Due to its importance in physics and applied mathematics, the non-linear Sturm-Liouville problems
witnessed massive attention since 1960. A powerful Mathematical technique called the Newton-Kantorovich
method is applied in this work to one of the non-linear Sturm-Liouville problems. To the best of the authors’
knowledge, this technique of Newton-Kantorovich has never been applied before to solve the non-linear
Sturm-Liouville problems under consideration. Accordingly, the purpose of this work is to show that this
important specific kind of non-linear Sturm-Liouville differential equations problems can be solved by
applying the well-known Newton-Kantorovich method. Also, to show the efficiency of appl

Statisticians often use regression models like parametric, nonparametric, and semi-parametric models to represent economic and social phenomena. These models explain the relationships between different variables in these phenomena. One of the parametric model techniques is conic projection regression. It helps to find the most important slopes for multidimensional data using prior information about the regression's parameters to estimate the most efficient estimator. R algorithms, written in the R language, simplify this complex method. These algorithms are based on quadratic programming, which makes the estimations more accurate.

Experimental investigations have been carried out to investigate the pH-control problems of industrial electroplating wastewater treatment plants. The accurate and sensitive PID control system could treat most problem and disturbances in the normal operation of the water treatment. However, conventional treatment was replaced by proprietary treatment agent called a QUASIL which was found to be more effective for a wide range of pH.

An approximate solution of the liner system of ntegral cquations fot both fredholm(SFIEs)and Volterra(SIES)types has been derived using taylor series expansion.The solusion is essentailly