Abstract. Fibrewise micro-topological spaces be a useful tool in various branches of mathematics. These mathematical objects are constructed by assigning a micro-topology to each fibre from a fibre bundle. The fibrewise micro-topological space is then formed by taking the direct limit of these individual micro-topological spaces. It can be adapted to analyze various mathematical structures, from algebraic geometry to differential equations. In this study, we delve into the generalizations of fibrewise micro-topological spaces and explore the applications of these abstract structures in different branches of mathematics. This study aims to define the fibrewise micro topological space through the generalizations that we use in this paper, whi

The concept of Cech fuzzy soft bi-closure space ( ˇ Cfs bi-csp) ( ˇ U, L1, L2, S) is initiated and studied by the authors in [6]. The notion of pairwise fuzzy soft separated sets in Cfs bi-csp is defined in this study, and various features of ˇ this notion are proved. Then, we introduce and investigate the concept of connectedness in both Cfs bi-csps and its ˇ associated fuzzy soft bitopological spaces utilizing the concept of pairwise fuzzy soft separated sets. Furthermore, the concept of pairwise feebly connected is introduced, and the relationship between pairwise connected and pairwise feebly connected is discussed. Finally, we provide various instances to further explain our findings.

The idea of ech fuzzy soft bi-closure space ( bicsp) is a new one, and its basic features are defined and studied in [1]. In this paper, separation axioms, namely pairwise, , pairwise semi-(respectively, pairwise pseudo and pairwise Uryshon) - fs bicsp's are introduced and studied in both ech fuzzy soft bi-closure space and their induced fuzzy soft bitopological spaces. It is shown that hereditary property is satisfied for , with respect to ech fuzzy soft bi-closure space but for other mentioned types of separations axioms, hereditary property satisfies for closed subspaces of ech fuzzy soft bi-closure space.

The current research deals with the specificity of the interior design of the classes of art education in the schools of excellence for the province of Muthanna and its center of the city of Samawah. In the first chapter، the problem of research was determined by the lack of internal spaces of the classes of art education to designs that meet the requirements and needs of students in these educational stages.  The importance of the research in being an addition to knowledge in the field of interior design and engineering department of the general directorates of the Ministry of Education. The objectives of the research were determined through.

1. Identifying the reality of the halls of art education for sch

      In this study, simple, low cost, precise and speed spectrophotometric methods development for evaluation of sulfacetamide sodium are described. The primary approach contains conversion of sulfacetamide sodium to diazonium salt followed by a reaction with p-cresol as a reagent in the alkaline media.  The colored product has an orange colour with absorbance at λmax 450 nm. At the concentration range of (5.0-100 µg.mL^-1), the Beer̆ s Low is obeyed with correlation coefficient (R²= 0.9996), limit of detection as 0.2142 µg.mL^-1, limit of quantification as 0.707 µg.mL^-1 and molar absorptivity as 1488.249 L.mol^-1.cm^-1. The other approach, cloud point extraction w

We dealt with the nature of the points under the influence of periodic function chaotic functions associated functions chaotic and sufficient conditions to be a very chaotic functions Palace

The purpose of this study is to show the constants and variables geography in Russian
policy in light of variables geostrategic witnessed by the world, especially after the collapse
of the Soviet Union and the disintegration to fifteen Republic became the Russian Federation
and the heir to the Soviet Union, Geography particularly important because the impact of its
data in policy making less change ofothers, and explain the political choices cannot achieve
security through its relationship constants geographical (natural or human) paint forms of
economic activity and determine the points they national security. issue is the geographical
this or that country is determined by its policy also specifies the way in which

the study covered theoretical concering parial molal volume the applicability of jones-dole equation

As human societies grow, the problem of waste management becomes one of the pressing issues that need to be addressed. Recycling and reuse of waste are effective waste management measures that prevent pollution and conserve natural resources. In this study, the possibility of using glass waste as an alternative was used as a partial weight substitute for fine aggregates with replacement ratios of 10, 20, 30, and 40% by the weight, and formed into test models (15 cm * 15 cm ) cube and (15 cm * 30 cm) cylinder, then matured and tested their strength compression and tensile strength at the age of 7 and 28 days and compared with a reference or conventional concrete with a mixing ratio (1: 1.5: 3) as well as testing its worka

This work includes synthesis of new six membered heterocyclic rings with effective amino group using the reaction of benzylideneacetophenone (chalcone) (1) with thiourea or urea in alcoholic basic medium to form: 1,3-thiazen-2-amine (2), and 1,3-oxazin-2-amine (8) respectively. The diazotization reaction was carried out with sodium nitrite in presence of hydrochloric acid to form diazonium salts which suffered coupling reaction with naphthols and phenols in the presence of sodium hydroxide to form colored azo dyes (4-7, and 10-13). o-methylation reaction of compounds (7) and (10) yielded : 1,3-thiazin -2-yl-diazenyl (14), and 1,3-oxazin-2-yl-diazenyl (15) respectively.The new compounds were characterized using vario