This work aims to introduce and to study a new kind of divisor graph which is  called idempotent divisor graph, and it is  denoted by . Two non-zero distinct vertices v₁ and v₂ are adjacent if and only if , for some non-unit idempotent element . We establish some fundamental properties of ,  as well as it’s connection with . We also study planarity of this graph.

Background: Restoration of the gingival margin of Class II cavities with composite resin continues to be problematic, especially where no enamel exists for bonding to the gingival margin. The aim of study is to evaluate the marginal leakage at enamel and cementum margin of class II MOD cavities using amalgam restoration and modern composite restorations Filtek™ P90, Filtek™ Z250 XT (Nano Hybrid Universal Restorative) and SDR bulk fill with different restoratives techniques. Materials and method: Eighty sound maxillary first premolar teeth were collected and divided into two main groups, enamel group and cementum group (40 teeth) for each group. The enamel group was prepared with standardized Class II MOD cavity with gingival margin (1 m

The dual nature of asphalt binder necessitates improvements to mitigate rutting and fatigue since it performs as an elastic material under the regime of rapid loading or cold temperatures and as a viscous fluid at elevated temperatures. The present investigation assesses the effectiveness of Nano Alumina (NA), Nano Silica (NS), and Nano Titanium Dioxide (NT) at weight percentages of 0, 2, 4, 6, and 8% in asphalt cement to enhance both asphalt binder and mixture performance. Binder evaluations include tests for consistency, thermal susceptibility, aging, and workability, while mixture assessments focus on Marshall properties, moisture susceptibility, resilient modulus, permanent deformation, and fatigue characteristics. NS notably im

Background and aim: Pomegranate is a medicinal herb that can promote healing of periodontal tissue through differentiation of mesenchymal cells both in vivo and in vitro. Therefore, this study is to investigate the effect of oral supplementation of Punicagranatum L. peel extract on bone defect in rabbit. Methods: Forty five male rabbits were divided into 3 groups; group 1; baseline group(5 rabbits) left without bone defect. Group 2; study group (20 rabbits) with bone defect model that received daily 1ml of oral supplementation of pomegranate peel extract (PoPx). Group 3; control group (20 rabbits) with bone defect model that received distilled water. Bone defect was done into facial plate of lower right central incisor. Blood biopsies by

Let
be an
module, and let
be a set, let
be a soft set over
. Then
is said to be a fuzzy soft module over
iff
,
is a fuzzy submodule of
. In this paper, we introduce the concept of fuzzy soft modules over fuzzy soft rings and some of its properties and we define the concepts of quotient module, product and coproduct operations in the category of
modules.

Micro metal forming has an application potential in different industrial fields. Flexible tool-assisted sheet metal forming at micro scale is among the forming techniques that have increasingly attracted wide attention of researchers. This forming process is a suitable technique for producing micro components because of its inexpensive process, high quality products and relatively high production rate. This study presents a novel micro deep drawing technique through using floating ring as an assistant die with flexible pad as a main die. The floating ring designed with specified geometry is located between the process workpiece and the rubber pad. The function of the floating ring in this work is to produce SS304 micro cups with profile

Statistical learning theory serves as the foundational bedrock of Machine learning (ML), which in turn represents the backbone of artificial intelligence, ushering in innovative solutions for real-world challenges. Its origins can be linked to the point where statistics and the field of computing meet, evolving into a distinct scientific discipline. Machine learning can be distinguished by its fundamental branches, encompassing supervised learning, unsupervised learning, semi-supervised learning, and reinforcement learning. Within this tapestry, supervised learning takes center stage, divided in two fundamental forms: classification and regression. Regression is tailored for continuous outcomes, while classification specializes in c

The aim of this paper is to compare between classical and fuzzy filters for removing different types of noise in gray scale images. The processing used consists of three steps. First, different types of noise are added to the original image to produce a noisy image (with different noise ratios). Second, classical and fuzzy filters are used to filter the noisy image. Finally, comparing between resulting images depending on a quantitative measure called Peak Signal-to-Noise Ratio (PSNR) to determine the best filter in each case.
The image used in this paper is a 512 * 512 pixel and the size of all filters is a square window of size 3*3. Results indicate that fuzzy filters achieve varying successes in noise reduction in image compared to

    In this paper further properties of the fuzzy complete a-fuzzy normed algebra have been introduced. Then we found the relation between the maximal ideals of fuzzy complete a-fuzzy normed algebra and the associated multiplicative linear function space. In this direction we proved that if  is character on Z then ker is a maximal ideal in Z. After this we introduce the notion structure of the a-fuzzy normed algebra then we prove that the structure, st(Z) is -fuzzy closed subset of fb(Z, ) when  (Z,  , , ) is a commutative fuzzy complete a-fuzzy normed algebra with identity e.

In this paper the definition of fuzzy normed space is recalled and its basic properties. Then the definition of fuzzy compact operator from fuzzy normed space into another fuzzy normed space is introduced after that the proof of an operator is fuzzy compact if and only if the image of any fuzzy bounded sequence contains a convergent subsequence is given. At this point the basic properties of the vector space FC(V,U)of all fuzzy compact linear operators are investigated such as when U is complete and the sequence ( ) of fuzzy compact operators converges to an operator T then T must be fuzzy compact. Furthermore we see that when T is a fuzzy compact operator and S is a fuzzy bounded operator then the composition TS and ST are fuzzy compact