Journal of Mathematics最新文献

{"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":"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}

{"title":"Modeling and Analysis of an Age-Structured Malaria Model in the Sense of Atangana–Baleanu Fractional Operators","authors":"Dawit Kechine Menbiko, Chernet Tuge Deressa","doi":"10.1155/2024/6652037","DOIUrl":"https://doi.org/10.1155/2024/6652037","url":null,"abstract":"In this paper, integer- and fractional-order models are discussed to investigate the dynamics of malaria in a human host with a varied age distribution. A system of differential equation model with five human state variables and two mosquito state variables was examined. Preschool-age (0–5) and young-age individuals make up our model’s division of the human population. We investigated the existence of an area in which the model is both mathematically and epidemiologically well posed. According to the findings of our mathematical research, the disease-free equilibrium exists whenever the fundamental reproduction number &lt;svg height=\"11.927pt\" style=\"vertical-align:-3.291101pt\" version=\"1.1\" viewbox=\"-0.0498162 -8.6359 13.1624 11.927\" width=\"13.1624pt\" 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,-0.0091,8.086,3.132)\"&gt;&lt;/path&gt;&lt;/g&gt;&lt;/svg&gt; is smaller than one and is asymptotically stable. The disease-free equilibrium point is unstable when &lt;span&gt;&lt;svg height=\"11.927pt\" style=\"vertical-align:-3.291101pt\" version=\"1.1\" viewbox=\"-0.0498162 -8.6359 24.295 11.927\" width=\"24.295pt\" 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=\"#g113-83\"&gt;&lt;/use&gt;&lt;/g&gt;&lt;g transform=\"matrix(.0091,0,0,-0.0091,8.086,3.132)\"&gt;&lt;use xlink:href=\"#g50-49\"&gt;&lt;/use&gt;&lt;/g&gt;&lt;g transform=\"matrix(.013,0,0,-0.013,16.664,0)\"&gt;&lt;/path&gt;&lt;/g&gt;&lt;/svg&gt;&lt;span&gt;&lt;/span&gt;&lt;span&gt;&lt;svg height=\"11.927pt\" style=\"vertical-align:-3.291101pt\" version=\"1.1\" viewbox=\"27.8771838 -8.6359 6.422 11.927\" width=\"6.422pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"&gt;&lt;g transform=\"matrix(.013,0,0,-0.013,27.927,0)\"&gt;&lt;/path&gt;&lt;/g&gt;&lt;/svg&gt;.&lt;/span&gt;&lt;/span&gt; We showed that the endemic equilibrium point is unique for &lt;span&gt;&lt;svg height=\"11.927pt\" style=\"vertical-align:-3.291101pt\" version=\"1.1\" viewbox=\"-0.0498162 -8.6359 24.295 11.927\" width=\"24.295pt\" 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=\"#g113-83\"&gt;&lt;/use&gt;&lt;/g&gt;&lt;g transform=\"matrix(.0091,0,0,-0.0091,8.086,3.132)\"&gt;&lt;use xlink:href=\"#g50-49\"&gt;&lt;/use&gt;&lt;/g&gt;&lt;g transform=\"matrix(.013,0,0,-0.013,16.664,0)\"&gt;&lt;use xlink:href=\"#g117-92\"&gt;&lt;/use&gt;&lt;/g&gt;&lt;/svg&gt;&lt;span&gt;&lt;/span&gt;&lt;span&gt;&lt;svg height=\"11.927pt\" style=\"vertical-align:-3.291101pt\" version=\"1.1\" viewbox=\"27.8771838 -8.6359 6.422 11.927\" width=\"6.422pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"&gt;&lt;g transform=\"matrix(.013,0,0,-0.013,27.927,0)\"&gt;&lt;use xlink:href=\"#g113-50\"&gt;&lt;/use&gt;&lt;/g&gt;&lt;/svg&gt;.