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.

  Let L be a commutative ring with identity and let W be a unitary left L- module. A submodule D of an L- module W is called  s- closed submodule denoted by  D ≤sc W, if D has   no  proper s- essential extension in W, that is , whenever D ≤ W such that D ≤se H≤ W, then D = H. In  this  paper,  we study  modules which satisfies  the ascending chain  conditions (ACC) and descending chain conditions (DCC) on this kind of submodules.

This article aims to cast a shadow over the history of mental health education and training in Iraq and a projection of Islamic scientific heritage in Baghdad during the seventh century. It also discloses the foundation of first teaching and training centers in psychiatry focusing on the marked contribution of the pioneer psychiatrists. Introduction. Up to our knowledge there is no elaborate published literature focusing on historical role of Iraq in mental health education and training and its current reality apart from scares data about mental health in Mediterranean region as a whole. In this article, we try calling the attention to the outstanding contribution of Iraq in mental health and medical educati

          A novel median filter based on crow optimization algorithms (OMF) is suggested to reduce the random salt and pepper noise and improve the quality of the RGB-colored and gray images. The fundamental idea of the approach is that first, the crow optimization algorithm detects noise pixels, and that replacing them with an optimum median value depending on a criterion of maximization fitness function. Finally, the standard measure peak signal-to-noise ratio (PSNR), Structural Similarity, absolute square error and mean square error have been used to test the performance of suggested filters (original and improved median filter) used to removed noise from images. It achieves the simulation based on MATLAB R2019b and the resul

        In our research, we introduced new concepts, namely ^*and **-light mappings, after we knew ^*and **-totally disconnected mappings through the use of -open sets.

Many examples, facts, relationships and results have been given to support our work.

        In this paper, we introduce the notation of the soft bornological group to solve the problem of boundedness for the soft group. We combine soft set theory with bornology space to produce a new structure which is called    soft bornological group. So that both the product and inverse maps are soft bounded. As well as, we study the actions of the soft bornological group on the soft bornological sets. The aim soft bornological set is to partition into orbital classes by acting soft bornological group on the soft bornological set. In addition, we explain the centralizer, normalizer, and stabilizer in details. The main important results are to prove that the product of soft bornological groups is soft bornol

Studied red beetle life on each of the yen and wheat durum wheat, barley, corn, rice, chickpeas, ground peanuts and beans in Living situation constant temperature and relative humidity of 65% for a period of 66 days was the life cycle of the insect different from one substance to another ....

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

The world went through turmoil before the sixth century AD, and human societies were in conflict and rivalry, each strong state is a weak state-dependent, but the dominant societies made the slave societies to them .. And thus made many societies or civilizations system of classes, and differentiation between members of one community, Weakened its strength and go alone. As the Islamic society in the present weak and weak and falling to the lowest levels of civilizational underdevelopment in the organization of society and social security contrary to what it was Islamic civilization, because of our distance from the heavenly instructions, and this prompted many to walk behind Western ideas aimed at the demolition of Islamic civilization,