Let R be a commutative ring with identity and M be unitary (left) R-module. The principal aim of this paper is to study the relationships between relatively cancellation module and multiplication modules, pure submodules and Noetherian (Artinian) modules.

Imitation learning is an effective method for training an autonomous agent to accomplish a task by imitating expert behaviors in their demonstrations. However, traditional imitation learning methods require a large number of expert demonstrations in order to learn a complex behavior. Such a disadvantage has limited the potential of imitation learning in complex tasks where the expert demonstrations are not sufficient. In order to address the problem, we propose a Generative Adversarial Network-based model which is designed to learn optimal policies using only a single demonstration. The proposed model is evaluated on two simulated tasks in comparison with other methods. The results show that our proposed model is capable of completing co

      In this study, different methods were used for estimating location parameter  and scale parameter for extreme value distribution, such as maximum likelihood estimation (MLE) , method of moment  estimation (ME),and approximation  estimators based on percentiles which is called white method in estimation, as the extreme value distribution is one of exponential distributions. Least squares estimation (OLS) was used, weighted least squares estimation (WLS), ridge regression estimation (Rig), and adjusted ridge regression estimation (ARig) were used. Two parameters for expected value to the percentile  as estimation for distribution f

Transportation and distribution are the most important elements in the work system for any company, which are of great importance in the success of the chain work. Al-Rabee factory is one of the largest ice cream factories in Iraq and it is considered one of the most productive and diversified factories with products where its products cover most areas of the capital Baghdad, however, it lacks a distribution system based on scientific and mathematical methods to work in the transportation and distribution processes, moreover, these processes need a set of important data that cannot in any way be separated from the reality of fuzziness industrial environment in Iraq, which led to use the fuzzy sets theory to reduce the levels of uncertainty.

The aim of the research is to find out the availability of the requirements of applying the indicators of school performance system in the public schools in  Mahayel Asir educational directorate through the school planning indicator, the safety and security indicator, the active learning indicator, the student guidance indicator and determining the existence of statistically significant differences between the responses of the research community according to the variable of (scientific qualification - years of work as a principal - training courses). The questionnaire was used as a tool for data collection from the research community, which consists of all the public schools’ principals (n=180) Mahayel Asir educational directorate

Evolutionary algorithms are better than heuristic algorithms at finding protein complexes in protein-protein interaction networks (PPINs). Many of these algorithms depend on their standard frameworks, which are based on topology. Further, many of these algorithms have been exclusively examined on networks with only reliable interaction data. The main objective of this paper is to extend the design of the canonical and topological-based evolutionary algorithms suggested in the literature to cope with noisy PPINs. The design of the evolutionary algorithm is extended based on the functional domain of the proteins rather than on the topological domain of the PPIN. The gene ontology annotation in each molecular function, biological proce