Geodetic graphs of diameter two

We survey what is known on geodetic graphs of diameter two and discuss the implications of a new strong necessary condition for the existence of such graphs.     

Electron delocalization in the radical cation of 1,3,6,8-tetraazatricyclo[4.4.1.1(3,8)]dodecane, a 4-nitrogen-7-electron system.

The radical cation of 1,3,6,8-tetraazatricyclo [4.4.1.1(3,8)]dodecane (TTD) has been studied using magnetic resonance and optical spectroscopic methods and computational techniques. With the help of deuterated isotopomers, assignments of EPR and resonance Raman spectra could be unequivocally established. The results demonstrate that the radical cation has D(2d) symmetry, and instantaneous electron delocalization over the four equivalent nitrogen atoms occurs. This extensive delocalization in a completely saturated system is a unique feature of the TTD radical cation. The spectroscopy of TTD, in contrast to that of simpler diamines such as 1,4-diaza[2.2.2]bicyclooctane, simultaneously reveals the consequences of orbital interactions through space and through bonds. The relationship between nitrogen pyramidalization and hyperfine coupling constants in nitrogen-centered radical cations with a number of different bonding arrangements is reviewed.     

On-line trace enrichment — column liquid chromatography of polar pollutants in surface water using bifunctional membrane-based extraction-disk cartridges

Summary An on-line trace-enrichment system, using a bifunctional membrane extraction-disk cartridge, has been combined with a column liquid chromatography separation for the simultaneous determination of basic, neutral and acidic pollutants in surface water. The enrichment device consisted of a specially constructed holder containing both C-18 and cation-exchange disks. The holder can contain up to 25 disks of 0.5 mm thickness and 4.6 mm diameter. Before trace enrichment of 20 ml of surface water (pH 3.0), calcium ions were removed from the sample by means of an oxalic acid precipitation. Desorption of the cartridge was at elevated temperature using reversed-phase gradient elution; detection was performed with a diode-array UV absorbance detector. The detection limits for the test compounds in surface water are typically 0.5–2 g/l; the calibration graphs are linear from the lower limit of determination up to 50 g/l.     

The direct observation of a highly mobile positive ion in nanosecond pulse irradiated liquid cyclohexane

The electrical conductivity induced by pulse irradiation of liquid cyclohexane has been studied by means of microwave absorption. The conductivity in pure cyclohexane, due principally to the excess electron, is reduced to less than 10% of the initial value on addition of 5 × 10^?4 M of the electron scavenger SF₆. The conductivity remaining after addition of SF₆ is however more than an order of magnitude larger than expected for massive ions in cyclohexane and, since it is almost completely removed by the addition of 4 × 10^?3 M of the positive ion scavenger NH₃, is attributed mainly to the high mobility of the positive hole in this liquid. The ratio of the electron to hole mobility is determined to be 15. The mean lifetime of the hole under the present conditions is 86 ns. The rate constant for reaction of the hole with NH₃ is determined to be 1.8 × 10¹¹ M^?1 s^?1. From the conductivity remaining after removal of both the electron and the hole the sum of the mobilities of the resulting molecular ions is determined to be 8.4 × 10^?4 cm² V^?1 s^?1.     

Trace enrichment of polar pollutants from water and the influence of humic substances

Summary A practical liquid chromatographic early-warning system for polar pollutants in water ought to have detection limits at a level below a microgram per litre. Using ultraviolet absorbance detection this normally necessitates trace enrichment of the samples. In this study ten different sorbents have been tested with respect to their enrichment capacity. The hydrophobic polymeric PLRP-S material, in combination with a C-18 modified analytical column, proved to be the best choice. The influence of humic substances, present in surface water, was also studied. Lowering of the sample pH, resulted in a significant increase in the interferences due to the humic substances.     

Expedient synthesis of a novel asymmetric selectively deprotectable derivative of the ATAC scaffold

An efficient multigram scale synthesis of a new asymmetric triazacyclophane scaffold, the ATAC (Asymmetric-TAC) scaffold, bearing three selectively removable groups is described. This scaffold is slightly more rigid than our frequently used TAC (TriAzaCyclophane) scaffold. The synthesis of the required triamine is very high yielding without difficult steps or purifications and was also applied to a much improved synthesis of our original TAC scaffold. Especially the tedious first reaction step, that is, mono-oNBS-protection of a triamine could be omitted. The rigidity of the triazacyclophane ring in both TAC- and ATAC scaffolds has also been investigated using variable temperature ¹H NMR experiments.     

Zur Begründung der intuitionistischen Mathematik. I.

Ohne ZusammenfassungDie Reihe von Aufsätzen, die ich unter diesem Titel in den Mathematischen Annalen veröffentlichen werde, soll eine erweiterte und wo nötig emendierte Wiedergabe bilden vom Inhalte meiner von 1918 an in den Verhandelingen der Amsterdamer Akademie erscheinenden Abhandlungen: Begründung der Mengenlehre unabhängig vom logischen Staz vom ausgeschlossenen Dritten und Begründung der Funktionenlehre unabhängig vom logischen Staz vom ausgeschlossenen Dritten.     

The generating rank of the space of short vectors in the Leech lattice mod 2

Consider the partial linear space on the images in Λ/2Λ of the shortest nonzero vectors in the Leech lattice Λ, where the lines are the triples of vectors adding up to zero. We determine the universal embedding dimension and the generating rank of this space (both are 24) and classify its hyperplanes.