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  studied  kinetics  of flotation   of  emulsified  paraffine  in  water  in  bubble  column  with  sodium .dodecylsulphate as a collector agent. The effects of oil drops and air bubble diameters on the flotation rate constant were studied. The removal rate for each oil drop size was first order with respect to oil drop concentration. An experimental procedure permitting determination of the first order rate constants for  removal due to bubble/drop interaction was developed, decreasing bubble diameter by adding NaCl and increasing oil drop diameter increased the rate constants. A comparison between the experimental and theoretical rate constants showed

Optimum perforation location selection is an important study to improve well production and hence in the reservoir development process, especially for unconventional high-pressure formations such as the formations under study. Reservoir geomechanics is one of the key factors to find optimal perforation location. This study aims to detect optimum perforation location by investigating the changes in geomechanical properties and wellbore stress for high-pressure formations and studying the difference in different stress type behaviors between normal and abnormal formations. The calculations are achieved by building one-dimensional mechanical earth model using the data of four deep abnormal wells located in Southern Iraqi oil fields. The magni

A Genetic Algorithm optimization model is used in this study to find the optimum flow values of the Tigris river branches near Ammara city, which their water is to be used for central marshes restoration after mixing in Maissan River. These tributaries are Al-Areed, AlBittera and Al-Majar Al-Kabeer Rivers. The aim of this model is to enhance the water quality in Maissan River, hence provide acceptable water quality for marsh restoration. The model is applied for different water quality change scenarios ,i.e. , 10%,20% increase in EC,TDS and BOD. The model output are the optimum flow values for the three rivers while, the input data are monthly flows(1994-2011),monthly water requirements and water quality parameters (EC, TDS, BOD, DO and

In this paper we proposes the philosophy of the Darwinian selection as synthesis method called Genetic algorithm ( GA ), and include new merit function with simple form then its uses in other works for designing one of the kinds of multilayer optical filters called high reflection mirror. Here we intend to investigate solutions for many practical problems. This work appears designed high reflection mirror that have good performance with reduction the number of layers, which can enable one to controlling the errors effect of the thickness layers on the final product, where in this work we can yield such a solution in a very shorter time by controlling the length of the chromosome and optimal genetic operators . Res

Due to the need for controlling and regulating of feed pellet. Pellet that is imported or locally manufactured is accompanied by cracking and crumbling percentage that occur during transporting and distributing to animals, using conveyors and mechanical feeders. This study aimed to determine the effect of particle size and die holes diameter in the machine on broiler feed pellets quality in pellet durability, pellet direct measurement, pellet expansion, and pellet length. Three particle size 2, 4, and 6 mm, and three diameters of die holes in the machine 3, 4, and 5 mm, have been used. The results showed that changing the particle size from 2 to 4 then to 6 mm led to a significant decrease in pellet durability and pellet lengths, pe

The present work is concerned with the finding of the optimum conditions for biochemical wastewater treatment for a local tannery. The water samples were taken from outline areas (the wastewater of the chrome and vegetable tannery) in equal volumes and subjected to sedimentation, biological treatment, and chemical and natural sedimentation treatment.
The Box-Wilson method of experimental design was adopted to find useful relationships between three operating variables that affect the treatment processes (temperature, aeration period and phosphate concentration) on the Biochemical Oxygen Demand (BOD5).
The experimental data collected by this method were successfully fitted to a second order polynomial mathematical model. The most fa

The effect of the magnetic abrasive finishing (MAF) method on the temperature rise (TR), and material removal rate (MRR) has been investigated in this paper. Sixteen runs were to determine the optimum temperature in the contact area (between the abrasive powder and surface of workpiece) and the MRR according to Taguchi orthogonal array (OA). Four variable technological parameters (cutting speed, finishing time, working gap, and the current in the inductor) with four levels for each parameter were used, the matrix is known as a L16 (4⁴) OA. The signal to noise ratio (S/N) ratio and analysis of the variance (ANOVA) were utilized to analyze the results using (MINITAB17) to find the optimum condition and identify the significant p