In this paper we introduce a lot of concepts in bitopological spaces which are ij-ω-converges to a subset, ij-ω-directed toward a set, ij-w-closed functions, ij-w-rigid set, ij-w-continuous functions and the main concept in this paper is ij-w-perfect functions between bitopological spaces. Several theorems and characterizations concerning these concepts are studied.

In this study, we present a new steganography method depend on quantizing the perceptual color spaces bands. Four perceptual color spaces are used to test the new method which is HSL, HSV, Lab and Luv, where different algorithms to calculate the last two-color spaces are used. The results reveal the validity of this method as a steganoic method and analysis for the effects of quantization and stegano process on the quality of the cover image and the quality of the perceptual color spaces bands are presented.

In this research, a new application has been developed for games by using the generalization of the separation axioms in topology, in particular regular, Sg-regular and SSg- regular spaces. The games under study consist of two players and the victory of the second player depends on the strategy and choice of the first player. Many regularity, Sg, SSg regularity theorems have been proven using this type of game, and many results and illustrative examples have been presented

The main objective of this work is to introduce and investigate fixed point (F. p) theorems for maps that satisfy contractive conditions in weak partial metric spaces (W.P.M.S), and give some new generalization of the fixed point theorems of Mathews and Heckmann. Our results extend, and unify a multitude of (F. p) theorems and generalize some results in (W.P.M.S). An example is given as an illustration of our results.

 The internal administrative spaces of the interior designer formed an obsession for their development and for finding solutions and treatments to advance to enhance the state of adaptation for their employees by providing a healthy, appropriate and sound environment for work and production. . The first chapter focuses on laying theoretical foundations to show what health materials are used in the administrative spaces of the training directorates of the Ministry of Education in Baghdad. The second chapter dealt with the knowledge of health materials, their impact and effectiveness in the interior space, and the variables of their functional characteristics and their work in the interior spaces in a way that enhances the development of

This paper is concerned with introducing and studying the o-space by using out degree system (resp. i-space by using in degree system) which are the core concept in this paper. In addition, the m-lower approximations, the m-upper approximations and ospace and i-space. Furthermore, we introduce near supraopen (near supraclosed) d. g.'s. Finally, the supra-lower approximation, supraupper approximation, supra-accuracy are defined and some of its properties are investigated.

A complete metric space is a well-known concept. Kreyszig shows that every non-complete metric space  can be developed into a complete metric space , referred to as completion of .

We use the b-Cauchy sequence to form  which “is the set of all b-Cauchy sequences equivalence classes”. After that, we prove  to be a 2-normed space. Then, we construct an isometric by defining the function from  to ; thus  and  are isometric, where  is the subset of  composed of the equivalence classes that contains constant b-Cauchy sequences. Finally, we prove that  is dense in ,  is complete and the uniqueness of  is up to isometrics

The pharmacy is the face for the health buildings and hospitals, The linking professional relationships and functional, it is been from the important places that most people go it, so according to that we must format its interior design in form that suitable with the need of most people use it or work in it, and this the search goal, dashing from the search subject which to hide finding designer treatment for the pharmacies interior spaces, to give share in the functional improvement performance or aesthetic. We define the search goals to share in educate the pharmacist in the effect of interior design for improvement of interior environment, in addition to the search consider as designer trying add to the other trying the interior desig