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"Salama, Mohammad"
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On Numerical Simulations of Variable-Order Fractional Cable Equation Arising in Neuronal Dynamics
In recent years, various complex systems and real-world phenomena have been shown to include memory and hereditary properties that change with respect to time, space, or other variables. Consequently, fractional partial differential equations containing variable-order fractional operators have been extensively resorted for modeling such phenomena accurately. In this paper, we consider the two-dimensional fractional cable equation with the Caputo variable-order fractional derivative in the time direction, which is preferable for describing neuronal dynamics in biological systems. A point-wise scheme, namely, the Crank–Nicolson finite difference method, along with a group-wise scheme referred to as the explicit decoupled group method are proposed to solve the problem under consideration. The stability and convergence analyses of the numerical schemes are provided with complete details. To demonstrate the validity of the proposed methods, numerical simulations with results represented in tabular and graphical forms are given. A quantitative analysis based on the CPU timing, iteration counting, and maximum absolute error indicates that the explicit decoupled group method is more efficient than the Crank–Nicolson finite difference scheme for solving the variable-order fractional equation.
Journal Article
Islam and the culture of modern Egypt from the monarchy to the republic
Telling a new story of modern Egypt, Mohammad Salama uses textual and cinematic sources to construct a clear and accessible narrative of the dynamics of Islam and culture in the first half of the twentieth century. The conflict between tradition and secular values in modern Egypt is shown in a stimulating and challenging new light as Salama bridges analysis of nationalism and its connection to Islamism, and outlines the effects of secular education versus traditional Islamic teaching on varied elements of Egyptian society. These include cultural production, politics, economic, identity, and gender relations. All of this helps to discern the harbingers that led to Egypt's social transition from the monarchy to the republic and opens the possibility of Islam as an inspiring and inspirational force. This illuminating, provocative and informative study will be of use to anyone interested in the period, whether general readers, students, or researchers.
Book
A new implicit high-order iterative scheme for the numerical simulation of the two-dimensional time fractional Cable equation
In this article, we developed a new higher-order implicit finite difference iterative scheme (FDIS) for the solution of the two dimension (2-D) time fractional Cable equation (FCE). In the new proposed FDIS, the time fractional and space derivatives are discretized using the Caputo fractional derivative and fourth-order implicit scheme, respectively. Moreover, the proposed scheme theoretical analysis (convergence and stability) is also discussed using the Fourier analysis method. Finally, some numerical test problems are presented to show the effectiveness of the proposed method.
Journal Article
Impact of Bone Morphogenetic Protein 7 and Prostaglandin receptors on osteoblast healing and organization of collagen
This study seeks to investigate the impact of co-administering either a Prostaglandin EP2 receptor agonist or an EP1 receptor antagonist alone with a low dose BMP7 on in vitro healing process, collagen content and maturation of human osteoblasts.
Human osteoblast cells were used in this study. These cells were cultured and subjected to different concentrations of Prostaglandin EP2 receptor agonist, EP1 receptor antagonist, BMP7, Control (Ct) (Vehicle alone), and various combinations treatments. Cell viability at 24, 48 and 72 hours (h) was evaluated using the XTT assay. A wound healing assay was conducted to observe the migration ability of human osteoblast cells. Additionally, Sirius red staining and Fourier-Transform Infrared Spectroscopy Imaging (FT-IR) was employed to analyze various parameters, including total protein concentration, collagen production, mature collagen concentration, and mineral content.
The combination of low dose BMP7 and Prostaglandin EP2 receptor agonist resulted to the lowest cell viability when compared to both the Ct and individual treatments. In contrast, the Prostaglandin EP1 receptor antagonist alone showed the highest cellular viability at 72 h. In the wound healing assay, the combined treatment of low dose BMP7 with the Prostaglandin EP2 receptor agonist and EP1 receptor antagonist showed a decrease in human osteoblast healing after 24 h. Analysis of FT-IR data indicated a reduction in total protein content, collagen maturity, collagen concentration and mineral content in combination treatment compared to the single or Ct treatments.
The combination of a Prostaglandin EP2 receptor agonist or an EP1 receptor antagonist when combined with low dose BMP7 significantly hinders both human osteoblast healing and collagen maturity/concentration in comparison to low dose BMP7 treatment alone.
Journal Article
Efficient hybrid group iterative methods in the solution of two-dimensional time fractional cable equation
In this paper, the development of new hybrid group iterative methods for the numerical solution of a two-dimensional time-fractional cable equation is presented. We use Laplace transform method to approximate the time fractional derivative which reduces the problem into an approximating partial differential equation. The obtained partial differential equation is solved by four-point group iterative methods derived from two implicit finite difference schemes. Matrix norm analysis together with mathematical induction are utilized to investigate the stability and convergence properties. A comparative study with the recently developed hybrid standard point (HSP) iterative method accompanied by their computational cost analysis are also given. Numerical experiments are conducted to demonstrate the superiority of the proposed hybrid group iterative methods over the HSP iterative method in terms of the number of iterations, computational cost as well as the CPU times.
