In this paper we define and study new concepts of fibrewise topological spaces over B namely, fibrewise Lindelöf and locally Lindelöf topological spaces, which are generalizations of will-known concepts: Lindelöf topological space (1) "A topological space X is called a Lindelöf space if for every open cover of X has a countable subcover" and locally Lindelöf topological space (1) "A topological space X is called a locally Lindelöf space if for every point x in X, there exist a nbd U of x such that the closure of U in X is Lindelöf space". Either the new concepts are: "A fibrewise topological space X over B is called a fibrewise Lindelöf if the projection function p : X→B is Lindelöf" and "The fibrewise topological space X over B

This study delves into the properties of the associated act V over the monoid S of sinshT. It examines the relationship between faithful, finitely generated, and separated acts, as well as their connections to one-to-one and onto operators. Additionally, the correlation between acts over a monoid and modules over a ring is explored. Specifically, it is established that  functions as an act over S if and only if  functions as module, where T represents a nilpotent operator. Furthermore, it is proved that when T is onto operator and  is finitely generated, is guaranteed to be finite-dimensional. Prove that for any bounded operator the following,  is acting over S if and only if  is a module where T is a nilpotent operator, is a

 الأثر V بالنسبة إلى   sinshT و خواصه قد تم دراسته في هذا البحث حيث تم دراسة علاقة الأثر المخلص والاثر المنتهى التولد والاثر المنفصل وربطها بالمؤثرات المتباينة حيث تم بهنة العلاقات التالية ان الاثر اذا وفقط اذا مقاس في حالة كون المؤثر هو عديم القوة وكذلك في حالة كون المؤثر شامل فان الاثر هو منتهي التولد اي ان الغضاء هو منتهي التولد وايضا تم برهن ان الاثر مخلص لكل مؤثر مقيد وك\لك قد تم التحقق من انه لاي مؤثر مقي

The ability of using aluminum filings which is locally solid waste was tested as a mono media in gravity rapid filter. The present study was conducted to evaluate the effect of variation of influent water turbidity (10, 20and 30 NTU); flow rate(30, 40, and 60 l/hr) and bed height (30and60)cm on the performance of aluminum filings filter media for 5 hours run time and compare it with the conventional sand filter. The results indicated that aluminum filings filter showed better performance than sand filter in the removal of turbidity and in the reduction of head loss. Results showed that the statistical model developed by the multiple linear regression was proved to be
valid, and it could be used to predict head loss in aluminum filings

Background: The aim of this national oral health survey was to determine the prevalence of malocclusions due to some anomalies in the dentition among the 13 years old Kurdish students in sulaimani intermediate school. Materials and methods: The total sample was 950 (455 males and 495 females) which assessed by diagnostic set and special instrument. The clinical examination was mainly based on the definitions of Björk et al. Some variables were recorded as present or absent sometimes denoting the tooth or the teeth involved in malocclusion and their distribution according to the whole sample. Results: The results showed that 1)The most common extracted tooth was the mandibular first molar (2.9%). 2) At this age group the most common partial