Suppose that <svg height="8.68572pt" style="vertical-align:-0.0498209pt" version="1.1" viewbox="-0.0498162 -8.6359 9.2729 8.68572" width="9.2729pt" 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> is a Banach algebra and <svg height="11.5564pt" style="vertical-align:-2.26807pt" version="1.1" viewbox="-0.0498162 -9.28833 26.2232 11.5564" width="26.2232pt" 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,-0.013,7.895,0)"></path></g><g transform="matrix(.013,0,0,-0.013,12.393,0)"><use xlink:href="#g113-66"></use></g><g transform="matrix(.013,0,0,-0.013,21.528,0)"></path></g></svg> is its enveloping dual Banach algebra, we show that <svg height="11.5564pt" style="vertical-align:-2.26807pt" version="1.1" viewbox="-0.0498162 -9.28833 26.2232 11.5564" width="26.2232pt" 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="#g113-71"></use></g><g transform="matrix(.013,0,0,-0.013,7.895,0)"><use xlink:href="#g113-41"></use></g><g transform="matrix(.013,0,0,-0.013,12.393,0)"><use xlink:href="#g113-66"></use></g><g transform="matrix(.013,0,0,-0.013,21.528,0)"><use xlink:href="#g113-42"></use></g></svg> is approximately contractible (approximately amenable) if <svg height="8.68572pt" style="vertical-align:-0.0498209pt" version="1.1" viewbox="-0.0498162 -8.6359 9.2729 8.68572" width="9.2729pt" 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="#g113-66"></use></g></svg> has the same property. Also, we study the relation between the pseudoamenability of <svg height="11.5564pt" style="vertical-align:-2.26807pt" version="1.1" viewbox="-0.0498162 -9.28833 26.2232 11.5564" width="26.2232pt" 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="#g113-71"></use></g><g transform="matrix(.013,0,0,-0.013,7.895,0)"><use xlink:href="#g113-41"></use></g><g transform="matrix(.013,0,0,-0.013,12.393,0)"><use xlink:href="#g113-66"></use></g><g transform="matrix(.013,0,0,-0.013,21.528,0)"><use xlink:href="#g113-42"></use></g></svg> and the pseudoamenability of the second dual <svg height="10.1524pt" style="vertical-align:-0.04990005pt" version="1.1" viewbox="-0.0498162 -10.1025 20.9329 10.1524" width="20.9329pt" 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="#g113-66"></use></g><g transform="matrix(.0091,0,0,-0.0091,9.135,-5.741)"></path></g><g transform="matrix(.0091,0,0,-0.0091,14.695,-5.741)"><use xlink:href="#g50-43"></use></g></svg> and we also characterize approximate biflatness and approximate biprojectivity of <svg height="11.5564p
{"title":"Enveloping Dual Banach Algebras and Approximate Properties","authors":"N. Razi, A. Pourabbas","doi":"10.1155/2024/6300080","DOIUrl":"https://doi.org/10.1155/2024/6300080","url":null,"abstract":"Suppose that <svg height=\"8.68572pt\" style=\"vertical-align:-0.0498209pt\" version=\"1.1\" viewbox=\"-0.0498162 -8.6359 9.2729 8.68572\" width=\"9.2729pt\" 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> is a Banach algebra and <svg height=\"11.5564pt\" style=\"vertical-align:-2.26807pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 26.2232 11.5564\" width=\"26.2232pt\" 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,-0.013,7.895,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,12.393,0)\"><use xlink:href=\"#g113-66\"></use></g><g transform=\"matrix(.013,0,0,-0.013,21.528,0)\"></path></g></svg> is its enveloping dual Banach algebra, we show that <svg height=\"11.5564pt\" style=\"vertical-align:-2.26807pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 26.2232 11.5564\" width=\"26.2232pt\" 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=\"#g113-71\"></use></g><g transform=\"matrix(.013,0,0,-0.013,7.895,0)\"><use xlink:href=\"#g113-41\"></use></g><g transform=\"matrix(.013,0,0,-0.013,12.393,0)\"><use xlink:href=\"#g113-66\"></use></g><g transform=\"matrix(.013,0,0,-0.013,21.528,0)\"><use xlink:href=\"#g113-42\"></use></g></svg> is approximately contractible (approximately amenable) if <svg height=\"8.68572pt\" style=\"vertical-align:-0.0498209pt\" version=\"1.1\" viewbox=\"-0.0498162 -8.6359 9.2729 8.68572\" width=\"9.2729pt\" 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=\"#g113-66\"></use></g></svg> has the same property. Also, we study the relation between the pseudoamenability of <svg height=\"11.5564pt\" style=\"vertical-align:-2.26807pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 26.2232 11.5564\" width=\"26.2232pt\" 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=\"#g113-71\"></use></g><g transform=\"matrix(.013,0,0,-0.013,7.895,0)\"><use xlink:href=\"#g113-41\"></use></g><g transform=\"matrix(.013,0,0,-0.013,12.393,0)\"><use xlink:href=\"#g113-66\"></use></g><g transform=\"matrix(.013,0,0,-0.013,21.528,0)\"><use