Stieltjes transform method

Sips in 1948 was able to solve the integral equation for F U) using a Stieltjes transform method (see Section 2). He assumed that the internal partition function for the adsorbed phase (incorporated in K) is independent of the adsorption energy and obtained a solution of the form shown in equation (10). However the normalization integral ... 

If Bdistribution function is translated to lower adsorption energies.A difficulty arises when using the Sips procedure since the distribution function so determined is temperature dependent. Honig and Hill have repeated the analysis but with a constraint requiring the distribution to be independent of temperature thus leading to severe restrictions on the form of the total isotherm function that can be handled by the Stieltjes transform method. 

Toth et have noted the wide applicability of another total isotherm equation, the Toth equation,and by using the Stieltjes transform method... 

Misra (1970) used the Langmuir equation as the local isotherm (which is also used by many because of the simplicity of the such equation), and for some specific overall isotherms they obtained the energy distribution by using the method of Stieltjes transform to solve the inverse problem. 

One of the most effective methods of evaluation of the energy distribution function %(e) relating to the overall adsorption isotherm assumed a priori was proposed by Sips [21,22], He proved that the integral equation (10) with the Langmuir local isotherm [Eq. (11)] could be rewritten as the Stieltjes transform [105] ... 

The Sips method, based the theory of Stieltjes transform and requiring the analytic extension of 9(0 [24,25]. 

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