On the difference between consecutive zeros of the Riemann zeta function

Let 0 < γ₁ ≤ γ₂ ≤ … be the imaginary part of the zeros, $\text{λ =}\text{lim}{}_{\mathrm{n}}\text{(γ}{}_{\mathrm{n}}\text{? γ}{}_{\mathrm{n\; ?\; 1}}\text{)(}\text{log}\text{γ}{}_{\mathrm{n}}\text{2π}\text{)}$ and $\text{μ =}\text{lim}{}_{\mathrm{n}}\text{(γ}{}_{\mathrm{n}}\text{? γ}{}_{\mathrm{n\; ?\; 1}}\text{)(}\text{log}\text{γ}{}_{\mathrm{n}}\text{2π}\text{)}$. Assuming the Riemann hypothesis, it is known that μ ≤ 0.68 and λ > 1. One suspects that μ = 0 and λ = +∞. The object of this note is to show that λ ≥ 1.9.     

Proton-proton coupling constants in the unsubstituted pyrylium cation

An iterative analysis of the PMR spectrum of the title compound was performed and the calculated values of spectral parameters, relative chemical shifts, proton-proton and direct carbon-proton couplings are compared with those of pyridine.     

Calculated molecular structures and electronic spectra of the geometric isomers of a model carotenoid molecule, 6,11-dimethylhexadecaheptaene

The molecular structures and the electronic spectra of the geometric isomers of a model carotenoid polyene, 6,11-dimethylhexadecaheptaene, were calculated. It was concluded that solvent effects and conformational isomerization must be taken into account in order to satisfactorily explain the observed spectra. Molecular structures were calculated using molecular mechanics (MM2), and electronic spectra using the VESCF-MO-CI method including all singly-excited configurations. A method based on the calculated and observed spectra of simple linear polyenes was devised to estimate the solvent effects.     

A comparison of T2*-weighted magnitude and phase imaging for measuring the arterial input function in the rat aorta following intravenous injection of gadolinium contrast agent

The arterial input function (AIF) is important for quantitative MR imaging perfusion experiments employing Gd contrast agents. This study compared the accuracy of T(2)*-weighted magnitude and phase imaging for noninvasive measurement of the AIF in the rat aorta. Twenty-eight in vivo experiments were performed involving simultaneous arterial blood sampling and MR imaging following Gd injection. In vitro experiments were also performed to confirm the in vivo results. At 1.89 T and TE=3 ms, the relationship between changes in 1/T(2)* in blood (estimated from MR signal magnitude) and Gd concentration ([Gd]) was measured to be approximately 19 s(-1) mM(-1), while that between phase and [Gd] was approximately 0.19 rad mM(-1). Both of these values are consistent with previously published results. The in vivo phase data had approximately half as much scatter with respect to [Gd] than the in vivo magnitude data (r(2)=.34 vs. r(2)=.17, respectively). This is likely due to the fact that the estimated change in 1/T(2)* is more sensitive than the phase to a variety of factors such as partial volume effects and T(1) weighting. Therefore, this study indicates that phase imaging may be a preferred method for measuring the AIF in the rat aorta compared to T(2)*-weighted magnitude imaging.     

Dietary lipid content influences the activity of lipogenic enzymes in the liver and on whole body delta13C values of Nile tilapia, Oreochromis niloticus (L.)

The use of stable isotope techniques for the reconstruction of diets has increased over the last decade. However, isotopic ratios in an animal are not only affected by the composition of the feed, but also by the amount of feed consumed. An uncertainty of up to 1 per thousand for both delta13C and delta15N values has been observed when the feeding level is unknown. This may have substantial effects on the results of back-calculation. As the feeding level of animals is unknown in nature, an additional indicator for their nutritional status is needed. High feeding levels and a consequent surfeit of dietary energy lead to the synthesis of lipids. In order to test whether the level of lipogenesis could be used as an indicator, Nile tilapia (Oreochromis niloticus) were fed four isonitrogenous and isoenergetic wheat-based semi-synthetic diets with different lipid contents (2.0 %, 4.5 %, 9.5 % and 13.3 %) for eight weeks. Body composition, gross energy content and delta13C values in the lipids and the lipid-free material were determined in diets and fish bodies. The livers of three fish per feeding group were assayed for the activity of two lipogenic enzymes, ATP-citrate lyase and malic enzyme. There was a strong negative correlation between delta13C values in the lipids of the individual fish and the apparent lipid conversion. The activities of lipogenic enzymes decreased with rising lipid content in the diet. The delta13C values in the lipids decreased significantly with increasing specific activity for both enzymes. In this experiment where lipogenesis was influenced by the composition of the diet, it was possible to determine the exact value for the trophic shift in relation to the enzyme activities. Further experiments to investigate the use of enzyme activities in situations where the feeding level of an animal is unknown are recommended.     

Multi-echo imaging in highly inhomogeneous magnetic fields

A new pulsed field gradient multi-echo imaging technique to encode position in the phase of every echo generated by a CPMG sequence in the presence of a strongly inhomogeneous static magnetic field is presented. It was applied to improve the sensitivity in an imaging experiment by adding the echo train acquired during the CPMG sequence and to spatially resolve relaxation times of inhomogeneous specimens using single-sided probes. The sequence was implemented in a new bar-magnet MOUSE equipped with a gradient coil system to apply a pulsed magnetic field with a constant gradient along one spatial coordinate. An important reduction by a factor larger than two orders of magnitude in the acquisition time was obtained compared to the previously published single-point imaging technique.