Filling Length in Finitely Presentable Groups

We study the filling length function for a finite presentation of a group , and interpret this function as an optimal bound on the length of the boundary loop as a van Kampen diagram is collapsed to the basepoint using a combinatorial notion of a null-homotopy. We prove that filling length is well behaved under change of presentation of . We look at 'AD-pairs' (f,g) for a finite presentation : that is, an isoperimetric function f and an isodiametric function g that can be realised simultaneously. We prove that the filling length admits a bound of the form [g+1][log (f+1)+1] whenever (f,g) is an AD-pair for . Further we show that (up to multiplicative constants) if is an isoperimetric function ( ) for a finite presentation then ( ) is an AD-pair. Also we prove that for all finite presentations filling length is bounded by an exponential of an isodiametric function.Partially supported by NSF grant DMS-9800158Supported by EPSRC Award No. 98001683 and Corpus Christi College, Oxford.     

Use of labelled nitrogen to measure gross and net rates of mineralization and microbial activity in permanent pastures following fertilizer applications at different time intervals

Measurements of some of the main internal N-cycling processes in soil were obtained by labelling the inorganic N pool with the stable isotope of nitrogen ((15)N). The (15)N mean pool dilution technique, combined with other field measurements, enabled gross and net N-mineralization rates to be resolved in grassland soils, which had previously either received fertilizer N (F), or had remained unfertilized (U) for many years. The two soils were subdivided into plots that received N at different time intervals (over 3 weeks), prior to (15)N measurements being made. By this novel approach, possible 'priming' effects over time were investigated to try to overcome some of the temporal problems of isotopic labelling of soil N (native plus fertilizer) and to identify possible changes in a range of primary N-transformation processes. The results suggested that an overall stimulation of microbially mediated processes occurred with all N treatments, but there were inconsistencies associated with the release of N, both in the timing and the degree to which different processes responded to the application of fertilizer N. The rates of these processes were, however, within the range of previously reported data and the (15)N measurements were not adversely affected by the differences in N pools created by the treatments. Thus, the mean pool dilution technique was shown to be applicable to agricultural soils, under conditions relevant to grass swards receiving fertilizer. For example, between the U and F treatments, the size of inorganic N pools increased by five-fold and gross rates of mineralization reached 3.5 and 4.8 microg N g(-1) (dry soil) d(-1), respectively, but did not vary greatly with the timing of N applications. A correlation (r(2) = 0.57) was found between soil respiration (which is relatively simple to measure) and net mineralization (which is more time consuming), suggesting that the former might be used as an indicator of the latter. Although this relationship was stronger in previously unfertilized soils, the similarities found with fertilized soils suggest that this approach could be used to obtain information of wider agronomic value and would, therefore, warrant further work under a range of soil conditions.     

Placement and characterization of pairs of luminescent molecules in spatially separated regions of nanostructured thin films

Methods of making mesostructured sol-gel silicate thin films containing two different molecules deliberately placed in two different spatially separated regions in a one-step, one-pot preparation are developed and demonstrated. When the structure-directing agent is the surfactant cetyltrimethylammonium bromide, the structure is 2-D hexagonal with lattice spacings between 31.6 and 42.1 angstroms depending on the dopant molecules and their concentrations. The three general strategies that are used to place the molecules are philicity (like dissolves like), bonding, and bifunctionality. These strategies take advantage of the different chemical and physical properties of the regions of the films. These regions are the inorganic silicate framework, the hydrophobic organic interior of the micelles, and the ionic interface between them. Luminescent molecules that possess the physical and chemical properties appropriate for the desired strategies are chosen. Lanthanide and ruthenium complexes with condensable trialkoxysilane groups are incorporated into the silicate framework. 1,4-Naphthoquinone, pyrene, rhodamine 6G and coumarin 540A, and lanthanides with no condensable trialkoxysilanes occupy the hydrophobic core of micelles by virtue of their hydrophobicity. The locations of the molecules are determined by luminescence spectroscopy and by luminescence lifetime measurements. In all cases, the long-range order templated into the thin film is verified by X-ray diffraction. The simultaneous placement of two molecules in the structured film and the maintenance of long-range order require a delicate balance among film preparation methodology, design of the molecules to be incorporated in specific regions, and concentrations of all of the species.     