xlink:href=\"#g113-42\"></use></g></svg> and the pseudoamenability of the second dual <svg height=\"10.1524pt\" style=\"vertical-align:-0.04990005pt\" version=\"1.1\" viewbox=\"-0.0498162 -10.1025 20.9329 10.1524\" width=\"20.9329pt\" 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=\"#g113-66\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,9.135,-5.741)\"></path></g><g transform=\"matrix(.0091,0,0,-0.0091,14.695,-5.741)\"><use xlink:href=\"#g50-43\"></use></g></svg> and we also characterize approximate biflatness and approximate biprojectivity of <svg height=\"11.5564p","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":"16 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140574954","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}
The influence of consumer psychological effects on customer needs has become a normal state of product sales models in the consumer goods supply chain field. The literature lacks systematic research on the mechanism through which consumer psychological effects affect customer needs. On the basis of analyzing and sorting out the literature and viewpoints, this paper establishes a mathematical model to investigate how manufacturers design and plan product supply strategies based on nonessential demand patterns under three different sales models. Finally, by solving the mathematical model, the optimal production volume, the optimal commodity price, and the maximum profit that can be obtained by the manufacturer are obtained, and the correctness of the model is verified via numerical calculation. The study results explain the relationships among commodity costs, demand, and commodity pricing, which are significant for the study of consumer psychology and can further provide a beneficial reference for manufacturers in various industries.
{"title":"Mathematical Modelling of B2C Consumer Product Supply Strategy Based on Nonessential Demand Pattern","authors":"Zhiyi Zhuo, Shuhong Chen, Hong Yan","doi":"10.1155/2024/7711868","DOIUrl":"https://doi.org/10.1155/2024/7711868","url":null,"abstract":"The influence of consumer psychological effects on customer needs has become a normal state of product sales models in the consumer goods supply chain field. The literature lacks systematic research on the mechanism through which consumer psychological effects affect customer needs. On the basis of analyzing and sorting out the literature and viewpoints, this paper establishes a mathematical model to investigate how manufacturers design and plan product supply strategies based on nonessential demand patterns under three different sales models. Finally, by solving the mathematical model, the optimal production volume, the optimal commodity price, and the maximum profit that can be obtained by the manufacturer are obtained, and the correctness of the model is verified via numerical calculation. The study results explain the relationships among commodity costs, demand, and commodity pricing, which are significant for the study of consumer psychology and can further provide a beneficial reference for manufacturers in various industries.","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":"57 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140574952","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}
In the classroom teaching of Chinese international education (CIE), teachers will face different types of problems. Teachers should focus on each teaching link, identify key and difficult points, teach students in line with their aptitude, and emphasize communication with students to improve the classroom teaching quality in CIE. The classroom teaching quality evaluation of CIE in higher-education institutions is regarded as multiple-attribute decision-making (MADM). Recently, the EDAS and CRITIC model was employed to put forward the MADM. The double-valued neutrosophic sets (DVNSs) are employed as the optimal decision tool for expressing the uncertain data during the classroom teaching quality evaluation of CIE in higher-education institutions. In this paper, EDAS is founded for MADM under DVNSs. Then, the double-valued neutrosophic number EDAS (DVNN-EDAS) model is constructed for MADM. Finally, a numerical example for classroom teaching quality evaluation of CIE is employed to verify the DVNN-EDAS model. The main decision contribution of this study is that (1) the novel MADM technique is established in line with EDAS and CRITIC under DVNSs. (2) The objective weights are constructed through CRITIC. (3) A numerical example for classroom teaching quality evaluation of CIE in higher-education institutions in line with the DVNN-EDAS is constructed.
