Abstract. The objective of this paper is to introduce a general scheme for the construction of interpolatory approximation formulas and compactly supported wavelets by using spline functions with arbitrary (nonuniform) knots. Both construction procedures are based on certain "optimally local" interpolatory fundamental spline functions which are not required to possess any approximation property.

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Synthetic aluminosilica gels fixed potassium in varying amounts against replacement by common alkali and alkaline earth cations; the larger the solvated size of the replacing cation the greater was the amount of K retained. Replacing power thus followed the lyotropic series NH4 > Na > Ba > Ca > Mg. The amounts of K fixed against exchange by a particular ion increased with total cation‐exchange capacity (in turn dependent on gel composition) and with the pH value at which K‐saturation originally took place. A marked increase in capacity to fix K was shown to result from drying the gels prior to K‐saturation. Drying presumably increased the rigidity of channels in the gel structure which restrict the passage of larger hydrated cations and which, as with zeolites, are responsible for the fixation phenomenon. For xerogels, wet‐ and dry‐fixation measurements yielded results of the same order of magnitude.

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