Pub Date : 2024-07-16DOI: 10.9734/arjom/2024/v20i7812
Clayton Suguio Hida
We consider irredundant and almost irredundant subsets in the *-algebra (mathbb{M}_2)((mathbb{C})) of all 2 X 2 matrices with coefficients in (mathbb{C}). We prove that the largest size of an irredundant subset is two, and that (mathbb{M}_2)((mathbb{C})) has an infinite almost irredundant subset.
{"title":"Irredundant and Almost Irredundant Sets in (mathbb{M}_2)((mathbb{C}))","authors":"Clayton Suguio Hida","doi":"10.9734/arjom/2024/v20i7812","DOIUrl":"https://doi.org/10.9734/arjom/2024/v20i7812","url":null,"abstract":"We consider irredundant and almost irredundant subsets in the *-algebra (mathbb{M}_2)((mathbb{C})) of all 2 X 2 matrices with coefficients in (mathbb{C}). We prove that the largest size of an irredundant subset is two, and that (mathbb{M}_2)((mathbb{C})) has an infinite almost irredundant subset.","PeriodicalId":281529,"journal":{"name":"Asian Research Journal of Mathematics","volume":"10 41","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141640274","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-11DOI: 10.9734/arjom/2024/v20i7811
Mirgichan Khobocha James, C. Ngari, Stephen Karanja, Robert Muriungi
HIV/AIDS and Hepatitis B co-infection complicates population dynamics and brings forth a wide range of clinical outcomes which makes it a difficult situation for public health. In particular designing treatment plans for the co-infection. A Stochastic Differential Equation (SDE) model is a special class of a stochastic model with continuous parameter space and continuous state space. Deterministic model lacks randomness while an SDE model accounts for randomness and uncertainties. In this study, an SDE model was formulated from an existing deterministic model to examine the variability of dynamic behavior. The analysis and numerical schemes were derived based on Euler-Maruyama SDE algorithms. The model utilized epidemiological insights with current developments in mathematical modeling approaches to represent the interaction between these two viruses. Matlab software was used to obtain SDE numerical results alongside the deterministic solution. Descriptive statistics of the sample paths indicated that the variability of infection outcomes oscillates around the deterministic trajectory. None of the sample paths are absorbed during the time steps. This shows the persistence of the co-infection in the population, in particular The variability of the infections ranges between 1.972 and 202.4, being lowest in AIDS infectives and highest in acute Hepatitis B infectives. An indication that variability cannot be ignored in designing control interventions of co-infections. These results provide new insights into the dynamics of co-infection through in-depth research and simulation, which helps to understand the inherent nature of deterministic model by incorporating the stochastic effects. These understanding will further help the policy makers in health sector to take care of the variability and uncertainty in designing treatment and management strategies.
{"title":"Modeling HIV-HBV Co-infection Dynamics: Stochastic Differential Equations and Matlab Simulation with Euler-Maruyama Numerical Method","authors":"Mirgichan Khobocha James, C. Ngari, Stephen Karanja, Robert Muriungi","doi":"10.9734/arjom/2024/v20i7811","DOIUrl":"https://doi.org/10.9734/arjom/2024/v20i7811","url":null,"abstract":"HIV/AIDS and Hepatitis B co-infection complicates population dynamics and brings forth a wide range of clinical outcomes which makes it a difficult situation for public health. In particular designing treatment plans for the co-infection. A Stochastic Differential Equation (SDE) model is a special class of a stochastic model with continuous parameter space and continuous state space. Deterministic model lacks randomness while an SDE model accounts for randomness and uncertainties. In this study, an SDE model was formulated from an existing deterministic model to examine the variability of dynamic behavior. The analysis and numerical schemes were derived based on Euler-Maruyama SDE algorithms. The model utilized epidemiological insights with current developments in mathematical modeling approaches to represent the interaction between these two viruses. Matlab software was used to obtain SDE numerical results alongside the deterministic solution. Descriptive statistics of the sample paths indicated that the variability of infection outcomes oscillates around the deterministic trajectory. None of the sample paths are absorbed during the time steps. This shows the persistence of the co-infection in the population, in particular The variability of the infections ranges between 1.972 and 202.4, being lowest in AIDS infectives and highest in acute Hepatitis B infectives. An indication that variability cannot be ignored in designing control interventions of co-infections. These results provide new insights into the dynamics of co-infection through in-depth research and simulation, which helps to understand the inherent nature of deterministic model by incorporating the stochastic effects. These understanding will further help the policy makers in health sector to take care of the variability and uncertainty in designing treatment and management strategies.","PeriodicalId":281529,"journal":{"name":"Asian Research Journal of Mathematics","volume":"63 9","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141658333","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-06DOI: 10.9734/arjom/2024/v20i7810
Xinlong Zhang
This article mainly focuses on investigating finite-time synchronization(FTS) of fractional-order quaternionvalued neural networks(FOQVNNs) with time-varying delay via aperiodically intermittent control. Firstly, a new group of fractional differential inequalities during aperiodically intermittent times is proposed, which provides a formula for calculating stable time (tilde{t}) related to a parameter (varpi) about aperiodically intermittent control strategy. It can make the stable time (tilde{t}) even shorter than that of many existing literature results. Secondly, the theoretical analysis of the entire paper is conducted in a nonseparable method, and a quaternion-valued aperiodically intermittent controller based on 1-norm is directly designed to ensure the synchronization of FOQVNNs. By constructing a suitable Lyapunov function, the FTS criterion is derived. Finally, the validity of the proposed theoretical results is confirmed by numerical simulations.
