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Ultrafiltration of a polymer-electrolyte mixture

We present a mathematical model to describe the ultrafiltration behaviour of polymer-electrolyte mixtures. The model combines the proper thermodynamic forces (pressure, chemical potential and electrical potential differences) with multicomponent diffusion theory. The model is verified with experimental data on the ultrafiltration of aqueous solutions of PEG-4000 and potassium phosphate. The single solute rejection of PEG-4000 goes through a maximum as also found by others. The single solute rejection of potassium phosphate depends on the ionic strength of the solution. At low ionic strength rejections are found of 50%. Solutions containing a high concentration of PEG-4000 and potassium phosphate show a negative rejection for potassium phosphate. This is caused by the strongly non-ideal behaviour of these aqueous solutions. The model predicts the behaviour of single solute experiments quite well, but some deviations are found with the mixed solute experiments. However, negative rejections found in the mixed solute experiments are predicted by the model.     

Finding nonnormal bent functions

The question if there exist nonnormal bent functions was an open question for several years. A Boolean function in n variables is called normal if there exists an affine subspace of dimension n/2 on which the function is constant. In this paper we give the first nonnormal bent function and even an example for a nonweakly normal bent function. These examples belong to a class of bent functions found in [J.F. Dillon, H. Dobbertin, New cyclic difference sets with Singer parameters, in: Finite Fields and Applications, to appear], namely the Kasami functions. We furthermore give a construction which extends these examples to higher dimensions. Additionally, we present a very efficient algorithm that was used to verify the nonnormality of these functions.