Abstract. In this study, we shall research the fibrewise micro ideal topological spaces over Ḃ, as well as the relationship between fibrewise micro ideal topological spaces over Ḃ and fibrewise micro topological spaces over Ḃ. At first present introduces a novel notion from fibrewise micro ideal topological spaces over Ḃ, and differentiates it from fibrewise micro topological spaces over Ḃ. Some fundamental characteristics from these spaces are studied. Then show discussed the fibrewise micro ideal closed and micro ideal open topologies. Many propositions relating to these ideas are offered. In the next part will study defines and investigates novel conceptions from fibrewise micro ideal topological spaces over Ḃ, particularly f

The primary objective of this paper is to present a new concept of fibrewise topological spaces over B is said to be fibrewise slightly topological spaces over B. Also, we introduce the concepts of fibrewise slightly perfect topological spaces, filter base, contact point, slightly convergent, slightly directed toward a set, slightly adherent point, slightly rigid, fibrewise slightly weakly closed, H.set, fibrewise almost slightly perfect, slightly∗ .continuous fibrewise slightly∗ topological spaces respectively, slightly Te, locally QHC, In addition, we state and prove several propositions related to these concepts.

Form the series of generalization of the topic of supra topology is the generalization of separation axioms . In this paper we have been introduced (S * - SS *) regular spaces . Most of the properties of both spaces have been investigated and reinforced with examples . In the last part we presented the notations of supra *- -space ( =0,1) and we studied their relationship with (S * - SS *) regular spaces.

In this work we explain and discuss new notion of fibrewise topological spaces, calledfibrewise soft ideal topological spaces, Also, we show the notions of fibrewise closed soft ideal topological spaces, fibrewise open soft ideal topological spaces and fibrewise soft near ideal topological spaces.

Background: Imprelon® Biostar foils are new alternative tray material that has become increasingly popular because oftheir several advantages. Also, (Duran®) is another type of Biostar foils which is used in splint therapy. This study assessed some mechanical properties of these two types Biostar sheets in comparison with some types of acrylic resins used for construction of trays and splints. Materials and Methods: A total of 150 specimens were prepared, 30 specimens for each test, 10 for each group material in order to assess some mechanical properties of the Imprelon® Biostar foil (dimension stability, surface roughness and shear bond strength of Imprelon® materialto zinc oxide impression material) and compare them to that of the oth

This paper aims to introduce certain new kinds of ideals on pseudo-BG-Algebra (P-BG-A), such as pseudo-closed ideal (P-CI), pseudo-completely closed ideal (P-CCI), and pseudo-n-ideal (P-n-I). Firstly, a (P-n-I) is defined and its pertinent properties are explored. Some important properties have been proven, for example, any pseudo-ideal is a (P-n-I), but the opposite is not generally true, an example was given of the opposite direction. Also, every pseudo-subalgebra of a (P-BG-A) is a pseudo ideal and it is a (P-n-I). Secondly, (P-CI) and a (P-CCI) ideal are defined. After that, we prove that every pseudo-subalgebra of a (P-BG-A) is a (P-CI) and the converse is true. The relationship between (P-BG-A) and pseudo-BH-algebra is demonstrated un

This paper is concerned with introducing and studying the M-space by using the mixed degree systems which are the core concept in this paper. The necessary and sufficient condition for the equivalence of two reflexive M-spaces is super imposed. In addition, the m-derived graphs, m-open graphs, m-closed graphs, m-interior operators, m-closure operators and M-subspace are introduced. From an M-space, a unique supratopological space is introduced. Furthermore, the m-continuous (m-open and m-closed) functions are defined and the fundamental theorem of the m-continuity is provided. Finally, the m-homeomorphism is defined and some of its properties are investigated.

This study showed that the lens in baloot muluki fish Chondrostoma regium is transparent, spherical shape, and solid in textures, while in the tree frog Hyla arborea savignyi, freshwater turtles Clemmys caspia caspia, white–eared bulbul Pycnonotus leucotis and brown rat Rattus norvegicus are transparent, soft and biconvex, it is very soft in white–eared bulbul. There are many significant differences have been recorded between the average weight lens and the total concentration of the protein in the lens all studied animals. Electrical migration process for lens proteins showed that there is one bundle of crystalline –? and one bundle also crystalline–? in all studied species, either crystalline–? may represent one bundle character