Necessary and sufficient conditions for the operator equation I AXAX n*, to have a real positive definite solution X are given. Based on these conditions, some properties of the operator A as well as relation between the solutions X andAare given.

In this paper, three approximate methods namely the Bernoulli, the Bernstein, and the shifted Legendre polynomials operational matrices are presented to solve two important nonlinear ordinary differential equations that appeared in engineering and applied science. The Riccati and the Darcy-Brinkman-Forchheimer moment equations are solved and the approximate solutions are obtained. The methods are summarized by converting the nonlinear differential equations into a nonlinear system of algebraic equations that is solved using Mathematica®12. The efficiency of these methods was investigated by calculating the root mean square error (RMS) and the maximum error remainder (𝑀𝐸𝑅n) and it was found that the accuracy increases with increasi

A huge potential from researchers was presented for enhancing the nonlinear optical response for materials that interacts by light. In this work, we study the nonlinear optical response for chemically prepared nano- fluid of silver nanoparticles in de-ionized water with TSC (Tri-sodium citrate) protecting agent. By the means of self-defocusing technique and under CW 473 nm blue laser, the reflected diffraction pattern were observed and recorded by CCD camera. The results demonstrate that, the Ag nano-fluid shows a good third order nonlinear response and the magnitude of the nonlinear refractive index was in the order of 10−7 cm2/W. We determine the maximum change of the nonlinear refractive index and the related phase shift for the mat

The research aims to derive the efficient industrial plans for Al – shaheed public company under risk by using Target MOTAD as a linear alternative  model for the quadratic programming models.

The results showed that there had been a sort of (trade- off) between risk and the expected gross margins. And if the studied company strives to get high gross margin, it should tolerate risk and vice versa. So the management  of Al- Shaheed Company to be invited to apply the suitable procedures in the production process, in order to get efficient plans that improves it's  performance .

In the present study, the effect of new cross-section fin geometries on overall thermal/fluid performance had been investigated. The cross-section included the base original geometry of (triangular, square, circular, and elliptical pin fins) by adding exterior extra fins along the sides of the origin fins. The present extra fins include rectangular extra fin of 2 mm (height) and 4 mm (width) and triangular extra fin of 2 mm (base) 4 mm (height). The use of entropy generation minimization method (EGM) allows the combined effect of thermal resistance and pressure drop to be assessed through the simultaneous interaction with the heat sink. A general dimensionless expression for the entropy generation rate is obtained by con

In a connected graph , the distance function between each pair of two vertices from a set vertex  is the shortest distance between them and the vertex degree  denoted by  is the number of edges which are incident to the vertex  The Schultz and modified Schultz polynomials of  are have defined as:

 respectively, where the summations are taken over all unordered pairs of distinct vertices in  and  is the distance between  and  in  The general forms of Schultz and modified Schultz polynomials shall be found and indices of the edge – identification chain and ring – square graphs in the present work.

Based on nonlinear self- diffraction technique, the nonlinear optical properties of thin slice of matter can be obtained. Here, nonlinear characterization of nano-fluids consist of hybrid Single Wall Carbon Nanotubes and Silver Nanoparticles (SWCNTs/Ag-NPs) dispersed in acetone at volume fraction of 6x10-6, 9x10-6, 18x10-6 have been investigated experimentally. Therefore, CW DPSS laser at 473 nm focused into a quartz cuvette contains the previous nano-fluid was utilized. The number of diffraction ring patterns (N) has been counted using Charge - Coupled- Device (CCD) camera and Pc with a certain software, in order to find the maximum change of refractive index ( of fluids. Our result show that the fraction volume of 18x10-6 is more nonli

The development of information systems in recent years has contributed to various methods of gathering information to evaluate IS performance. The most common approach used to collect information is called the survey system. This method, however, suffers one major drawback. The decision makers consume considerable time to transform data from survey sheets to analytical programs. As such, this paper proposes a method called ‘survey algorithm based on R programming language’ or SABR, for data transformation from the survey sheets inside R environments by treating the arrangement of data as a relational format. R and Relational data format provide excellent opportunity to manage and analyse the accumulated data. Moreover, a survey syste