This article examines and proposes a dietary chain model with a prey shelter and alternative food sources. It is anticipated that mid-predators' availability is positively correlated with the number of refuges. The solution's existence and exclusivity are examined. It is established that the solution is bounded. It is explored whether all potential equilibrium points exist and are locally stable. The Lyapunov approach is used to investigate the equilibrium points' worldwide stability. Utilizing a Sotomayor theorem application, local bifurcation is studied. Numerical simulation is used to better comprehend the dynamics of the model and define the control set of parameters.
{"title":"The Effect of Alternative Resource and Refuge on the Dynamical Behavior of Food Chain Model","authors":"Z. M. Hadi, D. K. Bahlool","doi":"10.47836/mjms.17.4.13","DOIUrl":"https://doi.org/10.47836/mjms.17.4.13","url":null,"abstract":"This article examines and proposes a dietary chain model with a prey shelter and alternative food sources. It is anticipated that mid-predators' availability is positively correlated with the number of refuges. The solution's existence and exclusivity are examined. It is established that the solution is bounded. It is explored whether all potential equilibrium points exist and are locally stable. The Lyapunov approach is used to investigate the equilibrium points' worldwide stability. Utilizing a Sotomayor theorem application, local bifurcation is studied. Numerical simulation is used to better comprehend the dynamics of the model and define the control set of parameters.","PeriodicalId":43645,"journal":{"name":"Malaysian Journal of Mathematical Sciences","volume":"2005 22","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139001738","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}
In this paper, we establish the block matrix decomposition of kth order slant Toeplitz operators. We also establish some relations between the compressions of kth order slant Toeplitz and kth order slant Hankel operators on H2. In the last section, we introduce the notion of kth order slant Toeplitz graphs.
{"title":"Decomposition of kth Order Slant Toeplitz Operators","authors":"K. P. Singh, M. P. Singh,, A. J. Sanasam,","doi":"10.47836/mjms.17.4.14","DOIUrl":"https://doi.org/10.47836/mjms.17.4.14","url":null,"abstract":"In this paper, we establish the block matrix decomposition of kth order slant Toeplitz operators. We also establish some relations between the compressions of kth order slant Toeplitz and kth order slant Hankel operators on H2. In the last section, we introduce the notion of kth order slant Toeplitz graphs.","PeriodicalId":43645,"journal":{"name":"Malaysian Journal of Mathematical Sciences","volume":"20 4","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139002798","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}
The k-token graph of a given graph G, is the graph which vertex set consists of all k− subsets of the vertex set of G and two vertices are connected by an edge exactly when their difference corresponds to an edge of G. In this paper, we give a description on the structure of the 2-token graph of disjoint union of multiple graphs. This result complements the previous findings regarding the properties of the k-token graphs.
给定图 G 的 k 标记图是指顶点集由 G 的顶点集的所有 k 个子集组成的图，当两个顶点的差值对应于 G 的一条边时，这两个顶点正好通过一条边相连。这一结果补充了之前关于 k 标记图性质的发现。
{"title":"On the 2-Token Graphs of Some Disjoint Union of Graphs","authors":"Y. Susanti,","doi":"10.47836/mjms.17.4.12","DOIUrl":"https://doi.org/10.47836/mjms.17.4.12","url":null,"abstract":"The k-token graph of a given graph G, is the graph which vertex set consists of all k−\u0000subsets of the vertex set of G and two vertices are connected by an edge exactly when their difference corresponds to an edge of G. In this paper, we give a description on the structure of the 2-token graph of disjoint union of multiple graphs. This result complements the previous findings regarding the properties of the k-token graphs.","PeriodicalId":43645,"journal":{"name":"Malaysian Journal of Mathematical Sciences","volume":"166 3","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139002353","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}
In this paper, we propose a Blind Identity-Based Identification (Blind IBI) scheme based on the Guillou-Quisquater (GQ) scheme. Our proposed scheme combines the benefits of traditional Identity-Based Identification (IBI) schemes that can authenticate a user's identity without relying on a trusted third party with the Blind Signature (BS) scheme that provides anonymity. As a result, the proposed scheme assures absolute user privacy during the authentication process. It does not rely on a third party, yet the verifier can still be assured of the user's identity without the user actually revealing it. In our work, we show that the proposed scheme is provably secure under the random oracle model, with the assumption that the one-more-RSA-inversion problem is difficult. Furthermore, we demonstrate that the proposed scheme is secure against passive, active, and concurrent impersonation attacks. In conclusion, the proposed scheme is able to achieve the desired blindness property without compromising the security of the GQ-IBI scheme it is based upon.
