\"matrix(.013,0,0,-0.013,37.564,0)\"><use xlink:href=\"#g113-47\"></use></g><g transform=\"matrix(.013,0,0,-0.013,42.74,0)\"><use xlink:href=\"#g113-45\"></use></g></svg><span></span><span><svg height=\"11.5564pt\" style=\"vertical-align:-2.26807pt\" version=\"1.1\" viewbox=\"47.8331838 -9.28833 13.089 11.5564\" width=\"13.089pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,47.883,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,56.21,0)\"></path></g></svg>,</span></span> where <svg height=\"8.68572pt\" style=\"vertical-align:-0.0498209pt\" version=\"1.1\" viewbox=\"-0.0498162 -8.6359 8.46388 8.68572\" width=\"8.46388pt\" 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=\"#g113-133\"></use></g></svg> is the sum of the number of nodes and links. Assume that the induced link assignment <svg height=\"10.1524pt\" style=\"vert","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":"9 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139561814","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Geometric Characterization of the Numerical Range of Parallel Sum of Two Orthogonal Projections","authors":"Weiyan Yu, Ran Wang, Chen Zhang","doi":"10.1155/2024/1448498","DOIUrl":"https://doi.org/10.1155/2024/1448498","url":null,"abstract":"Let <svg height=\"9.25986pt\" style=\"vertical-align:-0.2455397pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.01432 13.1092 9.25986\" width=\"13.1092pt\" 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></svg> be a complex separable Hilbert space and <svg height=\"11.5564pt\" style=\"vertical-align:-2.26807pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 34.5353 11.5564\" width=\"34.5353pt\" 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,-0.013,12.35,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,16.848,0)\"><use xlink:href=\"#g198-9\"></use></g><g transform=\"matrix(.013,0,0,-0.013,29.809,0)\"></path></g></svg> be the algebra of all bounded linear operators from <svg height=\"9.25986pt\" style=\"vertical-align:-0.2455397pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.01432 13.1092 9.25986\" width=\"13.1092pt\" 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=\"#g198-9\"></use></g></svg> to <span><svg height=\"9.25986pt\" style=\"vertical-align:-0.2455397pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.01432 13.1092 9.25986\" width=\"13.1092pt\" 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=\"#g198-9\"></use></g></svg>.</span> Our goal in this article is to describe the closure of numerical range of parallel sum operator <span><svg height=\"10.9105pt\" style=\"vertical-align:-2.15716pt\" version=\"1.1\" viewbox=\"-0.0498162 -8.75334 14.622 10.9105\" width=\"14.622pt\" 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,-0.013,11.658,0)\"></path></g></svg><span></span><svg height=\"10.9105pt\" style=\"vertical-align:-2.15716pt\" version=\"1.1\" viewbox=\"18.204183800000003 -8.75334 17.203 10.9105\" width=\"17.203pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,18.254,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,25.573,0)\"></path></g></svg></span> for two orthogonal projections <svg height=\"8.68572pt\" style=\"vertical-align:-0.0498209pt\" version=\"1.1\" viewbox=\"-0.0498162 -8.6359 8.15071 8.68572\" width=\"8.15071pt\" 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=\"#g113-81\"></use></g></svg> and <svg height=\"10.7866pt\" style=\"vertical-align:-2.150701pt\" version=\"1.1\" viewbox=\"-0.0498162 -8.6359 9.52083 10.7866\" width=\"9.52083pt\" 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></svg> in <svg height=\"11.5564pt\" style=\"vertical-align:-2.26807pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 34.5353 11.5564","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":"6 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139561734","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Solution Approach to Nonlinear Integral Equations in Generalized b-Metric Spaces","authors":"Mohammed M. M. Jaradat, Abeeda Ahmad, Saif Ur Rehman, Nabaa Muhammad Diaa, Shamoona Jabeen, Muhammad Imran Haider, Iqra