In this article, an implementation of an efficient numerical method for solving the system of coupled non-linear fractional (Caputo sense) dynamical model of marriage (FDMM) is introduced. The proposed system describes the dynamics of love affair between couples. The method is based on the spectral collocation method using Legendre polynomials. The proposed method reduces FDMM to a system of algebraic equations, which solved using Newton iteration method. Special attention is given to study the convergence analysis and deduce an error upper bound of the resulting approximate solution. Numerical simulation is given to show the validity and the accuracy of the proposed method. 

The objective of this paper is to link the second phase with the third phase of the man-made river project at the connecting point near the SEDADA area. The flow rate in the second phase of the project will increase from 1.666 million cubic meters of water per day to 2.646 million cubic meters of water per day, by increasing 0.98 million cubic meters of water from the first phase through the third phase. It was necessary to study the effect of this increase in the flow rate and how to obtain the optimum way to transfer this quantity of water in terms of hydraulic and specifically the effect of change in pressure and pipe diameters. Therefore, the options studied which were proposed, namely the construction of the ALKHOMS pumping station, the linear pipeline, and the independent pipe line. The analysis is carrying by applying COLEBROOK-WHITE equation with using excel program to evaluate the hydraulic gradient at each point of study along the pipe line. The Optimum flow rate and pipe diameters was found are 30.625 m3 / sec and (3.4m-3.8m) respectively, which allows the water flow from the point of connection to the TAMALLAH  (RS) with natural flow.

In this paper we establish the existence of integrable solution of boundary value problems of (mixed type) Fredholm - volterra functional integro-differential equations  with nonlocal boundary conditions.

In this paper we define the Weyl algebra by two ways, and we study some theorems related to this algebra. We also study it widely as a ring of differential operators.

In this study, the cellular viability and function of immortalized human cervical and dermal cells are monitored and compared in conventional 2D and two commercial 3D membranes, Collagen and Geltrex, of varying working concentration and volume. Viability was monitored with the aid of the Alamar Blue assay, cellular morphology was monitored with confocal microscopy, and cell cycle studies and cell death mechanism studies were performed with flow cytometry. The viability studies showed apparent differences between the 2D and 3D culture systems, the differences attributed in part to the physical transition from 2D to 3D environment causing alterations to effective resazurin concentration, uptake and conversion rates, which was dependent on exposure time, but also due to the effect of the membrane itself on cellular function. These effects were verified by flow cytometry, in which no significant differences in viable cell numbers between 2D and 3D systems were observed after 24 h culture. The results showed the observed effect was different after shorter exposure periods, was also dependent on working concentration of the 3D system and could be mediated by altering the culture vessel size. Cell cycle analysis revealed cellular function could be altered by growth on the 3D substrates and the alterations were noted to be dependent on 3D membrane concentration. The use of 3D culture matrices has been widely interpreted to result in “improved viability levels” or “reduced” toxicity or cellular “resistance” compared to cells cultured on traditional 2D systems. The results of this study show that cellular health and viability levels are not altered by culture in 3D environments, but their normal cycle can be altered as indicated in the cell cycle studies performed and such variations must be accounted for in studies employing 3D membranes for in vitro cellular screening.

Bacterial infections are one of the most dangerous infections that threaten the existence and continuity of life.

Despite the discovery and manufacturing of effective antibiotics to tackle these menaces, bacteria have developed

resistance against such treatments and transformed into new mutant resistant strains. Bacteriophages, or phages, are

regarded as effective alternative antibacterial agents. Recently, scientists have been taking a closer look at the variety of

different phages that attack bacteria. This review primarily focuses on the potential of phage therapy as an alternative

treatment to overcome a wide spectrum of resistant bacterial infections, as well as current phage therapy advancement. It

also proposes the idea of engineering “broad-spectrum phage” to overcome a wide range of resistant bacterial infections,

and its advantages over antibiotics, individual phage, and phage cocktails.

Mathematical modelling of real-life problems usually results in functional equations, like ordinary or partial differential equations, integral and integro- differential equations, stochastic equations. Many mathematical formulation of physical phenomena contain integro-differential equations, these equations arises in many fields like fluid dynamics, biological models and chemical kinetics integro-differential equations are usually difficult to solve analytically so it is required to obtain an efficient approximate solution.