{"title":"Research on Classroom Teaching Quality Evaluation of Chinese International Education in Higher-Education Institutions Based on EDAS Method and Euclidean Distance","authors":"Wei Li, Jia Song, Gangling Liu","doi":"10.1155/2024/5577601","DOIUrl":"https://doi.org/10.1155/2024/5577601","url":null,"abstract":"In the classroom teaching of Chinese international education (CIE), teachers will face different types of problems. Teachers should focus on each teaching link, identify key and difficult points, teach students in line with their aptitude, and emphasize communication with students to improve the classroom teaching quality in CIE. The classroom teaching quality evaluation of CIE in higher-education institutions is regarded as multiple-attribute decision-making (MADM). Recently, the EDAS and CRITIC model was employed to put forward the MADM. The double-valued neutrosophic sets (DVNSs) are employed as the optimal decision tool for expressing the uncertain data during the classroom teaching quality evaluation of CIE in higher-education institutions. In this paper, EDAS is founded for MADM under DVNSs. Then, the double-valued neutrosophic number EDAS (DVNN-EDAS) model is constructed for MADM. Finally, a numerical example for classroom teaching quality evaluation of CIE is employed to verify the DVNN-EDAS model. The main decision contribution of this study is that (1) the novel MADM technique is established in line with EDAS and CRITIC under DVNSs. (2) The objective weights are constructed through CRITIC. (3) A numerical example for classroom teaching quality evaluation of CIE in higher-education institutions in line with the DVNN-EDAS is constructed.","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":"20 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140311206","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}
The rapid advancements in metamaterial research have brought forth a new era of possibilities for controlling and manipulating light at the nanoscale. In particular, the design and engineering of optical metamaterials have created advances in the field of photonics, enabling the development of advanced devices with unprecedented functionalities. Among the myriad of intriguing metamaterial structures, the nonlinear directional couplers with beta derivative evolution have emerged as a significant avenue of exploration, offering remarkable potential for light propagation and manipulation. This study obtains the solitary wave solutions for twin-core couplers having spatial-temporal fractional beta derivative evolution by using two different methods, the Bernoulli method and the complete polynomial discriminant system method. By graphing some of the obtained solutions, the effect of the beta derivative has been shown. The findings would be beneficial to understand physical behaviours in nonlinear optics, particularly twin-core couplers with optical metamaterials.
{"title":"Solitons of the Twin-Core Couplers with Fractional Beta Derivative Evolution in Optical Metamaterials via Two Distinct Methods","authors":"Meryem Odabasi Koprulu, Zehra Pinar Izgi","doi":"10.1155/2024/8852337","DOIUrl":"https://doi.org/10.1155/2024/8852337","url":null,"abstract":"The rapid advancements in metamaterial research have brought forth a new era of possibilities for controlling and manipulating light at the nanoscale. In particular, the design and engineering of optical metamaterials have created advances in the field of photonics, enabling the development of advanced devices with unprecedented functionalities. Among the myriad of intriguing metamaterial structures, the nonlinear directional couplers with beta derivative evolution have emerged as a significant avenue of exploration, offering remarkable potential for light propagation and manipulation. This study obtains the solitary wave solutions for twin-core couplers having spatial-temporal fractional beta derivative evolution by using two different methods, the Bernoulli method and the complete polynomial discriminant system method. By graphing some of the obtained solutions, the effect of the beta derivative has been shown. The findings would be beneficial to understand physical behaviours in nonlinear optics, particularly twin-core couplers with optical metamaterials.","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":"116 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140311196","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}
In this paper, we give the forms of local automorphisms (resp. superderivations) of model filiform Lie superalgebra in the matrix version. Linear 2-local automorphisms (resp. superderivations) of are also characterized. We prove that each linear 2-local automorphism of is an automorphism.
