Nanofluids are said to have high potential applicability as an enhanced thermophysical heat transfer fluid and are also related to CMC (carboxymethyl cellulose) due to their increased thermal conductivities. The intention of this research is to investigate and analyze the free convection flow of a second grade MHD heat transfer of CNTs on a vertically static plate with a constant wall temperature. The two types of CNTs are immersed in CMC, named multiple wall carbon nanotubes (MWCNTs) and single-wall carbon nanotubes (SWC-NTs). Nanofluids have been determined to offer a great potential application as an improved thermophysical heat transfer fluid, also due to their higher thermal conductivities. The problem is formulated as PDEs with initial and boundary conditions that are transformed into dimensionless structures by using unique non-dimensional variables. The general solution to the problem is achieved by utilizing the Laplace Transformation approach and obtaining the exact solutions for velocity, temperature, and shear stress. We compared the solutions of SWCNTs and MWCNTs regarding parameters such as Grashof number, relaxation time, Prandtl number, and volume fraction of nanoparticles. The results are significantly influenced by the differences in SWCNTs andMWCNTs.
{"title":"Heat transfer enhancement in free convection flow of MHD second grade fluid with carbon nanotubes (CNTS) over a vertically static plate","authors":"Afreen Roohani, Muhammad Usman, None Saima Zainab","doi":"10.52700/msa.v2i1.10","DOIUrl":"https://doi.org/10.52700/msa.v2i1.10","url":null,"abstract":"Nanofluids are said to have high potential applicability as an enhanced thermophysical heat transfer fluid and are also related to CMC (carboxymethyl cellulose) due to their increased thermal conductivities. The intention of this research is to investigate and analyze the free convection flow of a second grade MHD heat transfer of CNTs on a vertically static plate with a constant wall temperature. The two types of CNTs are immersed in CMC, named multiple wall carbon nanotubes (MWCNTs) and single-wall carbon nanotubes (SWC-NTs). Nanofluids have been determined to offer a great potential application as an improved thermophysical heat transfer fluid, also due to their higher thermal conductivities. The problem is formulated as PDEs with initial and boundary conditions that are transformed into dimensionless structures by using unique non-dimensional variables. The general solution to the problem is achieved by utilizing the Laplace Transformation approach and obtaining the exact solutions for velocity, temperature, and shear stress. We compared the solutions of SWCNTs and MWCNTs regarding parameters such as Grashof number, relaxation time, Prandtl number, and volume fraction of nanoparticles. The results are significantly influenced by the differences in SWCNTs andMWCNTs.","PeriodicalId":42896,"journal":{"name":"Annals of Mathematical Sciences and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136365486","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}
Muhammad Owais Tariq, Muhammad Irfan Mushtaq, None Amir Hamza
In this paper, we will discuss the controllability and observability conditions for some fractional electrical circuits, using the controllability and observability of Gramian matrix conditions derived for fractional continuous time linear systems with regular pencil. These results are obtained with the help of the Drazin inverse method.
{"title":"Fractional electrical circuits: A drazin Inverse Technique","authors":"Muhammad Owais Tariq, Muhammad Irfan Mushtaq, None Amir Hamza","doi":"10.52700/msa.v2i1.11","DOIUrl":"https://doi.org/10.52700/msa.v2i1.11","url":null,"abstract":"In this paper, we will discuss the controllability and observability conditions for some fractional electrical circuits, using the controllability and observability of Gramian matrix conditions derived for fractional continuous time linear systems with regular pencil. These results are obtained with the help of the Drazin inverse method.","PeriodicalId":42896,"journal":{"name":"Annals of Mathematical Sciences and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136365490","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 : 2023-06-22DOI: 10.4310/amsa.2023.v8.n2.a4
Ching-Jou Liao, Chih-Neng Liu, Jung-Hui Liu, N. Wong
Let $mathrm{Lip}(X)$, $mathrm{Lip}^b(X)$, $mathrm{Lip}^{mathrm{loc}}(X)$ and $mathrm{Lip}^mathrm{pt}(X)$ be the vector spaces of Lipschitz, bounded Lipschitz, locally Lipschitz and pointwise Lipschitz (real-valued) functions defined on a metric space $(X, d_X)$, respectively. We show that if a weighted composition operator $Tf=hcdot fcirc varphi$ defines a bijection between such vector spaces preserving Lipschitz constants, local Lipschitz constants or pointwise Lipschitz constants, then $h= pm1/alpha$ is a constant function for some scalar $alpha>0$ and $varphi$ is an $alpha$-dilation. Let $U$ be open connected and $V$ be open, or both $U,V$ are convex bodies, in normed linear spaces $E, F$, respectively. Let $Tf=hcdot fcircvarphi$ be a bijective weighed composition operator between the vector spaces $mathrm{Lip}(U)$ and $mathrm{Lip}(V)$, $mathrm{Lip}^b(U)$ and $mathrm{Lip}^b(V)$, $mathrm{Lip}^mathrm{loc}(U)$ and $mathrm{Lip}^mathrm{loc}(V)$, or $mathrm{Lip}^mathrm{pt}(U)$ and $mathrm{Lip}^mathrm{pt}(V)$, preserving the Lipschitz, locally Lipschitz, or pointwise Lipschitz constants, respectively. We show that there is a linear isometry $A: Fto E$, an $alpha>0$ and a vector $bin E$ such that $varphi(x)=alpha Ax + b$, and $h$ is a constant function assuming value $pm 1/alpha$. More concrete results are obtained for the special cases when $E=F=mathbb{R}^n$, or when $U,V$ are $n$-dimensional flat manifolds.
