Throughout this paper we introduce the notion of coextending module as a dual of the class of extending modules. Various properties of this class of modules are given, and some relationships between these modules and other related modules are introduced.

Abstract: In recent times, global attention has increasingly focused on the critical issue of environmental sustainability, owing to escalating environmental degradation exacerbated by the utilization of green spaces and technological innovation. This phenomenon necessitates thorough examination, prompting the present study to scrutinize the impact of various factors, namely green spaces, technological innovation, environmental taxes, renewable energy consumption (REC), inflation, and economic growth (EG), on environmental sustainability within the context of Iraq. Secondary data extracted from the World Development Indicators (WDI) spanning the period from 1991 to 2022 served as the foundation for this investigation. Methodologically, the

In the present paper, a simply* compact spaces was introduced it defined over simply*- open set previous knowledge and we study the relation between the simply* separation axioms and the compactness, in addition to introduce a new types of functions known as 𝛼𝑆 𝑀∗ _irresolte , 𝛼𝑆 𝑀∗ __𝑐𝑜𝑛𝑡𝑖𝑛𝑢𝑜𝑢𝑠 and 𝑅 𝑆 𝑀∗ _ continuous, which are defined between two topological spaces.

This study aims to Statement of the relationship between Total Quality Management philosophy and Organizational performance from the point of view of the internal customer. A comparison has been made between two companies, one of which applies the requirements of TQM well and the other does not apply these requirements as the (General Company for Electrical Industries/ Diyala) and (General Company for Electrical Industries/ Baghdad) to conduct the search, During the questionnaire prepared for this purpose and distributed to a sample of 30 employees in the General Company for Electric Industries/ Diyala and (20) employees of the General Company for Electrical Industries/ Baghdad. Their answers were analyzed using a simple correlation coef

Form the series of generalization of the topic of supra topology is the generalization of separation axioms . In this paper we have been introduced (S * - SS *) regular spaces . Most of the properties of both spaces have been investigated and reinforced with examples . In the last part we presented the notations of supra *- -space ( =0,1) and we studied their relationship with (S * - SS *) regular spaces.

Background: Radial neck fractures in children account for 5 to 10% of all elbow fractures in children. They are extra-articular fractures of the radius proximal to the bicipital tuberosity. The physis is typically involved as a Salter-Harris I or II pattern. Alternatively, the fracture sometimes is extraphyseal, through the metaphysis. In children there is considerable potential for remodeling after these fractures. Up to 30° of radial head tilt and up to 3 mm of transverse displacement are acceptable. Many modalities of treatment are available regarding Surgical &Non-Surgical treatments. Objectives: To evaluate the functional outcome after surgical percutaneous joystick reduction therapy of severely angulated radial neck fracture i

Background: Radial neck fractures in children account for 5 to 10% of all elbow fractures in children. They are extra-articular fractures of the radius proximal to the bicipital tuberosity. The physis is typically involved as a Salter-Harris I or II pattern. Alternatively, the fracture sometimes is extraphyseal, through the metaphysis. In children there is considerable potential for remodeling after these fractures. Up to 30° of radial head tilt and up to 3 mm of transverse displacement are acceptable. Many modalities of treatment are available regarding Surgical &Non-Surgical treatments. Objectives: To evaluate the functional outcome after surgical percutaneous joystick reduction therapy of severely angulated radial neck fracture i

The primary aim of this paper, is to introduce the rough probability from topological view. We used the Gm-topological spaces which result from the digraph on the stochastic approximation spaces to upper and lower distribution functions, the upper and lower mathematical expectations, the upper and lower variances, the upper and lower standard deviation and the upper and lower r th moment. Different levels for those concepts are introduced, also we introduced some results based upon those concepts.

In this paper, some basic notions and facts in the b-modular space similar to those in the modular spaces as a type of generalization are given.  For example, concepts of convergence, best approximate, uniformly convexity etc. And then, two results about relation between semi compactness and approximation are proved which are used to prove a theorem on the existence of best approximation for a semi-compact subset of b-modular space.

In this paper, we introduce an exponential of an operator defined on a Hilbert space H, and we study its properties and find some of properties of T inherited to exponential operator, so we study the spectrum of exponential operator e^T according to the operator T.