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.

Background: It has been established that several filling techniques can affect apical leakage, which is responsible for 59% of endodontic failures. The primary goal of endodontic therapy is to create a tight seal that aids in repairing the periapical tissues, prevents apical periodontitis, and shields against root canal infection. The study aims to compare the apical sealing ability of epoxy resin based sealer  (AH plus), which is an epoxy-resin-based root canal sealer, GuttaFlow 2, which is a silicone-based root canal sealer, GuttaFlow bioseal is a bioactive glass-based root canal sealer, TotalFill HiFlow bioceramic (BC) sealer is a silicate-based root canal sealer (bioceramic sealer) using a single cone techn

Concentrations of radon were measured in this study for twenty-four samples of soil distributed in six locations on the north part of Iraq. The radon concentrations in soil samples measured by using alpha-emitters registration that emits from Radon (222Rn) in (CR-39) track detector. The concentrations values were calculated by a comparison with standard samples. The results shows that the radon gas concentrations in Darbandikhan City varies from (16.60-34.04 Bq/m3), Halabja City (16.51-23.32 Bq/m3), Al Sulaimaniya City (17.61-32.25 Bq/m3), Koisnjaq City (22.04-35.65 Bq/m3), Shaqlaua City (21.10-29.10 Bq/m3) and Erbil City (22.30-34.63 Bq/m3). The average radon gas concentration in Al Sulaimaniya and Erbil governorate are (22.30 Bq/m3)

The effect of high energy radiation on the energy gap of compound semiconductor Silicon Carbide (SiC) are viewed. Emphasis is placed on those effects which can be interpreted in terms of energy levels. The goal is to develop semiconductors operating at high temperature with low energy gaps by induced permanent damage in SiC irradiated by gamma source. TEACO2 laser used for producing SiC thin films. Spectrophotometer lambda - UV, Visible instrument is used to determine energy gap (Eg). Co-60, Cs-137, and Sr-90 are used to irradiate SiC samples for different time of irradiation. Possible interpretation of the changing in Eg values as the time of irradiation change is discussed

Rutting is mainly referring to pavement permanent deformation, it is a major problem for flexible pavement and it is a complicated process and highly observed along with many segments of asphalt pavement in Iraq. The occurrence of this defect is related to several variables such as elevated temperatures and high wheel loads. Studying effective methods to reduce rutting distress is of great significance for providing a safe and along-life road. The asphalt mixture used to be modified by adding different types of additives. The addition of additives typically excesses stiffness, improves temperature susceptibility, and reduces moisture sensitivity. For this work, steel fibres have been used for modifying asphalt mixture as they incorp

In this paper activated carbon adsorbents produced from waste tires by chemical activation methods and application of microwave assisted KOH activation. The influence of radiation time, radiation power, and impregnation ratio on the yield and oil removal which is one of the major environmental issues nowadays and considered persistent environmental contaminants and many of them are suspected of being carcinogenic. Based on Box-Wilson central composite design, polynomial models were developed to correlate the process variables to the two responses. From the analysis of variance the significant variables on each response were identified.  Optimum conditions of 4 min radiation time, 700 W radiation power and 0.5 g/g impregnation ratio

The optimal combination of aluminum quality, sufficient strength, high stress to weight ratio and clean finish make it a good choice in driveshafts fabrication. This study has been devoted to experimentally investigate the effect of applying laser shock peening (LSP) on the fatigue performance for 6061-T6 aluminum alloy rotary shafts. Q-switched pulsed Nd:YAG laser was used with operating parameters of 500 mJ and 600 mJ pulse energies, 12 ns pulse duration and 10 Hz pulse repetition rate. The LSP is applied at the waist of the prepared samples for the cyclic fatigue test. The results show that applying 500 mJ pulse energy yields a noticeable effect on enhancing the fatigue strength by increasing the required number of cycles to fracture the

In this work, plasma parameters such as, the electron temperature )Te(, electron density ne, plasma frequency )fp(, Debye length )λD(
and Debye number )ND), have been studied using optical emission spectroscopy technique. The spectrum of plasma with different values of energy, Pb doped CuO at different percentage (X=0.6, 0.7, 0.8) were recorded. The spectroscopic study for these mixing under vacuum with pressure down to P=2.5×10-2 mbar. The results of electron temperature for X=0.6 range (1.072-1.166) eV, for X=0.7 the Te range (1.024-0.855) eV and X=0.8 the Te is (1.033-0.921) eV. Optical properties of CuO:Pb thin films were determined through the optical transmission method using ultraviolet visible spectrophotometer within the ra