Ultralow-energy excitations and prospects for spatially resolved spectroscopy.

The key contribution of electron microscopy methods to condensed matter spectroscopy is undoubtedly spatial resolution. So far this has mainly been manifest through electron energy loss spectroscopy in the 1-eV to 10-keV energy range and has not seriously challenged the dominance of optical, X-ray, and neutron spectroscopy methods over most of the vast field at lower energies. At frequencies up to a few megahertz, corresponding to energies of a few nanoelectron volts and below, direct excitation by pulsed electron beams or electric fields has proved effective. Prospects are discussed for extending spatially resolved spectroscopy to the intermediate energy region, mainly by combining the advantages of electrons with those of photons.     

6,6‐Diphenyl‐6,7‐dihydro‐5H‐1,3,4,8‐tetrathia‐6‐stannazulene‐2‐thione and 6,6′‐spirobi[6,7‐dihydro‐5H‐1,3,4,8‐tetrathia‐6‐stannazulene]‐2,2′‐dithione

The title compounds, [Sn(C₆H₅)₂(C₅H₄S₅)] and [Sn(C₅H₄S₅)₂], respectively, are of interest because they can be regarded as intermediate in nature between chelates and heterocyclic compounds containing the C₃S₅ fragment. In contrast with the essentially normal bond lengths and angles within the mol­ecules, the molecular conformations are somewhat unexpected, as are the intermolecular contacts found in the case of the latter compound.     

A re‐examination of supra­molecular aggregation in two polymorphs of acetone 2,4‐dinitro­phenyl­hydrazone

The structure of the triclinic polymorph of acetone 2,4‐dinitrophenylhydrazone, C₉H₁₀N₄O₄, has been redetermined from diffraction data collected at 120 (2) K; the mol­ecules are linked by C—H⋯O hydrogen bonds into centrosymmetric R₂²(10) dimers which are themselves linked into a chain by an aromatic π–π stacking inter­action. In the monoclinic polymorph, which crystallizes with Z′ = 2 in the space group P2₁/n, one type of mol­ecule forms dimers exactly as in the triclinic polymorph, while the other forms C(6) chains.     

On the Asphericity of Length Five Relative Group Presentations

We investigate asphericity of the relative group presentation G,t |atbtctdtet=1 and prove it aspherical provided thesubgroupof G generated by ab^–1, bc^–1, cd^–1, de^–1is neither finite cyclic nor a finite triangle group. We alsoprove a similar result for the closely related relative grouppresentation G,s,t | sßst=1=tts^–1. 2000 MathematicsSubject Classification: 20F05, 57M05.     

Rank Properties in Finite Semigroups II: The Small Rank and the Large Rank

This paper is concerned with the application of two possible definitions of rank to certain well-known semigroups.AMS Subject Classification (2000), 20M10