The significance fore supra topological spaces as a subject of study cannot be overstated, as they represent a broader framework than traditional topological spaces. Numerous scholars have proposed extension to supra open sets, including supra semi open sets, supra per open and others. In this research, a notion for ⱨ-supra open created within the generalizations of the supra topology of sets. Our investigation involves harnessing this style of sets to introduce modern notions in these spaces, specifically supra ⱨ - interior, supra ⱨ - closure, supra ⱨ - limit points, supra ⱨ - boundary points and supra ⱨ - exterior of sets. It has been examining the relationship with supra open. The research was also enriched with many

The primary aim of this paper, is to introduce the rough probability from topological view. We used the Gm-topological spaces which result from the digraph on the stochastic approximation spaces to upper and lower distribution functions, the upper and lower mathematical expectations, the upper and lower variances, the upper and lower standard deviation and the upper and lower r th moment. Different levels for those concepts are introduced, also we introduced some results based upon those concepts.

The topic of supra.topological.spaces considered one of the important topics because it is a generalization to topological.spaces. Many researchers have presented generalizations to supra open sets such as supra semi.open and supra pre.open sets and others. In this paper, the concept of δ∼open sets was employed and introduced in to the concept of supra topology and a new type of open set was extracted, which was named S∼δ∼open. Our research entails the utilization of this category of sets to form a new concepts in these spaces, namely S∼δ∼limit points and S∼δ∼derive points, and examining its relationship with S∼open and S∼reg∼open. Based on this class of sets, we have introduced other new concepts such as S∼isolate

Banks represents financial institutions that influence the economy of any country and their evolution and development is the need to seek all states , communities, maintain and control a guarantee of the beneficiaries investors and to promote confidence, so the specialized organizations trying to set principles and rules must be adhered to and are Basel (II) of the necessary effects to be introduced and work on their application.  Banks exposed by various risks one of them operational risks that have multiple effects on the activity of the institution itself, as well as the national economy, so this study was to find out what those effects and to find solutions and appropriate proposals to avoid Iraqi banks from the effects of risk,

In this paper, an approach for object tracking that is inspired from human oculomotor system is proposed and verified experimentally. The developed approach divided into two phases, fast tracking or saccadic phase and smooth pursuit phase. In the first phase, the field of the view is segmented into four regions that are analogue to retinal periphery in the oculomotor system. When the object of interest is entering these regions, the developed vision system responds by changing the values of the pan and tilt angles to allow the object lies in the fovea area and then the second phase will activate. A fuzzy logic method is implemented in the saccadic phase as an intelligent decision maker to select the values of the pan and tilt angle based

Background: Complete removal of filling material from the root canal is an essential requirement for endodontic retreatment. The purpose of the present study is to evaluate and compare the dissolving capabilities of various solvents (Xylene, Eugenate Desobturator, Eucalyptol, EDTA and Distilled water (as a control)) on four different types of sealer (Endofill, Apexit Plus, AH Plus and EndoSequence bioceramic sealer). Materials and method: Eighty samples of each sealer were prepared according to the manufacturers' instructions and then divided into ten groups (of 8 samples) for immersion in the respective solvents for 2 and 5 min immersion periods. Each sealer specimen was weighed to obtain its initial mass. The specimens were immersed in

The Research is interested in the detailed comparative study of certain selection of
Imam Alsamarqandi in some subjects of washing and touching the Gracious Quran.
The value of this study is that it is related to one aspect of the duties obliged on Muslim
like parity.
The study has tried to collect certain scholars’ opinions of eight doctrines with the
selection of Alsamarqandi to make a comp arson between them and to show how
Alsamarqandi is able to create legal laws from his sources to lead the researchers nto have
knowledge about the syllabi of the famous scientists.
Finally we ask God to bless to what is right and to accept this study and make it part of
our good deeds, Ameen.

The main idea of this research is to consider fibrewise pairwise versions of the more important separation axioms of ordinary bitopology named fibrewise pairwise - spaces, fibrewise pairwise - spaces, fibrewise pairwise - spaces, fibrewise pairwise -Hausdorff spaces, fibrewise pairwise functionally -Hausdorff spaces, fibrewise pairwise -regular spaces, fibrewise pairwise completely -regular spaces, fibrewise pairwise -normal spaces and fibrewise pairwise functionally -normal spaces. In addition we offer some results concerning it.

The theory of Topological Space Fiber is a new and essential branch of mathematics, less than three decades old, which is created in forced topologies. It was a very useful tool and played a central role in the theory of symmetry. Furthermore, interdependence is one of the main things considered in topology fiber theory. In this regard, we present the concept of topological spaces α associated with them and study the most important results.

The main purpose of this paper is to introduce a some concepts in fibrewise bitopological spaces which are called fibrewise , fibrewise -closed, fibrewise −compact, fibrewise -perfect, fibrewise weakly -closed, fibrewise almost -perfect, fibrewise ∗-bitopological space respectively. In addition the concepts as - contact point, ij-adherent point, filter, filter base, ij-converges to a subset, ij-directed toward a set, -continuous, -closed functions, -rigid set, -continuous functions, weakly ijclosed, ij-H-set, almost ij-perfect, ∗-continuous, pairwise Urysohn space, locally ij-QHC bitopological space are introduced and the main concept in this paper is fibrewise -perfect bitopological spaces. Several theorems and characterizations c