The aim of this paper is to present a method for solving high order ordinary differential equations with two point's boundary condition, we propose semi-analytic technique using two-point oscillatory interpolation to construct polynomial solution. The original problem is concerned using two-point oscillatory interpolation with the fit equal numbers of derivatives at the end points of an interval [0 , 1] . Also, many examples are presented to demonstrate the applicability, accuracy and efficiency of the method by comparing with conventional methods.

In many applications such as production, planning, the decision maker is important in optimizing an objective function that has fuzzy ratio two functions which can be handed using fuzzy fractional programming problem technique. A special class of optimization technique named fuzzy fractional programming problem is considered in this work when the coefficients of objective function are fuzzy. New ranking function is proposed and used to convert the data of the fuzzy fractional programming problem from fuzzy number to crisp number so that the shortcoming when treating the original fuzzy problem can be avoided. Here a novel ranking function approach of ordinary fuzzy numbers is adopted for ranking of triangular fuzzy numbers with simpler an

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

The need to constantly and consistently improve the quality and quantity of the educational system is essential. E-learning has emerged from the rapid cycle of change and the expansion of new technologies. Advances in information technology have increased network bandwidth, data access speed, and reduced data storage costs. In recent years, the implementation of cloud computing in educational settings has garnered the interest of major companies, leading to substantial investments in this area. Cloud computing improves engineering education by providing an environment that can be accessed from anywhere and allowing access to educational resources on demand. Cloud computing is a term used to describe the provision of hosting services

Objective To investigate the accuracy of gingival crevicular fluid (GCF) E-cadherin and total antioxidant capacity (TAC) to discriminate periodontal health from disease. Subjects and Methods GCF samples were collected from participants with periodontal health (control), gingivitis, and periodontitis (n = 25 each group). The latter group was further subdivided according to stage (S) and grade. Periodontal parameters were recorded then levels of biomarkers were assayed using ELISA and antioxidant status by use of the Total Antioxidant Capacity Assay for E-cadherin and TAC, respectively. Results All periodontal parameters were significantly higher in periodontally diseased groups than controls. The GCF E-cadherin significantly increased

The preparation of the title compound, C₂₆H₂₅N, was achieved by the condensation of an ethanolic mixture of benzaldehyde, cyclohexanone and ammonium acetate in a 2:1:1 molar ratio. There are two crystallographically independent molecules in the asymmetric unit. The two cyclohexyl rings adopt ananti-envelope conformation with the benzyl moiety adopting acisconformation with respect to the nitrogen atom of the phenanthridine segment. In the crystal, molecules are linked through C—H...N interactions into hydrogen-bonded chains that are further arranged into distinct layers by weak offset π–π interactions.