In this paper, we obtain a complete characterization for the norm and the minimum norm attainment sets of bounded linear operators on a real Banach spaces at a vector in the unit sphere, using approximate 𝜖-Birkhoff-James orthogonality techniques. As an application of the results, we obtained a useful characterization of
bounded linear operators on a real Banach spaces. Also, using approximate 𝜖-Birkhoff -James orthogonality proved that a Banach space is a reflexive if and only if for any closed hyperspace of , there exists a rank one linear operator such that , for some vectors in and such that 𝜖 .Mathematics subject classification (2010): 46B20, 46B04, 47L05.

In this paper, new concepts which are called: left derivations and generalized left derivations in nearrings have been defined. Furthermore, the commutativity of the 3-prime near-ring which involves some
algebraic identities on generalized left derivation has been studied.

The continuous growth in technology and technological devices has led to the development of machines to help ease various human-related activities. For instance, irrespective of the importance of information on the Steam platform, buyers or players still get little information related to the application. This is not encouraging despite the importance of information in this current globalization era. Therefore, it is necessary to develop an attractive and interactive application that allows users to ask questions and get answers, such as a chatbot, which can be implemented on Discord social media. Artificial Intelligence is a technique that allows machines to think and be able to make their own decisions. This research showed that the dis

Our aim in this paper is to study the relationships between min-cs modules and some other known generalizations of cs-modules such as ECS-modules, P-extending modules and n-extending modules. Also we introduce and study the relationships between direct sum of mic-cs modules and mc-injectivity.

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 pure relative to submodule T of M (Simply T-pure) if for each ideal A of R, N?AM=AN+T?(N?AM). In this paper, the properties of the following concepts were studied: Pure essential submodules relative to submodule T of M (Simply T-pure essential),Pure closed submodules relative to submodule T of M (Simply T-pure closed) and relative pure complement submodule relative to submodule T of M (Simply T-pure complement) and T-purely extending. We prove that; Let M be a T-purely extending module and let N be a T-pure submodule of M. If M has the T-PIP, then N is T-purely extending.

      Finding similarities in texts is important in many areas such as information retrieval, automated article scoring, and short answer categorization. Evaluating short answers is not an easy task due to differences in natural language. Methods for calculating the similarity between texts depend on semantic or grammatical aspects. This paper discusses a method for evaluating short answers using semantic networks to represent the typical (correct) answer and students' answers. The semantic network of nodes and relationships represents the text (answers). Moreover, grammatical aspects are found  by measuring the similarity of parts of speech between the answers. In addition, finding hierarchical relationships between nodes in netwo

The research team seeks to study the phenomena of random housing in Iraqi society in general and Baghdad city in particular by standing on the causes behind this phenomena and its relation with security situation in Baghdad. The researchers adopted a theoretical and practical framework. The main objective is to diagnose the risks caused by the escalation of slums in Baghdad city. 

We report a method of converting non-conductive plastic surfaces into conductive by plating either copper electroless or copper electroplating -carbon black containing bending Agent onto Perspex plastics . Various approaches have been studied in order to comparing properties of the plated copper for two methods such as scanning electron microscopy (SEM),thickness, roughness, porosity, tensile Strength and elongation. The results show that the surface of electroplating was uniform, compact, and continuous and it had an obvious metallic sheen, while the surface of plated copper for electroless for it had many pores. Also observed that the coating was composed of small cells. Thes

Praise be to God, Lord of the worlds, and prayers and peace be upon our master Muhammad and upon his family and companions.
       We see human societies differ from one society to another in organizing social life, and each according to the foundations and rules prepared by the main thing in the welfare and prosperity.
That is why we see eastern societies differ from western societies in many patterns and various ways of reaching that sophistication, until Islam came and gave the proper model in raising society at that time to the best and highest social levels, because it is based on heavenly rules and foundations and not status as in previous civilizations.
And when the Islamic community has

 The corrosion of metals is of great economic importance. Estimates show that the quarter of the iron and the steel produced is destroyed in this way. Rubber lining has been used for severe corrosion protection because NR and certain synthetic rubbers have a basic resistance to the very corrosive chemicals particularly acids. The present work includes producing ebonite from both natural and synthetic rubbers ; therefore, the following materials were chosen to produce ebonite rubber: a) Natural rubber (NR). b) Styrene butadiene rubber (SBR). c) Nitrile rubber (NBR). d) Neoprene rubber (CR) [WRT]. The best ebonite vulcanizates are obtained in the presence of 30 Pphr sulfur, and carbon black as reinforcing filler. The relation between