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

The effect of air injection device on the performance of airlift pump used for water pumping has been studied numerically and experimentally. An airlift pump of dimensions 42mm diameter and 2200 mm length with conventional and modified air injection device was considered. A modification on conventional injection device (normal air-jacket type) was carried out by changing injection angle from 90  (for conventional) to 22.5  (for modified). Continuity and Navier-Stokes equations in turbulent regime with an appropriate two-phase flow model (VOF) and turbulent model (   ) in two dimensions axisymmetry flow were formulated and solved by using the known package FLUENT version (14.5). The numerical and experimental investiga

A load flow program is developed using MATLAB and based on the Newton–Raphson method,which shows very fast and efficient rate of convergence as well as computationally the proposed method is very efficient and it requires less computer memory through the use of sparsing method and other methods in programming to accelerate the run speed to be near the real time.
The designed program computes the voltage magnitudes and phase angles at each bus of the network under steady–state operating conditions. It also computes the power flow and power losses for all equipment, including transformers and transmission lines taking into consideration the effects of off–nominal, tap and phase shift transformers, generators, shunt capacitors, sh

In this study, a cholera model with asymptomatic carriers was examined. A Holling type-II functional response function was used to describe disease transmission. For analyzing the dynamical behavior of cholera disease, a fractional-order model was developed. First, the positivity and boundedness of the system's solutions were established. The local stability of the equilibrium points was also analyzed. Second, a Lyapunov function was used to construct the global asymptotic stability of the system for both endemic and disease-free equilibrium points. Finally, numerical simulations and sensitivity analysis were carried out using matlab software to demonstrate the accuracy and validate the obtained results.

In this research we study a variance component model, Which is the one of the most important models widely used in the analysis of the data, this model is one type of a multilevel models, and it is considered as linear models , there are three types of linear variance component models ,Fixed effect of linear variance component model, Random effect of linear variance component model and Mixed effect of linear variance component model . In this paper we will examine the model of mixed effect of linear variance component model with one –way random effect ,and the mixed model is a mixture of fixed effect and random effect in the same model, where it contains the parameter (μ) and treatment effect (τ_i ) which  has

Background: The vaginal microbial ecosystem stability preclude many other organisms but sometimes the vaginal micro biota is disturbed and this cause change in the normal

balance causing symptoms of vulvuvaginitis like abnormal or increased vaginal discharge, redness and itching.

Objective: To prove C. albicans presence in their vagina clinically and laboratory by culture of vaginal swab on two media.

Type of the study: This study is a case control study

Methods: This study is a case control study in which 100 clinically patient women admitted to maternity hospital in kalar city and khanaqin hospital during the pe