{"title":"Weighted composition operators preserving various Lipschitz constants","authors":"Ching-Jou Liao, Chih-Neng Liu, Jung-Hui Liu, N. Wong","doi":"10.4310/amsa.2023.v8.n2.a4","DOIUrl":"https://doi.org/10.4310/amsa.2023.v8.n2.a4","url":null,"abstract":"Let $mathrm{Lip}(X)$, $mathrm{Lip}^b(X)$, $mathrm{Lip}^{mathrm{loc}}(X)$ and $mathrm{Lip}^mathrm{pt}(X)$ be the vector spaces of Lipschitz, bounded Lipschitz, locally Lipschitz and pointwise Lipschitz (real-valued) functions defined on a metric space $(X, d_X)$, respectively. We show that if a weighted composition operator $Tf=hcdot fcirc varphi$ defines a bijection between such vector spaces preserving Lipschitz constants, local Lipschitz constants or pointwise Lipschitz constants, then $h= pm1/alpha$ is a constant function for some scalar $alpha>0$ and $varphi$ is an $alpha$-dilation. Let $U$ be open connected and $V$ be open, or both $U,V$ are convex bodies, in normed linear spaces $E, F$, respectively. Let $Tf=hcdot fcircvarphi$ be a bijective weighed composition operator between the vector spaces $mathrm{Lip}(U)$ and $mathrm{Lip}(V)$, $mathrm{Lip}^b(U)$ and $mathrm{Lip}^b(V)$, $mathrm{Lip}^mathrm{loc}(U)$ and $mathrm{Lip}^mathrm{loc}(V)$, or $mathrm{Lip}^mathrm{pt}(U)$ and $mathrm{Lip}^mathrm{pt}(V)$, preserving the Lipschitz, locally Lipschitz, or pointwise Lipschitz constants, respectively. We show that there is a linear isometry $A: Fto E$, an $alpha>0$ and a vector $bin E$ such that $varphi(x)=alpha Ax + b$, and $h$ is a constant function assuming value $pm 1/alpha$. More concrete results are obtained for the special cases when $E=F=mathbb{R}^n$, or when $U,V$ are $n$-dimensional flat manifolds.","PeriodicalId":42896,"journal":{"name":"Annals of Mathematical Sciences and Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46038576","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}
A variety of graphical invariants have been described and tested, offering lots of applications in the fields of Nano chemistry, computational networks and different scientific research areas. One commonly studied group of invariants is the topological index, which allows the prediction of the chemical, biological and physical properties of a chemical structure. Topological indexes are numerical quantities that can be used to describe the properties of the molecular graph. In this article, we computed the face index formula for certain molecular structures of benzenoid series such as polycyclic aromatic hydrocarbon (PAH), jagged-rectangle benzenoid system (JRB[m,n]) and the series of concealed non-kekulean benzenoid system.