{"title":"A Pairing-free Provable Secure and Efficient Identity-based Identification Scheme with Anonymity","authors":"R. Kannan, J. J. Chin,, V. T. Goh, S. C. Yip","doi":"10.47836/mjms.17.4.11","DOIUrl":"https://doi.org/10.47836/mjms.17.4.11","url":null,"abstract":"In this paper, we propose a Blind Identity-Based Identification (Blind IBI) scheme based on the Guillou-Quisquater (GQ) scheme. Our proposed scheme combines the benefits of traditional Identity-Based Identification (IBI) schemes that can authenticate a user's identity without relying on a trusted third party with the Blind Signature (BS) scheme that provides anonymity. As a result, the proposed scheme assures absolute user privacy during the authentication process. It does not rely on a third party, yet the verifier can still be assured of the user's identity without the user actually revealing it. In our work, we show that the proposed scheme is provably secure under the random oracle model, with the assumption that the one-more-RSA-inversion problem is difficult. Furthermore, we demonstrate that the proposed scheme is secure against passive, active, and concurrent impersonation attacks. In conclusion, the proposed scheme is able to achieve the desired blindness property without compromising the security of the GQ-IBI scheme it is based upon.","PeriodicalId":43645,"journal":{"name":"Malaysian Journal of Mathematical Sciences","volume":"12 4","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139003068","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}
S. M. Al-Omari,, Akhtar Hussain, Muhammad Usman, F. D. Zaman,
Our research focuses on a fourth-order partial differential equation (PDE) that arises from the Timoshenko model for beams. This PDE pertains to situations where the elastic moduli remain constant and an external load, represented as F, is applied. We thoroughly analyze Lie symmetries and categorize the various types of applied forces. Initially, the principal Lie algebra is two-dimensional, but in certain noteworthy cases, it extends to three dimensions or even more. For each specific case, we derive the optimal system, which serves as a foundation for symmetry reductions, transforming the original PDE into ordinary differential equations. In certain instances, we successfully identify exact solutions using this reduction process. Additionally, we delve into the conservation laws using a direct method proposed by Anco, with a particular focus on specific classes within the equation. The findings we have presented in our study are indeed original and innovative. This study serves as compelling evidence for the robustness and efficacy of the Lie symmetry method, showcasing its ability to provide valuable insights and solutions in the realm of mathematical analysis.
我们的研究重点是梁的季莫申科模型中产生的四阶偏微分方程（PDE）。该偏微分方程适用于弹性模量保持恒定，并施加以 F 表示的外部载荷的情况。我们深入分析了李对称性，并对各种外力进行了分类。最初，主李代数是二维的，但在某些值得注意的情况下，它扩展到三维甚至更多维。对于每种特定情况，我们都会推导出最优系统，作为对称性还原的基础，将原始 PDE 转换为常微分方程。在某些情况下，我们利用这一还原过程成功找出了精确解。此外，我们还利用 Anco 提出的直接方法深入研究了守恒定律，并特别关注方程中的特定类别。我们在研究中提出的发现确实具有原创性和创新性。这项研究有力地证明了李对称方法的稳健性和有效性，展示了它在数学分析领域提供有价值的见解和解决方案的能力。
{"title":"Invariance Analysis and Closed-form Solutions for The Beam Equation in Timoshenko Model","authors":"S. M. Al-Omari,, Akhtar Hussain, Muhammad Usman, F. D. Zaman,","doi":"10.47836/mjms.17.4.05","DOIUrl":"https://doi.org/10.47836/mjms.17.4.05","url":null,"abstract":"Our research focuses on a fourth-order partial differential equation (PDE) that arises from the Timoshenko model for beams. This PDE pertains to situations where the elastic moduli remain constant and an external load, represented as F, is applied. We thoroughly analyze Lie symmetries and categorize the various types of applied forces. Initially, the principal Lie algebra is two-dimensional, but in certain noteworthy cases, it extends to three dimensions or even more. For each specific case, we derive the optimal system, which serves as a foundation for symmetry reductions, transforming the original PDE into ordinary differential equations. In certain instances, we successfully identify exact solutions using this reduction process. Additionally, we delve into the conservation laws using a direct method proposed by Anco, with a particular focus on specific classes within the equation. The findings we have presented in our study are indeed original and innovative. This study serves as compelling evidence for the robustness and efficacy of the Lie symmetry method, showcasing its ability to provide valuable insights and solutions in the realm of mathematical analysis.","PeriodicalId":43645,"journal":{"name":"Malaysian Journal of Mathematical Sciences","volume":"31 6","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138972005","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}
This paper investigates the two fifth-order Fujimoto-Watanabe equations from the perspective of the group theoretic approach. We identify the reduced equations that lead to the solutions of these high order equations. Furthermore, the corresponding solutions are found by power series due to their nonlinear characteristics. As a result, the findings of the study demonstrate the convergence of solutions for such models and identifies the travelling wave solutions.
