Strong and ∆-convergence for a two-step iteration process utilizing asymptotically nonexpansive and total asymptotically nonexpansive noneslf mappings in the CAT(0) spaces have been studied. As well, several strong convergence theorems under semi-compact and condition (M) have been proved. Our results improve and extend numerous familiar results from the existing literature.

This research deals with the concept of space in the theatrical performance and how the director works between two different spaces, the closed space and the open space. The question was how to use space according to the director's vision in the presentation. The problem of the research was whether the director of the Iraqi filmmaker could see the variable in the architectural space Or the place or space within the exhibition between open and closed, through the formation of the vision of the external components of intellectual and aesthetic and aesthetic, and impact on the relationship between the actor and the recipient to produce a new aesthetic space, and then the purpose of research and importance and limits and terminology The seco

In the present work, asphaltenes and resins separated from emulsion samples collected from two Iraqi oil wells, Nafut Kana (Nk) and Basrah were used to study the emulsion stability. The effect of oil resins to asphaltene (R/A) ratio, pH of the aqueous phase, addition of paraffinic solvent (n-heptane), aromatic solvent (toluene), and blend of both (heptol) in various proportions on the stability of emulsions had been investigated. The conditions of experiments were specified as an agitation speed of 1000 rpm for 30 minutes, heating at 50 °C, and water content of 30%.  The results showed that as the R/A ratio increases, the emulsion will be unstable and the amount of water separated from emulsion increases. It was noticed that the em

     The linear instability and nonlinear stability analyses are performed for the model of bidispersive local thermal non-equilibrium flow. The effect of local thermal non-equilibrium on the onset of convection in a bidispersive porous medium of Darcy type is investigated.  The temperatures in the macropores and micropores are allowed to be different. The effects of various interaction parameters on the stability of the system are discussed. In particular, the effects of the porosity modified conductivity ratio parameters,  and , with the int

     Fractional calculus has paid much attention in recent years, because it plays an essential role in many fields of science and  engineering, where the study of stability theory of fractional differential equations emerges to be very important. In this paper, the stability of fractional order ordinary differential equations will be studied and introduced the backstepping method. The Lyapunov function  is easily found by this method. This method also gives a guarantee of stable solutions for the fractional order differential equations. Furthermore it gives asymptotically stable.

Nonlinear differential equation stability is a very important feature of applied mathematics, as it has a wide variety of applications in both practical and physical life problems. The major object of the manuscript is to discuss and apply several techniques using modify the Krasovskii's method and the modify variable gradient method which are used to check the stability for some kinds of linear or nonlinear differential equations. Lyapunov function is constructed using the variable gradient method and Krasovskii’s method to estimate the stability of nonlinear systems. If the function of Lyapunov is positive, it implies that the nonlinear system is asymptotically stable. For the nonlinear systems, stability is still difficult even though

In this work, samples of Cd2Si1-xGexO4 prepared by powder technology for (x = 0, 0.3, 0.6) were studied. The effect of (Ge) additives at different ratio of Ge (x=0, 0.3, 0.6) on the behavior of dielectric constant, dielectric loss and a,c conductivity were measured as a function of temperature at a selected frequencies (0.01 – 10) MHz in the temperature range 298 K to 473 K. The dielectric constant and dielectric loss obtained different behavior with the additives of (Ge). The activation energy for the electrical conduction process was studied.

Lithium–Manganese ferrites having the chemical formula (Li0.5-0.5x Mnx Fe2.5-0.5x O4), (0 ≤ x ≤ 1) were prepared by double sintering powder processing. The density of the ferrite increased with Mn content while the porosity was noticed to decrease. The dielectric constant was found to increase at high frequencies more rapidly than the low ones. The dielectric constant found to decrease with Mn content. The decrease in loss factor with frequency agreed with Deby’s type relaxation process. A maximum of dielectric loss factor was observed when the hopping frequency is equal to the external electric field frequency. Manganese substitution reduced the dielectric loss in ferrite. The variation of tanδ with frequency shows a similar na

     Charge extraction layers play a crucial role in developing the performance of the inverted organic solar cells. Using a transparent metal oxide with appropriate work function to the photoactive layer can significantly decrease interface recombination and enhance charge transport mechanism. Therefore, electron selective films that consist of aluminium-doped titanium dioxide (TiO₂:Al) with different concentrations of Al (0.4, 0.8, and 1.2)wt %  were prepared using sol-gel technique. The inverted organic solar cells PCPDTBT: PCBM with Al doped TiO2 as electron extraction layer were fabricated. It is well known that Al doping concentration potentially affects the physical characteristics of the TiO₂ by control