Linde Type-A (LTA) zeolite was modified by adding lead sulfide into cavities of zeolite. The zeolite and zeolite –pbs were characterized by FTIR, XRD, AFM and SEM. The adsorption of congo red (CR) dye from aqueous solution by zeolite and zeolite – pbs were studied. Different parameters like contact time, temperature and concentration of (CR) dye were investigated. The results show that at contact time of 45, 30 min for maximum adsorption of (CR) dye onto zeolite and zeolite -pbs respectively were observed. The kinetic data was analyzed using pseudo-first-order and pseudo-second-order kinetic models. The adsorption kinetics of (CR) dye were fitted well with the pseudo-second-order kinetic model for both adsorbents. Experimental equilibrium data onto adsorption of C-R dye on zeolite and zeolite –pbs were analyzed by the Langmuir, Freundlich and temkin isotherm models .The calculated thermodynamic parameters, namely ΔGο, ΔHο, and ΔSο for zeolite showed that adsorption of C-R dye onto zeolite was spontaneous , endothermic and increase in the randomness and for zeolite –pbs showed that adsorption of C-R dye onto zeolite -pbs was spontaneous and ,exothermic and decreasing randomness under examined conditions ,The results of analysis errors and R2 values shows that the best fit was achieved with the Langmuir isotherm equation and were followed order:- ( Big R2) langmuir > temkin > freundlich( small R2) ( small error) Langmuir < temkin < freundlich( big error)
Longitudinal data is becoming increasingly common, especially in the medical and economic fields, and various methods have been analyzed and developed to analyze this type of data.
In this research, the focus was on compiling and analyzing this data, as cluster analysis plays an important role in identifying and grouping co-expressed subfiles over time and employing them on the nonparametric smoothing cubic B-spline model, which is characterized by providing continuous first and second derivatives, resulting in a smoother curve with fewer abrupt changes in slope. It is also more flexible and can pick up on more complex patterns and fluctuations in the data.
The longitudinal balanced data profile was compiled into subgroup
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