Background: Metal ions can be released from metallic orthodontic appliances due to corrosion in the oral cavity; prophylactic mouthwashes may have an effect on ion release from orthodontic wires. Materials and Methods: Thirty six orthodontic sets of half maxillary fixed appliance with 2 types of arch wires SS and NiTi(Morelli) were constructed and immersed in 2 types of mouthwashes; Claradone (non-fluoridated) and Silver Care (fluoridated) for 28 days at 37°C, then the released Ni and Cr ionswere measured using atomic absorption spectrophotometer and compared statistically. Results: Ni ion release was higher from NiTi wire group than SS wire group for both mouthwashes and also was higher for Silver Care group than for Claradone group.

In the present paper, a simply* compact spaces was introduced it defined over simply*- open set previous knowledge and we study the relation between the simply* separation axioms and the compactness, in addition to introduce a new types of functions known as 𝛼𝑆 𝑀∗ _irresolte , 𝛼𝑆 𝑀∗ __𝑐𝑜𝑛𝑡𝑖𝑛𝑢𝑜𝑢𝑠 and 𝑅 𝑆 𝑀∗ _ continuous, which are defined between two topological spaces.

The aim of this research is to use the class of soft simply open set to define new types of separation axioms in soft topological spaces. We also introduce and study the concept of soft simply compactness.

Fibrewise topological spaces theory is a relatively new branch of mathematics, less than three decades old, arisen from algebraic topology. It is a highly useful tool and played a pivotal role in homotopy theory. Fibrewise topological spaces theory has a broad range of applications in many sorts of mathematical study such as Lie groups, differential geometry and dynamical systems theory. Moreover, one of the main objects, which is considered in fibrewise topological spaces theory is connectedness. In this regard, we of the present study introduce the concept of connected fibrewise topological spaces and study their main results.

  In this paper, we define the bg**-connected space and study the relation between this space and other kinds of connected spaces .Also we study some types of continuous functions and study the relation among (connected space, b-connected space,  bg-connected  space and bg**-connected space) under these types of continuous functions.  

     We introduce and discuss the modern type of fibrewise topological spaces, namely fibrewise fuzzy topological spaces. Also, we introduce the concepts of fibrewise closed fuzzy topological spaces, fibrewise open fuzzy topological spaces, fibrewise locally sliceable fuzzy topological spaces and fibrewise locally sectionable fuzzy topological spaces. Furthermore, we state and prove several theorems concerning these concepts.

The purpose of this research is to introduce a concept of general partial metric spaces as a generalization of partial metric space. Give some results and properties and find relations between general partial metric space, partial metric spaces and D-metric spaces.

  The purpose of this work is to determine the points and planes of 3-dimensional projective space PG(3,2) over Galois field GF(q), q=2,3 and 5 by designing a computer program.