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 β-normed app- spaces are norm bounded with a condition. We show that functions of β-normed Banach spaces are β- contraction, with some results and properties. The sequentially β-contraction is also explained and the relation between metric β- app- space and Hausdorff space is studied.
Television white spaces (TVWSs) refer to the unused part of the spectrum under the very high frequency (VHF) and ultra-high frequency (UHF) bands. TVWS are frequencies under licenced primary users (PUs) that are not being used and are available for secondary users (SUs). There are several ways of implementing TVWS in communications, one of which is the use of TVWS database (TVWSDB). The primary purpose of TVWSDB is to protect PUs from interference with SUs. There are several geolocation databases available for this purpose. However, it is unclear if those databases have the prediction feature that gives TVWSDB the capability of decreasing the number of inquiries from SUs. With this in mind, the authors present a reinforcement learning-ba
... Show MoreHuman interest in negative space has existential roots, in addition to its cognitive value of things. In the environment, it includes space features from facts and activities, as negative space plays an active role in the field of visual perception, and this value comes from the need to absorb vital relationships in its environment, Man represents the positive part of negative space through his presence in this environment, and therefore this is reflected in the design of its types and the function of each element in the design, for the real effectiveness that the elements gain and their impact comes through the negative space that surrounds them and organizes their relationships with other elements, that the orientation is distributed a
... Show MorePhilosophy of Abstraction and Construction of Space in Contemporary Iraqi Theater Abstract The aesthetic and stylistic features in the theatrical play develop according to the changes of the age and its developments. Stylistic forms different from the prevailing and familiar in the visions of contemporary theatre directors emerged which adopt the removal of traditional awareness in the creation of the visual space of theatrical discourse, through adopting contemporary formats and structures which depend on the abstraction representations in the aesthetic construction of the contemporary theatre show which is one of the prerequisites of the postmodern theater, that produces aesthetic data based on abstract metaphors in the formation of th
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The research aimed to test the relationship between the size of investment allocations in the agricultural sector in Iraq and their determinants using the Ordinary Least Squares (OLS) method compared to the Error Correction Model (ECM) approach. The time series data for the period from 1990 to 2021 was utilized. The analysis showed that the estimates obtained using the ECM were more accurate and significant than those obtained using the OLS method. Johansen's test indicated the presence of a long-term equilibrium relationship between the size of investment allocations and their determinants. The results of th
... Show MoreThe aim of this paper is to introduces and study the concept of CSO-compact space via the notation of simply-open sets as well as to investigate their relationship to some well known classes of topological spaces and give some of his properties.
The definition of semi-preopen sets were first introduced by "Andrijevic" as were is defined by :Let (X , ï´ ) be a topological space, and let A ⊆, then Ais called semi-preopen set if ⊆∘ . In this paper, we study the properties of semi-preopen sets but by another definition which is equivalent to the first definition and we also study the relationships among it and (open, α-open, preopen and semi-p-open )sets.
Graceful labeling of a graph with q edges is assigned the labels for its vertices by some integers from the set such that no two vertices received the same label, where each edge is assigned the absolute value of the difference between the labels of its end vertices and the resulting edge labeling running from 1 to inclusive. An edge labeling of a graph G is called vertex anntimagic, if all vertex weights are pairwise distinct, where the vertex weight of a vertex under an edge labeling is the sum of the label of all edges incident with that vertex. In this paper, we address the problem of finding graceful antimagic labelin for split of the star graph , graph, graph, jellyfish graph , Dragon graph , ki
... Show MoreThroughout this paper R represents commutative ring with identity and M is a unitary left R-module. The purpose of this paper is to investigate some new results (up to our knowledge) on the concept of weak essential submodules which introduced by Muna A. Ahmed, where a submodule N of an R-module M is called weak essential, if N ? P ? (0) for each nonzero semiprime submodule P of M. In this paper we rewrite this definition in another formula. Some new definitions are introduced and various properties of weak essential submodules are considered.
In this paper we define and study new concepts of functions on fibrewise topological spaces over B namely, fibrewise weakly (resp., closure, strongly) continuoac; funttions which are analogous of weakly
(resp., closure, strongly) continuous functions and the main result is : Let <p : XY be a fibrewise closure (resp., weakly, closure, strongly, strongly) continuous function, where Y is fibrewise topological space over B and X is a fibrewise set which has the
in
... Show MoreA class of hyperrings known as divisible hyperrings will be studied in this paper. It will be presented as each element in this hyperring is a divisible element. Also shows the relationship between the Jacobsen Radical, and the set of invertible elements and gets some results, and linked these results with the divisible hyperring. After going through the concept of divisible hypermodule that presented 2017, later in 2022, the concept of the divisible hyperring will be related to the concept of division hyperring, where each division hyperring is divisible and the converse is achieved under conditions that will be explained in the theorem 3.14. At the end of this paper, it will be clear that the goal of this paper is to study the concept
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