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

The research aims to determine the effectiveness of auditing in light of the relationship between the governance of investment policy and the cost of debt in companies listed on the Iraqi Stock Exchange. The problem of the research is to raise the question about the effect of the governance of investment policy and the cost of debt on the effectiveness of auditing and auditors. During the research, the most important of them were: the existence of an impact relationship on the effectiveness of auditing through the relationship between the governance of investment policy and the cost of debt. The companies listed in the Iraqi Stock Exchange lack an effective proposed guide or framework dealing with the governance of investment policy desp

      Political Discourse Analysis is an important linguistic study approach used by politicians to gain people support. The present paper sheds light on the figures of speech  of emphasis in the televised debate between the two presidential elections candidates, Emmanuel Macron and Marine Le Pen and the distinctive effect they add to the political discourse to win general public support as well as the presidential elections.

       The present paper provides a rudimentary definition and an analysis of the terms “discourse” and “political discourse” and traces the significant role played by politically directed televised Media and internet to support political pa

The purpose of this interview study was to explore teachers’ perceptions of Response to Intervention (RtI) implementation in their school. Particularly, the study explored teachers’ knowledge of RtI, teachers’ perceptions of RtI their intervention/instruction in school, and teachers’ suggestions of RtI implementation in their school. The study design was a qualitative interview in nature and data were collected from face-to-face interviews with four teachers in one school. The findings revealed that RtI means to identify students’ problems; the positive teachers’ perceptions of their implementation included: (a) students who demonstrate progress through RtI are those who receive private education services, (b) progress monito

Corpus linguistics is a methodology in studying language through corpus-based research. It differs from a traditional approach in studying a language (prescriptive approach) in its insistence on the systematic study of authentic examples of language in use (descriptive approach).A “corpus” is a large body of machine-readable structurally collected naturally occurring linguistic data, either written texts or a transcription of recorded speech, which can be used as a starting-point of linguistic description or as a means of verifying hypotheses about a language.  In the past decade, interest has grown tremendously in the use of language corpora for language education. The ways in which corpora have been employed in language pedago

Management is considered as most important resource of the society ones in modern era and an exchange
point in societies’ lives in order to achieve its goals and wishes. So far, management behinds the new
electronic society has become different in shape and nature due to the force of the nature of information
technology that shapes the relationships between the world’s individuals at the national level but it goes
beyond the international ones. The study aims at identifying the impact of the electronic management’s
components upon the improvement of the quality of nursing care in Baghdad’s hospitals. The descriptive
design, with a sample-survey approach, is used as appropriate ones for the field study of social

In this work, we study two species of predator with two species of prey model, where the two species of prey live in two diverse habitats and have the ability to group-defense. Only one of the two predators tends to switch between the habitats. The mathematical model has at most 13 possible equilibrium points, one of which is the point of origin, two are axial, tow are interior points and the others are boundary points. The model with , where n is the switching index, is discussed regarding the boundedness of its solutions and the local stability of its equilibrium points. In addition, a basin of attraction was created for the interior point. Finally, three numerical examples were given to support the theoretical results.

In this paper, we propose a new approach of regularization for the left censored data (Tobit). Specifically, we propose a new Bayesian group Bridge for left-censored regression ( BGBRLC). We developed a new Bayesian hierarchical model and we suggest a new Gibbs sampler for posterior sampling. The results show that the new approach performs very well compared to some existing approaches.

This paper presents a hybrid approach for solving null values problem; it hybridizes rough set theory with intelligent swarm algorithm. The proposed approach is a supervised learning model. A large set of complete data called learning data is used to find the decision rule sets that then have been used in solving the incomplete data problem. The intelligent swarm algorithm is used for feature selection which represents bees algorithm as heuristic search algorithm combined with rough set theory as evaluation function. Also another feature selection algorithm called ID3 is presented, it works as statistical algorithm instead of intelligent algorithm. A comparison between those two approaches is made in their performance for null values estima