Aims to find out the (Extent of mathematics teachers' appreciation of the mathematical problem `multiple solutions) Research sample consisted of (100) mathematics teachers distributed on the General Directorates of Education in Baghdad (Rusafa 1/2/3) and (Karkh 1/2/ 3) There was two research approach which are: The first - two different answers of students to the same issue where teachers must assess each answer and explain which one the teacher will accept and why? The second - Different solutions of students' to the same issue, including wrong answers , Teachers should correct the answers and give them final grades (0-10). Descriptive and analytical Approch was used in this research methodology And zero hypotheses, which are as f

This paper aims to study the fractional differential systems arising in warm plasma, which exhibits traveling wave-type solutions. Time-fractional Korteweg-De Vries (KdV) and time-fractional Kawahara equations are used to analyze cold collision-free plasma, which exhibits magnet-acoustic waves and shock wave formation respectively. The decomposition method is used to solve the proposed equations. Also, the convergence and uniqueness of the obtained solution are discussed. To illuminate the effectiveness of the presented method, the solutions of these equations are obtained and compared with the exact solution. Furthermore, solutions are obtained for different values of time-fractional order and represented graphically.

      The research aims to study the corrosion of aluminum alloy(6061) in 0.6 mol. dm^-3 NaCl solution in base medium  was examined with out and with Gallic acid as environmentally – friendly corrosion inhibitor at temperature range (298-313)K. The inhibitive action of gallic acid on corrosion of aluminum alloy(6061)  in KOH solution was examined through electrochemical polarization method using potentiostatic technique and surface analysis by optical microscopy,  Polarization measurements indicate that the examined compound act as a mixed type inhibitor. Results appeared that the inhibition occurs through adsorption of the inhibitor molecules on the metal surface and it was obeyed

Room temperature ionic liquids show potential as an alternative to conventional organic membrane solvents mainly due to their properties of low vapour pressure, low volatility and they are often stable. In the present work, the technical feasibilities of room temperature ionic liquids as bulk liquid membranes for phenol removal were investigated experimentally. In this research several hydrophobic ionic liquids were synthesized at laboratory. These ionic liquids include (1-butyl-3-methylimidazolium bis (trifluoromethylsulfonyl) imide[Bmim][NTf₂], 1-Hexyl-3-methylimidazolium bis (trifluoromethylsulfonyl) imide[Hmim][NTf₂], 1-octyl-3-methylimidazolium bis (trifluoromethylsulfonyl)imide[Omim][NTf₂],1‐butyl

In this paper, Touchard polynomials (TPs) are presented for solving Linear Volterra integral equations of the second kind (LVIEs-2k) and the first kind (LVIEs-1k) besides, the singular kernel type of this equation. Illustrative examples show the efficiency of the presented method, and the approximate numerical (AN) solutions are compared with one another method in some examples. All calculations and graphs are performed by program MATLAB2018b.

The removal of chlorpyrifos pesticide from aqueous solutions was achieved by adsorption using low cost agricultural residue as adsorbent surface; barley husks. Several variables that affect the adsorption were studied including contact time, adsorbent weight, pH, ionic strength, particle size and temperature. The absorbance of the solution before and after adsorption was measured by using UV-Visible spectrophotometer. The equilibrium data was suitable with Langmuir model of adsorption and the linear regression coefficient R2 = 0.9785 at 37.5°C was used to knowledge the best fitting isotherm model. The general shape of the adsorption isotherm of chlorpyrifos on barley husks consistent with (H3-type) on the Giles classification. Several

The Wheat husk is one of the common wastes abundantly available in the Middle East countries especially in Iraq. The present study aimed to evaluate the Wheat husk as low cost material, eco-friendly adsorbents for the removal of the carcinogenic dye (Congo red dye) from wastewater by investigate the effect of, at different conditions such as, pH(3-10), amount of adsorbents (1-2.3gm/L),and particle size (125-1000) μm, initial Congo red dye concentration(10, 25 , 50 and 75mg/l)  by batch experiments. The results showed that the removal percentage of dye increased with increasing adsorbent dosage, and decreasing particle size. The maximum removal and uptake reached (91%) , 21.5mg/g, respectively for 25 initial concent

In the present study, a low cost adsorbent is developed from the naturally available sawdust
which is biodegradable. The removal capacity of chromium(VI) from the synthetically prepared
industrial effluent of electroplating and tannery industrial is obtained.
Two modes of operation are used, batch mode and fixed bed mode. In batch experiment the
effect of Sawdust dose (4- 24g/L) with constant initial chromium(VI) concentration of 50 mg/L and
constant particle size less than1.8 mm were studied.
Batch kinetics experiments showed that the adsorption rate of chromium(VI) ion by Sawdust
was rapid and reached equilibrium within 120 min. The three models (Freundlich, Langmuir and
Freundlich-Langmuir) were fitted to exper

   This paper applies the Modified Adomian Decomposition Method (MADM) for solving Integro-Differential Inequality, this method  is one of effective to construct analytic approximate solutions for linear and nonlinear integro-differential inequalities without solving many integrals and transformed or discretization. Several examples are presented, the analytic results show that this method is a promising and powerful for solving these problems.

ABSTRACT Pulmonary alveolar microlithiasis is rare infiltrative pulmonary disease characterized by intra-alveoli deposition of microliths. We present a familial case of an adult female with complaint of progressive shortness of breath on exertion. Chest radiograph showed innumerable tiny dense nodules, diffusely involving both lungs mainly the lower zones. High-resolution CT scan illustrated widespread intra-alveolar microliths, diffuse ground-glass attenuation areas and septal thickening predominantly in the basal regions. Chest radiograph is all that is needed for the diagnosis of this case but CT scan was done to demonstrate the extent and severity of this disease