R. Vasuki [1] proved fixed point theorems for expansive mappings in Menger spaces. R. Gujetiya and et al [2] presented an extension of the main result of Vasuki, for four expansive mappings in Menger space. In this article, an important lemma is given to prove that the iteration sequence is Cauchy under suitable condition in Menger probabilistic G-metric space (shortly, MPGM-space). And then, used to obtain three common fixed point theorems for expansive type mappings.

Background: Nasal obstruction is common in otorhinolaryngology outpatient visitors. The diagnosis of such compliant is by history, clinical examination and diagnostic procedures. Nasal endoscopy and computerized tomography scan are common diagnostic investigations. Nasal obstruction is either anterior or posterior (nasal septal deviations, hypertrophied turbinate pathological cyst, polyps, mass etc), or postnasal obstruction (hypertrophied turbinate, adenoid hypertrophy, nasopharyngeal cyst or nasopharyngeal tumors).

Aim of study: Prospective study to compare endoscopic finding and computerized tomography of nose, paranasal sinuses and postnasal space as diagnostic methods for nasal obstruction and other nose, p

This paper examines the gaps in Lebanese building law as well as the exploitation of contractors, stakeholders, and residents in order to make illegal profits at the expense of The Shape of urban agglomerations and their expansion in cities and rural areas, which is contrary to the principles of sustainable land development. It also emphasizes the amplification of the factors of vertical and horizontal building investments in the implementation of buildings contrary to the license, as well as the burden that this places on the city's resulting infrastructure and ability to absorb the activities and needs of its residents. The study then presents recommendations in the process of transformation in the technique of planning and application

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 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.

<p>In this paper, we prove there exists a coupled fixed point for a set- valued contraction mapping defined on X× X , where X is incomplete ordered G-metric. Also, we prove the existence of a unique fixed point for single valued mapping with respect to implicit condition defined on a complete G- metric.</p>

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

The digital revolution had greatly affected the methods through which we communicate, starting from the basic concepts of the internet technology and the web content in addition to the important issues that concern the culture of the digital media, the internet governance and the variation in the digital age in general and the graphic and internal design in particular.
This research addresses an important topic that goes along with the scientific development in the field of the digital design, especially in the internal and graphic designs. This study consists of two sections: the first includes the problem of the study and the need for it. Starting from the problem of the research, there is no clear perception of the formal characte

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.