{"title":"Finite-Time Synchronization of Fractional-Order Quaternion-Valued Neural Networks under Aperiodically Intermittent Control: A Non-Separation Method","authors":"Xinlong Zhang","doi":"10.9734/arjom/2024/v20i7810","DOIUrl":"https://doi.org/10.9734/arjom/2024/v20i7810","url":null,"abstract":"This article mainly focuses on investigating finite-time synchronization(FTS) of fractional-order quaternionvalued neural networks(FOQVNNs) with time-varying delay via aperiodically intermittent control. Firstly, a new group of fractional differential inequalities during aperiodically intermittent times is proposed, which provides a formula for calculating stable time (tilde{t}) related to a parameter (varpi) about aperiodically intermittent control strategy. It can make the stable time (tilde{t}) even shorter than that of many existing literature results. Secondly, the theoretical analysis of the entire paper is conducted in a nonseparable method, and a quaternion-valued aperiodically intermittent controller based on 1-norm is directly designed to ensure the synchronization of FOQVNNs. By constructing a suitable Lyapunov function, the FTS criterion is derived. Finally, the validity of the proposed theoretical results is confirmed by numerical simulations.","PeriodicalId":281529,"journal":{"name":"Asian Research Journal of Mathematics","volume":" 40","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141672802","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-06-14DOI: 10.9734/arjom/2024/v20i6807
Devine Fathy Mae S. Grino, I. S. Jr.
Let X be an arbitrary Banach space. For a nontrivial connected graph G and nonempty subset S (subseteq) V (G), S is a safe dominating set of G if and only if S is a dominating set of G and every component X of G[S] and every component Y of G[V (G) S] adjacent to X, |X| (ge) |Y|. Moreover, S is called a minimum safe dominating set if S is a safe dominating set of the smallest size in a given graph. The cardinality of the minimum safe dominating set of G is the safe domination number of G, denoted by (gamma s)(G). In this paper, we characterized the safe dominating set and determine its corresponding safe domination number in some special classes of graphs.