Journal Article
Computationally Efficient Hybrid Method for the Numerical Solution of the 2D Time Fractional Advection-Diffusion Equation
In this paper, a hybrid method based on the Laplace transform and implicit finite difference scheme is applied to obtain the numerical solution of the two-dimensional time fractional advection-diffusion equation (2D-TFADE). Some of the major limitations in computing the numerical solution for fractional differential equations (FDEs) in multi-dimensional space are the huge computational cost and storage requirement, which are O(N^2) cost and O(MN) storage, N and M are the total number of time levels and space grid points, respectively. The proposed method reduced the computational complexity efficiently as it requires only O(N) computational cost and O(M) storage with reasonable accuracy when numerically solving the TFADE. The method’s stability and convergence are also investigated. The Results of numerical experiments of the proposed method are obtained and found to compare well with the results of existing standard finite difference scheme.
Journal Article
Impact of Bone Morphogenetic Protein 7 and Prostaglandin receptors on osteoblast healing and organization of collagen
This study seeks to investigate the impact of co-administering either a Prostaglandin EP2 receptor agonist or an EP1 receptor antagonist alone with a low dose BMP7 on in vitro healing process, collagen content and maturation of human osteoblasts. Human osteoblast cells were used in this study. These cells were cultured and subjected to different concentrations of Prostaglandin EP2 receptor agonist, EP1 receptor antagonist, BMP7, Control (Ct) (Vehicle alone), and various combinations treatments. Cell viability at 24, 48 and 72 hours (h) was evaluated using the XTT assay. A wound healing assay was conducted to observe the migration ability of human osteoblast cells. Additionally, Sirius red staining and Fourier-Transform Infrared Spectroscopy Imaging (FT-IR) was employed to analyze various parameters, including total protein concentration, collagen production, mature collagen concentration, and mineral content. The combination of low dose BMP7 and Prostaglandin EP2 receptor agonist resulted to the lowest cell viability when compared to both the Ct and individual treatments. In contrast, the Prostaglandin EP1 receptor antagonist alone showed the highest cellular viability at 72 h. In the wound healing assay, the combined treatment of low dose BMP7 with the Prostaglandin EP2 receptor agonist and EP1 receptor antagonist showed a decrease in human osteoblast healing after 24 h. Analysis of FT-IR data indicated a reduction in total protein content, collagen maturity, collagen concentration and mineral content in combination treatment compared to the single or Ct treatments. The combination of a Prostaglandin EP2 receptor agonist or an EP1 receptor antagonist when combined with low dose BMP7 significantly hinders both human osteoblast healing and collagen maturity/concentration in comparison to low dose BMP7 treatment alone.
Journal Article
Impact of Bone Morphogenetic Protein 7 and Prostaglandin receptors on osteoblast healing and organization of collagen
This study seeks to investigate the impact of co-administering either a Prostaglandin EP2 receptor agonist or an EP1 receptor antagonist alone with a low dose BMP7 on in vitro healing process, collagen content and maturation of human osteoblasts. Human osteoblast cells were used in this study. These cells were cultured and subjected to different concentrations of Prostaglandin EP2 receptor agonist, EP1 receptor antagonist, BMP7, Control (Ct) (Vehicle alone), and various combinations treatments. Cell viability at 24, 48 and 72 hours (h) was evaluated using the XTT assay. A wound healing assay was conducted to observe the migration ability of human osteoblast cells. Additionally, Sirius red staining and Fourier-Transform Infrared Spectroscopy Imaging (FT-IR) was employed to analyze various parameters, including total protein concentration, collagen production, mature collagen concentration, and mineral content. The combination of low dose BMP7 and Prostaglandin EP2 receptor agonist resulted to the lowest cell viability when compared to both the Ct and individual treatments. In contrast, the Prostaglandin EP1 receptor antagonist alone showed the highest cellular viability at 72 h. In the wound healing assay, the combined treatment of low dose BMP7 with the Prostaglandin EP2 receptor agonist and EP1 receptor antagonist showed a decrease in human osteoblast healing after 24 h. Analysis of FT-IR data indicated a reduction in total protein content, collagen maturity, collagen concentration and mineral content in combination treatment compared to the single or Ct treatments. The combination of a Prostaglandin EP2 receptor agonist or an EP1 receptor antagonist when combined with low dose BMP7 significantly hinders both human osteoblast healing and collagen maturity/concentration in comparison to low dose BMP7 treatment alone.
Journal Article