Intermolecular additions of cyclobutylchlorocarbene

Cyclobutylchlorocarbene can be intercepted by simple alkenes in successful competition with intramolecular ring expansion and hydride migration reactions.     

Enhanced photoluminescence from very thin double-wall carbon nanotubes synthesized by the zeolite-CCVD method

Photoluminescence (PL) from purified (>90%) double-wall carbon nanotubes (DWNTs), which have been synthesized by zeolite catalyst-supported chemical vapor deposition (zeolite-CCVD), of very small diameters (0.8-nm average inner tube) is reported. The PL contour mappings for various ratios (1-90%) of double- versus single-wall carbon nanotubes by thermal oxidation have enabled us to unambiguously identify the chirality of inner tubes for the DWNTs synthesized. After the extensive high-temperature oxidation at 700 degrees C, high-purity (>90%) DWNTs of approximately 0.8 nm inner diameter are obtained, and most of these correspond to the DWNTs having inner tubes with chiralities of (7,5), (7,6), and (9,4).     

Subtle stereochemical and electronic effects in iridium-catalyzed isomerization of C-allyl glycosides

[reaction: see text] Stereoselective isomerization of C-allyl glycosides into (E)-C-vinyl glycosides or (Z)-exo-glycals was carried out in the presence of the cationic iridium(I) catalyst [(Ph(2)MeP)(2)Ir(cod)PF(6)]. The products of the isomerization were affected by the relative 1,2-stereochemical relationships and by the nature of the protecting groups. These effects are discussed along with a plausible reaction mechanism.     

Simple pulse-acquire NMR methods for the quantitative analysis of calcium, magnesium and sodium in human serum

Simple pulse-acquire NMR methods are presented for accurate quantitation of calcium (Ca(2+)), magnesium (Mg(2+)) and sodium (Na(+)) in human serum. Ca(2+) and Mg(2+) can be determined simultaneously by (1)H NMR via their EDTA (ethylenediaminetetraacetic acid) complexes. Spectra are acquired before and after addition of EDTA, and the difference spectrum is used for integration of the signals from the complexes relative to an internal reference. Serum sodium can also be determined through pulse-acquire (23)Na NMR by integration of the free sodium signal relative to a reference signal (Na(+)+EDTA in a coaxial capillary tube). The method shows excellent accuracy and precision for all three metal ions. Slow chemical exchange between complexed and free EDTA at the natural pH of serum does not limit the accuracy of the determination of Ca(2+) and Mg(2+), and the large errors associated with spin-echo spectral editing methods are avoided.     

On the minimum degree,edge-connectivity and connectivity of power graphs of finite groups

In this paper, the minimum degree of power graphs of certain cyclic groups, abelian p-groups, dihedral groups and dicyclic groups are obtained. It is ascertained that the edge-connectivity and minimum degree of power graphs are equal, and consequently, the minimum disconnecting sets of power graphs of the aforementioned groups are determined. In order to investigate the equality of connectivity and minimum degree of power graphs, certain necessary conditions for finite groups and a necessary and su?cient condition for finite cyclic groups are obtained. Moreover, the equality is discussed for the power graphs of abelian p-groups, dihedral groups and dicyclic groups.     

Projection methods for computing Moore-Penrose inverses of unbounded operators

In this article we give a characterization of the convergence of projection methods which are useful for approximating the Moore-Penrose inverse of a closed densely defined operator between Hilbert spaces. We illustrate the main theorem with an example. Also a procedure for constructing the admissible sequence of projections is discussed.     

Local dependence functions for some families of bivariate distributions and total positivity

The purpose of this paper is to investigate a very useful application of a certain local dependence function γ_f(x,y), which was considered recently by Holland and Wang [20]. An interesting property of γ_f(x,y) is that the underlying joint density f(x,y) is TP₂ (that is, totally positive of order 2) if and only if . This gives an elegant way to investigate the TP₂ property of any bivariate distribution. For the Saramanov family, the Ali-Mikhail-Haq family of bivariate distributions and the family of bivariate elliptical distributions, we derive the local dependence function and obtain conditions for f(x,y) to be TP₂. These families are quite rich and include many other large classes of bivariate distributions as their special cases. Similar conditions are obtained for bivariate distributions with exponential conditionals and bivariate distributions with Pareto conditionals.     

The biogenetic law

We develop one criterion for the selection of the content of a mathematics syllabus. We advocate the importance of the biogenetic law and stress the importance of a historical perspective in mathematical education.