让 X 是一个任意的巴拿赫空间。对于一个非难连通图 G 和非空子集 S (subseteq) V (G)，当且仅当 S 是 G 的支配集且 G[S] 的每个分量 X 和 G[V (G) S] 的每个分量 Y 都与 X 相邻时，S 是 G 的安全支配集，|X| (ge) |Y|。此外，如果 S 是给定图中最小的安全支配集，那么 S 称为最小安全支配集。G 的最小安全支配集的心数就是 G 的安全支配数，用 (gamma s)(G) 表示。在本文中，我们将描述安全支配集的特征，并确定其在一些特殊图类中的相应安全支配数。
{"title":"Conditions of Safe Dominating Set in Some Graph Families","authors":"Devine Fathy Mae S. Grino, I. S. Jr.","doi":"10.9734/arjom/2024/v20i6807","DOIUrl":"https://doi.org/10.9734/arjom/2024/v20i6807","url":null,"abstract":"Let X be an arbitrary Banach space. For a nontrivial connected graph G and nonempty subset S (subseteq) V (G), S is a safe dominating set of G if and only if S is a dominating set of G and every component X of G[S] and every component Y of G[V (G) S] adjacent to X, |X| (ge) |Y|. Moreover, S is called a minimum safe dominating set if S is a safe dominating set of the smallest size in a given graph. The cardinality of the minimum safe dominating set of G is the safe domination number of G, denoted by (gamma s)(G). In this paper, we characterized the safe dominating set and determine its corresponding safe domination number in some special classes of graphs.","PeriodicalId":281529,"journal":{"name":"Asian Research Journal of Mathematics","volume":"80 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141342338","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-06-13DOI: 10.9734/arjom/2024/v20i6806
Osei-Asibey Eunice
In the field of mathematics education, it is essential to grasp teachers' competence in recognizing cognitive domains, as it plays a pivotal role in elevating teaching methods, evaluation techniques, and ultimately enhancing student academic achievements. This study examines the proficiency of basic school teachers in Ghana in identifying the cognitive domains of mathematics questions using Bloom's Taxonomy. A sample of 338 teachers from across the regions of Ghana participated, selected through random sampling. Teachers were assessed using a set of 50 Basic Education Certificate Examination (BECE) past questions spanning a decade (2010-2022), covering Algebra, Geometry and Measurement, Data, and Number strands. Participants categorized each question according to Bloom's Taxonomy. Poisson regression analysis and Confirmatory Factor Analysis were employed to evaluate teachers' proficiency. Results indicated a statistically significant intercept term, suggesting a baseline performance level among teachers. Significant interaction effects between demographic and professional characteristics (Class:category, Class:SchTyp, TeachEx:SchTyp, TeachEx:Domain, and the main effect of Domain) influenced teachers' ability to identify mathematics domains. Teaching experience positively influenced scores, while school type had a negative impact. The model demonstrated high discriminatory power and strong predictive performance with an AUC of 0.996. Dependency analysis revealed that understanding Bloom's taxonomy domains influenced the identification of mathematics strands. Primary level teachers’ consistently demonstrated higher proficiency compared to Junior High School (JHS) level teachers. Additionally, experienced and qualified professionals performed better than pupil teachers. These findings highlight the importance of targeted interventions and professional development programs to enhance teachers' competency in identifying mathematics domains, thus improving mathematics education in Ghana.
{"title":"Correlates of Ghanaian Teachers' Understanding of Mathematics Strands and Cognitive Domains in Basic Education Certificate Examination","authors":"Osei-Asibey Eunice","doi":"10.9734/arjom/2024/v20i6806","DOIUrl":"https://doi.org/10.9734/arjom/2024/v20i6806","url":null,"abstract":"In the field of mathematics education, it is essential to grasp teachers' competence in recognizing cognitive domains, as it plays a pivotal role in elevating teaching methods, evaluation techniques, and ultimately enhancing student academic achievements. This study examines the proficiency of basic school teachers in Ghana in identifying the cognitive domains of mathematics questions using Bloom's Taxonomy. A sample of 338 teachers from across the regions of Ghana participated, selected through random sampling. Teachers were assessed using a set of 50 Basic Education Certificate Examination (BECE) past questions spanning a decade (2010-2022), covering Algebra, Geometry and Measurement, Data, and Number strands. Participants categorized each question according to Bloom's Taxonomy. Poisson regression analysis and Confirmatory Factor Analysis were employed to evaluate teachers' proficiency. Results indicated a statistically significant intercept term, suggesting a baseline performance level among teachers. Significant interaction effects between demographic and professional characteristics (Class:category, Class:SchTyp, TeachEx:SchTyp, TeachEx:Domain, and the main effect of Domain) influenced teachers' ability to identify mathematics domains. Teaching experience positively influenced scores, while school type had a negative impact. The model demonstrated high discriminatory power and strong predictive performance with an AUC of 0.996. Dependency analysis revealed that understanding Bloom's taxonomy domains influenced the identification of mathematics strands. Primary level teachers’ consistently demonstrated higher proficiency compared to Junior High School (JHS) level teachers. Additionally, experienced and qualified professionals performed better than pupil teachers. These findings highlight the importance of targeted interventions and professional development programs to enhance teachers' competency in identifying mathematics domains, thus improving mathematics education in Ghana.","PeriodicalId":281529,"journal":{"name":"Asian Research Journal of Mathematics","volume":"43 8","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141349742","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-06-10DOI: 10.9734/arjom/2024/v20i6805
Revathi G, G. Ilango
Persistent homology, an algebraic topology-based mathematical framework, presents an innovative method for capturing and characterizing the inherent topological features present in time series datasets. The research aims to evaluate the efficacy of features derived from persistent homology in enhancing the accuracy and interpretability of classification models. This investigation contributes to the expanding convergence of topology and time series analysis, providing valuable insights into the potential of persistent homology for extracting information from temporal data. The study specifically focuses on the analysis of region-wise solar production data obtained from India for the year 2022. The examination of this data is conducted using R-Software, and the resulting topological properties are represented through persistent diagrams.
