The computational method based on using the operational matrix of an orthogonal function for solving variational problems is computer-oriented. In this approach, a truncated Hartley series together with the operational matrix of integration and integration of the cross product of two case vectors are used for finding the solution of variational problems. Two illustrative examples are included to demonstrate the validity and applicability of the technique.

Direct ophthalmoscopy is a medical examination used in emergency departments and clinics to diagnose important systematic diseases and screen chronic diseases. Despite the importance of this examination, studies have shown that medical staff is not enough enabled perform it. In this article, we will discuss the novel medical simulation that helps to learn how to examine patients' eyes with a Direct ophthalmoscope. This cutting-edge technology is designed to mimic details of the human eye in various pathological conditions with providing realistic and immersive experiences for users. Helps medical students and medical staff to practice repeatably Direct ophthalmoscopy in different diseases.

Light spectrum is one of the environmental cues that influence plant growth and development. Light is a stimulating factor for induction of somatic embryos during tissue culture practices. To accelerate the Direct embryogenesis, six different light spectra including: white (W), red (R), blue (B), green (G), red + blue (R+B) and red + far red (R+FR) together with dark condition (D), in combination with thidiazuron (TDZ) in four concentrations (0, 0. 5, 1. 5 and 3 mg L-1) were used. Inter-simple sequence repeat was used for identification and genetic stability analysis of somatic regenerated plantlets. Intact protocorm explants showed higher potential for Direct somatic embryogenesis (DSE) than the other explants. The rate of DSE was highly dependent on the concentration of TDZ and its interaction with light spectra. R and R + FR spectra with 3 mg L-1 TDZ on intact protocorms and R+FR with 3 mg L-1 TDZ were efficient treatments to induce DSE without somaclonal variation. G light spectrum has also significant effects on DSE of protocorm explants. The amplified products showed 26 scorable bands and regenerates were completely identical to the mother plant. In conclusion, this protocol provides way to regenerate plants through embryogenesis, and is a reliable protocol to obtain proper development and genetic stable Phalaenopsis embryos.

In this paper, we propose Direct methods to solve linear delay di erential equations (LDDEs) based on vector forms of Block-Pulse Functions (BPFs) and Triangular Functions (TFs). Operational matrix of integration of BPFs and TFs is applied to transform LDDE to a linear system of algebraic equations. Furthermore, some numerical examples are presented to indicate the reliability and the accuracy of these methods. Convergence analysis of the present method has been discussed, too.