in this study, catalyst of rutile titanium dioxide nanoparticles (rtio2-np) has been investigated for the removal and reduction of unburned hydrocarbons as benzopyran. to evaluate and calculate the thermodynamic properties of this aim, pollutants are closed to the nanoparticles and converted them into other products and the carbon dioxide molecules are simulated in the 12th steps. the geometric...

In this paper, we propose a variable metric method for unconstrained multiobjective optimization problems (MOPs). First, sequence of points is generated using different positive definite matrices in the generic framework. It proved that accumulation are Pareto critical points. Then, without convexity assumption, strong convergence established proposed method. Moreover, use common matrix to appr...