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The results obtained after measuring the responses were fitted as a two variable second order equation and the corresponding contour plots were plotted and analyzed.
The order of this reaction was determined using Lagergren's rate equation and linear pseudo second order equation and was found to be pseudo second order reaction.
The sorption process followed the pseudo-second order equation and the sorption data were fitted well with the Langmuir isotherm equations.
Two kinetic models, namely, pseudo first order equation and pseudo second order equations were applied for the adsorption of dyes onto calcined eggshell powder.
The adsorption kinetic followed the pseudo-second order equation, and was limited by internal diffusion and/or adsorbate external transfer, depending on chromate concentration, clay amount and temperature.
The results are more general and can be applied to other problems such as fourth order equation and vector valued systems of gradient type.
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See also [11 16] for related results regarding second order equations and first order systems, and [17 21] for high-order differential equations and systems.
The Larsen model first order equations and solutions are given below.
The interplay of convex and concave nonlinearities is studied both for second order equations and for problems involving thep-Laplacian.
Complex geometrical optics for first order equations and systems under different regularity assumptions of the coefficients have been constructed in [142, 144, 162, 163, 197].
Our method essentially simplifies the examination of the third order equations and what is more, it supports backward the research on the second order delay/advanced differential equations and inequalities.
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