In this paper, we introduce and study the notation of approximaitly quasi-primary submodules of a unitary left -module  over a commutative ring  with identity. This concept is a generalization of prime and primary submodules, where a proper submodule  of an -module  is called an approximaitly quasi-primary (for short App-qp) submodule of , if , for , , implies that either  or , for some . Many basic properties, examples and characterizations of this concept are introduced.

Let R be a commutative ring with identity and M be a unitary R- module. We shall say that M is a primary multiplication module if every primary submodule of M is a multiplication submodule of M. Some of the properties of this concept will be investigated. The main results of this paper are, for modules M and N, we have M N and HomR (M, N) are primary multiplications R-modules under certain assumptions.

Background: Since the periodontal disease Index of Ramfjord (Ramfjord index) can potentially shorten the examination time by almost half, many studies evaluated Ramfjord teeth in predicting full-mouth periodontal status of an adult population. The aim of this study was to evaluate the benefit of Ramfjord teeth in predicting the full-mouth clinical attachment level of an adult population in patients attending the college of dentistry- Baghdad University. Materials and methods: The study participants were 100 patients with age range from 30-60 years old which represent group zero. The patients were divided into three main groups according to the age of the patients. Group I and group II each of them composed of 30 patients while group III co

Abstract. Full-waveform airborne laser scanning data has shown its potential to enhance available segmentation and classification approaches through the additional information it can provide. However, this additional information is unable to directly provide a valid physical representation of surface features due to many variables affecting the backscattered energy during travel between the sensor and the target. Effectively, this delivers a mis-match between signals from overlapping flightlines. Therefore direct use of this information is not recommended without the adoption of a comprehensive radiometric calibration strategy that accounts for all these effects. This paper presents a practical and reliable radiometric calibration r

In this paper, a fusion of K models of full-rank weighted nonnegative tensor factor two-dimensional deconvolution (K-wNTF2D) is proposed to separate the acoustic sources that have been mixed in an underdetermined reverberant environment. The model is adapted in an unsupervised manner under the hybrid framework of the generalized expectation maximization and multiplicative update algorithms. The derivation of the algorithm and the development of proposed full-rank K-wNTF2D will be shown. The algorithm also encodes a set of variable sparsity parameters derived from Gibbs distribution into the K-wNTF2D model. This optimizes each sub-model in K-wNTF2D with the required sparsity to model the time-varying variances of the sources in the s

Dora petroleum refinery waste water is the one of the important source of pollution by priority pollutant aromatic compound discharged to Tigris river in Iraq. the station has waste water treatment unit contains many treatment subunits The most important sub units is :skimmer units ,physiochemical unit ,daf unit, biological unit. The aim of research project is to study the ability of unit to remove the priority pollutant aromatic compound and follow up these compounds in river to study ability of river to self removal. A solid phase extraction (SPE) followed by high performance liquid chromatography-ultra violet (HPLC-UV) technique is depicted for the quantitative estimation of benzidines and phenols. Experimental studies were performed to

Due to the deterioration of water quality within the last few years because of the increase of water consumption and the waste water production and disposal into the river The water quality in both surface and ground water resources was negatively affected .The concept of water quality index is used as a tool for water quality classification in Tigris River within Baghdad City .Twenty two parameters of pollution were selected to measure the water quality indices of Tigris river within Baghdad city .Those parameters were measured during (2000-2004)as average monthly values ,three water treatment plants were selected out of the eight water treatment plants that exist along the river.Al Kharkh water treatment plant to reflect the water quality

Most studies on deep beams have been made with reinforced concrete deep beams, only a few studies investigate the response of prestressed deep beams, while, to the best of our knowledge, there is not a study that investigates the response of full scale (T-section) prestressed deep beams with large web openings. An experimental and numerical study was conducted in order to investigate the shear strength of ordinary reinforced and partially prestressed full scale (T-section) deep beams that contain large web openings in order to investigate the prestressing existence effects on the deep beam responses and to better understand the effects of prestressing locations and opening depth to beam depth ratio on the deep beam performance and b