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).     

基于时频分布的盲信号分离方法研究长骨中的多模式导波信号

由于超声导波对长骨皮质骨的材料特性及厚度变化非常敏感,因此用导波评价长骨状况的研究已成为近年来的一个研究热点。在接收到的导波中,往往多种模式混叠在一起,使得进一步求取每种导波模式的群速度等与骨质状况密切相关的参数时遇到困难。本文采用基于时频分布的盲信号分离(TFBSS)方法对长骨中混叠的多模式进行分离,然后对分离后的单一导波模式求取群速度。研究结果表明TFBSS方法能够准确的分离出混叠的多模式导波,且实验测量的群速度与其理论值吻合。利用导波的群速度就可以得到长骨皮质骨的厚度,这对诊断其骨质状况具有重要意义。     

The hall effect in some liquid alloys

The Hall coefficient has been measured for (a) liquid CuTe, AgTe and AuTe₂ and (b) liquid Cu-Sn alloy. The results are discussed in terms of the possible semiconducting nature of liquids comprising group (a) and in terms of bound state formation around the Sn atoms for those in group (b).     

Phase Transfer Catalysis Preparation of Acyl Isothiocyanates

The use of phase transfer catalysis, PTC, for nucleophillic substitution reactions is well documented.^1,2 Included among these reactions is the preparation of both alkyl³ and aryl⁴ thiocyanates. However, PTC reactions at an acyl carbon are much less common. Brándstróm⁵ has reported the preparation of acyl azides and Weber⁶ has used PTC to prepare benzoyl cyanide. Recently Illi⁷ has used PTC to acylate sterically crowded phenols.