Rays and time dispersion in multimode graded core fibres

The propagation of a bundle of rays in a multimode graded core fibre is investigated. The analytical conditions for minimizing time dispersion for the bundle of rays are found and tested on a number of profiles including the so called alpha profile. Finally an estimate of the width of the impulse response is given and applied to different profiles.     

Technical considerations for the use of 15N-DNA stable-isotope probing for functional microbial activity in soils

Stable-isotope DNA probing is a culture-independent technique that may provide a link between function and phylogeny of active microorganisms. The technique has been used in association with 13C substrates while here we evaluate feasibility and limitations of 15N-DNA stable-isotope probing (SIP) using labelled and unlabelled pure microbial cultures or soil extracts. Our results showed that (15)N-DNA probing is feasible for cultures as well as soil samples. Limitations of 15N-DNA-SIP are (a) the need for relatively large quantities of DNA to visualise bands (although molecular resolution is much higher) and (b) 15N-DNA enrichment needed to ideally be >50 at%; however, this requirement can be lowered to approx. 40 atom% 15N with pure cultures using a modified CsCl centrifugation method (140K g for 69 h). These advances in 15N-DNA-SIP methodology open new opportunities to trace active microbial populations utilising specific N substrates in situ.     

Extension of Simons' inequality

We prove the following extended version of Simons' inequality and present its applications. Let be a set and be a subset of . Let be a subset of a Hausdorff topological vector space which is invariant under infinite convex combinations. Let be a bounded function such that the functions are convex for all and whenever 0$">, and Let be a sequence in . Assume that, for every , there exists satisfying . Then

If , then the set in the above inequality can be replaced by .

     

Organometallic derivatives of penicillins and cephalosporins a new class of semi-synthetic antibiotics

Novel semi-synthetic derivatives of penicillin and cephalosporin have been prepared in which the conventional phenyl or heteroaromatic group has been replaced by a ferrocene moiety, and in which the metal atom is in close proximity to the β-lactam ring of the antibiotic; several of the compounds exhibit high antibiotic activity and others are potent β-lactamase inhibitors.     

New theoretical and experimental infrared results on formaldehyde in solution

An extension of our combined procedure to determine a complete quartic force field and to resolve a vibrational problem thanks to a variational treatment is proposed for quantitative calculations of vibrational spectra in solution. Energies and gradients are obtained through a polarizable continuum model (PCM), the so-called self-consistent isodensity (SCI)-PCM. We present in this paper new experimental results dealing with formaldehyde in solution in cyclohexane, chloroform, THF, acetonitrile, DMSO and water; the obtained vibrational spectra are then compared with CCSD(T)/cc-pVQZ calculations. In addition, density functional theory (DFT) calculations have been carried out with the aim of both anticipating and positioning these approaches for larger sized molecules.     

Compactness of operators acting from a Lorentz sequence space to an Orlicz sequence space

LetX andY be closed subspaces of the Lorentz sequence spaced(v, p) and the Orlicz sequence spacel _M , respectively. It is proved that every bounded linear operator fromX toY is compact whenever

On a separable weak version of the bounded approximation property

Recently, Lee introduced and studied the separable weak bounded approximation property (BAP). Lee proved that the separable weak BAP of \({X^*}\), the dual space of a Banach space \({X}\), coincides with the BAP of \({X^*}\) whenever \({X^{**}}\) has the weak Radon–Nikodým property. We show that the separable weak BAP and the BAP are always the same properties.