{"title":"Local Automorphisms and Local Superderivations of Model Filiform Lie Superalgebras","authors":"Yuqiu Sheng, Wende Liu, Yang Liu","doi":"10.1155/2024/6650997","DOIUrl":"https://doi.org/10.1155/2024/6650997","url":null,"abstract":"In this paper, we give the forms of local automorphisms (resp. superderivations) of model filiform Lie superalgebra <svg height=\"12.9866pt\" style=\"vertical-align:-4.3507pt\" version=\"1.1\" viewbox=\"-0.0498162 -8.6359 23.1172 12.9866\" width=\"23.1172pt\" 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,-0.0091,8.294,3.132)\"></path></g><g transform=\"matrix(.0091,0,0,-0.0091,12.953,3.132)\"></path></g><g transform=\"matrix(.0091,0,0,-0.0091,15.11,3.132)\"></path></g></svg> in the matrix version. Linear 2-local automorphisms (resp. superderivations) of <svg height=\"12.9866pt\" style=\"vertical-align:-4.3507pt\" version=\"1.1\" viewbox=\"-0.0498162 -8.6359 23.1172 12.9866\" width=\"23.1172pt\" 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=\"#g113-77\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,8.294,3.132)\"><use xlink:href=\"#g50-111\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,12.953,3.132)\"><use xlink:href=\"#g50-45\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,15.11,3.132)\"><use xlink:href=\"#g50-110\"></use></g></svg> are also characterized. We prove that each linear 2-local automorphism of <svg height=\"12.9866pt\" style=\"vertical-align:-4.3507pt\" version=\"1.1\" viewbox=\"-0.0498162 -8.6359 23.1172 12.9866\" width=\"23.1172pt\" 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=\"#g113-77\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,8.294,3.132)\"><use xlink:href=\"#g50-111\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,12.953,3.132)\"><use xlink:href=\"#g50-45\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,15.11,3.132)\"><use xlink:href=\"#g50-110\"></use></g></svg> is an automorphism.","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":"9 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140311343","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}
Mohammad Imam Pasha, Kotha Rama Koteswara Rao, Gunaseelan Mani, Arul Joseph Gnanaprakasam, Santosh Kumar
In this paper, we propose the notion of the bipolar parametric metric space and prove fixed point theorems. The proved results generalize and extend some of the well-known results in the literature. An example and application to support our result is presented.
{"title":"Solving a Fractional Differential Equation via the Bipolar Parametric Metric Space","authors":"Mohammad Imam Pasha, Kotha Rama Koteswara Rao, Gunaseelan Mani, Arul Joseph Gnanaprakasam, Santosh Kumar","doi":"10.1155/2024/5533347","DOIUrl":"https://doi.org/10.1155/2024/5533347","url":null,"abstract":"In this paper, we propose the notion of the bipolar parametric metric space and prove fixed point theorems. The proved results generalize and extend some of the well-known results in the literature. An example and application to support our result is presented.","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":"16 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140311271","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}
In this paper, we investigate the observability of the fractional resolvent family, and we prove two main results: the first result shows a generalization of the Hautus-type test for observable exponentially stable semigroups to the fractional resolvent family and the second result shows the equivalence of the observability and the below boundedness of the linear operator on the wave packet when the generator conforms to a specific form.
