Most real-life situations need some sort of approximation to fit mathematical models. The beauty of using topology in approximation is achieved via obtaining approximation for qualitative subgraphs without coding or using assumption. The aim of this paper is to apply near concepts in the -closure approximation spaces. The basic notions of near approximations are introduced and sufficiently illustrated. Near approximations are considered as mathematical tools to modify the approximations of graphs. Moreover, proved results, examples, and counterexamples are provided.
The primary objective of this paper is to present a new concept of fibrewise topological spaces over B is said to be fibrewise slightly topological spaces over B. Also, we introduce the concepts of fibrewise slightly perfect topological spaces, filter base, contact point, slightly convergent, slightly directed toward a set, slightly adherent point, slightly rigid, fibrewise slightly weakly closed, H.set, fibrewise almost slightly perfect, slightly∗ .continuous fibrewise slightly∗ topological spaces respectively, slightly Te, locally QHC, In addition, we state and prove several propositions related to these concepts.
In this paper, certain types of regularity of topological spaces have been highlighted, which fall within the study of generalizations of separation axioms. One of the important axioms of separation is what is called regularity, and the spaces that have this property are not few, and the most important of these spaces are Euclidean spaces. Therefore, limiting this important concept to topology is within a narrow framework, which necessitates the use of generalized open sets to obtain more good characteristics and preserve the properties achieved in general topology. Perhaps the reader will realize through the research that our generalization preserved most of the characteristics, the most important of which is the hereditary property. Two t
... Show MoreCement-based adhesive (CBA) is used as a bonding agent in Carbon Fibre Reinforced Polymer (CFRP) applications as an alternative to epoxy-based adhesive due to the drawbacks of the epoxy system under severe service conditions which negatively affect the bond between the CFRP and strengthened elements. This paper reports the results of, an investigation carried out to develop two types of CBA using magnetized water (MW) for mixing and curing. Two magnetic devices (MD-I and MD-II), with different magnetic field strengths (9000 and 6000 Gauss) respectively, were employed for water magnetization. Different water flows with different water circulation times in the magnetizer were used for each device. Compressive and splitting tensile strength te
... Show MoreStraight tendons in pretensioned members can cause high-tensile stresses in the concrete extreme fibers at end sections because of the absence of the bending stresses due to self-weight and superimposed loads and the dominance of the moment due to prestressing force alone. Accordingly, the concrete tensile stresses at the ends of a member prestressed with straight tendons may limit the service load capacity of the member. It is therefore important to establish limiting zone in the concrete section within which the prestressing force can be applied without causing tension in the extreme concrete fibers. Two practical methods are available to reduce the stresses at the end sections due to the prestressing force. The first method based
... Show MoreObjectives: Recently, there have been important advances in the clinical application of targeted hybrid near-infrared (NIR) fluorescent-radioactive tracers. ICG-99mTc-nanocolloid, for example, is already being used by some centres for sentinel lymph node biopsy in head and neck cancer. The radioactive component allows imaging at depths which would not be possible with NIR alone and, once exposed, the NIR fluorescence reporter can be imaged at very high resolution. Gamma detection is currently carried out with a separate hand-held gamma camera or with a non-imaging probe. Visualisation of NIR fluorescence during surgery requires a dedicated NIR camera, several of which are available commercially. We describe a novel hand-held hybrid NIR-gamm
... Show MoreThis paper is concerned with introducing and studying the o-space by using out degree system (resp. i-space by using in degree system) which are the core concept in this paper. In addition, the m-lower approximations, the m-upper approximations and ospace and i-space. Furthermore, we introduce near supraopen (near supraclosed) d. g.'s. Finally, the supra-lower approximation, supraupper approximation, supra-accuracy are defined and some of its properties are investigated.
studied, and its important properties and relationship with both closed and open Nano sets were investigated. The new Nano sets were linked to the concept of Nano ideal, the development of nano ideal mildly closed set and it has been studied its properties. In addition to the applied aspect of the research, a sample was taken from patients infected with viral hepatitis, and by examining the infected people and using closed and open (nano mildly. and nano ideal mildly) sets, the important symptoms that constitute the core of this dangerous examining the infected people and using closed and open (nano mildly. and nano ideal mildly) sets, the important symptoms that constitute the core of this dangerous disease.
The internal administrative spaces of the interior designer formed an obsession for their development and for finding solutions and treatments to advance to enhance the state of adaptation for their employees by providing a healthy, appropriate and sound environment for work and production. . The first chapter focuses on laying theoretical foundations to show what health materials are used in the administrative spaces of the training directorates of the Ministry of Education in Baghdad. The second chapter dealt with the knowledge of health materials, their impact and effectiveness in the interior space, and the variables of their functional characteristics and their work in the interior spaces in a way that enhances the development of
... Show MoreThe main objective of this work is to introduce and investigate fixed point (F. p) theorems for maps that satisfy contractive conditions in weak partial metric spaces (W.P.M.S), and give some new generalization of the fixed point theorems of Mathews and Heckmann. Our results extend, and unify a multitude of (F. p) theorems and generalize some results in (W.P.M.S). An example is given as an illustration of our results.