{"title":"On the Optimal System and Series Solutions of Fifth-Order Fujimoto-Watanabe Equations","authors":"B. Gwaxa, S. Jamal,, A. G. Johnpillai","doi":"10.47836/mjms.17.4.03","DOIUrl":"https://doi.org/10.47836/mjms.17.4.03","url":null,"abstract":"This paper investigates the two fifth-order Fujimoto-Watanabe equations from the perspective of the group theoretic approach. We identify the reduced equations that lead to the solutions of these high order equations. Furthermore, the corresponding solutions are found by power series due to their nonlinear characteristics. As a result, the findings of the study demonstrate the convergence of solutions for such models and identifies the travelling wave solutions.","PeriodicalId":43645,"journal":{"name":"Malaysian Journal of Mathematical Sciences","volume":"27 18","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138975060","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}
High level of greenhouse gases emission in fossil fuels has induced a significant transition from conventional energy sources to renewable energy. However, using renewable energy in electricity grids has limitations, such as intermittency and lack of efficient energy storage. This paper focuses on constructing the quanto options contract to help renewable energy producers hedge the risk against low photovoltaic (PV) production and electricity prices. To achieve our objective, we first model the interday PV power production with a combination of a deterministic and stochastic model. We analyse empirical data for daily solar production in three operators in Germany ranging from 1 January 2016 to 31 December 2020. We discovered that all estimated parameters of the deterministic process are highly significant. Meanwhile, we use an autoregressive (AR) process to describe the random behavior in the production. The results demonstrated that AR(2) is suitable enough to explain its stochastic factor. For the error terms analysis, we observed a clear sign of seasonal heteroskedasticity supported by the left skewed density. In addition, we observed a clear seasonal pattern in the squared error terms, where we suggest using seasonal variance and skewed normal distribution to describe its dynamic. As for an application, we embed the PV model in the power price modeling. We found that AR(3) process is sufficient to explain the price behavior and that normal distribution best fits the error terms. Using the suggested PV and power price model, we construct the quanto options contract for renewable energy producers using Monte Carlo simulations. We discovered that the electricity price payoffs are consistent throughout the year, whereas PV and quanto options payoffs vary greatly depending on the season. The quanto options price result shows that the prices vary during four seasons, with the highest variation in July.
