Researchers have identified and defined β- approach normed space if some conditions are  satisfied. In this work, we show that every approach normed space is a normed space.However, the converse is not necessarily true by giving an example. In addition, we define β – normed Banach space, and some examples are given. We also solve some problems. We discuss a finite β-dimensional app-normed space is β-complete and consequent Banach app- space. We explain that every approach normed space is a metric space, but the converse is not true by giving an example. We define β-complete and give some examples and propositions. If we have two normed vector spaces, then we get two properties that are equivalent. We also explain that

In this work, two different structures are proposed which is fuzzy real normed space (FRNS) and fuzzy real Pre-Hilbert space (FRPHS). The basic concept of fuzzy norm on a real linear space is first presented to construct  space, which is a FRNS with some modification of the definition introduced by G. Rano and T. Bag. The structure of fuzzy real Pre-Hilbert space (FRPHS) is then presented which is based on the structure of FRNS. Then, some of the properties and related concepts for the suggested space FRN such as -neighborhood, closure of the set  named , the necessary condition for separable, fuzzy linear manifold (FLM) are discussed. The definition for a fuzzy seminorm on  is also introduced with the prove that a fuzzy seminorm on

The process of converting gray images or videos to color ones by adding colors to them and transforming them from one-dimension to three-dimension is called colorization. This process is often used to make the image appear more visually appealing. The main problem with the colorization process is the lack of knowledge of the true colors of the objects in the picture when it is captured. For that, there is no a unique solution. In the current work, the colorization of gray images is proposed based on the utilization of the YCbCr color space. Reference image (color image) is selected for transferring the color to a gray image. Both color and gray images are transferred to YCbCr color space. Then, the Y value of the gray image is combined w

The artistic concepts differ in their expressive and semantic relations, among these concepts are the artistic values, as there are points of view, social concepts and historical values interacted from one generation to another over the time. These values represent symbols and indications reflect reality, which has passed through the time to reach us with environmental forms saved by the history at the Natural History Museum, has an impact on the receives mind with its formal and sensory dimensions and connecting with that history as an environment that lacks to the current reality which has immortal means particularly in the cognitive thinking , and the reflection of that in the Iraqi culture and with the associated concepts of interior

problem of the research is the decline of the role of urban space with time as an influential system in societal relations. The research aims to define indicators for achieving social interaction in the city, and to determine indicators for achieving integration in the urban space, and to study the relationship between the integration of urban space and community interaction over time. the research assumed that by distinguishing the social interaction space from the urban space and developing urban spaces in order to be truly interactive spaces, this will help us achieve social interaction and build a positive relationship between them, which enables us to achieve integration within the urban spaces leading to social interaction. Because

The elements of theater formation that fall within the spatial experience of the scenography of the show, which the directors work in in the imaginary theater, are important and have an aesthetic, intellectual and cognitive dimension, working to highlight reality in an aesthetic image surrounding space and space. And its relationship to the distinct, multiple and variable spaces above the stage, to produce theatrical signals and endless meanings through the possibility of infinite reconfiguration of the theater's space and its public and private space through the distribution of a group of blocks within the scenic image.
I dealt with in the first chapter (the methodological framework), which includes the research problem identified

The research dealt with the study (interpretation of space in the art of installation), and it is located in four frameworks, the first is devoted to clarifying the research problem, its importance and the need for it, its goal, and its limits, and determining the most important terms contained therein.The research problem was determined from the question, does space embody those different and diverse materials that were formulated and installed by the artist into modern forms? Is the product of synthetic arts an appropriation of these spaces and domination of them?The problematic of interpreting space in its conceptual dimension in (synthetic) art in its multiplicity, diversity and difference, or objecting to the work of artistic system

   This paper aims to prove an existence theorem for Voltera-type equation in a generalized G- metric space, called the -metric space, where the fixed-point theorem in - metric space is discussed and its application.  First, a new contraction of Hardy-Rogess type is presented and also then fixed point theorem is established for these contractions in the setup of -metric spaces. As application, an existence result for Voltera integral equation is obtained.  

This paper presents a new transform method to solve partial differential equations, for finding suitable accurate solutions in a wider domain. It can be used to solve the problems without resorting to the frequency domain. The new transform is combined with the homotopy perturbation method in order to solve three dimensional second order partial differential equations with initial condition, and the convergence of the solution to the exact form is proved. The implementation of the suggested method demonstrates the usefulness in finding exact solutions. The practical implications show the effectiveness of approach and it is easily implemented in finding exact solutions.

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