In this work, we give an identity that leads to establishing the operator . Also, we introduce the polynomials . In addition, we provide Operator proof for the generating function with its extension and the Rogers formula for . The generating function with its extension and the Rogers formula for the bivariate Rogers-Szegö polynomials  are deduced. The Rogers formula for  allows to obtain the inverse linearization formula for , which allows to deduce the inverse linearization formula for . A solution to a q-difference equation is introduced and the solution is expressed in terms of the operators . The q-difference method is used to recover an identity of the operator  and the generating function for the polynomials

The study the problem emerged in the inability of local companies to enter the field of active competition with other companies operating in the same economic sector due to the high cost of their products, hence, the companies that want to apply this technique can effectively compete in order to achieve those objectives.

  So this study focused on the goal of reducing the cost of products by reducing the cost product to a minimum , as the study was based in its hypothesis on the ability of companies to application this technique which in turn leads to increased profits under conditions of normal working and the power available and their potential in improving the quality of its products, as well as the need for full coordina

Background: University dental students perceived a higher level of stress prior to the final exam associated with raised salivary cortisol levels which could be considered as a useful noninvasive biomarker for measuring acute stress. Using a Helkimo anamnestic and clinical dysfunction scoring for temporomandibular disorders can give a better insight about the association of this marker and temporomandibular joint disorders. The aim of this study was to evaluation level of salivary cortisol in stressor students with temporomandibular disorder and the relation between this marker in relation to temporomandibular disorder severity. This might give a better understanding to the role of psychological stress as an etiological factor for developin

Background: During pregnancy many physiological, anatomical and biochemical changes take place that affect almost all body systems. In the oral pregnant women have serious changes such as more sever dental caries. This study was conducted to measure dental caries severity and selected salivary variables (salivary flow rate, PH and viscosity)and to find the relation of dental caries with these salivary variables. Subjects, materials and methods: The study group consisted of 60 pregnant women that were divided into three equal groups according to trimester (20 pregnant women in each trimester).They were selected randomly from the Maternal and Child Health Care Centers in Baghdad city, the age range was 20-25 years. In addition to 20 unmarried

Background: Nutrition can affect the development and integrity of the oral cavity as well as the progression of oral diseases such as dental caries which was the most predominant and wide spread not life threatening human diseases especially in developing countries as in Iraq. This study was conducted to assess the occurrence, prevalence and severity of dental caries condition and their relations to nutritional status among intermediate schools females in Al-Najaf city in Iraq. Materials and methods: This study was conducted among intermediate schools females aged 13, 14 and15 years old and the total sample consisted of 754 students. The assessment of nutritional status was performed using body mass index (BMI) following Centers for Diseas

In this research local wheat peel was used as an adsorbent surface for removal of Azure B (AB) dye from the aqueous solution. The adsorption process was performed at different experimental parameters, equilibrium time, temperature, ionic strength and solution pH. The isotherms of adsorption are of H-type as compared with Giles curves and the adsorption data were coincide with Freundlich equation. The adsorption kinetic data were analyzed using pseudo- first and second order kinetic models. The effect of temperature was studied and the amount of dye adsorbed was found to increase with the increasing of temperature from 25 to 50 oC. The values of thermodynamic functions like enthalpy and entropy have been estimated. The quantity of adso

Background: Rheumatoid arthritis is a chronic destructive inflammatory disease associated with destruction of joint connective tissues and bones, affecting 0.5%–1% of the population worldwide reporting higher prevalence of periodontitis among rheumatoid arthritis patients. The purpose of this study is to estimate level of salivary C-reactive protein in relation to the occurrence and severity of the periodontal disease and other oral parameters among group of patients with rheumatoid arthritis Material and methods: Fifty women patients with rheumatoid arthritis; twenty five on Methotrexate treatment and twenty five on combination treatment of Methotrexate and Etanercept selected as study groups with an age range (30-40) years old and

This study synthesized zeolite 4A, and hierarchical composite structure consisting of zeolite 4A- carbon were successfully prepared. Hydrothermal method was used to grow a layer of zeolite 4A over porous carbon surfaces to enhance mass transfer and increase surface area of zeolite. The products then were used to remove radioactive cesium¹³⁷Cs from liquid wastewater. Iraqi dates leaves midribs (DM) were used as locally available agricultural waste to prepare low- cost porous carbon, using carbonization method in tubular furnace at 900C for two hours. Hierarchical porous structures including zeolite are prepared by mechanically activating the carbon surface via Ultrasonicating nanoparticles suspension of ground zeolite type 4A.F

     The electrical resistivity method is one of the geophysical methods for detecting weak subsurface zone. The 2D resistivity data were used to compare three electrode configurations, Wenner, Dipole-dipole, and Schlumberger, to detect weak subsurface zones along a profile south of Baghdad near the Bismayah pumping station. The results show many zones of low resistivity that may be weak zones. A dipole-dipole array is a large number of measurements and is more sensitive than others. The Wenner-Schlumberger array has a depth also higher than other arrays. Wenner array has higher signal strength than other arrays. Because it is more sensitive to horizontal and vertical structures, the dipole-dipole array is the optimum for mapping sub