Numerical iterative method for Volterra equations of the convolution type

The objective of this paper is to present an algorithm from which a rapidly convergent solution is obtained for Volterra integral equations of Hammerstein type. Such equations are often encountered when describing the response of viscoelastic materials where the time dependency of the material properties is often expressed in the form of a convolution integral. Frequently, singularity is encountered and often ignored when dealing with the constitutive equations of viscoelastic materials. In this paper, the singularity is incorporated in the solution and the iterative scheme used to solve the equation converges within six iterations to a typical toleration error of 10^?5. The algorithm is applied to the strain response of a polymer under impulsive (constant) loading and the results show excellent correlation between the experimental and analytical solution. Copyright © 2010 John Wiley & Sons, Ltd.     

New single isomer negatively charged β‐cyclodextrin derivatives as chiral selectors in capillary electrophoresis

To improve resolution power of chiral selector and enantiomeric peak efficiency in CE, single isomer negatively charged β‐CD derivatives, mono(6‐deoxy‐6‐sulfoethylthio)‐β‐CD (SET‐β‐CD) bearing one negative charge and mono[6‐deoxy‐6‐(6‐sulfooxy‐5,5‐bis‐sulfooxymethyl)hexylthio]‐β‐CD (SMHT‐β‐CD) carrying three negative charges, were synthesized. The structure of these two β‐CD derivatives was confirmed by ¹H NMR and MS. SET‐β‐CD and SMHT‐β‐CD successfully resolved the enantiomers of several basic model compounds. SMHT‐β‐CD provided for a significantly greater enantioseparation than SET‐β‐CD at lower concentrations. This appears to be due to the higher binding affinity of SMHT‐β‐CD to the model compounds and the wider separation window resulting from an increased countercurrent mobility of the selector. Overall, the new chiral selectors provided enantioseparations with high peak efficiency while avoiding peak distortion due to polydispersive and electrodispersive effects. The information obtained from an apparent binding constant study suggested that the enantioseparation of the model compounds followed the predictions of charged resolving agent migration model and that the observed degree of enantioseparation difference were due to the magnitude of differences in both enantiomer‐chiral selector binding affinities (ΔK) and the mobilities of the complexed enantiomers (Δμ_c).