Abstract. The purpose of this work is to introduce and investigate new concepts of mappings namely nano paracompactmappings, nano locally limited, nano h-locally limited and finally nano-perfect in nano topology by using nano-closed sets. As well as, the relation between these concepts of mappings have been study in nano topology. Additionally, the nano topology groups of the types and advances results which are introduces in this work are very vital. We also presented the type of nano Lindeloff mappings, and the relations of them was introduce and discussed with several characteristics related it. Nano morphism also introduce.

In this paper, we will introduce and study the concept of nano perfect mappings by using the definition of nano continuous mapping and nano closed mapping, study the relationship between them, and discuss them with many related theories and results. The k-space and its relationship with nano-perfect mapping are also defined.

The soft sets were known since 1999, and because of their wide applications and their great flexibility to solve the problems, we used these concepts to define new types of soft limit points, that we called soft turning points.Finally, we used these points to define new types of soft separation axioms and we study their properties.

Graph  is a tool that can be used to simplify and solve network problems. Domination is a typical network problem that graph theory is well suited for. A subset of nodes in any network is called dominating if every node is contained in this subset, or is connected to a node in it via an edge. Because of the importance of domination in different areas, variant types of domination have been introduced according to the purpose they are used for. In this paper, two domination parameters the first is the restrained and the second is secure domination have been chosn. The secure domination, and some types of restrained domination in one type of trees is called complete ary tree  are determined.

 Most of the propositions, after the Arabic letter reached a position of integrity and proficiency, the calligrapher turned to the production of calligraphic formations in various aesthetic and expressive forms, investing the spiritual energies in what these calligraphic compositions show in artistic paintings. It carries a lot of meanings that are embodied in linear formations, and in order to reach these expressions and know the effective positions of space, this research is concerned with studying these technical treatments. The first chapter included the research problem, which included a question about the effectiveness of space in the linear painting, the importance of research and the temporal and spatial boundaries. As for the s

In this study, the behavior of square helical piles models (5×5) mm² embedded in expansive soil bed overlaying a layer of sandy soil was investigated. The sand layer 200mm thickness was compacted into four sub layers in a steel container with diameter 400mm in size. Sandy soil layer was compacted into two relative densities 40% and 80%. The bed of ثءحties 40% and 80%.The bed of o00mm in size.Sandy soil layer was compacted into two relative densities 40% and 80%.The bed of oexpansive soil 300mm thickness was compacted into six sub layers on sandy soil layer. Model tests are performed with helical pile length 350mm, 400mm and 450mm and with helix diameter 15mm and 20mm. Also, one helix and double helix were

It is the dynamic tension between the relatively fixed built environment and the constantly changing in social life that determines the nature of urban spaces belonging to different historical periods, and considered as a tool for diagnosing transformations in urban spaces, that’s why, the characteristics of urban space became unclear between positive spaces and negative spaces, so emerged the need to study contemporary urban space belonging to the current period of time and show the most important transformations that have occurred in contemporary urban space to reach urban spaces that meet the current  life requirements. Therefore, the research dealt with a study of the characteristics of contemporary urban space and the most pr

The best proximity point is a generalization of a fixed point that is beneficial when the contraction map is not a self-map. On other hand, best approximation theorems offer an approximate solution to the fixed point equation . It is used to solve the problem in order to come up with a good approximation. This paper's main purpose is to introduce new types of proximal contraction for nonself mappings in fuzzy normed space and then proved the best proximity point theorem for these mappings. At first, the definition of fuzzy normed space is given. Then the notions of the best proximity point and - proximal admissible in the context of fuzzy normed space are presented. The notion of α ̃–ψ ̃- proximal contractive mapping is introduced.

This paper including a gravitational lens time delays study for a general family of lensing potentials, the popular singular isothermal elliptical potential (SIEP), and singular isothermal elliptical density distribution (SIED) but allows general angular structure. At first section there is an introduction for the selected observations from the gravitationally lensed systems. Then section two shows that the time delays for singular isothermal elliptical potential (SIEP) and singular isothermal elliptical density distributions (SIED) have a remarkably simple and elegant form, and that the result for Hubble constant estimations actually holds for a general family of potentials by combining the analytic results with data for the time dela