In this paper, we introduce a new type of functions in bitopological spaces, namely, (1,2)*-proper functions. Also, we study the basic properties and characterizations of these functions . One of the most important of equivalent definitions to the (1,2)*-proper functions is given by using (1,2)*-cluster points of filters . Moreover we define and study (1,2)*-perfect functions and (1,2)*-compact functions in bitopological spaces and we study the relation between (1,2)*-proper functions and each of (1,2)*-closed functions , (1,2)*-perfect functions and (1,2)*-compact functions and we give an example when the converse may not be true .
 

Research studies show that urban green spaces promote physical activity, the health of urban residents, and psychological well-being. Taking the community park in Duhok city as the research object, the spatial service area in terms of accessibility of to the Community Park under the mode of pedestrian transportation is analyzed by using the network analysis service area function of the geographic information system (GIS). The results show that under the walking mode in the research area, Parks are concentrated in the north and south of the city, but community parks are few in disadvantaged neighborhoods. In addition, there is a significant disparity between the number of community parks and the number of communities. Only 11 communities

  We study one example of hyperbolic problems it's Initial-boundary string problem with two ends. In fact we look for the solution in weak sense in some sobolev spaces. Also we use energy technic with Galerkin's method to study some properties for our problem as existence and uniqueness

Abstract. Nano-continuous mappings have a wide range of applications in pure and applied sciences. This paper aims to study and investigate new types of mappings, namely nano-para-compact, completely nano-regular, nano-para-perfect, and countably nano-para-perfect mappings in nano-topological spaces using nano-open sets. We introduce several properties and basic characterizations related to these mappings, which are essential for proving our main results. Additionally, we discuss the relationships among these types of mappings in nano-topological spaces. We also introduce the concept of nano-Ti-mapping, where i = 0, 1, 2, nano-neighborhood separated, and nano-functionally separated, along with various other definitions. We explore the relat

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 work, a weighted H lder function that approximates a Jacobi polynomial which solves the second order singular Sturm-Liouville equation is discussed. This is generally equivalent to the Jacobean translations and the moduli of smoothness. This paper aims to focus on improving methods of approximation and finding the upper and lower estimates for the degree of approximation in weighted H lder spaces by modifying the modulus of continuity and smoothness. Moreover, some properties for the moduli of smoothness with direct and inverse results are considered.

This paper deals with founding an estimation of best approximation of unbounded functions which satisfied weighted Lipschitz condition with respect to the convex polynomials by means of weighted moduli of smoothness of fractional order  , ( , ) p f t . In addition we prove some properties of weighted moduli of smoothness of fractional order.

In this thesis, we introduced the simply* compact spaces which are defined over simply* open set, and study relation between the simply* separation axioms and the compactness were studied and study 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. On the other hand we use the class of soft simply open set to define a new types of separation axioms in soft topological spaces and we introduce the concept of soft simply compactness and study it. We explain and discuss some new concepts in soft topological spaces such as soft simply separated, soft simply disjoint, soft simply division, soft simply limit point and we define soft simply c

Since the beginning of mankind, the view of the sky was present through observations with the naked eye, then it developed with time, and the sciences and tools of astronomical observations developed, including photometric measurements, which reached a high degree of accuracy in describing various cosmic phenomena, including the study of galaxies, their composition, and the differences between them, and from here the importance of this study emerged, to determine the differences between two distinct types of classification of galaxies, which are normal and barred spiral galaxies, where two galaxies NGC 4662 and NGC 2649 were chosen that represented certain types of galaxies to study the morphological structure of the two galaxies, a