{"title":"Topological Properties of some Benzenoid Chemical Structures by Using Face Index","authors":"M. Naeem, Muhammad Sajid, M. Ishtiaq","doi":"10.52700/msa.v2i1.8","DOIUrl":"https://doi.org/10.52700/msa.v2i1.8","url":null,"abstract":"A variety of graphical invariants have been described and tested, offering lots of applications in the fields of Nano chemistry, computational networks and different scientific research areas. One commonly studied group of invariants is the topological index, which allows the prediction of the chemical, biological and physical properties of a chemical structure. Topological indexes are numerical quantities that can be used to describe the properties of the molecular graph. In this article, we computed the face index formula for certain molecular structures of benzenoid series such as polycyclic aromatic hydrocarbon (PAH), jagged-rectangle benzenoid system (JRB[m,n]) and the series of concealed non-kekulean benzenoid system.","PeriodicalId":42896,"journal":{"name":"Annals of Mathematical Sciences and Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77461852","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}
Fractional calculus is one of the evolving fields in applied sciences. Delay differential equation of non-integer order plays a vital role in epidemiology, population growth, physiology economy, medicine, chemistry, control, and electrodynamics and many mathematical modeling problems Fractional Delay differential equations usually lacks analytic solutions and some of these equations can only be solved by some numerical methods. In this review article we present a comparative study on some standard numerical methods applied to solve linear fractional order differential equations with time delay. Fractional finite difference method (FFDM), Predictor-corrector method (PCM) with new and extended versions has been discussed in this article. All above mentioned methods use the Caputo type fractional differential operator to define fractional derivatives. Solution of a real-life problem formulated by FDDEs has been discussed under these methods. Results have been presented in tabular and graphical form to analyze the efficiency and scarcity of mentioned methods. These graphical and numerical comparisons are provided to illustrate and corroborate the similarity and differences between these methods.
{"title":"A Comparative Study on Solution Methods for Fractional order Delay Differential Equations and its Applications","authors":"Faiza Chishti, Fozia Hanif, Rehan Shams","doi":"10.52700/msa.v2i1.6","DOIUrl":"https://doi.org/10.52700/msa.v2i1.6","url":null,"abstract":"Fractional calculus is one of the evolving fields in applied sciences. Delay differential equation of non-integer order plays a vital role in epidemiology, population growth, physiology economy, medicine, chemistry, control, and electrodynamics and many mathematical modeling problems Fractional Delay differential equations usually lacks analytic solutions and some of these equations can only be solved by some numerical methods. In this review article we present a comparative study on some standard numerical methods applied to solve linear fractional order differential equations with time delay. Fractional finite difference method (FFDM), Predictor-corrector method (PCM) with new and extended versions has been discussed in this article. All above mentioned methods use the Caputo type fractional differential operator to define fractional derivatives. Solution of a real-life problem formulated by FDDEs has been discussed under these methods. Results have been presented in tabular and graphical form to analyze the efficiency and scarcity of mentioned methods. These graphical and numerical comparisons are provided to illustrate and corroborate the similarity and differences between these methods.","PeriodicalId":42896,"journal":{"name":"Annals of Mathematical Sciences and Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83645888","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}
Computation of Topological indices (TI) is useful in the analysis of the chemical as well as physical properties of different molecular structures. Among the TIs, the eccentricity connectivity index shows an effective role of estimating medicament properties. In our article, we computed eccentricity-based entropies (Eccentric-connectivity and Total eccentric-connectivity entropy) for the molecular structure of Water Soluble Dendritic Unimolecular Polyether Micelle.
{"title":"Eccentricity Based Entropy Indices of Water Soluble Dendritic Unimolecular Polyether Micelle","authors":"Rukhsar Zireen, Saima Noureen, Amir Hussain","doi":"10.52700/msa.v2i1.7","DOIUrl":"https://doi.org/10.52700/msa.v2i1.7","url":null,"abstract":"Computation of Topological indices (TI) is useful in the analysis of the chemical as well as physical properties of different molecular structures. Among the TIs, the eccentricity connectivity index shows an effective role of estimating medicament properties. In our article, we computed eccentricity-based entropies (Eccentric-connectivity and Total eccentric-connectivity entropy) for the molecular structure of Water Soluble Dendritic Unimolecular Polyether Micelle.","PeriodicalId":42896,"journal":{"name":"Annals of Mathematical Sciences and Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85759658","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 : 2023-04-13DOI: 10.4310/amsa.2023.v8.n2.a3
B. Forrest, J. Sawatzky, Aasaimani Thamizhazhagan
Let $G$ be a locally compact group. In this paper, we study various invariant subspaces of the duals of the algebras $A_M(G)$ and $A_{cb}(G)$ obtained by taking the closure of the Fourier algebra $A(G)$ in the multiplier algebra $MA(G)$ and completely bounded multiplier algebra $M_{cb}A(G)$ respectively. In particular, we will focus on various functorial properties and containment relationships between these various invariant subspaces including the space of uniformly continuous functionals and the almost periodic and weakly almost periodic functionals. Amongst other results, we show that if $mathcal{A}(G)$ is either $A_M(G)$ or $A_{cb}(G)$, then $UCB(mathcal{A}(G))subseteq WAP(G)$ if and only if $G$ is discrete. We also show that if $UCB(mathcal{A}(G))=mathcal{A}(G)^*$, then every amenable closed subgroup of $G$ is compact. Let $i:A(G)to mathcal{A}(G)$ be the natural injection. We show that if $X$ is any closed topologically introverted subspace of $mathcal{A}(G)^*$ that contains $L^1(G)$, then $i^*(X)$ is closed in $A(G)$ if and only if $G$ is amenable.
