studied, and its important properties and relationship with both closed and open Nano sets were investigated. The new Nano sets were linked to the concept of Nano ideal, the development of nano ideal mildly closed set and it has been studied its properties. In addition to the applied aspect of the research, a sample was taken from patients infected with viral hepatitis, and by examining the infected people and using closed and open (nano mildly. and nano ideal mildly) sets, the important symptoms that constitute the core of this dangerous examining the infected people and using closed and open (nano mildly. and nano ideal mildly) sets, the important symptoms that constitute the core of this dangerous disease.

The basic concepts of some near open subgraphs, near rough, near exact and near fuzzy graphs are introduced and sufficiently illustrated. The Gm-closure space induced by closure operators is used to generalize the basic rough graph concepts. We introduce the near exactness and near roughness by applying the near concepts to make more accuracy for definability of graphs. We give a new definition for a membership function to find near interior, near boundary and near exterior vertices. Moreover, proved results, examples and counter examples are provided. The Gm-closure structure which suggested in this paper opens up the way for applying rich amount of topological facts and methods in the process of granular computing.

This research deals with the topic (Fantasy Parody in the Design of the Advertisement) in view of the important role that fantasia plays in designing the most creative and attractive advertisements to the recipients. The research problem lies in accordance with the following question:
What is the Fantasy Parody in the Design of the Advertisement?
It means the imagination, the unfamiliar; and features that emerge for it that distinguish it from other concepts. Fantasy advertisement is creativity in innovative ways, either through collage, merging, or the use of various artistic expressions in terms of intellectual and cultural awareness. When uses in the parody of advertisement, it has helped to come up with an aesthetic experie

The concept of -closedness, a kind of covering property for topological spaces, has already been studied with meticulous care from different angles and via different approaches. In this paper, we continue the said investigation in terms of a different concept viz. grills. The deliberations in the article include certain characterizations and a few necessary conditions for the -closedness of a space, the latter conditions are also shown to be equivalent to -closedness in a - almost regular space. All these and the associated discussions and results are done with grills as the prime supporting tool.

We introduce and discus recent type of fibrewise topological spaces, namely fibrewise bitopological spaces, Also, we introduce the concepts of fibrewise closed bitopological spaces, fibrewise open bitopological spaces, fibrewise locally sliceable bitopological spaces and fibrewise locally sectionable bitopological spaces. Furthermore, we state and prove several propositions concerning with these concepts.

The significance fore supra topological spaces as a subject of study cannot be overstated, as they represent a broader framework than traditional topological spaces. Numerous scholars have proposed extension to supra open sets, including supra semi open sets, supra per open and others. In this research, a notion for ⱨ-supra open created within the generalizations of the supra topology of sets. Our investigation involves harnessing this style of sets to introduce modern notions in these spaces, specifically supra ⱨ - interior, supra ⱨ - closure, supra ⱨ - limit points, supra ⱨ - boundary points and supra ⱨ - exterior of sets. It has been examining the relationship with supra open. The research was also enriched with many

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

 A simulation study is used to examine the robustness of some estimators on a multiple linear regression model with problems of multicollinearity and non-normal errors, the Ordinary least Squares (LS) ,Ridge Regression, Ridge Least Absolute Value (RLAV), Weighted Ridge (WRID), MM and a robust ridge regression estimator MM estimator, which denoted as RMM this is the modification of the Ridge regression by incorporating robust MM estimator . finialy, we show that RMM is the best among the other estimators

Here, we found an estimation of best approximation of unbounded functions which satisfied weighted Lipschitz condition with respect to convex polynomial by means of weighted Totik-Ditzian modulus of continuity