Throughout this work we introduce the notion of Annihilator-closed submodules, and we give some basic properties of this concept. We also introduce a generalization for the Extending modules, namely Annihilator-extending modules. Some fundamental properties are presented as well as  we discuss the relation between this concept and some other related concepts.

The aim of this paper is to generate topological structure on the power set of vertices of digraphs using new definition which is Gm-closure operator on out-linked of digraphs. Properties of this topological structure are studied and several examples are given. Also we give some new generalizations of some definitions in digraphs to the some known definitions in topology which are Ropen subgraph, α-open subgraph, pre-open subgraph, and β-open subgraph. Furthermore, we define and study the accuracy of these new generalizations on subgraps and paths.

Abstract

Research title: The legal ruling of advice.

This research deals with the topic of advice, as the research included the following:

Preamble: I explained in it the meaning of advice in the Qur’an and Sunnah, and that what is meant by it is a good performance of the duty, then explaining its importance, importing it, and the difference between advice and what is similar to it, from enjoining good, denial, reproach and reprimand, backbiting and the will.

The first topic: It dealt with the ruling on advice, whether it is recommended or disliked, or forbidden, because what is meant by it is to give advice to others may be an obligation in kind, or it may be desirable or dislike

Many codiskcyclic operators on infinite-dimensional separable Hilbert space do not satisfy the criterion of codiskcyclic operators. In this paper, a kind of codiskcyclic operators satisfying the criterion has been characterized, the equivalence between them has been discussed and the class of codiskcyclic operators satisfying their direct summand is codiskcyclic. Finally, this kind of operators is used to prove that every codiskcyclic operator satisfies the criterion if the general kernel is dense in the space.

Weibull Distribution is one of most important distribution and it is mainly used in reliability and in distribution of life time. The study handled two parameter and three-parameter Weibull Distribution in addition to five –parameter Bi-Weibull distribution. The latter being very new and was not mentioned before in many of the previous references. This distribution depends on both the two parameter and the three –parameter Weibull distributions by using the scale parameter (α) and the shape parameter (b) in the first and adding the location parameter (g)to the second and then joining them together to produce a distribution with five parameters.

Gabriel Garcia Marquez, the Nobel laureate of literature in 1982, is one of the most famous Latin American writers who have been distinguished by the magic of realism. We can say the months in the world and he is almost the most controversial for many reasons and for these reasons he did not accept that his novels turn into movies Marquez agreed to turn one of his most important and most beautiful novels, "Love in the Time of Cholera," which he wrote in 1985 and agreed to convert to a film in 2006 after the novel was bought by the author for $ 3 million. Mike Noel to bring out

This study deals with the Spatial and Periodical Variation of the Economical Activities for the
Population of Al – Anbar Province on the level of districts , according to the Population
Computation for the period 1987 and 1997 and the results of determinations and numberings
for the year of 2011 .
This study depends on the Details Classifications of the 17th Activities for 1997 and 2011
beside the Triple Classification of the Economical Activities for the three study years .
The study proves that there is a spatial and periodical variation on the level of study area , and
that’s because of many factors , one of the most important of them was the distribution of
economical siege, as well as the weakness of the

Design of experiments (DOE) was made by Minitab software for the study of three factors used in the precipitation process of the Sodium Aluminate solution prepared from digestion of α-Al₂O₃  to determine the optimum conditions to a produce Boehmite which is used in production of ɤ-Al₂O₃ during drying and calcination processes, the factors are; the temperature of the sodium aluminate solution, concentration of HCl acid added for the precipitation and the pH of the solution at which the precipitation was ended. The design of the experiments leads to 18 experiments.

   The results show that the optimum conditions for the precipitation of the sodium aluminate solution which

Abstract

This study deals with the fluctuations of oil revenues and its effect on the public debt. This can be studied through the indicators of debt sustainability, the financial, and economic indicators which express the risk of debt. The study focuses on clarification of the public debt path and its management both domestic and foreign. The sustainability of debt takes an important role according the macroeconomic variables. This study stresses the relationship between the rental economy in Iraq and the risk of the public debt, it is very important to work high oil prices, and on investigating during high work to establish a fund to support the budget deficit. This will reduce future risks arising from the use of publi