{"title":"Invariant subspaces in the dual of $A_{cb}(G)$ and $A_M (G)$","authors":"B. Forrest, J. Sawatzky, Aasaimani Thamizhazhagan","doi":"10.4310/amsa.2023.v8.n2.a3","DOIUrl":"https://doi.org/10.4310/amsa.2023.v8.n2.a3","url":null,"abstract":"Let $G$ be a locally compact group. In this paper, we study various invariant subspaces of the duals of the algebras $A_M(G)$ and $A_{cb}(G)$ obtained by taking the closure of the Fourier algebra $A(G)$ in the multiplier algebra $MA(G)$ and completely bounded multiplier algebra $M_{cb}A(G)$ respectively. In particular, we will focus on various functorial properties and containment relationships between these various invariant subspaces including the space of uniformly continuous functionals and the almost periodic and weakly almost periodic functionals. Amongst other results, we show that if $mathcal{A}(G)$ is either $A_M(G)$ or $A_{cb}(G)$, then $UCB(mathcal{A}(G))subseteq WAP(G)$ if and only if $G$ is discrete. We also show that if $UCB(mathcal{A}(G))=mathcal{A}(G)^*$, then every amenable closed subgroup of $G$ is compact. Let $i:A(G)to mathcal{A}(G)$ be the natural injection. We show that if $X$ is any closed topologically introverted subspace of $mathcal{A}(G)^*$ that contains $L^1(G)$, then $i^*(X)$ is closed in $A(G)$ if and only if $G$ is amenable.","PeriodicalId":42896,"journal":{"name":"Annals of Mathematical Sciences and Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42949108","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 : 2023-01-01DOI: 10.4310/amsa.2023.v8.n1.a5
A. Kaplan, Mulla Veli Ablay
{"title":"Numerical solution of boundary value problem for the Bagley–Torvik equation using Hermite collocation method","authors":"A. Kaplan, Mulla Veli Ablay","doi":"10.4310/amsa.2023.v8.n1.a5","DOIUrl":"https://doi.org/10.4310/amsa.2023.v8.n1.a5","url":null,"abstract":"","PeriodicalId":42896,"journal":{"name":"Annals of Mathematical Sciences and Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70392898","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 : 2023-01-01DOI: 10.4310/amsa.2023.v8.n2.a7
Bing Tan, X. Qin
{"title":"An alternated inertial algorithm with weak and linear convergence for solving monotone inclusions","authors":"Bing Tan, X. Qin","doi":"10.4310/amsa.2023.v8.n2.a7","DOIUrl":"https://doi.org/10.4310/amsa.2023.v8.n2.a7","url":null,"abstract":"","PeriodicalId":42896,"journal":{"name":"Annals of Mathematical Sciences and Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70392613","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 : 2023-01-01DOI: 10.4310/amsa.2023.v8.n1.a6
Z. Anwar, Z. Ali, M. Faizan, M. A. Khan
{"title":"A note on moments of order statistics from the Pareto–Weibull distribution","authors":"Z. Anwar, Z. Ali, M. Faizan, M. A. Khan","doi":"10.4310/amsa.2023.v8.n1.a6","DOIUrl":"https://doi.org/10.4310/amsa.2023.v8.n1.a6","url":null,"abstract":"","PeriodicalId":42896,"journal":{"name":"Annals of Mathematical Sciences and Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70392916","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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