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.     

Composition and thermal stability of SiO2-based hybrid materials TEOS-MTEOS system

Hybrid materials with different amounts of organics permanently bound on the inorganic network obtained in the TEOS-MTEOS (tetraethoxysilan-methyltriethoxysilan) system are used for obtaining coatings with different optical and mechanical properties. To study the thermal stability of the mentioned materials, compositions with different molar ratios of the precursors were prepared. The influence of the solvent and water amounts on the gelation process was also investigated. The gels obtained were characterised by IR spectrometry and their decomposition temperatures were determined by DTA/TG. Thermal stability of the gels is rather influenced by their composition than the conditions of the gelation process. This revised version was published online in July 2006 with corrections to the Cover Date.     

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.     

Radiation dose contribution from coal-slags used as structural building material

A significant dose contribution on the population could be derived from coal slags used as isolation material. Extremely high natural activities are measured in the coal slag, derived from the region of the settlement Ajka, Hungary. In some buildings monitored, the elevated -doses were nearly 5–10 times higher than the world average ones. The annual average indoor radon concentrations from the slag exceeded 400 Bq/m³ and in some cases up to 1200 Bq/m³. Due to the elevated exposure and the radon concentrations in the dwellings the annual dose was estimated to 8–24 mSv/y more than 5–10 times of the world average one.     

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.