Brachytherapy treatment is primarily used for the certain handling kinds of cancerous tumors. Using radionuclides for the study of tumors has been studied for a very long time, but the introduction of mathematical models or radiobiological models has made treatment planning easy. Using mathematical models helps to compute the survival probabilities of irradiated tissues and cancer cells. With the expansion of using HDR-High dose rate Brachytherapy and LDR-low dose rate Brachytherapy for the treatment of cancer, it requires fractionated does treatment plan to irradiate the tumor. In this paper, authors have discussed dose calculation algorithms that are used in Brachytherapy treatment planning. Precise and less time-consuming calculations

Poly vinyl alcohol has been studied for its ability to form crystallites by using annealing method. Semicrystalline films of poly vinyl alcohol (PVA) were prepared by casting 11.5 wt. % and 13 wt. % PVA aqueous solution onto glass slides at annealing temperature range 90 -120°C and duration time 15- 60 minute. This allowed the macromolecules to form crystallites, small regions of folded and compacted chains separated by amorphous regions where single PVA chain may pass through several of these crystallites. Degree of crystallinity of PVA films (hydrogels) was determined by method of density; on the other hand the swelling behavior was conducted by the determination of water uptake, wet degree of crystallinity, gel fraction and solubilit

In this paper flotation method experiments were performed to investigate the removal of lead and zinc. Various parameters such as pH, air flow rate, collector concentrations, collector type and initial metal concentrations were tested in a bubble column of 6 cm inside diameter. High recoveries of the two metals have been obtained by applying the foam flotation process, and at relatively short time 45 minutes . The results show that the best removal of lead about 95% was achieved at pH value of 8 and the best removal of zinc about 93% was achieved
at pH value of 10 by using 100 mg/l of Sodium dodecylsulfate (SDS) as a collector and 1% ethanol as a frother. The results show that the removal efficiency increased with increasing initial m

     In this article, a new efficient approach is presented to solve a type of partial differential equations, such (2+1)-dimensional differential equations non-linear, and nonhomogeneous. The procedure of the new approach is suggested to solve important types of differential equations and get accurate analytic solutions i.e., exact solutions. The effectiveness of the suggested approach based on its properties compared with other approaches has been used to solve this type of differential equations such as the Adomain decomposition method, homotopy perturbation method, homotopy analysis method, and variation iteration method. The advantage of the present method has been illustrated by some examples.

     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.

Many numerical approaches have been suggested to solve nonlinear problems. In this paper, we suggest a new two-step iterative method for solving nonlinear equations. This iterative method has cubic convergence. Several numerical examples to illustrate the efficiency of this method by Comparison with other similar methods is given.

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.