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.     

An ESR study of some group IVB free radical adducts of diethylketomalonate

The formation of the compound RSnX(acac)₂ (acac = 2,4-pentanedionato) by reaction of bis(2,4-pentanedionato)tin(II) on a halide RX with R = CH₃, C₂H₅, C₄H₉, C₆H₅, CH₂I, (C₆H₅)₃SnCH₂, (C₂H₅)₃SnCH₂ and X = I, Br has been studied by polarography. At 25°C, it is in fact an equilibrium whose constant has been measured. The intermediate formation of the ion-pair [RSn(acac)₂⁺X^?] has allowed us to explain the experimental results.     

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).     

Discovery of a new phosphotyrosine mimetic for PTP1B using breakaway tethering

Protein tyrosine phosphatases play important roles in many signaling cascades involved in human disease. The identification of druglike inhibitors for these targets is a major challenge, and the discovery of suitable phosphotyrosine (pY) mimetics remains one of the key difficulties. Here we describe an extension of tethering technology, "breakaway tethering", which is ideally suited for discovering such new chemical entities. The approach involves first irreversibly modifying a protein with an extender that contains both a masked thiol and a known pY mimetic. The extender is then cleaved to release the pY mimetic, unmasking the thiol. The resulting protein is screened against a library of disulfide-containing small molecule fragments; any molecules with inherent affinity for the pY binding site will preferentially form disulfides with the extender, allowing for their identification by mass spectrometry. The ability to start from a known substrate mimimizes perturbation of protein structure and increases the opportunity to probe the active site using tethering. We applied this approach to the anti-diabetic protein PTP1B to discover a pY mimetic which belongs to a new molecular class and which binds in a novel fashion.     

Novel perturbation expansion for the Langevin equation

We discuss the randomly driven systemdx/dt= -W(x) +f(t), wheref(t) is a Gaussian random function or stirring force withf(t)f(t)=2(t–t), andW(x) is of the formgx ¹⁺². The parameter is a measure of the nonlinearity of the equation. We show how to obtain the correlation functionsx(t)f(t)···x(t( n)) _f as a power series in. We obtain three terms in the expansion and show how to use Padé approximants to analytically continue the answer in the variable. By using scaling relations, we show how to get a uniform approximation to the equal-time correlation functions valid for allg and.     

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.