Letters to the Editor

The Mathematical Intelligencer encourages comments about the material in this issue. Letters to the editor should be sent to either of the editors-in-chief, Chandler Davis or Marjorie Senechal.     

Scaling of the energy gap withT c in Bi2Sr2CaCu2O8+δ

The results of a high-resolution photoemission study using synchrotron radiation of two single crystals of Bi₂Sr₂CaCu₂O₈₊, with different critical temperaturesT _c due to a variation in oxygen stoichiometry are reported. Within experimental accuracy, the energy gap 2 is found to scale withT _c , amounting to a reduced gap parameter of 2/k _BT_c7.4. Employing resonant photoemission at the O–2s and Cu–3p thresholds, two spectral peaks at binding energies of 180 meV and 320 meV were identified as predominantly O–2p-and Cu–3d 4s-derived states, respectively.     

Another look at complete positivity in generalized quantum dynamics: Reply to Raggio and Primas

In this rejoinder to a critique by Raggio and Primas of our paper, On Completely Positive Maps in Generalized Quantum Dynamics, we acknowledge that, contrary to our original assertion, the Bloch equations are indeed completely positive. We then explain briefly why this modification of our analysis does not alter its main conclusions.     

A comparative study on methods of optimal sample preparation for the analysis of oligonucleotides by matrix-assisted laser desorption/ionization mass spectrometry

Metal adducts (e.g., Na+ and K+) significantly hinder the analysis of oligonucleotides by matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOF-MS). Although a number of sample purification methods exist, to date no comparative study exists to determine the most efficient method for purifying oligonucleotides. The objective of this work was to perform such a study. Several different oligonucleotide samples were synthesized. Aliquots of these samples were then purposely contaminated with sodium acetate to generate representative contaminated (salted) oligonucleotide samples. A number of popular oligonucleotide purification techniques were then tested as to their effectiveness at removing Na+ from the salted samples. The effectiveness of Na+ removal was qualitatively assessed by comparing the MALDI mass spectra of the original sample, the salted sample, and the salted sample after purification. Micropipet tips packed with C18 reversed-phase packing material (e.g., Zip Tips) appear to be the most effective means of purifying the oligonucleotides investigated. Minidialysis was found to be an effective alternative for purifying higher molecular weight oligonucleotides (> 10,000 u).     

Pyrrole β-amides: Synthesis and characterization of a dipyrrinone carboxylic acid and an N-Confused fluorescent dipyrrinone

Pyrrole β-amides are useful building blocks for the preparation of novel molecular architectures that can be used in supramolecular chemistry and sensor development. Under basic conditions, pyrrole β-amides with an α-aldehyde produce different condensation products when reacted with pyrrolinones depending on the amide substitution. Secondary amides form the expected dipyrrinones, but unexpectedly undergo a subsequent trans-amidation with the pyrrolinone nitrogen to produce an unsymmetrical imide (an N-confused fluorescent dipyrrinone). Under the same conditions, tertiary amides produce the expected dipyrrinone carboxylic acids, which have been shown to have strong self-association properties as determined by vapor pressure osmometry measurements, NMR studies, and X-ray crystal structure determination. Furthermore, an N-confused fluorescent dipyrrinone was produced from the same trans-amidation reaction during attempts to decarboxylate a dipyrrinone amide with a 9-carboxylic moiety.     

Amber‐Woody Scent: Alcohols with Divergent Structure Present Common Olfactory Characteristics and Sharp Enantiomer Differentiation

Only one out of the four possible trans isomers of the important perfumery alcohol Norlimbanol^® ( 1 ) possesses a very strong amber‐woody smell, the isomer 1A with (1′R,3S,6′S) absolute configuration. Its enantiomer 1B is almost odorless and devoid of amber‐woody character, whereas the diastereoisomers 1C and 1D are considerably weaker and perceptible only by the most‐sensitive persons. The same is true for a whole series of perceptual analogs of 1 , including β‐alkoxy alcohols. These ethers belong to two structural classes: [(2,2,6‐trimethylcyclohexyl)oxy]‐ (see 3, 4 , and 16 ) or {[2‐(tert‐butyl)cyclohexyl]oxy}alkan‐2‐ol derivatives (see 19 and 20 ; Table). A superimposition model allowing for good overlap of the respective hydroxylated side chains offers a tentative explanation for the shared perceptual characteristics of the two classes (Fig. 5). The lipophilic cyclohexane moieties present only a minimal overlap in this model, suggesting that quite larger molecules might possess the same smell. (S)‐Configured β‐alkoxy alcohols can conveniently be obtained on a larger scale by enantioselective reduction of the corresponding ketones (Scheme 9).