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 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 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

Iraq within the ranks of the fledgling communities characterized by a broad base of the population pyramid, because they pose the age group (under 15 years) of a large proportion of the community, as it exceeded the proportion (40%) during the years of research extended (1986-2010) Despite the relative decline in the rates fertility during that period, but the proportion of young people remained high, especially for groups of at least five years, amounting to about 14% in 2012, a little more than the proportion of what constitutes age group (5-9 above) years, where it was (13%) and this naturally predicts continuing population increases in coming decades, due to the entry of those numbers of individuals in the reproductive stage,

                 In this paper, we proved coincidence points theorems for two pairs mappings which are defined on nonempty subset   in metric spaces by using condition (1.1). As application, we established a unique common fixed points theorems for these mappings by using the concept weakly compatible (R-weakly commuting) between these mappings.

Keys to four genera and twelve species of the subfamily Phlaeothripinae (Phlaeothripidae) were constructed, these are: Haplothrips; Karnyothrips; Phlaeothrips; and Dolicholepta ,and the species are: Haplothrips cerealis Priesner; Haplothrips tritici kurdjumov, Haplothrips hukkineni Priesner; Haplothrips subtilissimus (Haliday) ؛ Haplothrips reuteri Karny; Haplothrips jasonis Priesner; Haplothrips sallloumensis Priesner ; Haplothrips pharao Priesner ; Phlaeothrips sycomri Priesner ; Karnyothrips flavipus (Jones); Karnyothrips melaleucus (Bagnall) ; Dolicholepta micrurus (Bagnall). These were collected from Baghdad

Rainfall in Nigeria is highly dynamic and variable on a temporal and spatial scale. This has taken a more pronounced dimension due to climate change. In this study, Standard Precipitation Index (SPI) and Mann-Kendall test statistical tools were employed to analyze rainfall trends and patterns in Gombe metropolis between 1990 and 2020 and the ARIMA model was used for making the forecast for ten (10) years. Daily rainfall data of 31 years obtained from Nigerian Meteorological Agency, (NIMET) was used for the study. The daily rainfall data was subjected to several analyses. Standard precipitation index showed that alternation of wet and dry period conditions had been witnessed in the study area. The result obtained showed that there is an u