Positivity of third order linear recurrence sequences

It is shown that the Positivity Problem for a sequence satisfying a third order linear recurrence with integer coefficients, i.e., the problem whether each element of this sequence is nonnegative, is decidable.     

Oligo-Quinolylene–Vinylene Foldamers

Quinoline based aromatic amide foldamers are known to adopt stable folded conformations. We have developed a synthetic approach to produce similar oligomers where all amide bonds, or part of them, have been replaced by an isosteric vinylene group. The results of solution and solid state structural studies show that oligomers exclusively containing vinylene linkages are not well folded, and adopt predominantly flat conformations. In contrast, a vinylene segment flanked by helical oligoamides also folds in a helix, albeit with a slightly lower curvature. The presence of vinylene functions also result in an extension of π-conjugation across the oligomer that may change charge transport properties. Altogether, these results pave the way to foldamers in which both structural control and specific electronic properties may be engineered.     

Improved solid-phase peptide synthesis of ‘difficult peptides’ by altering the microenvironment of the developing sequence

Three types of resins, related to the spacer, environmental and microenvironmental models were prepared by grafting commercial AMP polymer with 2-[2-(2-aminoethylamino)-2-oxoethoxy]acetic acid. All resins were highly loaded and functionalized with Rink-amide linker. A comparative synthesis of the classic difficult sequence ACP (65-74) on the prepared resins by Fmoc/t-Bu chemistry is presented. The ‘microenviromental’ model resin afforded the crude peptide in the highest purity (98%).     

The use of phase codes in ultrasound imaging: SNR gain and bandwidth requirements

Most of the literature on coded excitation describes the signal-to-noise ratio gain of a coded waveform in terms of the time-bandwidth product. We have shown that in the context of ultrasound imaging, the expression for the SNR gain provided by matched filtering a coded waveform, can be reduced to the total number of chips in the transmit signal. Hence, the SNR gain is independent of both the bandwidth and the duration of a single-chip. This concept is described in detail, clarifying this seeming contradiction. The impact of bandwidth and pulse duration on the SNR, SNR gain and axial resolution is described. Bandwidth requirements and the impact of regulatory peak-power limitations are also addressed.