{"title":"Pricing Quanto Options in Renewable Energy Markets","authors":"N. A. A. Arsat,, N. A. Ibrahim, C. M. I. C. Taib","doi":"10.47836/mjms.17.4.02","DOIUrl":"https://doi.org/10.47836/mjms.17.4.02","url":null,"abstract":"High level of greenhouse gases emission in fossil fuels has induced a significant transition from conventional energy sources to renewable energy. However, using renewable energy in electricity grids has limitations, such as intermittency and lack of efficient energy storage. This paper focuses on constructing the quanto options contract to help renewable energy producers hedge the risk against low photovoltaic (PV) production and electricity prices. To achieve our objective, we first model the interday PV power production with a combination of a deterministic and stochastic model. We analyse empirical data for daily solar production in three operators in Germany ranging from 1 January 2016 to 31 December 2020. We discovered that all estimated parameters of the deterministic process are highly significant. Meanwhile, we use an autoregressive (AR) process to describe the random behavior in the production. The results demonstrated that AR(2) is suitable enough to explain its stochastic factor. For the error terms analysis, we observed a clear sign of seasonal heteroskedasticity supported by the left skewed density. In addition, we observed a clear seasonal pattern in the squared error terms, where we suggest using seasonal variance and skewed normal distribution to describe its dynamic. As for an application, we embed the PV model in the power price modeling. We found that AR(3) process is sufficient to explain the price behavior and that normal distribution best fits the error terms. Using the suggested PV and power price model, we construct the quanto options contract for renewable energy producers using Monte Carlo simulations. We discovered that the electricity price payoffs are consistent throughout the year, whereas PV and quanto options payoffs vary greatly depending on the season. The quanto options price result shows that the prices vary during four seasons, with the highest variation in July.","PeriodicalId":43645,"journal":{"name":"Malaysian Journal of Mathematical Sciences","volume":"18 3","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138971005","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}
In the field of cheminformatics, the amalgamation of graph theory, chemistry, along with technology facilitates the establishment of connections between the structural as well as physiochemical attributes of organic compounds by employing certain valuable graph invariants including the corresponding molecular graph. In this work, we examine reverse topological indices, for instance, the reverse Zagreb index, the reverse arithmetic-geometric, the geometric-arithmetic, the reverse Nirmala indices for the bistar graphs B(n;m) , the reverse sum-connectivity index, the reverse Sombor as well as the corona product of Km∘K′n.
{"title":"A Study of Families of Bistar and Corona Product of Graph: Reverse Topological Indices","authors":"K. Gowtham, M. N. Husin,","doi":"10.47836/mjms.17.4.04","DOIUrl":"https://doi.org/10.47836/mjms.17.4.04","url":null,"abstract":"In the field of cheminformatics, the amalgamation of graph theory, chemistry, along with technology facilitates the establishment of connections between the structural as well as physiochemical attributes of organic compounds by employing certain valuable graph invariants including the corresponding molecular graph. In this work, we examine reverse topological indices, for instance, the reverse Zagreb index, the reverse arithmetic-geometric, the geometric-arithmetic, the reverse Nirmala indices for the bistar graphs B(n;m) , the reverse sum-connectivity index, the reverse Sombor as well as the corona product of Km∘K′n.","PeriodicalId":43645,"journal":{"name":"Malaysian Journal of Mathematical Sciences","volume":"22 3","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138971836","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}
In this paper, Richardson iterative method is employed to solve M-Equation. In order to guarantee the solution can be found, convergence theorems are established and confirmed numerically. The optimal α, which is a parameter of Richardson iterative method that can provide the best convergence rate, is also determined theoretically and numerically. Furthermore, a theorem establishing the range of initial vector for general splitting methods is extended from the range in past study. To further accelerate the convergence rate, Anderson accelerator and three preconditioners are incorporated into Richardson iterative method. Numerical results reveal that by including these accelerators, the convergence rates are enhanced. Finally, we show that Richardson iterative methods with optimal α perform better than the SOR type methods in past studies in terms of number of iterative steps and CPU time.