Electrophoresis in the presence of gradients: I. Viscosity gradients

In many cases, the resolution provided by capillary electrophoresis systems approaches that predicted for diffusion-limited separations. Once all device-related sources of band broadening have been eliminated or minimized, only thermal diffusion remains. In principle, peaks can be sharpened using gradients of various system characteristics such as gel concentration, buffer viscosity and electric field. However, it is not clear whether this can actually increase the resolution of the system. In this article, we focus our attention on viscosity gradients and we examine both continuous and step-like variations. Our results indicate that the performance of electrophoretic systems cannot be improved by viscosity gradients. They may provide extra stacking, and thus improve the resolution, when the injection width is non-negligible. However, for the systems considered here, the best resolution is obtained when the viscosity is uniform and the stacking is entirely performed at injection. We conclude by discussing the link between these results, the fundamental laws of thermodynamics, the nature of the detection process and the importance of having nonlinear effects in nonuniform systems.     

Total synthesis of the mycolactones

[structure: see text] The first total synthesis of the mycolactones is reported. This work unambiguously confirms our earlier relative and absolute stereochemical assignment of the mycolactones.     

Materials science of the gel to fluid phase transition in a supported phospholipid bilayer

We report the results of in situ AFM measurements examining the phase transition of bilayers formed from the zwitterionic phospholipid, DMPC, 1,2-dimyristoyl-sn-glycero-3-phosphocholine, supported on mica. The images show that the fluid to gel phase transition process features substantial tearing of the bilayer due to the density change between the two phases. The gel to fluid transition is strongly affected by the resultant stress introduced into the gel phase, which changes the degree of cooperativity, the shape of developing fluid phase regions, and the course of the transition.     

Contrasting friction and diffusion in molecularly thin confined films

We study, using fluorescence correlation spectroscopy, translational diffusion in molecularly thin liquids confined within a surface forces apparatus. The diffusion coefficient decreases exponentially from the edges towards the center of the Hertzian contact and further suggests the presence of a small number of distinct diffusion processes. This holds alike a crystallizable fluid (OMCTS) and a glass-former (1,2-propane diol), both of which displayed static friction. We conclude that friction, the average of an ensemble of molecules, masked massively heterogeneous molecular mobility.     

Beyond the absorption-limited nonlinear phase shift with microring resonators

We show that the nonlinear phase shift produced by a ring resonator constructed from a given nonlinear optical material can be greater than the phase shift produced by a single pass through an infinite length of the same material when linear and nonlinear absorption are taken into consideration. The figure of merit (defined by the phase shift times the throughput) also improves for the ring resonator over that of the native nonlinear absorbing material. We finally show that these benefits of using the ring resonator as a nonlinear phase-shifting element can enhance the switching characteristics of a Mach-Zehnder interferometer.     

Demonstration of transient gain x-ray lasers near 20nm for nickellike yttrium, zirconium, niobium, and molybdenum

We demonstrate strong lasing on the Ni-like 4d(1)S(0)?4p(1)P(1) transition at 18.9, 20.3, 22.0, and 24.0 nm for Mo, Nb, Zr, and Y ions, respectively, using the transient collisional excitation scheme. Approximately 5 J of laser energy in a combination of a 600-ps pulse and a 1-ps pulse from the Compact Multipulse Terawatt (COMET) tabletop laser system is used to irradiate slab targets of these materials. Small-signal gains of 17-26cm (-1) are determined on the 4d?4p transition, with overall gain-length products gL of 11-12. Lasing is observed and gain is measured on the 4f(1)P(1)?4d(1)P(1) transition, which is pumped by collisional excitation combined with self-photopumping, for what is to our knowledge the first time.     

Continuous-wave optical parametric oscillator based on periodically poled KTiOPO(4) and its application to spectroscopy

We report a continuous-wave, doubly resonant optical parametric oscillator (OPO) based on the nonlinear material periodically poled KTiOPO(4) and its application to spectroscopy. The OPO, which is pumped by a diode-pumped frequency-doubled Nd:YLF laser at 523 nm, has a low pump-power threshold of 25 mW and can deliver 10 mW of single-frequency output at 1.65 mum for a pump power of 200 mW. The idler wavelength can be temperature tuned at a rate of 0.73 nm/( degrees )C , and smooth tuning of the output frequency over ~3 GHz is achieved by smooth tuning of the pump laser. We demonstrate the practicality of the OPO by recording the absorption spectrum of methane near 1649 nm.