A non-polynomial spline (NPS) is an approximation method that relies on the triangular and polynomial parts, so the method has infinite derivatives of the triangular part of the NPS to compensate for the loss of smoothness inherited by the polynomial. In this paper, we propose polynomial-free linear and quadratic spline types to solve fuzzy Volterra integral equations (FVIE) of the 2nd kind with the weakly singular kernel (FVIEWSK) and Abel's type kernel. The linear type algorithm gives four parameters to form a linear spline. In comparison, the quadratic type algorithm gives five parameters to create a quadratic spline, which is more of a credit for the exact solution. These algorithms process kernel singularities with a simple techniqu

Background. “Polyetheretherketone (PEEK)” is a biocompatible, high-strength polymer that is well-suited for use in dental applications due to its unique properties. However, achieving good adhesion between PEEK and hydrophilic materials such as dental adhesives or cement can be challenging. Also, this hydrophobicity may affect the use of PEEK as an implant material. Surface treatment or conditioning is often necessary to improve surface properties. The piranha solution is the treatment of choice to be explored for this purpose. Methods. PEEK disks of 10 mm diameter and 2 mm thickness were used in this study. Those samples were divided into five groups (each group has five samples). The first is the control group, in which no

In this study, a new technique is considered for solving linear fractional Volterra-Fredholm integro-differential equations (LFVFIDE's) with fractional derivative qualified in the Caputo sense. The method is established in three types of Lagrange polynomials (LP’s), Original Lagrange polynomial (OLP), Barycentric Lagrange polynomial (BLP), and Modified Lagrange polynomial (MLP). General Algorithm is suggested and examples are included to get the best effectiveness, and implementation of these types. Also, as special case fractional differential equation is taken to evaluate the validity of the proposed method. Finally, a comparison between the proposed method and other methods are taken to present the effectiveness of the proposal meth

    Fuzzy numbers are used in various fields such as fuzzy process methods, decision control theory, problems involving decision making, and systematic reasoning. Fuzzy systems, including fuzzy set theory. In this paper, pentagonal fuzzy variables (PFV) are used to formulate linear programming problems (LPP). Here, we will concentrate on an approach to addressing these issues that uses the simplex technique (SM). Linear programming problems (LPP) and linear programming problems (LPP) with pentagonal fuzzy numbers (PFN) are the two basic categories into which we divide these issues. The focus of this paper is to find the optimal solution (OS) for LPP with PFN on the objective function (OF) and right-hand side. New ranking f

Attention has recently been given to finding alternative and sustainable raw material sources for wood and metal adhesives, such as polyvinyl alcohol (PVA), corn starch (CS), arabic gum (AG), and dextrins (D). Modifying polymer dispersion using unique substances, such as modifying reactive elastomer liquid (EL) using PVA, CS, AG, or D results in sufficiently moisture-resistant adhesive joins. In the present study, the physical characteristics of EL/blended with the natural polymers PVA, CS, AG, and D, based on high-density fiberboard (HDF) wood and aluminum (Al) adhesives and coatings, were investigated and compared to those of pure EL. The EL was blended with PVA, CS, AG, or D at a ratio of 60/40 (w/w) to form EL/blends. The che

The purpose of this research is to investigate the impact of corrosive environment (corrosive ferric chloride of 1, 2, 5, 6% wt. at room temperature), immersion period of (48, 72, 96, 120, 144 hours), and surface roughness on pitting corrosion characteristics and use the data to build an artificial neural network and test its ability to predict the depth and intensity of pitting corrosion in a variety of conditions. Pit density and depth were calculated using a pitting corrosion test on carbon steel (C-4130). Pitting corrosion experimental tests were used to develop artificial neural network (ANN) models for predicting pitting corrosion characteristics. It was found that artificial neural network models were shown to be

Abstract The surface of kaolin was diagnosed by an AFM and the results were shown The height of the highest peak reached by a quantity of Kaolin ‎surface is 2.5 µm, the granules, and their diameter with an average diameter of 666.1nm. Using Kaolin's adsorption properties, erythrosine was removed of its aqueous solution. It was determined that the maximal dye adsorption ranged 36.53–40.61%. ‎‎‎‎The results of using the Freundlich, Langmuir, and Temkin adsorption isotherms revealed that at temperatures of (298,308,318) K, the Freundlich model was followed, the Langmuir model did not match, and the Temkin model could only be partially applied. There is also physical adsorption. One of the three kinetic models of the