This paper contains an equivalent statements of a pre-  space, where  are considered subsets of with the product topology. An equivalence relation between the preclosed set  and a pre-  space, and a relation between a pre-  space and the preclosed set  with some conditions on a function  are found. In addition, we have proved that the graph  of  is preclosed in if  is a pre-  space, where the equivalence relation  on  is open.

     On the other hand, we introduce the definition of a pre-stable ( pre-stable) set by depending on the concept of a pre-neighborhood, where we get that every stable set is pre-stable. Moreover, we obtain that

    The main objective of this work is to generalize the concept of  fuzzy algebra by introducing the notion of  fuzzy algebra. Characterization and examples of the proposed generalization are presented, as well as several different properties of  fuzzy algebra are proven. Furthermore, the relationship between fuzzy algebra and fuzzy algebra is studied, where it is shown that the fuzzy algebra is a generalization of fuzzy algebra too. In addition, the notion of restriction, as an important property in the study of measure theory, is studied as well. Many properties of restriction of a nonempty family of fuzzy subsets of fuzzy power set are investigated and it is shown that the restriction of fuzzy algebra is fuzzy algebra too.

The goal of this discussion is to study the twigged of pure-small (pr-small) sub- moduleof a module W as recirculation of a small sub-module, and we give some basic idiosyncrasy and instances of this kind of sub-module. Also, we give the acquaint of pure radical of a module W (pr-radical) with peculiarities.

Petrography and physicomechanical characteristics of Iyuku granite from southwestern Nigeria were investigated. Rock and aggregate samples were obtained from five different quarry sites for thin-sectioning and physical and mechanical tests. The rock slides were subjected to petrographic analysis, while the aggregates were tested for the parameters of specific gravity (S.G), water absorption, aggregate impact value (AIV), aggregate crushing value (ACV), Los Angeles abrasion value (LAAV), and flakiness and elongation indices in accordance with the British Standards (B.S), American Standards for Testing Materials (ASTM) and Federal Ministry of Works Standards (FMWS). The petrographic, physical, and mechanical characteristics were described

     Various document types play an influential role in a lot of our lives activities today; hence preserving their integrity is an important matter. Such documents have various forms, including texts, videos, sounds, and images.  The latter types' authentication will be our concern here in this paper. Images can be handled spatially by doing the proper modification directly on their pixel values or spectrally through conducting some adjustments to some of the addressed coefficients. Due to spectral (frequency) domain flexibility in handling data, the domain coefficients are utilized for the watermark embedding purpose. The integer wavelet transform (IWT), which is a wavelet transform based on the lifting scheme,

Consider the (p,q) simple connected graph . The sum absolute values of the spectrum of quotient matrix of a graph  make up the graph's quotient energy. The objective of this study is to examine the quotient energy of identity graphs and zero-divisor graphs  of commutative rings using group theory, graph theory, and applications. In this study, the identity graphs  derived from the group  and a few classes of zero-divisor graphs  of the commutative ring R are examined.

New substituted anthraquinones with amino derivations fragments were synthesized through the substitution of bromine atom by different amines using the Ullmann coupling reaction. Obtained compounds based on anthraquinone used for experimental antimicrobial studies. The structure of the synthesized compounds was confirmed by LC-MS and ¹H, ¹³C NMR spectroscopy. Studies on planktonic microorganisms have shown that the first synthesized anthraquinone derivatives have an inhibitory effect against bacteria and fungi. The triazene 1-(3-(benzoic acid(triaz-1-en-1-ol(-4-(1H-imidazol-1-yl(-9,10-dioxo-9,10-dihydroanthracene -2-sulfonic acid, have wide spectrum of activity, growth retardation zones against gram-positive micro

A comprehensive review focuses on 3D network-on-chip (NoC) simulators and plugins while paying attention to the 2D simulators as the baseline is presented. Discussions include the programming languages, installation configuration, platforms and operating systems for the respective simulators. In addition, the simulator’s properties and plugins for design metrics evaluations are addressed. This review is intended for the early career researchers starting in 3D NoC, offering selection guidelines on the right tools for the targeted NoC architecture, design, and requirements.