本文采用理查森迭代法求解 M 方程。为了保证求解的准确性，本文建立了收敛定理并进行了数值确认。同时还从理论和数值上确定了 Richardson 迭代法中能提供最佳收敛速度的参数 α。此外，还在过去研究的基础上扩展了建立一般分裂方法初始向量范围的定理。为了进一步加快收敛速度，在 Richardson 迭代方法中加入了 Anderson 加速器和三个前置条件器。数值结果表明，加入这些加速器后，收敛速度得到了提高。最后，我们证明了具有最优 α 的 Richardson 迭代方法在迭代步数和 CPU 时间方面的表现优于以往研究中的 SOR 类型方法。
{"title":"Richardson Iterative Method for Solving Multi-Linear System with M-Tensor","authors":"Y. Liang,, A. Ibrahim,, Z. Omar,","doi":"10.47836/mjms.17.4.08","DOIUrl":"https://doi.org/10.47836/mjms.17.4.08","url":null,"abstract":"In this paper, Richardson iterative method is employed to solve M-Equation. In order to guarantee the solution can be found, convergence theorems are established and confirmed numerically. The optimal α, which is a parameter of Richardson iterative method that can provide the best convergence rate, is also determined theoretically and numerically. Furthermore, a theorem establishing the range of initial vector for general splitting methods is extended from the range in past study. To further accelerate the convergence rate, Anderson accelerator and three preconditioners are incorporated into Richardson iterative method. Numerical results reveal that by including these accelerators, the convergence rates are enhanced. Finally, we show that Richardson iterative methods with optimal α perform better than the SOR type methods in past studies in terms of number of iterative steps and CPU time.","PeriodicalId":43645,"journal":{"name":"Malaysian Journal of Mathematical Sciences","volume":"58 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139001846","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}
Rough set theory is commonly used to handle uncertainty in various applications. In order to broaden its application scope, the classical rough set model based on equivalence relations, it has been extended to include an additional partial order relation. This partial order relation represents an m-nano flou set, as defined in Section 5, between rough sets and is particularly useful in determining the levels of impact that key factors have on heart failure. The primary objective of the current research is to introduce a novel approximation method based on equivalence relations and partial order relations (ordered approximation spaces), which extends Pawlak's method and investigates related results. The paper establishes the equivalence between our approach and Pawlak's approach under the condition that we have an equivalence relation and a partial order relation that satisfies the criteria required for it to be considered an equality relation. The second objective is to extend the concept of nano topology to include nano ordered topology, which involves nano increasing or decreasing topological spaces. The research indicates that incorporating nano increasing or decreasing topological spaces results in enhanced data analysis accuracy when compared to solely utilizing nano topological spaces. This observation aligns with the discussions in the referenced work by Jayalakshmi. The findings of this research have the potential to significantly impact medical research related to heart failure. Improved methods for handling uncertainty and quantifying the influence of various factors can lead to more accurate and reliable predictions and diagnoses. Ultimately, this work aims to contribute to advancements in heart failure treatment and prevention. By bridging the gap between traditional rough set theory and the nuanced intricacies of heart failure analysis, our research strives to advance our comprehension of this critical medical condition and, in turn, support progress in heart failure treatment and prevention.
{"title":"An Application on an Information System via Nano Ordered Topology","authors":"S. H. Shalil, S. A. El-Sheikh, S. A. Kandil","doi":"10.47836/mjms.17.4.01","DOIUrl":"https://doi.org/10.47836/mjms.17.4.01","url":null,"abstract":"Rough set theory is commonly used to handle uncertainty in various applications. In order to broaden its application scope, the classical rough set model based on equivalence relations, it has been extended to include an additional partial order relation. This partial order relation represents an m-nano flou set, as defined in Section 5, between rough sets and is particularly useful in determining the levels of impact that key factors have on heart failure. The primary objective of the current research is to introduce a novel approximation method based on equivalence relations and partial order relations (ordered approximation spaces), which extends Pawlak's method and investigates related results. The paper establishes the equivalence between our approach and Pawlak's approach under the condition that we have an equivalence relation and a partial order relation that satisfies the criteria required for it to be considered an equality relation. The second objective is to extend the concept of nano topology to include nano ordered topology, which involves nano increasing or decreasing topological spaces. The research indicates that incorporating nano increasing or decreasing topological spaces results in enhanced data analysis accuracy when compared to solely utilizing nano topological spaces. This observation aligns with the discussions in the referenced work by Jayalakshmi. The findings of this research have the potential to significantly impact medical research related to heart failure. Improved methods for handling uncertainty and quantifying the influence of various factors can lead to more accurate and reliable predictions and diagnoses. Ultimately, this work aims to contribute to advancements in heart failure treatment and prevention. By bridging the gap between traditional rough set theory and the nuanced intricacies of heart failure analysis, our research strives to advance our comprehension of this critical medical condition and, in turn, support progress in heart failure treatment and prevention.","PeriodicalId":43645,"journal":{"name":"Malaysian Journal of Mathematical Sciences","volume":"13 9","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139002501","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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