In this paper mildly-regular topological space was introduced via the concept of mildly g-open sets. Many properties of mildly - regular space are investigated and the interactions between mildly-regular space and certain types of topological spaces are considered. Also the concept of strong mildly-regular space was introduced and a main theorem on this space was proved.

In this thesis, we study the topological structure in graph theory and various related results. Chapter one, contains fundamental concept of topology and basic definitions about near open sets and give an account of uncertainty rough sets theories also, we introduce the concepts of graph theory. Chapter two, deals with main concepts concerning topological structures using mixed degree systems in graph theory, which is M-space by using the mixed degree systems. In addition, the m-derived graphs, m-open graphs, m-closed graphs, m-interior operators, m-closure operators and M-subspace are defined and studied. In chapter three we study supra-approximation spaces using mixed degree systems and primary object in this chapter are two topological

Recently, new generalizations have been presented for the hyponormal operators, which are (N, k)-hyponormal operators and (h, M)-hyponormal operators. Some properties of these concepts have also been proved, one of these properties is that the product of two (N, k)-hyponormal operator is also (N, k)- hyponormal operator and the product of two (h, M)-hyponormal operators is (h, M)-hyponormal operator. In our research, we will reprove these properties by using the (l,m)-commuting operator equations, in addition to that we will solve the (l, m)-commuting operator equations for (N, k)-hyponormal operators and (h, M)-hyponormal operators.

This dissertation depends on study of the topological structure in graph theory as well as introduce some concerning concepts, and generalization them into new topological spaces constructed using elements of graph. Thus, it is required presenting some theorems, propositions, and corollaries that are available in resources and proof which are not available. Moreover, studying some relationships between many concepts and examining their equivalence property like locally connectedness, convexity, intervals, and compactness. In addition, introducing the concepts of weaker separation axioms in α-topological spaces than the standard once like, α-feebly Hausdorff, α-feebly regular, and α-feebly normal and studying their properties. Furthermor

The importance of topology as a tool in preference theory is what motivates this study in which we characterize topologies generating by digraphs. In this paper, we generalized the notions of rough set concepts using two topological structures generated by out (resp. in)-degree sets of vertices on general digraph. New types of topological rough sets are initiated and studied using new types of topological sets. Some properties of topological rough approximations are studied by many propositions.

order to increase the level of security, as this system encrypts the secret image before sending it through the internet to the recipient (by the Blowfish method). As The Blowfish method is known for its efficient security; nevertheless, the encrypting time is long. In this research we try to apply the smoothing filter on the secret image which decreases its size and consequently the encrypting and decrypting time are decreased. The secret image is hidden after encrypting it into another image called the cover image, by the use of one of these two methods" Two-LSB" or" Hiding most bits in blue pixels". Eventually we compare the results of the two methods to determine which one is better to be used according to the PSNR measurs

This paper includes a comparison between denoising techniques by using statistical approach, principal component analysis with local pixel grouping (PCA-LPG), this procedure is iterated second time to further improve the denoising performance, and other enhancement filters were used. Like adaptive Wiener low pass-filter to a grayscale image that has been degraded by constant power additive noise, based on statistics estimated from a local neighborhood of each pixel. Performs Median filter of the input noisy image, each output pixel contains the Median value in the M-by-N neighborhood around the corresponding pixel in the input image, Gaussian low pass-filter and Order-statistic filter also be used.

Experimental results shows LPG-

     In a previous work, Ali and Ghawi studied closed Rickart modules. The main purpose of this paper is to define and study the properties of y-closed Rickart modules .We prove that, Let  and   be two -modules such that  is singular. Then  is -y-closed Rickart module if and only if   Also, we study the direct sum  of  y-closed Rickart modules.

This paper includes a comparison between denoising techniques by using statistical approach, principal component analysis with local pixel grouping (PCA-LPG), this procedure is iterated second time to further improve the denoising performance, and other enhancement filters were used. Like adaptive Wiener low pass-filter to a grayscale image that has been degraded by constant power additive noise, based on statistics estimated from a local neighborhood of each pixel. Performs Median filter of the input noisy image, each output pixel contains the Median value in the M-by-N neighborhood around the corresponding pixel in the input image, Gaussian low pass-filter and Order-statistic filter also be used. Experimental results shows LPG-PCA method