{"title":"The Hautus-Type Inequality for Abstract Fractional Cauchy Problems and Its Observability","authors":"Li Chen-Yu","doi":"10.1155/2024/6179980","DOIUrl":"https://doi.org/10.1155/2024/6179980","url":null,"abstract":"In this paper, we investigate the observability of the fractional resolvent family, and we prove two main results: the first result shows a generalization of the Hautus-type test for observable exponentially stable semigroups to the fractional resolvent family and the second result shows the equivalence of the observability and the below boundedness of the linear operator on the wave packet when the generator conforms to a specific form.","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":"4 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140201298","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}
Keneni Abera Tola, V. N. Srinivasa Rao Repalle, Mamo Abebe Ashebo
Neutrosophic graphs are used to model inconsistent information and imprecise data about any real-life problem. It is regarded as a generalization of intuitionistic fuzzy graphs. Since interval-valued neutrosophic sets are more accurate, compatible, and flexible than single neutrosophic sets, interval-valued neutrosophic graphs (IVNGs) were defined. The interval-valued neutrosophic graph is a fundamental issue in graph theory that has wide applications in the real world. Also, problems may arise when partial ignorance exists in the datasets of membership [0, 1], and then, the concept of IVNG is crucial to represent the problems. Line graphs of neutrosophic graphs are significant due to their ability to represent and analyze uncertain or indeterminate information about edge relationships and complex networks in graphs. However, there is a research gap on the line graph of interval-valued neutrosophic graphs. In this paper, we introduce the theory of an interval-valued neutrosophic line graph (IVNLG) and its application. In line with that, some mathematical properties such as weak vertex isomorphism, weak edge isomorphism, effective edge, and other properties of IVNLGs are proposed. In addition, we defined the vertex degree of IVNLG with some properties, and by presenting several theorems and propositions, the relationship between fuzzy graph extensions and IVNLGs was explored. Finally, an overview of the algorithm used to solve the problems and the practical application of the introduced graphs were provided.
{"title":"Theory and Application of Interval-Valued Neutrosophic Line Graphs","authors":"Keneni Abera Tola, V. N. Srinivasa Rao Repalle, Mamo Abebe Ashebo","doi":"10.1155/2024/5692756","DOIUrl":"https://doi.org/10.1155/2024/5692756","url":null,"abstract":"Neutrosophic graphs are used to model inconsistent information and imprecise data about any real-life problem. It is regarded as a generalization of intuitionistic fuzzy graphs. Since interval-valued neutrosophic sets are more accurate, compatible, and flexible than single neutrosophic sets, interval-valued neutrosophic graphs (IVNGs) were defined. The interval-valued neutrosophic graph is a fundamental issue in graph theory that has wide applications in the real world. Also, problems may arise when partial ignorance exists in the datasets of membership [0, 1], and then, the concept of IVNG is crucial to represent the problems. Line graphs of neutrosophic graphs are significant due to their ability to represent and analyze uncertain or indeterminate information about edge relationships and complex networks in graphs. However, there is a research gap on the line graph of interval-valued neutrosophic graphs. In this paper, we introduce the theory of an interval-valued neutrosophic line graph (IVNLG) and its application. In line with that, some mathematical properties such as weak vertex isomorphism, weak edge isomorphism, effective edge, and other properties of IVNLGs are proposed. In addition, we defined the vertex degree of IVNLG with some properties, and by presenting several theorems and propositions, the relationship between fuzzy graph extensions and IVNLGs was explored. Finally, an overview of the algorithm used to solve the problems and the practical application of the introduced graphs were provided.","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":"100 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140168875","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}
Ismail T. Shbair, Amgad S. Salama, Osama A. Embaby, Abdelfattah A. El-Atik
Rough set has an important role to deal with uncertainty objects. The aim of this article is to introduce some kinds of generalization for rough sets through minimal neighborhoods using special kinds of binary relations. Moreover, four different types of dual approximation operators will be constructed in terms of minimal neighborhoods. The comparison between these types of approximation operators is discussed. Some new kinds of topological structures induced by minimal neighborhoods are established and some of their properties are studied. Finally, we give a comparison between these topologies that help for determining the major components of COVID-19 infections. In this application, the components of infections help the expert in decision making in medicine.
