This paper is concerned with introducing and studying the new approximation operators based on a finite family of d. g. 'swhich are the core concept in this paper. In addition, we study generalization of some Pawlak's concepts and we offer generalize the definition of accuracy measure of approximations by using a finite family of d. g. 's.

synthesis and characterization of New Bidentate schiff base Ligand Type(NO)Donor Atoms Derived from isatin and 3-Amino benzoic acid and Its complexes with Co(||),Cu(||),Cd(||)and Hg(||)Ions

This book includes four main chapters: 1. Indefinite Integral. 2. Methods of Integration. 3. Definite Integral. 4. Multiple Integral. In addition to many examples and exercises for the purpose of acquiring the student's ability to think correctly in solving mathematical questions.

Reflection cracking in asphalt concrete (AC) overlays is a common form of pavement deterioration that occurs when underlying cracks and joints in the pavement structure propagate through an overlay due to thermal and traffic-induced movement, ultimately degrading the pavement’s lifespan and performance. This study aims to determine how alterations in overlay thickness and temperature conditions, the incorporation of chopped fibers, and the use of geotextiles influence the overlay’s capacity to postpone the occurrence of reflection cracking. To achieve the above objective, a total of 36 prism specimens were prepared and tested using an overlay testing machine (OTM). The variables considered in this study were the thickness of the

Reflection cracking in asphalt concrete (AC) overlays is a common form of pavement deterioration that occurs when underlying cracks and joints in the pavement structure propagate through an overlay due to thermal and traffic-induced movement, ultimately degrading the pavement’s lifespan and performance. This study aims to determine how alterations in overlay thickness and temperature conditions, the incorporation of chopped fibers, and the use of geotextiles influence the overlay’s capacity to postpone the occurrence of reflection cracking. To achieve the above objective, a total of 36 prism specimens were prepared and tested using an overlay testing machine (OTM). The variables considered in this study were the thickness of the

Background: The displacement of artificial teeth during complete denture construction presents major processing errors in the occlusal vertical dimension which were verified at the previous trial denture stage. The aim of this study was to assess the effect of delay in processing after final flask closure and tension application on the vertical acrylic and porcelain teeth displacement of complete dentures constructed from heat cured acrylic and the results were compared with the conventional processing method. Materials and methods: forty samples of identical maxillary complete dentures were constructed from heat polymerized acrylic resin. These samples were subdivided into the following experimental subgroups in which each subgroup contai

Background: This study aimed to apply a high-power pulsed alexandrite laser in vitro, the researchers tested different exposure periods, pulse lengths, and laser fluencies to see which dosage was most successful against S. aureus bacteria, which had developed resistance to many antibiotics. Method: Three bacteria samples were exposed to laser beams for 30 seconds with a 5ms pulse duration and a laser fluency of 5J/cm2. The process was repeated with laser fluencies of 10, 15, and 20. Results: The study was carried out by using different doses of Alexandrite laser. Results: There are significant differences (p = 0.05) in the mean number of bacteria colonies exposed for 30 and 60 seconds at any laser fluencies utilized in the present i

This study aimed to investigate the effect of total suspended solids (TSS) on the performance of a continuously operated dual-chamber microbial fuel cell (MFC) proceeded by primary clarifier to treat actual potato chips processing wastewater. The system was also tested in the absence of the primary clarifier and the results demonstrated a significant effect of TSS on the polarization curve of the MFC which was obtained by operating the graphite anodic electrode against Ag/AgCl reference electrode. The maximum observed power and current densities were decreased form 102.42 mW/m² and 447.26 mA/m² to 80.16 mW/m² and 299.10 mA/m², respectively due to the adverse effect of TSS. Also

The complexes of the 2-hydroxy-4-Nitro phenyl piperonalidene with metal ions Cr(III), Ni(II), Pt(IV) and Zn(II) were prepared in ethanolic solution. These complexes were characterized by spectroscopic methods, conductivity, metal analyses and magnetic moment measurements. The nature of the complexes formed in ethanolic solution was study following the molar ratio method. From the spectral studies, monomer structures proposed for the nickel (II) and Zinc (II) complexes while dimeric structures for the chromium (III) and platinum (IV) were proposed. Octahedral geometry was suggested for all prepared complexes except zinc (II) has tetrahedral geometry, Structural geometries of these compounds were also suggested in gas phase by using