Gauss on infinity

In opposing the use of completed infinity in mathematics, Gauss was making a valid criticism of one particular kind of argument. His celebrated statement has no connection with the set theory to which it was later applied.     

Pieces of eight in class groups of quadratic fields

This paper gives an elementary method to determine the number of cyclic summands with order divisible by eight in the ideal class group of a quadratic number field.     

A general thermolabile protecting group strategy for organocatalytic metal-organic frameworks

We present a general strategy for incorporating organocatalytic moieties into metal-organic frameworks (MOFs). The organocatalytic units are protected by a thermolabile protecting group during MOF synthesis and then unveiled by a simple postsynthetic heating step. The strategy is exemplified using a thermolabile tert-butoxycarbonyl (Boc) protecting group for a proline moiety, the removal of which endows the resulting cubic zinc(II) IRMOF with catalytic activity for asymmetric aldol reactions. The bulky Boc groups also prevent framework interpenetration, producing open MOFs that can admit relatively large substrates.     

Book review

Skew Fields, by P. K. Draxl. London Mathematical Society Lecture Notes No. 18, Cambridge University Press, 1983, ix + 182 pp.     

Experimental determination of the lifetime for the 2p3d(1P0) helium doubly excited state

Two recent theoretical studies [C. Liu, Phys. Rev. A 64, 010501 (2001)]; M. Zitnik, ibid. 65, 032520 (2002)]] predict that the fluorescence lifetimes of helium doubly excited states converging to He+ N=2 should be longer than that of the He+ 2p ion state. This effect is caused by the electric field of the outer electron which, through Stark mixing, gives the inner fluorescing electron some series specific, stabilizing 2s character. We have obtained the first experimental evidence that confirms this effect by measuring the lifetime of the 2p3d(1P0) doubly excited state. This was determined to be 190+/-30 ps compared to 100 ps for the He+ 2p ion state. The measurements were performed using short pulses of synchrotron radiation to form doubly excited states and recording the arrival time of photons from fluorescence.     

Use of S-pentafluorophenyl tris(2,4,6-trimethoxyphenyl)phosphonium acetate bromide and (4-hydrazino-4-oxobutyl) [tris(2,4,6-trimethoxyphenyl)phosphonium bromide for the derivatization of alcohols,aldehydes and ketones for detection by liquid chromatography/electrospray mass spectrometry

The synthesis of S-pentafluorophenyl tris(2,4,6-trimethoxyphenyl)phosphonium acetate bromide (TMPP-AcPFP) and the novel compound (4-hydrazino-4-oxobutyl) [tris(2,4,6-trimethoxyphenyl)phosphonium bromide (TMPP-PrG) is described and the use of these compounds as derivatizing reagents for alcohols, aldehydes and ketones evaluated. Methods have been developed for the pre-column derivatization of alcohols using TMPP-AcPFP and for aldehydes and ketones using TMPP-PrG. The reactions were investigated by the use of a variety of individual test compounds containing the target functional groups. The TMPP acetyl ester and TMPP propyl hydrazone derivatives formed with their respective target analytes produced an enhanced response in electrospray ionization mass spectrometry (ESI-MS), and reproducible chromatography. The use of these two reagents to derivatize and facilitate detection of alcohols (including sugars and steroids), aldehydes and ketones (including steroids) by LC/ESI-MS was investigated.     

Quantifier problems beyond uniformity

An error in the work of W. H. Young is used to show how quantification problems still arose after uniformity was well understood.