Arithmetical conservation results

In this paper we present a proof of Goodman’s Theorem, a classical result in the metamathematics of constructivism, which states that the addition of the axiom of choice to Heyting arithmetic in finite types does not increase the collection of provable arithmetical sentences. Our proof relies on several ideas from earlier proofs by other authors, but adds some new ones as well. In particular, we show how a recent paper by Jaap van Oosten can be used to simplify a key step in the proof. We have also included an interesting corollary for classical systems pointed out to us by Ulrich Kohlenbach.     

Liquid-core waveguide technology for coupling column liquid chromatography and Raman spectroscopy

The on-line coupling of liquid chromatography (LC) and Raman spectroscopy (RS) via an entirely plastic liquid-core waveguide (LCW) was optimized in terms of excitation wavelength of the laser, especially in relation to the fluorescence background, and the length of the LCW. Excitation at 632.8 nm (He-Ne laser) was found to be a good compromise between a wavelength long enough to strongly reduce the fluorescence background and, on the other hand, short enough to avoid (re)-absorption of laser light and Raman signals by H2O in LCWs of considerable length. This conclusion is supported by a theoretical discussion on the optimization of LCW lengths as function of the excitation wavelength for H2O and 2H2O. When using the He-Ne laser the optimum length is approximately 50 cm for H2O; this corresponds to a detection cell volume of 19 microl for an LCW of 220 microm I.D., which is fully compatible with conventional-size LC. The influence of an organic modifier, usually necessary for reversed-phase LC, on the free spectral window was evaluated. The potential applicability of LC-LCW-RS was shown for a mixture of adenosine 5'-monophosphate (AMP), guanosine 5'-monophosphate (GMP) and uridine 5'-monophosphate (UMP), utilizing an aqueous eluent without the addition of a modifier. Improved detectability was achieved by using the stopped-flow mode and applying a large-volume-injection procedure (injection volume: 200 microl). Under these conditions, the limit of identification for AMP, GMP and UMP was in the 0.1-0.5-mg/ml range.     

The first three anisotropy constants of nickel

The technique of ferromagnetic resonance at 23 GHz has been used to determine the first three anisotropy constants of pure Ni down to 4.2K. A temperature and orientation dependent linewidth has also been observed.     

Measuring body length of male sperm whales from their clicks: the relationship between inter-pulse intervals and photogrammetrically measured lengths

Sperm whales (Physeter macrocephalus) emit short, broadband clicks which often include multiple pulses. The time interval between these pulses [inter-pulse interval (IPI)] represents the two-way time for a pulse to travel between the air sacs located at either end of the sperm whale's head. The IPI therefore, is a proxy of head length which, using an allometric relationship, can be used to estimate total body length. Previous studies relating IPI to an independent measure of length have relied on very small sample sizes and manual techniques for measuring IPI. Sound recordings and digital stereo photogrammetric measurements of 21 individuals were made off Kaikoura, New Zealand, and, in addition, archived recordings of whales measured with a previous photogrammetric system were reanalyzed to obtain a total sample size of 33 individuals. IPIs were measured automatically via cepstral analysis implemented via a software plug-in for pamguard, an open-source software package for passive acoustic monitoring. IPI measurements were highly consistent within individuals (mean CV=0.63%). The new regression relationship relating IPI (I) and total length (T) was found to be T=1.258I+5.736 (r(2)=0.77, p<0.001). This new regression provides a better fit than previous studies of large (> 11 m) sperm whales.