Let R be a commutative ring with identity 1 and M be a unitary left R-module. A submodule N of an R-module M is said to be approximately pure submodule of an R-module, if for each ideal I of R. The main purpose of this paper is to study the properties of the following concepts: approximately pure essentialsubmodules, approximately pure closedsubmodules and relative approximately pure complement submodules. We prove that: when an R-module M is an approximately purely extending modules and N be Ap-puresubmodulein M, if M has the Ap-pure intersection property then N is Ap purely extending.

Let R be an associative ring with identity and let M be a unitary left R–module. As a generalization of small submodule , we introduce Jacobson–small submodule (briefly J–small submodule ) . We state the main properties of J–small submodules and supplying examples and remarks for this concept . Several properties of these submodules are given . Also we introduce Jacobson–hollow modules ( briefly J–hollow ) . We give a characterization of J–hollow modules and gives conditions under which the direct sum of J–hollow modules is J–hollow . We define J–supplemented modules and some types of modules that are related to J–supplemented modules and int

In this paper, certain types of regularity of topological spaces have been highlighted, which fall within the study of generalizations of separation axioms. One of the important axioms of separation is what is called regularity, and the spaces that have this property are not few, and the most important of these spaces are Euclidean spaces. Therefore, limiting this important concept to topology is within a narrow framework, which necessitates the use of generalized open sets to obtain more good characteristics and preserve the properties achieved in general topology. Perhaps the reader will realize through the research that our generalization preserved most of the characteristics, the most important of which is the hereditary property. Two t

With the great development in the field of the Internet, the talk about the new media and its implications began, And its interactive services have made the future of media material sometimes participating in it and manufacturing it at other times,
the public is seeking information and choosing the appropriate ones, as well as exchanging messages with the sender after what the role of the receiver is just receiving information only.
This study aims to demonstrate the effects of using digital media in various forms and types to construct the value system of Iraqi society through the identification of the following aims:
Identify the most popular digital media for the Iraqi public in their daily lives on the Internet.
Identify

This research sheds light on one of the important and vital topics for the banking sectors (technical requirements for the application of economic intelligence) namely by (Hardware, equipment, communication networks, software, databases). And the dimensions of the strategic success of the banks represented by(Customer satisfaction, customer trust, quality of service, growth) In the three Iraqi private banks, namely(Assyria International Investment, Mansour Investment, International Development Investment and Finance). Its implementation is an urgent necessity in order to improve the quality of its banking services to win the satisfaction of its customers and their confidence and then grow to achieve stra

The multi-focus image fusion method can fuse more than one focused image to generate a single image with more accurate description. The purpose of image fusion is to generate one image by combining information from many source images of the same scene. In this paper, a multi-focus image fusion method is proposed with a hybrid pixel level obtained in the spatial and transform domains. The proposed method is implemented on multi-focus source images in YCbCr color space. As the first step two-level stationary wavelet transform was applied on the Y channel of two source images. The fused Y channel is implemented by using many fusion rule techniques. The Cb and Cr channels of the source images are fused using principal component analysis (PCA).

Aerial manipulation of objects has a number of advantages as it is not limited by the morphology of the terrain. One of the main problems of the aerial payload process is the lack of real-time prediction of the interaction between the gripper of the aerial robot and the payload. This paper introduces a digital twin (DT) approach based on impedance control of the aerial payload transmission process. The impedance control technique is implemented to develop the target impedance based on emerging the mass of the payload and the model of the gripper fingers. Tracking the position of the interactional point between the fingers of gripper and payload, inside the impedance control, is achieved using model predictive control (MPD) approach.

The performance of sewage pumps stations affected by many factors through its work time which produce undesired transportation efficiency. This paper is focus on the use of artificial neural network and multiple linear regression (MLR) models for prediction the major sewage pump station in Baghdad city. The data used in this work were obtained from Al-Habibia sewage pump station during specified records- three years in Al-Karkh district, Baghdad. Pumping capability of the stations was recognized by considering the influent input importance of discharge, total suspended solids (TSS) and biological oxygen demand (BOD).  In addition, the chemical oxygen demands (COD), pH and chloride (Cl). The proposed model performanc

In this paper, we give new results and proofs that include the notion of norm attainment set of bounded linear operators on a smooth Banach spaces and using these results to characterize a bounded linear operators on smooth Banach spaces that preserve of approximate - -orthogonality. Noting that this work takes brief sidetrack in terms of approximate - -orthogonality relations characterizations of a smooth Banach spaces.