This work describes two efficient and useful methods for solving fractional pantograph delay equations (FPDEs) with initial and boundary conditions. These two methods depend mainly on orthogonal polynomials, which are the method of the operational matrix of fractional derivative that depends on Bernstein polynomials and the operational matrix of the fractional derivative with Shifted Legendre polynomials. The basic procedure of this method is to convert the pantograph delay equation to a system of linear equations and by using, the operational matrices we get rid of the integration and differentiation operations, which makes solving the problem easier. The concept of Caputo has been used to describe fractional derivatives. Finally, some

Hard water does not pose a threat to human health but may cause precipitation of soap or results stone in the boilers. These reactions are caused by the high concentrations of Ca and Mg. In the industry they are undesirable because of higher fuel consumption for industrial use .Electromagnetic polarization water treatment is a method which can be used for increasing the precipitation of Ca ²⁺ and CO₃ ^2- ions in hard water to form CaCO₃ which leads to decrease the water hardness is research has been conducted by changing the number of coil turns and voltage of the system. The spectroscopy electron microscope was used for imaging the produced crystals. Results of the investigation indicated that

Levofloxacin belongs to the fluoroquinolone family; it is a potent broad-spectrum bactericidal agent. The pharmacophore required for significant antibacterial activity is the C-3 carboxylic acid group and the 4-pyridine ring with the C-4 carbonyl group, into which binding to the DNA bases occur. In this work, we tried to show that by masking the carboxyl group through amide formation using certain amines to form levofloxacin carboxamides, an interesting activity is kept. Levofloxacin carboxamides on the C-3 group were prepared, followed by the formation of their copper complexes. The target compounds were characterized by FT-IR, elemental analysis. The antimicrobial activity of the target compounds was evaluated and showed satisfactory resu

generator the metal conductor is replaced by conducting gas plasma.

The current research aims to identify the level of digital skills of kindergarten teachers, identify the level of professional competence of kindergarten teachers, as well as to identify the relationship between digital skills and the professional competence of kindergarten teachers. The current research was determined by kindergarten teachers in the second Baghdad / Karkh Education Directorate for the academic year (2021-2022). The research sample consisted of (100) teachers chosen in a simple random way. To achieve the objectives of the research, the researcher developed a digital skills scale of (20) items and a scale of professional competence consisting of (22) items. The results revealed that kindergarten teachers have a high level

Hypothyroidism is the decrease in thyroid hormones production and thyroid gland function. Hashimoto’s thyroiditis is the most common cause of hypothyroidism with production of autoantibodies directed toward autoantigens thyroglobulin (Tg) and thyroid peroxidase (TPO). This study was carried out to determine and compare serum and salivary levels of thyroid antibodies (TPO-Ab and Tg- Ab) in hypothyroid patients (with and without periodontitis) and healthy control; as well as to estimate the possibility to evaluate and measured these antibodies in the saliva as measured in the serum. Serum and saliva samples were collected from sixty hypothyroid patients with age ranged (20-64) years (30 of patients were with periodontitis and 30 without per

Breast cancer (BC) is the most common malignant tumor in women and the leading cause of cancer deaths worldwide. This work was conducted to estimate the roles of oxidative stress, vitamin B12, homocysteine (HCY), and DNA methylation in BC disease progression. Sixty BC patients (age range 33–80 years) and 30 healthy controls were recruited for this study. Patients with BC were split to group 1 consisted of stage II BC women (low level), and group 2 consisted of patients in stages III and IV (high level). Malondialdehyde (MDA), glutathione peroxidase 3 (GPX3), HCY, and vitamin B12 levels in the study groups were measured. Also, the 5-methylcytosine (5mC) global DNA methylation levels were evaluated. The results showed a significant

Background: Periodontitis and type 2 diabetes mellitus are both considered as a chronic disease that affect many people and have an interrelationship in their pathogenesis. Objective: The aim is to evaluate the salivary levels of interleukin-17 (IL-17) and galectin-3 in patients with periodontitis and type-2 diabetes mellitus. Materials and Methods: The samples were gathered from 13 healthy (control group) and 75 patients split into 3 groups, 25 patients with type 2 diabetes mellitus and healthy periodontium (T2DM group), 25 patients with generalized periodontitis (P group), and 25 patients with generalized periodontitis and type 2 diabetes mellitus (P-T2DM group). Clinical periodontal parameters were documented. The concentration of IL-17