&lt;/span&gt;&lt;/span&gt; Also, the most influential control parameters of the spread of malaria were identified. Numerical simulations of both classical and fractional order were conducted, and we used ODE (45) for classical part and numerical technique developed by Toufik and Atangana for fractional order. The infected population ","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":"54 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139396392","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":"Composition-Differentiation Operators on Derivative Hardy Spaces","authors":"A. Abkar, A. Babaei","doi":"10.1155/2024/8222237","DOIUrl":"https://doi.org/10.1155/2024/8222237","url":null,"abstract":"We first explore conditions under which every weighted composition-differentiation operator on the Hardy space <svg height=\"13.8595pt\" style=\"vertical-align:-2.2681pt\" version=\"1.1\" viewbox=\"-0.0498162 -11.5914 34.4579 13.8595\" width=\"34.4579pt\" 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(.0091,0,0,-0.0091,10.923,-5.741)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,15.87,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,20.368,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,29.754,0)\"></path></g></svg> is completely continuous. We then discuss necessary and sufficient conditions for these operators to be Hilbert–Schmidt on the derivative Hardy space <span><svg height=\"13.8595pt\" style=\"vertical-align:-2.2681pt\" version=\"1.1\" viewbox=\"-0.0498162 -11.5914 29.656 13.8595\" width=\"29.656pt\" 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(.0091,0,0,-0.0091,6.136,-5.741)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,11.083,0)\"><use xlink:href=\"#g113-41\"></use></g><g transform=\"matrix(.013,0,0,-0.013,15.581,0)\"><use xlink:href=\"#g197-15\"></use></g><g transform=\"matrix(.013,0,0,-0.013,24.967,0)\"><use xlink:href=\"#g113-42\"></use></g></svg>.</span>","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":"4 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139094706","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 Note on Approximation of Blending Type Bernstein–Schurer–Kantorovich Operators with Shape Parameter α","authors":"Mohammad Ayman-Mursaleen, Nadeem Rao, Mamta Rani, Adem Kilicman, Ahmed Ahmed Hussin Ali Al-Abied, Pradeep Malik","doi":"10.1155/2023/5245806","DOIUrl":"https://doi.org/10.1155/2023/5245806","url":null,"abstract":"The objective of this paper is to construct univariate and bivariate blending type &lt;span&gt;&lt;svg height=\"6.1673pt\" style=\"vertical-align:-0.2063904pt\" version=\"1.1\" viewbox=\"-0.0498162 -5.96091 7.51131 6.1673\" width=\"7.51131pt\" 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;/svg&gt;-&lt;/span&gt;Schurer–Kantorovich operators depending on two parameters &lt;span&gt;&lt;svg height=\"11.439pt\" style=\"vertical-align:-2.15067pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 17.881 11.439\" width=\"17.881pt\" 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=\"#g113-223\"&gt;&lt;/use&gt;&lt;/g&gt;&lt;g transform=\"matrix(.013,0,0,-0.013,11.017,0)\"&gt;&lt;/path&gt;&lt;/g&gt;&lt;/svg&gt;&lt;span&gt;&lt;/span&gt;&lt;svg height=\"11.439pt\" style=\"vertical-align:-2.15067pt\" version=\"1.1\" viewbox=\"21.463183800000003 -9.28833 26.836 11.439\" width=\"26.836pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"&gt;&lt;g transform=\"matrix(.013,0,0,-0.013,21.513,0)\"&gt;&lt;/path&gt;&lt;/g&gt;&lt;g transform=\"matrix(.013,0,0,-0.013,25.998,0)\"&gt;&lt;/path&gt;&lt;/g&gt;&lt;g transform=\"matrix(.013,0,0,-0.013,32.238,0)\"&gt;&lt;/path&gt;&lt;/g&gt;&lt;g transform=\"matrix(.013,0,0,-0.013,37.381,0)\"&gt;&lt;/path&gt;&lt;/g&gt;&lt;g transform=\"matrix(.013,0,0,-0.013,43.621,0)\"&gt;&lt;/path&gt;&lt;/g&gt;&lt;/svg&gt;&lt;/span&gt; and &lt;span&gt;&lt;svg height=\"11.7782pt\" style=\"vertical-align:-3.42938pt\" version=\"1.1\" viewbox=\"-0.0498162 -8.34882 18.273 11.7782\" width=\"18.273pt\" 