持久同源性是一种基于代数拓扑的数学框架，它提出了一种创新方法，用于捕捉和描述时间序列数据集中存在的固有拓扑特征。这项研究旨在评估从持久同源性中提取的特征在提高分类模型的准确性和可解释性方面的功效。这项研究有助于拓扑学和时间序列分析不断扩大的融合，为持久同源性从时间数据中提取信息的潜力提供有价值的见解。本研究特别关注对 2022 年印度地区太阳能生产数据的分析。使用 R 软件对这些数据进行了检查，并通过持久图来表示由此产生的拓扑特性。
{"title":"Persistent Homology in Solar Production","authors":"Revathi G, G. Ilango","doi":"10.9734/arjom/2024/v20i6805","DOIUrl":"https://doi.org/10.9734/arjom/2024/v20i6805","url":null,"abstract":"Persistent homology, an algebraic topology-based mathematical framework, presents an innovative method for capturing and characterizing the inherent topological features present in time series datasets. The research aims to evaluate the efficacy of features derived from persistent homology in enhancing the accuracy and interpretability of classification models. This investigation contributes to the expanding convergence of topology and time series analysis, providing valuable insights into the potential of persistent homology for extracting information from temporal data. The study specifically focuses on the analysis of region-wise solar production data obtained from India for the year 2022. The examination of this data is conducted using R-Software, and the resulting topological properties are represented through persistent diagrams.","PeriodicalId":281529,"journal":{"name":"Asian Research Journal of Mathematics","volume":" 56","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141365798","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-06-07DOI: 10.9734/arjom/2024/v20i6804
Okoh Ufuoma
The question as to whether a CNF Boolean formula is satisfiable is referred to as Boolean satisfiability problem (SAT). For decades now, this problem has attracted a great deal of attention. A well-known algorithm for solving this problem is the DPLL algorithm. However, this algorithm may run in an exponential (long) time. The great plan embraced in this work is to show how the satisfiability of any CNF Boolean formula can be decided in a very short time. This is achieved by the modification of the DPLL algorithm and the introduction of a quick algorithm.
{"title":"Deciding Satisfiability in the Twinkling of an Eye","authors":"Okoh Ufuoma","doi":"10.9734/arjom/2024/v20i6804","DOIUrl":"https://doi.org/10.9734/arjom/2024/v20i6804","url":null,"abstract":"The question as to whether a CNF Boolean formula is satisfiable is referred to as Boolean satisfiability problem (SAT). For decades now, this problem has attracted a great deal of attention. A well-known algorithm for solving this problem is the DPLL algorithm. However, this algorithm may run in an exponential (long) time. The great plan embraced in this work is to show how the satisfiability of any CNF Boolean formula can be decided in a very short time. This is achieved by the modification of the DPLL algorithm and the introduction of a quick algorithm.","PeriodicalId":281529,"journal":{"name":"Asian Research Journal of Mathematics","volume":" 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141371021","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-06-07DOI: 10.9734/arjom/2024/v20i6803
B. Olabode, S. Kayode, O. J. Olatubi, A. Momoh
This work presents advancing numerical methods of block multi-derivative approaches for ordinary differential equations (ODEs) of Various Orders. The derivation of the methods is achieved by applying the techniques of interpolation and collocation to a power series polynomial, which is considered an approximate solution to the problems. Higher derivative terms are introduced to improve the accuracy of the method, giving room to modify the method for solving second and third-order initial value problems (IVPs) of ordinary differential equations (ODEs). Details conformation of the block method is presented, showing that the method is zero stable, consistent and convergent. The method is applied block-by-block to first, second and third-order initial value problems (IVPs) of ordinary differential equations. The application of the method to a real-life example also yields accurate results.