Shamas, Rawan A. Shlaka","doi":"10.1155/2024/8847058","DOIUrl":"https://doi.org/10.1155/2024/8847058","url":null,"abstract":"In this paper, we study some generalized contraction conditions for three self-mappings on generalized b-metric spaces to prove the existence of some unique common fixed-point results. To unify our results, we establish a supportive example for three self-mappings to show the uniqueness of a common fixed point for a generalized contraction in the said space. In addition, we present a supportive application of nonlinear integral equations for the validation of our work. The concept presented in this paper will play an important role in the theory of fixed points in the context of generalized metric spaces with applications.","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":"14 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139561738","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Singular Value and Matrix Norm Inequalities between Positive Semidefinite Matrices and Their Blocks","authors":"Feng Zhang, Rong Ma, Chunwen Zhang, Yuxin Cao","doi":"10.1155/2024/6652793","DOIUrl":"https://doi.org/10.1155/2024/6652793","url":null,"abstract":"In this paper, we obtain some inequalities involving positive semidefinite <span><svg height=\"8.69875pt\" style=\"vertical-align:-0.3499298pt\" version=\"1.1\" viewbox=\"-0.0498162 -8.34882 16.776 8.69875\" width=\"16.776pt\" 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,-0.013,9.145,0)\"></path></g></svg><span></span><svg height=\"8.69875pt\" style=\"vertical-align:-0.3499298pt\" version=\"1.1\" viewbox=\"19.6321838 -8.34882 6.415 8.69875\" width=\"6.415pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,19.682,0)\"><use xlink:href=\"#g113-51\"></use></g></svg></span> block matrices and their blocks.","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":"54 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139561822","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Exact Null Controllability of String Equations with Neumann Boundaries","authors":"Lizhi Cui, Jing Lu","doi":"10.1155/2024/8890544","DOIUrl":"https://doi.org/10.1155/2024/8890544","url":null,"abstract":"This article focuses on the exact null controllability of a one-dimensional wave equation in noncylindrical domains. Both the fixed endpoint and the moving endpoint are Neumann-type boundary conditions. The control is put on the moving endpoint. When the speed of the moving endpoint is less than the characteristic speed, we can obtain the exact null controllability of this equation by using the Hilbert uniqueness method. In addition, we get a sharper estimate on controllability time that depends on the speed of the moving endpoint.","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":"74 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139517147","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Performance Analysis of Two Different Types of Waiting Queues with Working Vacations","authors":"M. Sundararaman, D. Narasimhan, P. Rajadurai","doi":"10.1155/2024/5829171","DOIUrl":"https://doi.org/10.1155/2024/5829171","url":null,"abstract":"This work examines a new class of working vacation queueing models that contain regular (original) and retrial waiting queues. Upon arrival, a customer either starts their service instantly if the server is available, or they join the regular queue if the server is occupied. When it is empty, the server departs the system to take a working vacation (WV). The server provides services more slowly during the WV period. New customers join the retry queue (orbit), if the server is on vacation. The supplementary variable technique (SVT) examines the steady-state probability generating functions (PGFs) of queue size for different server states. Several system performances are numerically displayed, including system state probabilities, mean busy cycles, mean queue lengths, sensitivity analysis, and cost optimization values. The motivation for this model in a pandemic situation is to analyze new healthcare service systems and reflect the characteristics of patient