In this paper, the Airfoil polynomials for solving the second order integro-differential equation with a singular kernel is considered. The collocation method is developed to obtain an approximate solution of the equation. We present an error analysis and conclude by providing numerical tests to verify our results.
{"title":"Solving Fredholm Second Order Integro-Differential Equation with Logarithmic Kernel Using the Airfoil Collocation Method","authors":"N. E. Ramdani, A. Hadj","doi":"10.47836/mjms.16.1.07","DOIUrl":"https://doi.org/10.47836/mjms.16.1.07","url":null,"abstract":"In this paper, the Airfoil polynomials for solving the second order integro-differential equation with a singular kernel is considered. The collocation method is developed to obtain an approximate solution of the equation. We present an error analysis and conclude by providing numerical tests to verify our results.","PeriodicalId":43645,"journal":{"name":"Malaysian Journal of Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41857583","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 main aim of this article is to establish some new refinements of Hermite Hadmard type inequalities via coordinate preinvex functions for fractional integrals. Here we give special cases to our results.
{"title":"Hermite-Hadamard Fejér Inequalities for Fractional Integrals for Functions Whose Second-Order Mixed Derivatives are Coordinated Preinvex","authors":"S. Mehmood, F. Zafar, H. Humza, A. Rasheed","doi":"10.47836/mjms.16.1.12","DOIUrl":"https://doi.org/10.47836/mjms.16.1.12","url":null,"abstract":"The main aim of this article is to establish some new refinements of Hermite Hadmard type inequalities via coordinate preinvex functions for fractional integrals. Here we give special cases to our results.","PeriodicalId":43645,"journal":{"name":"Malaysian Journal of Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42167088","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}
Kho L. C., Kasihmuddin M. S. M., Mansor M. A., Sathasivam S.
Minimizing the cost function that corresponds to propositional logic is vital to ensure the learning phase of HNN can occur optimally. In that regard, optimal and non-biased algorithm is required to ensure HNN will always converge to global solution. Ant Colony Optimization (ACO) is a population-based and nature-inspired algorithm to solve various combinatorial optimization problems. ACO simulates the behaviour of the real ants that forage for food and communication of ants through pheromone density. In this work, ACO will be used to minimize the cost function that corresponds to the logical rule in Hopfield Neural Network. ACO will utilize pheromone density to find the optimal path that leads to zero cost function without consuming more learning iteration. Performance for all learning models will be evaluated based on various performance metrics. Results collected from computer simulation implies that ACO outperformed conventional learning model in minimizing the logical cost function.
{"title":"Propositional Satisfiability Logic via Ant Colony Optimization in Hopfield\u0000Neural Network","authors":"Kho L. C., Kasihmuddin M. S. M., Mansor M. A., Sathasivam S.","doi":"10.47836/mjms.16.1.04","DOIUrl":"https://doi.org/10.47836/mjms.16.1.04","url":null,"abstract":"Minimizing the cost function that corresponds to propositional logic is vital to ensure the learning phase of HNN can occur optimally. In that regard, optimal and non-biased algorithm is required to ensure HNN will always converge to global solution. Ant Colony Optimization (ACO) is a population-based and nature-inspired algorithm to solve various combinatorial optimization problems. ACO simulates the behaviour of the real ants that forage for food and communication of ants through pheromone density. In this work, ACO will be used to minimize the cost function that corresponds to the logical rule in Hopfield Neural Network. ACO will utilize pheromone density to find the optimal path that leads to zero cost function without consuming more learning iteration. Performance for all learning models will be evaluated based on various performance metrics. Results collected from computer simulation implies that ACO outperformed conventional learning model in minimizing the logical cost function.","PeriodicalId":43645,"journal":{"name":"Malaysian Journal of Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46266594","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}
Numerical predictions of blood flow and hemodynamic properties through stenosis and aneurysm artery have been studied in the presence of blood clots at the constricted area. The finite element method has been used to solve the partial differential equations of continuity, momentum, Oldroyd-B, and bioheat transport in cartesian coordinates systems. The present investigation carries the potential to compute blood velocity, pressure, and drag coefficients with significance at the throat of stenosis and aneurysm. The models have also been employed to study simulation, blood clots, and hemodynamic characteristics for all modifications. The impact of shearthinning on blood flow is intensified compared to the viscoelastic properties. It is found that the maximum effect of the drag coefficient is visible at the hub of stenotic for nonclotting models. The highest pressure and the lowest velocity are gained for the presence of blood clots at the constraint area. The impact of stenosis and aneurysm artery, drag coefficient, and blood clots on blood flow is the main physical outcome that may be reported in medical science to identify atherosclerosis diseases. The quantitative analysis has been completed numerically with the physiological significance of hemodynamic factors of blood flow which shows the validity of the present model.
