This paper aims to explore the metallic structure J2=pJ+qI, where p and q are natural numbers, us... more This paper aims to explore the metallic structure J2=pJ+qI, where p and q are natural numbers, using complete and horizontal lifts on the tangent bundle TM over almost quadratic ϕ-structures (briefly, (ϕ,ξ,η)). Tensor fields F˜ and F* are defined on TM, and it is shown that they are metallic structures over (ϕ,ξ,η). Next, the fundamental 2-form Ω and its derivative dΩ, with the help of complete lift on TM over (ϕ,ξ,η), are evaluated. Furthermore, the integrability conditions and expressions of the Lie derivative of metallic structures F˜ and F* are determined using complete and horizontal lifts on TM over (ϕ,ξ,η), respectively. Finally, we prove the existence of almost quadratic ϕ-structures on TM with non-trivial examples.
The computational analysis of the second-order micropolar stagnation point flow of nanofluid over... more The computational analysis of the second-order micropolar stagnation point flow of nanofluid over an exponentially permeable stretching sheet is considered. The freestream velocity with the thermal slip effects is taken into account in this analysis. This model is developed on the basis of flow assumptions and reduced into partial differential equations before applying the boundary layer approximations. The governing equations as a mathematical model are simplified with the help of suitable transformations. The differential system is further solved by using the bvp4c. Both graphs and tables are used to report observations. The skin friction and Nusselt number are reported for both weak and strong concentrations. The magnitude of skin friction is noticed greater for strong concentration in comparison with weak concentration. Subject to couple stress, the values of skin friction are relatively high for the case of weak concentration in comparison with strong concentration. Micropolar profile admit the direct relation toward micropolar parameter and micro-gyration parameter. Both Sherwood number and Nusselt number admits higher values for strong concentration as compared to weak concentration.
The computational analysis of the second-order micropolar stagnation point flow of nanofluid over... more The computational analysis of the second-order micropolar stagnation point flow of nanofluid over an exponentially permeable stretching sheet is considered. The freestream velocity with the thermal slip effects is taken into account in this analysis. This model is developed on the basis of flow assumptions and reduced into partial differential equations before applying the boundary layer approximations. The governing equations as a mathematical model are simplified with the help of suitable transformations. The differential system is further solved by using the bvp4c. Both graphs and tables are used to report observations. The skin friction and Nusselt number are reported for both weak and strong concentrations. The magnitude of skin friction is noticed greater for strong concentration in comparison with weak concentration. Subject to couple stress, the values of skin friction are relatively high for the case of weak concentration in comparison with strong concentration. Micropolar ...
Let (M; g) be an n-dimensional compact and connected Riemannian manifold of constant scalar curva... more Let (M; g) be an n-dimensional compact and connected Riemannian manifold of constant scalar curvature. If the sectional curvatures of M are bounded below by a constant > 0, and the Ricci curvature satis es Ric (n 1) , 1, then it is shown that either M is isometric to the n-sphere S n () or else each nonzero eigenvalue of the Laplacian acting on the smooth functions of M satis es the following: 2 + 3n (2) + 2n 2 (1 + (n 1)) > 0
This paper aims to explore the metallic structure J2=pJ+qI, where p and q are natural numbers, us... more This paper aims to explore the metallic structure J2=pJ+qI, where p and q are natural numbers, using complete and horizontal lifts on the tangent bundle TM over almost quadratic ϕ-structures (briefly, (ϕ,ξ,η)). Tensor fields F˜ and F* are defined on TM, and it is shown that they are metallic structures over (ϕ,ξ,η). Next, the fundamental 2-form Ω and its derivative dΩ, with the help of complete lift on TM over (ϕ,ξ,η), are evaluated. Furthermore, the integrability conditions and expressions of the Lie derivative of metallic structures F˜ and F* are determined using complete and horizontal lifts on TM over (ϕ,ξ,η), respectively. Finally, we prove the existence of almost quadratic ϕ-structures on TM with non-trivial examples.
The computational analysis of the second-order micropolar stagnation point flow of nanofluid over... more The computational analysis of the second-order micropolar stagnation point flow of nanofluid over an exponentially permeable stretching sheet is considered. The freestream velocity with the thermal slip effects is taken into account in this analysis. This model is developed on the basis of flow assumptions and reduced into partial differential equations before applying the boundary layer approximations. The governing equations as a mathematical model are simplified with the help of suitable transformations. The differential system is further solved by using the bvp4c. Both graphs and tables are used to report observations. The skin friction and Nusselt number are reported for both weak and strong concentrations. The magnitude of skin friction is noticed greater for strong concentration in comparison with weak concentration. Subject to couple stress, the values of skin friction are relatively high for the case of weak concentration in comparison with strong concentration. Micropolar profile admit the direct relation toward micropolar parameter and micro-gyration parameter. Both Sherwood number and Nusselt number admits higher values for strong concentration as compared to weak concentration.
The computational analysis of the second-order micropolar stagnation point flow of nanofluid over... more The computational analysis of the second-order micropolar stagnation point flow of nanofluid over an exponentially permeable stretching sheet is considered. The freestream velocity with the thermal slip effects is taken into account in this analysis. This model is developed on the basis of flow assumptions and reduced into partial differential equations before applying the boundary layer approximations. The governing equations as a mathematical model are simplified with the help of suitable transformations. The differential system is further solved by using the bvp4c. Both graphs and tables are used to report observations. The skin friction and Nusselt number are reported for both weak and strong concentrations. The magnitude of skin friction is noticed greater for strong concentration in comparison with weak concentration. Subject to couple stress, the values of skin friction are relatively high for the case of weak concentration in comparison with strong concentration. Micropolar ...
Let (M; g) be an n-dimensional compact and connected Riemannian manifold of constant scalar curva... more Let (M; g) be an n-dimensional compact and connected Riemannian manifold of constant scalar curvature. If the sectional curvatures of M are bounded below by a constant > 0, and the Ricci curvature satis es Ric (n 1) , 1, then it is shown that either M is isometric to the n-sphere S n () or else each nonzero eigenvalue of the Laplacian acting on the smooth functions of M satis es the following: 2 + 3n (2) + 2n 2 (1 + (n 1)) > 0
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Papers by Afifah Al-Eid