In this work, the modified Lyapunov-Schmidt reduction is used to find a nonlinear Ritz approximation of Fredholm functional defined by the nonhomogeneous Camassa-Holm equation and Benjamin-Bona-Mahony. We introduced the modified Lyapunov-Schmidt reduction for nonhomogeneous problems when the dimension of the null space is equal to two.  The nonlinear Ritz approximation for the nonhomogeneous Camassa-Holm equation has been found as a function of codimension twenty-four.

Abstract: This study aims to investigate the backscattering electron coefficient for SixGe1-x/Si heterostructure sample as a function of primary electron beam energy (0.25-20 keV) and Ge concentration in the alloy. The results obtained have several characteristics that are as follows: the first one is that the intensity of the backscattered signal above the alloy is mainly related to the average atomic number of the SixGe1-x alloy. The second feature is that the backscattering electron coefficient line scan shows a constant value above each layer at low primary electron energies below 5 keV. However, at 5 keV and above, a peak and a dip appeared on the line scan above Si-Ge alloy and Si, respectively, close to the interfacing line

The purpose of this research paper is to present the second-order homogeneous complex differential equation   , where   , which is defined on the certain complex domain depends on solution behavior. In order to demonstrate  the relationship between the solution of the second-order of the complex differential equation and its coefficient of function, by studying the solution in certain cases: a meromorphic function, a coefficient of function, and if the solution is considered to be a transformation with another complex solution. In addition, the solution has been provided as a power series with some  applications.

In this work, radon concentrations in the polluted environment were measured within the Baghdad sample surface soil conservation, and this was done using a RAD-7 mobile detector. The work consists of four parts:
The first part includes calculating the latitude and longitude of each point of the study area using the Global Positioning System (GPS). The second part of which includes Determination of 222Rn gas concentrations in surface soil samples. In the northeast part of Baghdad, the highest concentration of radon was found in Al-
Shaab area (3.11 ±175.33 Bq / m3), while the lowest gas concentration in AL Gzeera area (6.67±73.00 Bq/ m3), In the northwest part of Baghdad, the highest concentratio

Background: Laser is a novel physical therapy technique used to treat various conditions, including wound healing, inhibition of bacterial growth, and postoperative wounds. High-power pulsed alexandrite laser therapy is one of the most prevalent forms of laser therapy, which is a noninvasive method for treating various pathological conditions, thereby enhancing functional capacities and quality of life. It is a modern medical and physiotherapeutic technology. Generally, the Alexandrite laser emits infrared light with a wavelength of 755 nm, allowing it to propagate and penetrate tissues. Objective: This study focused on the application of a high-power pulsed alexandrite laser in vitro to evaluate the effect of a pulsed alexandrite l

     In this paper, we built a mathematical model for convection and thermal radiation heat transfer of fluid flowing through a vertical channel with porous medium under effects of horizontal magnetic field (MF) at the channel. This model represents a 2-dimensional system of non-linear partial differential equations. Then, we solved this system numerically by finite difference methods using Alternating Direction Implicit (ADI) Scheme in two phases (steady state and unsteady state). Moreover, we found the distribution and behaviour of the heat temperature inside the channel and studied the effects of Brinkman number, Reynolds number, and Boltzmann number on the heat temperature behaviour. We solved the system by buildi

During the winter, in the industry region (Shaikh Omer) and by applying a passive radon detector (CR-39), lung cancer risk has been measured in twelve rooms of different workshops of two old factories in this site. The radon concentration is ranged from (123.345 Bq/m³) to (328.985 Bq/m³) with an average of (244.19±61.52 Bq/m³). Lung cancer risk ranged from 55.993 to 149.346 per million people and with an average of (110.855 per million people) which were lower than the recommended values (170-230 per million people), so there was no cancer risk on workers in these locations.