services.","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":"38 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139516784","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Structure and Rank of a Cyclic Code over a Class of Nonchain Rings","authors":"Nikita Jain, Sucheta Dutt, Ranjeet Sehmi","doi":"10.1155/2024/8817721","DOIUrl":"https://doi.org/10.1155/2024/8817721","url":null,"abstract":"The rings &lt;span&gt;&lt;svg height=\"12.1436pt\" style=\"vertical-align:-3.18148pt\" version=\"1.1\" viewbox=\"-0.0498162 -8.96212 24.414 12.1436\" width=\"24.414pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"&gt;&lt;g transform=\"matrix(.013,0,0,-0.013,0,0)\"&gt;&lt;/path&gt;&lt;/g&gt;&lt;g transform=\"matrix(.0091,0,0,-0.0091,8.931,3.132)\"&gt;&lt;/path&gt;&lt;/g&gt;&lt;g transform=\"matrix(.013,0,0,-0.013,16.783,0)\"&gt;&lt;/path&gt;&lt;/g&gt;&lt;/svg&gt;&lt;span&gt;&lt;/span&gt;&lt;svg height=\"12.1436pt\" style=\"vertical-align:-3.18148pt\" version=\"1.1\" viewbox=\"27.2691838 -8.96212 19.997 12.1436\" width=\"19.997pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"&gt;&lt;g transform=\"matrix(.013,0,0,-0.013,27.319,0)\"&gt;&lt;/path&gt;&lt;/g&gt;&lt;g transform=\"matrix(.013,0,0,-0.013,33.221,0)\"&gt;&lt;use xlink:href=\"#g113-91\"&gt;&lt;/use&gt;&lt;/g&gt;&lt;g transform=\"matrix(.0091,0,0,-0.0091,42.152,3.132)\"&gt;&lt;use xlink:href=\"#g50-53\"&gt;&lt;/use&gt;&lt;/g&gt;&lt;/svg&gt;&lt;/span&gt; have been classified into chain rings and nonchain rings based on the values of &lt;span&gt;&lt;svg height=\"14.7729pt\" style=\"vertical-align:-3.181499pt\" version=\"1.1\" viewbox=\"-0.0498162 -11.5914 21.344 14.7729\" width=\"21.344pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"&gt;&lt;g transform=\"matrix(.013,0,0,-0.013,0,0)\"&gt;&lt;use xlink:href=\"#g185-47\"&gt;&lt;/use&gt;&lt;/g&gt;&lt;g transform=\"matrix(.0091,0,0,-0.0091,5.902,-5.741)\"&gt;&lt;/path&gt;&lt;/g&gt;&lt;g transform=\"matrix(.013,0,0,-0.013,14.48,0)\"&gt;&lt;/path&gt;&lt;/g&gt;&lt;/svg&gt;&lt;span&gt;&lt;/span&gt;&lt;svg height=\"14.7729pt\" style=\"vertical-align:-3.181499pt\" version=\"1.1\" viewbox=\"24.9261838 -11.5914 24.414 14.7729\" width=\"24.414pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"&gt;&lt;g transform=\"matrix(.013,0,0,-0.013,24.976,0)\"&gt;&lt;use xlink:href=\"#g113-91\"&gt;&lt;/use&gt;&lt;/g&gt;&lt;g transform=\"matrix(.0091,0,0,-0.0091,33.907,3.132)\"&gt;&lt;use xlink:href=\"#g50-53\"&gt;&lt;/use&gt;&lt;/g&gt;&lt;g transform=\"matrix(.013,0,0,-0.013,41.759,0)\"&gt;&lt;use xlink:href=\"#g117-36\"&gt;&lt;/use&gt;&lt;/g&gt;&lt;/svg&gt;&lt;span&gt;&lt;/span&gt;&lt;span&gt;&lt;svg height=\"14.7729pt\" style=\"vertical-align:-3.181499pt\" version=\"1.1\" viewbox=\"52.2461838 -11.5914 20.044 14.7729\" width=\"20.044pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"&gt;&lt;g transform=\"matrix(.013,0,0,-0.013,52.296,0)\"&gt;&lt;use xlink:href=\"#g185-47\"&gt;&lt;/use&gt;&lt;/g&gt;&lt;g transform=\"matrix(.013,0,0,-0.013,58.198,0)\"&gt;&lt;use xlink:href=\"#g113-91\"&gt;&lt;/use&gt;&lt;/g&gt;&lt;g transform=\"matrix(.0091,0,0,-0.0091,67.129,3.132)\"&gt;&lt;use xlink:href=\"#g50-53\"&gt;&lt;/use&gt;&lt;/g&gt;&lt;/svg&gt;.&lt;/span&gt;&lt;/span&gt; In this paper, the structure of a cyclic code of arbitrary length over the rings &lt;span&gt;&lt;svg height=\"12.1436pt\" style=\"vertical-align:-3.18148pt\" version=\"1.1\" viewbox=\"-0.0498162 -8.96212 24.414 12.1436\" width=\"24.414pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"&gt;&lt;g transform=\"matrix(.013,0,0,-0.013,0,0)\"&gt;&lt;use xlink:href=\"#g113-91\"&gt;&lt;/use&gt;&lt;/g&gt;&lt;g transform=\"matrix(.0091,0,0,-0.0091,8.931,3.132)\"&gt;&lt;use xlink:href=\"#g50-53\"&gt;&lt;/use&gt;&lt;/g&gt;&lt;g transform=\"matrix(.013,0,0,-0.013,16.783,0)\"&gt;&lt;use xlink:href=\"#g117-36\"&gt;&lt;/use&gt;&lt;/g&gt;&lt;/svg&gt;&lt;span&gt;&lt;/span&gt;&lt;svg height=\"12.1436pt\" style=","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":"21 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139496888","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The