On a packing problem for infinite graphs and independence spaces

In this paper several infinite extensions of the well-known results for packing bases in finite matroids are considered. A counterexample is given to a conjecture of Nash-Williams on edge-disjoint spanning trees of countable graphs, and a sufficient condition is proved for the packing problem in independence spaces over a countably infinite set.     

Nonlocality in imaging

We show how an effective nonlocality in imaging can lead to the sampling of a spatial region which is not significantly illuminated by an imaging probe. The nonlocality is embodied in the effective nonlocal potential describing inelastic scattering which occurs when coupled channel Schr?dinger equations are reduced to a single integro-differential equation. The context in which this prediction will be illustrated is atomic resolution imaging based on energy-loss spectroscopy in scanning transmission electron microscopy.     

A sharp bound on the size of a connected matroid

This paper proves that a connected matroid in which a largest circuit and a largest cocircuit have and elements, respectively, has at most elements. It is also shown that if is an element of and and are the sizes of a largest circuit containing and a largest cocircuit containing , then . Both these bounds are sharp and the first is proved using the second. The second inequality is an interesting companion to Lehman's width-length inequality which asserts that the former inequality can be reversed for regular matroids when and are replaced by the sizes of a smallest circuit containing and a smallest cocircuit containing . Moreover, it follows from the second inequality that if and are distinct vertices in a -connected loopless graph , then cannot exceed the product of the length of a longest -path and the size of a largest minimal edge-cut separating from .

     

Some synthetic approaches to ropinirole (sk&f 101468-a): A potent dopamine receptor agonist

Three new routes to ropinirole (SK&F 101468-A, 1 ) are described each involving the preparation of 3-chlorooxindole intermediates of type 3 from β-nitrostyrenes as the pivotal step. The superiority of sulphonate esters 17a-c as direct precursors to 1 over the bromide 11 is also described.     

Recent research using the Oxford electron beam ion trap

The presence of the σ-phase in Fe-Cr alloys (eg. Stainless steel) is important in industrial applications and from an academic point of view. The presence of the σ-phase in these alloys drastically affects their mechanical properties and their resistance to various corrosive media. In the present investigation Fe-Cr alloys containing different amounts of Mo were prepared and the transformation to the σ-phase was carried out by isothermally annealing the samples for various periods in an argon atmosphere. It will be shown that the presence of Mo has a dramatic accelerating effect on the rate of the σ-phase formation in these alloys. This revised version was published online in August 2006 with corrections to the Cover Date.     

Combinatorial geometries representable over GF(3) and GF(q). II. Dowling geometries

Letq be an odd prime power not divisible by 3. In Part I of this series, it was shown that the number of points in a rank-n combinatorial geometry (or simple matroid) representable over GF(3) and GF(q) is at mostn ². In this paper, we show that, with the exception ofn = 3, a rank-n geometry that is representable over GF(3) and GF(q) and contains exactlyn ² points is isomorphic to the rank-n Dowling geometry based on the multiplicative group of GF(3).This research was partially supported by the National Science Foundation under Grants DMS-8521826 and DMS-8500494.     

Proof of a conjecture of Kahn for non-binary matroids

This note proves a conjecture of Kahn by showing that ifX is a 3-element independent set in a 3-connected non-binary matroid M, thenM has a connected non-binary minor havingX as a basis. This research was partially supported by an LSU Summer Research Grant.     

Diffusion of HDO in pure and acid-doped ice films

In these experiments, a few bilayers of D(2)O were vapor-deposited on a pure crystalline H(2)O ice film or an ice film doped with a small amount of HCl. Upon deposition, H/D isotopic exchange quickly converted the D(2)O layer into an HDO-rich mixture layer. Infrared absorption spectroscopy followed the changes of the HDO from the initial HDO mixture layer to HDO isolated in the H(2)O ice film. This was possible because isolated HDO in H(2)O ice has a unique, sharp peak in the O-D stretch region that can be distinguished from the broad peak due to the initial HDO mixture layer. The absorbance of isolated HDO displayed first-order kinetics and was attributed to diffusion of HDO from the HDO-rich mixture layer into the underlying H(2)O ice film. While negligible diffusion was observed for pure ice films and for ice films with HCl concentrations up to 1 x 10(-4) mole fraction, diffusion of HDO occurred for higher concentrations of (2-20) x 10(-4) mole fraction HCl with a concentration-independent rate constant. The diffusion under these conditions followed Arrhenius behavior for T = 135-145 K yielding E(a) = 25 +/- 5 kJ/mol. The mechanism for the HDO diffusion involves either (i) molecular self-diffusion or (ii) long-range H/D diffusion by a series of multiple proton hop and orientational turn steps. While these spectroscopic results compare favorably with recent studies of molecular self-diffusion in low-temperature ice films, the diffusion results from all the ice film studies at low temperatures (ca. T < 170 K) differ from earlier bulk ice studies at higher temperatures (ca. T > 220 K). A comparison and discussion of the various diffusion studies are included in this report.