Efficient numerical methods in non-uniform sampling theory

Summary. We present a new ``second generation" reconstruction algorithm for irregular sampling, i\@.e\@. for the problem of recovering a band-limited function from its non-uniformly sampled values. The efficient new method is a combination of the adaptive weights method which was developed by the two first named authors and the method of conjugate gradients for the solution of positive definite linear systems. The choice of "adaptive weights" can be seen as a simple but very efficient method of preconditioning. Further substantial acceleration is achieved by utilizing the Toeplitz-type structure of the system matrix. This new algorithm can handle problems of much larger dimension and condition number than have been accessible so far. Furthermore, if some gaps between samples are large, then the algorithm can still be used as a very efficient extrapolation method across the gaps. Received December 22, 1993     

A coordinated approach towards the molecular weight determination of peptides by gel electrophoresis and fast-atom bombardment mass spectrometry

The molecular weight of peptides can be determined by fast-atom bombardment mass spectrometry (FAB-MS) following polyacrylamide gel electrophoresis (PAGE). Initial results combining the fast and efficient separation of peptides by PAGE and the unambiguous determination of molecular weights by FAB-MS have been demonstrated for the three peptides bradykinin, neurotensin and gramicidin S. This method has also been applied to the determination of the molecular weights of two fragments from the tryptic digest of horse-heart cytochrome c.     

A Modulated Differential Scanning Calorimetric study

Modulated Differential Scanning Calorimetry^? has been applied to frozen sucrose solutions in the concentration range 10–80% w/w. The results from this study present, for the first time, information on the reversing and non-reversing nature of events that occur in these solutions. The study demonstrates the potential benefits of this new technique to help separate complex transitions that can occur in the total heat-flow curves obtained using traditional differential scanning calorimetry. The results illustrate how this new technique can separate the different enthalpic events, which relate to the glass transition and the onset of ice dissolution that occurs during the heating of these frozen systems, by nature of their “reversing” and “non-reversing” contributions to the total heat flow.     

Electrochemical quantification of high-affinity halide binding by a steroid-based receptor

The strength of binding between a cholapod receptor and halide anions is quantified using voltammetry at the liquid/liquid interface, revealing very high affinities and size-selectivity peaking at chloride.     

Separation of T-MAZ ethoxylated sorbitan fatty acid esters by reverse phase chromatography

Summary The method for determination of T-MAZ ethoxylated sorbitan fatty acid esters is described. This work demonstrates that with a less retentive C₈ alkyl bonded phase packing, reverse phase chromatography can be used to analyze nonionic polymer mixtures with a molecular weight range of 900 to 1500. Using a gradient elution, a complete separation of T-MAZ oligomers was achieved, comparable to that obtained by Supercritical Fluid Chromatography (SFC). Isocratic elution is used to quantify T-MAZ and the detection limit is 321 ppm, which is acceptable for polymers with high molecular weights and no UV-absorbing chromophores. This work also shows the comparison of the separations of T-MAZ using gel permeation chromatography and reverse phase chromatography.     

Cyclopentene Synthesis from 1,3-Dienes via Base-Induced Ring Contraction of 3,6-Dihydro-2H-thiopyrans: Studies on Diastereoselection and Mechanism

An investigation of the scope and mechanism of a new synthesis of cyclopentenes from 3,6-dihydro-2H-thiopyrans is described. Alkyl halides substituted with an electron-withdrawing group in the alpha-position were reacted with sodium thiosulfate, yielding the corresponding Bunte salts, which could be transformed to reactive thiocarbonyl compounds by elimination of the elements of bisulfite with mild base treatment. In situ trapping by 1,3-dienes afforded in good yields a variety of 3,6-dihydro-2H-thiopyrans substituted with electron-withdrawing groups at the 2-position. Exposure of these cycloadducts to strong base at low temperature effected a novel ring contraction, affording 2-(methylthio)-3-cyclopentenes after quenching with methyl iodide. The level of diastereoselectivity exhibited during the generation of these cyclopentenes was found to be dependent on the nature of the electron-withdrawing group at the 2-position of the dihydrothiopyran as well as the substitution pattern originally present in the diene component. In some cases, reducing the temperature during the ring contraction resulted in the isolation of good yields of vinyl cyclopropanes of high isomeric purity. With one substrate, highly diastereoselective rearrangement of a vinyl cyclopropane to a cyclopentene was unambiguously demonstrated, suggesting that this might be a key feature of the overall ring contraction mechanism.     

Nucleophilic substitution at a saturated carbon atom with retention of configuration: The reaction of trans-2-halo-3-tert-butyloxiranes with phenolates

Whereas reaction of trans-2-chloro or 2-bromo-3-tert-butyloxirane with thiophenolate occurs at C-3 to give 2-phenylmercapto-3,3-dimethylbutanal, phenolates give substitution at C-2 with retention of the oxirane ring and retention of configuration with kinetics that indicate a bimolecular mechanism.