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.

The concerns about water contaminants affect most developing countries bypassing rivers over them. The issue is challenging to introduce water quality within the allowed limits for drinking, industrial and agricultural purposes. In the present study, physical-chemical parameters measurements of water samples taken from eleven stations were collected during six months in 2020 through flow path along the whole length of Tigris River inside AL Kut city (center of Wassit government) were investigated for six parameters are total hardness TH, hydrogen ion pH, biological oxygen demand BOD5, total dissolved solids TDS, nitrate NO3, and sulfate SO4. The water quality analysis results were compared with the maximum allowable limit concentrat

Enhancement of heat transfer in the tube heat exchanger is studied experimentally by using discrete twisted tapes. Three different positions were selected for inserting turbulators along tube section (horizontal position by α= 0⁰, inclined position by α= 45 ⁰ and vertical position by α= 90⁰). The space between turbulators was fixed by distributing 5 pieces of these turbulators with pitch ratio    PR = (0.44). Also, the factor of constant heat flux was applied as a boundary condition around the tube test section for all experiments of this investigation, while the flow rates were selected as a variable factor (Reynolds number values vary from 5000 to 15000). The results s

Background: Glass ionomers have good biocompatibility and the ability to adhere to both enamel and dentin. However, they have certain demerits, mainly low tensile and compressive strengths. Therefore, this study was done to assess consistency and compressive strength of glass ionomer reinforced by different amount of hydroxyapatite. Materials and Methods: In this study hydroxyapatite materials were added to glass ionomer cement at different ratios, 10%, 15%, 20%, 25% and 30% (by weight). The standard consistency test described in America dental association (ADA) specification No. 8 was used, so that all new base materials could be conveniently mixed and the results would be of comparable value and the compressive strength test described by

Cr2O3 thin films have been prepared by spray pyrolysis on a glass substrate. Absorbance and transmittance spectra were recorded in the wavelength range (300-900) nm before and after annealing. The effects of annealing temperature on absorption coefficient, refractive index, extinction coefficient, real and imaginary parts of dielectric constant and optical conductivity were expected. It was found that all these parameters increase as the annealing temperature increased to 550°C.

Nathaniel Hawthorne (1804-1864) has been widely known for his special interest in the female characters. In many of his novels, he narrates the conditions, values, and the institutions that surround and control the life of women, leading them to be victims. In “Rappaccini’s Daughter” (1844), the heroine, Beatrice is created to be victimized by her loved ones (her father and lover). This paper focuses on the term “victim,” it shows its aspects through the development of Beatrice’s character. The paper also studies a female character in the male-dominated society, to show the cruelty done to her, and how she is considered to be a second rate person, who is unable to live normally, or at least to save herself from dea

Brucella melitensis isolates were obtained from human infections , and milk which obtained from aborted sheep at Mosul city vicinity . One isolate from each source was used in carrying out this study. Brucella liquid culture was added to sheep milk at 2.5 % for treatments . To first treatment 2 % of yoghurt starter ( Lactobacillus delbrueckii subsp. bulgaricus and Streptococcus salivarius subsp. thermophilus ( 1: 1 ) ) . Second treatment was carried out without addition of yoghurt starter but the pH was lowered using lactic acid in pattern similar to first treatment . Third treatment was similar to the first treatment but contained buffer to alleviate the reduction in pH , which reduced to 6.1 in comparison to 4.9 of the first treatment .