In this paper, we define some generalizations of topological group namely -topological group, -topological group and -topological group with illustrative examples. Also, we define grill topological group with respect to a grill. Later, we deliberate the quotient on generalizations of topological group in particular -topological group. Moreover, we model a robotic system which relays on the quotient of -topological group.

      In this paper, we introduce the concepts of Large-lifting and Large-supplemented modules as a generalization of lifting and supplemented modules.  We also give some results and properties of this new kind of modules.

The research talks about the interest and its impact on polygamy as a legitimate social psychological issue, where she talked about the concept of polygamy, and evidence of the legitimacy of polygamy, and clarify the conditions, and then touched on the great interests for which the law allowed polygamy, and mentioned some practical models in polygamy, including What is in the interest of men in pluralism, including in the interest of women in pluralism, including in the interests of both sexes in pluralism . 

Abstract:
the system of Administrative Control in organizations meets the need to check on the optimal use and proper resources and conservation to achieve the objectives sought by the organization, hence the system of Administrative Control  is part of the overall system in any organization that has undergone evolution always to be able to keep up with progress in the development of other sciences, and that the growth of coherence between subordinates in the organization means the ability to influence the opinions, ideas and attitudes to change it for directions the organization and its values ​​and this is reflected positively on the coherence of the organization, the researcher interest of the imp

In this paper we show that if ? Xi is monotonically T2-space then each Xi is monotonically T2-space, too. Moreover, we show that if ? Xi is monotonically normal space then each Xi is monotonically normal space, too. Among these results we give a new proof to show that the monotonically T2-space property and monotonically normal space property are hereditary property and topologically property and give an example of T2-space but not monotonically T2-space.

The sintering behavior of Alumina was investigated by adding TiO2. The addition of TiO2 lowered the sintering temperature of the Alumina compared with those of pure Alumina. The result suggests that TiO2 acts as an activator for sintering of Alumina. Water absorption, apparent porosity and density were examined for both pure and TiO2 added to Alumina samples. The variations of sintering behavior were discussed in terms of shrinkage, porosity, water absorption and density. Thermal shock resistance was also examined. In term of this work, the way of improving the thermal shock resistance in oxide- based materials by adding reactive Titania powder to the Alumina samples. The laboratory results showed an improvement in thermal shock resistance

The notion of a Tˉ-pure sub-act and so Tˉ-pure sub-act relative to sub-act are introduced. Some properties of these concepts have been studied.

The main purpose of this work is to introduce the concept of higher N-derivation and study this concept into 2-torsion free prime ring we proved that:Let R be a prime ring of char. 2, U be a Jordan ideal of R and be a higher N-derivation of R, then , for all u U , r R , n N .