In this paper we use Bernstein polynomials for deriving the modified Simpson's 3/8 , and the composite modified Simpson's 3/8 to solve one dimensional linear Volterra integral equations of the second kind , and we find that the solution computed by this procedure is very close to exact solution.

The research aims to find approximate solutions for two dimensions Fredholm linear integral equation. Using the two-variables of the Bernstein polynomials we find a solution to the approximate linear integral equation of the type two dimensions. Two examples have been discussed in detail.

This study presents a practical method for solving fractional order delay variational problems. The fractional derivative is given in the Caputo sense. The suggested approach is based on the Laplace transform and the shifted Legendre polynomials by approximating the candidate function by the shifted Legendre series with unknown coefficients yet to be determined. The proposed method converts the fractional order delay variational problem into a set of (n ＋ 1) algebraic equations, where the solution to the resultant equation provides us the unknown coefficients of the terminated series that have been utilized to approximate the solution to the considered variational problem. Illustrative examples are given to show that the recommended appro

Background: Various fluids in the oral environment can affect the surface roughness of resin composites. This in vitro study was conducted to determine the influence of the mouth rinses on surface roughness of two methacrylate-based resin (nanofilled and packable composite) and siloraine-based resin composites.

Materials and methods: Disc-shaped specimens (12 mm in diameter and 2mm in height) were prepared from three types of composi

The security of message information has drawn more attention nowadays, so; cryptography has been used extensively. This research aims to generate secured cipher keys from retina information to increase the level of security. The proposed technique utilizes cryptography based on retina information. The main contribution is the original procedure used to generate three types of keys in one system from the retina vessel's end position and improve the technique of three systems, each with one key. The distances between the center of the diagonals of the retina image and the retina vessel's end (diagonal center-end (DCE)) represent the first key. The distances between the center of the radius of the retina and the retina vessel's end (ra

The convergence speed is the most important feature of Back-Propagation (BP) algorithm. A lot of improvements were proposed to this algorithm since its presentation, in order to speed up the convergence phase. In this paper, a new modified BP algorithm called Speeding up Back-Propagation Learning (SUBPL) algorithm is proposed and compared to the standard BP. Different data sets were implemented and experimented to verify the improvement in SUBPL.

Regression testing being expensive, requires optimization notion. Typically, the optimization of test cases results in selecting a reduced set or subset of test cases or prioritizing the test cases to detect potential faults at an earlier phase. Many former studies revealed the heuristic-dependent mechanism to attain optimality while reducing or prioritizing test cases. Nevertheless, those studies were deprived of systematic procedures to manage tied test cases issue. Moreover, evolutionary algorithms such as the genetic process often help in depleting test cases, together with a concurrent decrease in computational runtime. However, when examining the fault detection capacity along with other parameters, is required, the method falls sh

Solid waste is a major issue in today's world. Which can be a contributing factor to pollution and the spread of vector-borne diseases. Because of its complicated nonlinear processes, this problem is difficult to model and optimize using traditional methods. In this study, a mathematical model was developed to optimize the cost of solid waste recycling and management. In the optimization phase, the salp swarm algorithm (SSA) is utilized to determine the level of discarded solid waste and reclaimed solid waste. An optimization technique SSA is a new method of finding the ideal solution for a mathematical relationship based on leaders and followers. It takes a lot of random solutions, as well as their outward or inward fluctuations, t