{"title":"Advancing Numerical Methods of Block Multi-Derivative Approaches for ODEs of Various Orders","authors":"B. Olabode, S. Kayode, O. J. Olatubi, A. Momoh","doi":"10.9734/arjom/2024/v20i6803","DOIUrl":"https://doi.org/10.9734/arjom/2024/v20i6803","url":null,"abstract":"This work presents advancing numerical methods of block multi-derivative approaches for ordinary differential equations (ODEs) of Various Orders. The derivation of the methods is achieved by applying the techniques of interpolation and collocation to a power series polynomial, which is considered an approximate solution to the problems. Higher derivative terms are introduced to improve the accuracy of the method, giving room to modify the method for solving second and third-order initial value problems (IVPs) of ordinary differential equations (ODEs). Details conformation of the block method is presented, showing that the method is zero stable, consistent and convergent. The method is applied block-by-block to first, second and third-order initial value problems (IVPs) of ordinary differential equations. The application of the method to a real-life example also yields accurate results.","PeriodicalId":281529,"journal":{"name":"Asian Research Journal of Mathematics","volume":"8 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141375555","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-06-06DOI: 10.9734/arjom/2024/v20i5802
Kimtai Boaz Simatwo
Let u, v, w, z, k, m and I be any integers such that k = z - w = w - v = v - u . The study of integer I for which I = u2n + v2n + w2n + z2n = k2 + m2 + r2 is not known. This study is therefore, set to partially overcome this challenge by introducing new formula relating sums of four even powers as an exact sum of three squares.
设 u、v、w、z、k、m 和 I 是任意整数，使得 k = z - w = w - v = v - u 。关于 I = u2n + v2n + w2n + z2n = k2 + m2 + r2 的整数 I 的研究尚不清楚。因此，本研究通过引入有关四个偶数幂的和为三个平方的精确和的新公式来部分克服这一难题。
{"title":"Equal Sums of Four Even Powers","authors":"Kimtai Boaz Simatwo","doi":"10.9734/arjom/2024/v20i5802","DOIUrl":"https://doi.org/10.9734/arjom/2024/v20i5802","url":null,"abstract":"Let u, v, w, z, k, m and I be any integers such that k = z - w = w - v = v - u . The study of integer I for which I = u2n + v2n + w2n + z2n = k2 + m2 + r2 is not known. This study is therefore, set to partially overcome this challenge by introducing new formula relating sums of four even powers as an exact sum of three squares.","PeriodicalId":281529,"journal":{"name":"Asian Research Journal of Mathematics","volume":"54 s186","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141376374","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-04-11DOI: 10.9734/arjom/2024/v20i4794
Takaaki Fujita
The study of width parameters holds significant interest in both graph theory and algebraic settings. Among these, the tree-cut decomposition stands out as a key metric. The "Edge-tangle" concept is closely related to the "tree-cut width" width parameter in graph theory. This obstruction is often seen as vital for creating effective algorithms to calculate graph width, with the edge-tangle being the specific obstruction for tree-cut width. Meanwhile, the idea of an "Ultrafilter" is well-established in topology and algebra. Due to their versatile nature, ultrafilters hold significant and broad-ranging importance. In this paper, we introduce a new concept called Edge-Ultrafilters for graphs and demonstrate how they are equivalent to Edge-tangles.
{"title":"Novel Idea on Edge-Ultrafilter and Edge-Tangle","authors":"Takaaki Fujita","doi":"10.9734/arjom/2024/v20i4794","DOIUrl":"https://doi.org/10.9734/arjom/2024/v20i4794","url":null,"abstract":"The study of width parameters holds significant interest in both graph theory and algebraic settings. Among these, the tree-cut decomposition stands out as a key metric. The \"Edge-tangle\" concept is closely related to the \"tree-cut width\" width parameter in graph theory. This obstruction is often seen as vital for creating effective algorithms to calculate graph width, with the edge-tangle being the specific obstruction for tree-cut width. Meanwhile, the idea of an \"Ultrafilter\" is well-established in topology and algebra. Due to their versatile nature, ultrafilters hold significant and broad-ranging importance. In this paper, we introduce a new concept called Edge-Ultrafilters for graphs and demonstrate how they are equivalent to Edge-tangles.","PeriodicalId":281529,"journal":{"name":"Asian Research Journal of Mathematics","volume":"3 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140712799","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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