This paper deals with founding an estimation of best approximation of unbounded functions which satisfied weighted Lipschitz condition with respect to the convex polynomials by means of weighted moduli of smoothness of fractional order  , ( , ) p f t . In addition we prove some properties of weighted moduli of smoothness of fractional order.

               In this research, the semiparametric Bayesian method is compared with the classical  method to  estimate reliability function of three  systems :  k-out of-n system, series system, and parallel system. Each system consists of three components, the first one represents the composite parametric in which failure times distributed as exponential, whereas the second and the third components are nonparametric ones in which reliability estimations depend on Kernel method using two methods to estimate bandwidth parameter h method and Kaplan-Meier method. To indicate a better method for system reliability function estimation, it has be

A new class of higher derivatives  for harmonic univalent functions defined by a generalized fractional integral operator inside an open unit disk E is the aim of this paper.

The investigation of determining solutions for the Diophantine equation  over the Gaussian integer ring for the specific case of  is discussed. The discussion includes various preliminary results later used to build the resolvent theory of the Diophantine equation studied. Our findings show the existence of infinitely many solutions. Since the analytical method used here is based on simple algebraic properties, it can be easily generalized to study the behavior and the conditions for the existence of solutions to other Diophantine equations, allowing a deeper understanding, even when no general solution is known.

The objective of this study is to investigate the application of advanced oxidation processes (AOPs) in the treatment of wastewater contaminated with furfural. The AOPs investigated is the homogeneous photo-Fenton (UV/H₂O₂/Fe⁺²) process. The experiments were conducted by using cylindrical stainless steel batch photo-reactor. The influence of different variables: initial concentration of H₂O₂ (300-1300mg/L), Fe⁺²(20-70mg/L), pH(2-7) and initial concentration of furfural (50-300 mg/L) and their relationship with the mineralization efficiency were studied.

 Complete mineralization for the system UV/H₂O₂/Fe⁺² was achieved at: initi