{"title":"Some Topological Approaches of Rough Sets through Minimal Neighborhoods and Decision Making","authors":"Ismail T. Shbair, Amgad S. Salama, Osama A. Embaby, Abdelfattah A. El-Atik","doi":"10.1155/2024/2214422","DOIUrl":"https://doi.org/10.1155/2024/2214422","url":null,"abstract":"Rough set has an important role to deal with uncertainty objects. The aim of this article is to introduce some kinds of generalization for rough sets through minimal neighborhoods using special kinds of binary relations. Moreover, four different types of dual approximation operators will be constructed in terms of minimal neighborhoods. The comparison between these types of approximation operators is discussed. Some new kinds of topological structures induced by minimal neighborhoods are established and some of their properties are studied. Finally, we give a comparison between these topologies that help for determining the major components of COVID-19 infections. In this application, the components of infections help the expert in decision making in medicine.","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":"28 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140168606","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}
The conditions of the coronavirus epidemic have put much pressure on the healthcare system. This disease has hurt the blood supply through the reduction of blood donation and the reduction of access to suitable collection facilities due to dysfunction. Considering the importance of the subject, the purpose of this paper is to design a two-level supply chain network for blood products with the approach of reducing costs and the rate of contagion under the conditions of epidemic outbreaks (COVID-19). After examining the solution methods for multilevel supply chain networks of blood products under the conditions of the spread of the COVID-19 virus, three exact solution methods, including LP-metric, an improved version of the augmented ε-constraint (AUGMECON2), and an improved weighted Chebyshev, are proposed. They are used to solve the model in small dimensions. In order to compare the methods in the obtained solutions, several numerical examples of different sizes are generated and solved. Then, using the statistical assumption test, the obtained results are compared in all numerical examples by Tukey’s technique. Also, the TOPSIS is applied to select the best method. Finally, in order to investigate the reaction of the objectives to the changes in the contagion probability parameter, a sensitivity analysis has been performed. The results emphasize that improving the performance of the blood supply chain (BSC) can lead to a reduction in BSC costs and improved service to patients. Also, the adaptation of different components of the BSC and regular coordination between them play an efficient role in controlling and improving this disease and reducing the costs of the BSC. Also, receiving the plasma product of recovered people from type (II) donors can play a vital role in reducing the percentage of disease transmission.
{"title":"A Two-Objective Model for the Multilevel Supply Chain of Blood Products with the Approach of Reducing the Rate of Contagion under the (COVID-19) Epidemic Outbreak Conditions","authors":"Abolfazl Moghimi Esfandabadi, Davood Shishebori, Mohammad-Bagher Fakhrzad, Hassan Khademi Zare","doi":"10.1155/2024/9986541","DOIUrl":"https://doi.org/10.1155/2024/9986541","url":null,"abstract":"The conditions of the coronavirus epidemic have put much pressure on the healthcare system. This disease has hurt the blood supply through the reduction of blood donation and the reduction of access to suitable collection facilities due to dysfunction. Considering the importance of the subject, the purpose of this paper is to design a two-level supply chain network for blood products with the approach of reducing costs and the rate of contagion under the conditions of epidemic outbreaks (COVID-19). After examining the solution methods for multilevel supply chain networks of blood products under the conditions of the spread of the COVID-19 virus, three exact solution methods, including LP-metric, an improved version of the augmented <i>ε</i>-constraint (AUGMECON2), and an improved weighted Chebyshev, are proposed. They are used to solve the model in small dimensions. In order to compare the methods in the obtained solutions, several numerical examples of different sizes are generated and solved. Then, using the statistical assumption test, the obtained results are compared in all numerical examples by Tukey’s technique. Also, the TOPSIS is applied to select the best method. Finally, in order to investigate the reaction of the objectives to the changes in the contagion probability parameter, a sensitivity analysis has been performed. The results emphasize that improving the performance of the blood supply chain (BSC) can lead to a reduction in BSC costs and improved service to patients. Also, the adaptation of different components of the BSC and regular coordination between them play an efficient role in controlling and improving this disease and reducing the costs of the BSC. Also, receiving the plasma product of recovered people from type (II) donors can play a vital role in reducing the percentage of disease transmission.","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":"34 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140168527","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}
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