Reducibility behavior of polynomials with varying coefficients

LetK be a number field, and leth∈K[Y] be a polynomial of degreen. Fix an integer 0≤i≤n and compare the set ν of those integersa ofK such thath(Y)−aY ⁱhas a root inK with the set of those integersa, such thath(Y)−aY ⁱis reducible overK. Ifi is coprime ton, then we classify the rare cases where ν is not cofinite in . The main tools are a theorem of Siegel about integral points on algebraic curves and the theory of finite groups.     

Determination of heavy metal concentration in feed and permeate streams of polymer enhanced ultrafiltration process

Polymer enhanced ultrafiltration (PEUF) is a newly developed method for the removal of heavy metals from aqueous solutions. This method was applied for the removal of mercury and cadmium with the presence of polyethyleneimine (PEI) as a water soluble polymer. After ultrafiltration experiments for metal–polymer mixtures, two separate streams, namely, retentate and permeate, former of which contains mainly metal–polymer complex and free polymer molecules while latter of which mainly contains free metal ions, were obtained. At the end of PEUF experiments, performance of operation was determined by concentration analyses which was achieved by atomic absorption spectroscopy (AAS) applied in a different way for permeate and retentate streams considering the effect of presence of polymer. For mercury analysis, cold vapor AAS was applied. It was observed that the presence of PEI did not affect the atomic absorption signal when 10% HCl was added to the sample solutions. For calcium and cadmium, flame AAS was used. It was observed that change in PEI concentration results in change in measured concentration of calcium and cadmium. Therefore, two new approaches were developed for accurate measurement of concentrations of calcium and cadmium. It was also observed that presence of other metals did not affect the accuracy of the measurement of a particular metal in the concentration range studied.     

1H NMR study on the inclusion of bicyclo[3.3.1]nonanes in cyclodextrins

- and -cyclodextrins were found to form 1:1 inclusion complexes with 2,6- and 2,9-substituted bicyclo[3.3.1]nonanes. The binding constants and the structure of the complexes were estimated from titration studies and 2D ROESY experiments.