The basic concepts of some near open subgraphs, near rough, near exact and near fuzzy graphs are introduced and sufficiently illustrated. The Gm-closure space induced by closure operators is used to generalize the basic rough graph concepts. We introduce the near exactness and near roughness by applying the near concepts to make more accuracy for definability of graphs. We give a new definition for a membership function to find near interior, near boundary and near exterior vertices. Moreover, proved results, examples and counter examples are provided. The Gm-closure structure which suggested in this paper opens up the way for applying rich amount of topological facts and methods in the process of granular computing.

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.

This 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.

Abstract. This study gives a comprehensive analysis of the properties and interactions of fibrewise maximal and minimal topological spaces. Fibrewise topology extends classical topological concepts to structured spaces, providing a thorough understanding of spaces that vary across different dimensions. We study the basic theories, crucial properties, and characterizations of maximal and minimal fibrewise topological spaces. We investigate their role in different mathematical contexts and draw connections with related topological concepts. By providing exact mathematical formulations and comprehensive examples, this abstract advances the fields of topology and mathematical analysis by elucidating the unique properties and implications of fib

Wastewater treatment plants operators prefer to make adjustments because they are more cost effective, to use the existing tank instead of building new ones. In this case an imported materials would be  used as bio-loads to increase biomass and thus maintain efficiency as the next organic loading increases.In the present study, a local substance "pumice stone" was used as a biological carrier in the aeration tank, and the experiments were carried out in five stages: without biological carriers, filling ratio of 4%,10%,20%, and25% with pumice stone, the maximum organic loading at each stage (1.1884, 1.2144, 1.9432, 2.7768, 3.3141)g BOD /l.d respectively.Other experiments were carried out to determine the best filling ratio, the SS remova

New 1,2,4-triazole derivatives of 2-mercaptobenzimidazole (MB) are reported. Ethyl (benzimidazole-2-yl thio) acetate (1) has been prepared by condensing 2-mercaptobenzimidazole with ethylchloroacetate. The ester (1) on reacting with hydrazine hydrate gave the corresponding acetohydrazide(2)which was reacted separately with phenylisocyanate and phenylisothiocyanate, followed by ring closure in an alkaline medium giving 3-[(benzimidazole-2-yl thio) methyl]-4-phenyl-1,2,4-triazole-5-ol and 3-[(benzimidazole-2-yl thio) methyl]-4-phenyl-1,2,4-triazole-5-thiol respectively (6,7). Reaction of acetohydrazide (2) with CS2 and ethanol/KOH, gave dithiocarbazate salt (8). Cyclization of (8) with hydrazine hydrate gave 3-[(benzimi

Preparation of identical independent photons is the core of many quantum applications such as entanglement swapping and entangling process. In this work, Hong-Ou-Mandel experiment was performed to evaluate the degree of indistinguishability between independent photons generated from two independent weak coherent sources working at 640 nm. The visibility was 46%, close to the theoretical limit of 50%. The implemented setup can be adopted in quantum key distribution experiments carried out with free space as the channel link, as all the devices and components used are operative in the visible range of the electromagnetic spectrum.