Dandruff and seborrheic dermatitis (SD) are common skin disorders affecting the scalp and extending to other body sites in the case of SD. They are associated with pruritus and scaling, causing an esthetical disturbance in the population affected.   Treatment of such conditions involves using a variety of drugs for long terms, thus optimizing drug formulation is essential to improve therapeutic efficacy and patient compliance. Conventional topical formulations like shampoos and creams have been widely used but their use is associated with disadvantages. To overcome such effects, novel topical nanotechnology-based formulations are currently under investigation. In the following article, we highlight recently published formulatio

     The method of operational matrices is based on the Bernoulli and Shifted Legendre polynomials which is used to solve the Falkner-Skan equation. The nonlinear differential equation converting to a system of nonlinear equations is solved using Mathematica®12, and the approximate solutions are obtained. The efficiency of these methods was studied by calculating the maximum error remainder ( ), and it was found that their efficiency increases as  increases. Moreover, the obtained approximate solutions are compared with the numerical solution obtained by the fourth-order Runge-Kutta method (RK4), which gives  a good agreement.

In this article, the nonlinear problem of Jeffery-Hamel flow has been solved analytically and numerically by using reliable iterative and numerical methods. The approximate solutions obtained by using the Daftardar-Jafari method namely (DJM), Temimi-Ansari method namely (TAM) and Banach contraction method namely (BCM). The obtained solutions are discussed numerically, in comparison with other numerical solutions obtained from the fourth order Runge-Kutta (RK4), Euler and previous analytic methods available in literature. In addition, the convergence of the proposed methods is given based on the Banach fixed point theorem. The results reveal that the presented methods are reliable, effective and applicable to solve other nonlinear problems.

Background:sThe aims of this study were to evaluate and compare the ability of three different techniques to obdurate simulated lateral canals, evaluate the effect of the main canal curvature on obturation of lateral canals and compare the gutta-percha penetration between coronal and apical lateral canals. Materials and methods: Resin blocks with 30 straight and 30 curved were used in this study. Each canal has two parallel lateral canals. The main canal has 0.3 mm apical diameter and 0.04 taper. The canals were divided into six groups according to canal curvature and obturation techniques used (n=10): Groups C1 and C2: straight and curved canals obturated with continuous wave technique using E&Q masterTM system. Groups O1 and O2: straight