{"title":"Comparative Mathematical Study of Blood Flow Through Stenotic and Aneurysmatic Artery with the Presence and Absence of Blood Clots","authors":"M. Uddin, M. Uddin, Md. Monjarul Alam","doi":"10.47836/mjms.16.3.12","DOIUrl":"https://doi.org/10.47836/mjms.16.3.12","url":null,"abstract":"Numerical predictions of blood flow and hemodynamic properties through stenosis and aneurysm artery have been studied in the presence of blood clots at the constricted area. The finite element method has been used to solve the partial differential equations of continuity, momentum, Oldroyd-B, and bioheat transport in cartesian coordinates systems. The present investigation carries the potential to compute blood velocity, pressure, and drag coefficients with significance at the throat of stenosis and aneurysm. The models have also been employed to study simulation, blood clots, and hemodynamic characteristics for all modifications. The impact of shearthinning on blood flow is intensified compared to the viscoelastic properties. It is found that the maximum effect of the drag coefficient is visible at the hub of stenotic for nonclotting models. The highest pressure and the lowest velocity are gained for the presence of blood clots at the constraint area. The impact of stenosis and aneurysm artery, drag coefficient, and blood clots on blood flow is the main physical outcome that may be reported in medical science to identify atherosclerosis diseases. The quantitative analysis has been completed numerically with the physiological significance of hemodynamic factors of blood flow which shows the validity of the present model.","PeriodicalId":43645,"journal":{"name":"Malaysian Journal of Mathematical Sciences","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2020-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42012374","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}
F. A. Z. Shirazi, Fatemeh Ebrahimifar, Maryam Hagh Jooyan, A. Hosseini
In the following text, for finite discrete X with at least two elements, nonempty countable Γ, and φ:Γ→Γ we prove the generalized shift dynamical system (XΓ,σφ) is densely chaotic if and only if φ:Γ→Γ does not have any (quasi--)periodic point. Hence the class of all densely chaotic generalized shifts on XΓ is intermediate between the class of all Devaney chaotic generalized shifts on XΓ and the class of all Li--Yorke chaotic generalized shifts on XΓ. In addition, these inclusions are proper for infinite countable Γ. Moreover we prove (XΓ,σφ) is Li--Yorke sensitive (resp. sensitive, strongly sensitive, asymptotic sensitive, syndetically sensitive, cofinitely sensitive, multi--sensitive, ergodically sensitive, spatiotemporally chaotic, Li--Yorke chaotic) if and only if φ:Γ→Γ has at least one non--quasi--periodic point.
{"title":"On A Class Between Devaney Chaotic and Li-Yorke Chaotic Generalized Shift Dynamical Systems","authors":"F. A. Z. Shirazi, Fatemeh Ebrahimifar, Maryam Hagh Jooyan, A. Hosseini","doi":"10.47836/mjms.16.3.11","DOIUrl":"https://doi.org/10.47836/mjms.16.3.11","url":null,"abstract":"In the following text, for finite discrete X with at least two elements, nonempty countable Γ, and φ:Γ→Γ we prove the generalized shift dynamical system (XΓ,σφ) is densely chaotic if and only if φ:Γ→Γ does not have any (quasi--)periodic point. Hence the class of all densely chaotic generalized shifts on XΓ is intermediate between the class of all Devaney chaotic generalized shifts on XΓ and the class of all Li--Yorke chaotic generalized shifts on XΓ. In addition, these inclusions are proper for infinite countable Γ. Moreover we prove (XΓ,σφ) is Li--Yorke sensitive (resp. sensitive, strongly sensitive, asymptotic sensitive, syndetically sensitive, cofinitely sensitive, multi--sensitive, ergodically sensitive, spatiotemporally chaotic, Li--Yorke chaotic) if and only if φ:Γ→Γ has at least one non--quasi--periodic point.","PeriodicalId":43645,"journal":{"name":"Malaysian Journal of Mathematical Sciences","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2017-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41782636","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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