Y-Index of Some Complement Graph Structures and Their Applications of Nanotubes and Nanotorus","authors":"Mohammed Alsharafi, Abdu Alameri, Yusuf Zeren, Mahioub Shubatah, Anwar Alwardi","doi":"10.1155/2024/4269325","DOIUrl":"https://doi.org/10.1155/2024/4269325","url":null,"abstract":"Topological descriptors play a significant role in chemical nanostructures. These topological measures have explicit chemical uses in chemistry, medicine, biology, and computer sciences. This study calculates the &lt;i&gt;Y&lt;/i&gt;-index of some graphs and complements graph operations such as join, tensor and Cartesian and strong products, composition, disjunction, and symmetric difference between two simple graphs. Moreover, the &lt;i&gt;Y&lt;/i&gt;-polynomial of titania nanotubes and the formulae for the &lt;i&gt;Y&lt;/i&gt;-index, &lt;i&gt;Y&lt;/i&gt;-polynomial, &lt;i&gt;F&lt;/i&gt;-index, &lt;i&gt;F&lt;/i&gt;-polynomial, and &lt;i&gt;Y&lt;/i&gt;-coindex of the &lt;span&gt;&lt;svg height=\"12.7178pt\" style=\"vertical-align:-3.42947pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 59.544 12.7178\" width=\"59.544pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"&gt;&lt;g transform=\"matrix(.013,0,0,-0.013,0,0)\"&gt;&lt;/path&gt;&lt;/g&gt;&lt;g transform=\"matrix(.013,0,0,-0.013,9.475,0)\"&gt;&lt;/path&gt;&lt;/g&gt;&lt;g transform=\"matrix(.013,0,0,-0.013,18.529,0)\"&gt;&lt;/path&gt;&lt;/g&gt;&lt;g transform=\"matrix(.0091,0,0,-0.0091,27.174,3.132)\"&gt;&lt;/path&gt;&lt;/g&gt;&lt;g transform=\"matrix(.013,0,0,-0.013,32.121,0)\"&gt;&lt;use xlink:href=\"#g121-65\"&gt;&lt;/use&gt;&lt;/g&gt;&lt;g transform=\"matrix(.0091,0,0,-0.0091,40.766,3.132)\"&gt;&lt;/path&gt;&lt;/g&gt;&lt;g transform=\"matrix(.013,0,0,-0.013,45.712,0)\"&gt;&lt;/path&gt;&lt;/g&gt;&lt;g transform=\"matrix(.013,0,0,-0.013,50.197,0)\"&gt;&lt;/path&gt;&lt;/g&gt;&lt;g transform=\"matrix(.013,0,0,-0.013,56.58,0)\"&gt;&lt;/path&gt;&lt;/g&gt;&lt;/svg&gt;&lt;span&gt;&lt;/span&gt;&lt;svg height=\"12.7178pt\" style=\"vertical-align:-3.42947pt\" version=\"1.1\" viewbox=\"61.674183799999994 -9.28833 12.455 12.7178\" width=\"12.455pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"&gt;&lt;g transform=\"matrix(.013,0,0,-0.013,61.724,0)\"&gt;&lt;/path&gt;&lt;/g&gt;&lt;g transform=\"matrix(.013,0,0,-0.013,69.434,0)\"&gt;&lt;/path&gt;&lt;/g&gt;&lt;/svg&gt;&lt;/span&gt; and &lt;span&gt;&lt;svg height=\"12.7178pt\" style=\"vertical-align:-3.42947pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 73.136 12.7178\" width=\"73.136pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"&gt;&lt;g transform=\"matrix(.013,0,0,-0.013,0,0)\"&gt;&lt;use xlink:href=\"#g190-73\"&gt;&lt;/use&gt;&lt;/g&gt;&lt;g transform=\"matrix(.013,0,0,-0.013,9.475,0)\"&gt;&lt;use xlink:href=\"#g190-66\"&gt;&lt;/use&gt;&lt;/g&gt;&lt;g transform=\"matrix(.013,0,0,-0.013,18.529,0)\"&gt;&lt;use xlink:href=\"#g121-65\"&gt;&lt;/use&gt;&lt;/g&gt;&lt;g transform=\"matrix(.0091,0,0,-0.0091,27.174,3.132)\"&gt;&lt;use xlink:href=\"#g50-54\"&gt;&lt;/use&gt;&lt;/g&gt;&lt;g transform=\"matrix(.013,0,0,-0.013,32.121,0)\"&gt;&lt;use xlink:href=\"#g121-65\"&gt;&lt;/use&gt;&lt;/g&gt;&lt;g transform=\"matrix(.0091,0,0,-0.0091,40.766,3.132)\"&gt;&lt;/path&gt;&lt;/g&gt;&lt;g transform=\"matrix(.013,0,0,-0.013,45.712,0)\"&gt;&lt;use xlink:href=\"#g121-65\"&gt;&lt;/use&gt;&lt;/g&gt;&lt;g transform=\"matrix(.0091,0,0,-0.0091,54.357,3.132)\"&gt;&lt;use xlink:href=\"#g50-56\"&gt;&lt;/use&gt;&lt;/g&gt;&lt;g transform=\"matrix(.013,0,0,-0.013,59.304,0)\"&gt;&lt;use xlink:href=\"#g113-92\"&gt;&lt;/use&gt;&lt;/g&gt;&lt;g transform=\"matrix(.013,0,0,-0.013,63.789,0)\"&gt;&lt;use xlink:href=\"#g113-114\"&gt;&lt;/use&gt;&lt;/g&gt;&lt;g transform=\"matrix(.013,0,0,-0.013,70.172,0)\"&gt;&lt;use xlink:href=\"#g113-45\"&gt;&lt;/use&gt;&lt;/g&gt;&lt;/svg&gt;&lt;span&gt;&lt;/span&gt;&lt;svg height=\"12.7178pt\" style=\"vertical-align:-3.42947pt\" version=\"1.1\" viewbox=\"75.2651838 -9.2","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":"11 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139481493","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}