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,-0.013,10.642,0)\"&gt;&lt;/path&gt;&lt;/g&gt;&lt;/svg&gt;&lt;span&gt;&lt;/span&gt;&lt;svg height=\"11.7782pt\" style=\"vertical-align:-3.42938pt\" version=\"1.1\" viewbox=\"21.855183800000002 -8.34882 6.415 11.7782\" width=\"6.415pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"&gt;&lt;g transform=\"matrix(.013,0,0,-0.013,21.905,0)\"&gt;&lt;use xlink:href=\"#g113-49\"&gt;&lt;/use&gt;&lt;/g&gt;&lt;/svg&gt;&lt;/span&gt; to approximate a class of measurable functions on &lt;span&gt;&lt;svg height=\"12.7178pt\" style=\"vertical-align:-3.42947pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 32.645 12.7178\" width=\"32.645pt\" 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=\"#g113-92\"&gt;&lt;/use&gt;&lt;/g&gt;&lt;g transform=\"matrix(.013,0,0,-0.013,4.485,0)\"&gt;&lt;use xlink:href=\"#g113-49\"&gt;&lt;/use&gt;&lt;/g&gt;&lt;g transform=\"matrix(.013,0,0,-0.013,10.725,0)\"&gt;&lt;use xlink:href=\"#g113-45\"&gt;&lt;/use&gt;&lt;/g&gt;&lt;g transform=\"matrix(.013,0,0,-0.013,15.868,0)\"&gt;&lt;use xlink:href=\"#g113-50\"&gt;&lt;/use&gt;&lt;/g&gt;&lt;g transform=\"matrix(.013,0,0,-0.013,25.014,0)\"&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=\"35.500183799999995 -9.28833 13.832 12.7178\" width=\"13.832pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"&gt;&lt;g transform=\"matrix(.013,0,0,-0.013,35.55,0)\"&gt;&lt;/path&gt;&lt;/g&gt;&lt;g transform=\"matrix(.013,0,0,-0.013,41.","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":"17 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139069326","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":"On the Expected Discounted Penalty Function Using Physics-Informed Neural Network","authors":"Jiayu Wang, Houchun Wang","doi":"10.1155/2023/9950023","DOIUrl":"https://doi.org/10.1155/2023/9950023","url":null,"abstract":"We study the expected discounted penalty at ruin under a stochastic discount rate for the compound Poisson risk model with a threshold dividend strategy. The discount rate is modeled by a Poisson process and a standard Brownian motion. By applying the differentiation method and total expectation formula, we obtain an integrodifferential equation for the expected discounted penalty function. From this integrodifferential equation, a renewal equation and an asymptotic formula satisfied by the expected discounted penalty function are derived. In order to solve the integrodifferential equation, we use a physics-informed neural network (PINN) for the first time in risk theory and obtain the numerical solutions of the expected discounted penalty function in some special cases of the penalty at ruin.","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139052639","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":"Retracted: Research on the Spread Path and Evolution Causes of Oral Language in the Digital Era","authors":"Journal of Mathematics","doi":"10.1155/2023/9878209","DOIUrl":"https://doi.org/10.1155/2023/9878209","url":null,"abstract":"<jats:p />","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":"123 35","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138953713","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":"Retracted: Classification and Analysis of College Students’ Skills Using Hybrid AI Models","authors":"Journal of Mathematics","doi":"10.1155/2023/9842979","DOIUrl":"https://doi.org/10.1155/2023/9842979","url":null,"abstract":"<jats:p />","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":"62 21","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138957063","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}