The expansion factors of an outer automorphism and its inverse

A fully irreducible outer automorphism of the free group of rank  has an expansion factor which often differs from the expansion factor of . Nevertheless, we prove that the ratio between the logarithms of the expansion factors of and is bounded above by a constant depending only on the rank . We also prove a more general theorem applying to an arbitrary outer automorphism of and its inverse and their two spectrums of expansion factors.

     

Thick metric spaces,relative hyperbolicity,and quasi-isometric rigidity

We study the geometry of non-relatively hyperbolic groups. Generalizing a result of Schwartz, any quasi-isometric image of a non-relatively hyperbolic space in a relatively hyperbolic space is contained in a bounded neighborhood of a single peripheral subgroup. This implies that a group being relatively hyperbolic with non-relatively hyperbolic peripheral subgroups is a quasi-isometry invariant. As an application, Artin groups are relatively hyperbolic if and only if freely decomposable. We also introduce a new quasi-isometry invariant of metric spaces called metrically thick, which is sufficient for a metric space to be non-hyperbolic relative to any non-trivial collection of subsets. Thick finitely generated groups include: mapping class groups of most surfaces; outer automorphism groups of most free groups; certain Artin groups; and others. Non-uniform lattices in higher rank semisimple Lie groups are thick and hence non-relatively hyperbolic, in contrast with rank one which provided the motivating examples of relatively hyperbolic groups. Mapping class groups are the first examples of non-relatively hyperbolic groups having cut points in any asymptotic cone, resolving several questions of Drutu and Sapir about the structure of relatively hyperbolic groups. Outside of group theory, Teichmüller spaces for surfaces of sufficiently large complexity are thick with respect to the Weil–Peterson metric, in contrast with Brock–Farb’s hyperbolicity result in low complexity.     

Development of a sodium-pump/neo-lasant photopumped soft X-raylaser

An intense source of sodium pump-line radiation has been created and used to photopump a neon plasma for application to a pulsed-power driven sodium/neo X-ray laser. Properties of the sodium-pump plasma and the neon-lasant plasma required to optimize fluorescence and lasing are determined. The implosion of a sodium-bearing plasma with a megampere pulsed-power driver (Gamble II) is used to produce a linear Z-pinch with up to 25 GW of sodium-pump-line radiation. A separate neon plasma, driven by part of the return current from the imploding sodium plasma, is created parallel to the sodium line source at a distance of 5 cm. Evidence for population inversion is indicated by fluorescence enhancement of the 11-Å resonance line from the n =4 level of neon when pumped by sodium     

The reaction of lead tetraacetate with hydrocarbons

The free radical reaction of lead tetraacetate with hydrocarbons has been investigated. The products of these reactions are the acetate esters. The hydrogen abstracting species from lead tetraacetate is found to have a primary to secondary to tertiary selectivity of 1:27:123 based upon relative reactivities.     

N,N'-bis(substituted phenyl)-1,2,4,5-benzenetetracarboxylic-1,2:4,5-diimides

The preparation of N,N'-bis(substituted phenyl)-1,2,4,5-benzenetetracarboxylic-1,2:4,5-di-imides by the reaction of 1,2,4,5-benzenetetracarboxylic-1,2:4,5-dianhydride ( 1 ) with aryl-amines and with aryl isocyanates is described. Correlations are made between the properties of these diimides and the nature and position of the substituents in the phenyl ring. The condensation of dianhydride 1 with diisocyanates yields polymers varying from soft elastomers to tough films, depending upon the amount of imide structure in the polymer chain.     

Distribution of a major surface-associated glycoprotein, fibronectin, in cultures of adherent cells

Fibronectin was present in media and cell layers of cultures of adherent cells from human skin, kidney, lung, chest wall, liver, and heart. Cell-surface fibronectin, visualized by immunofluorescence, was in dense fibrillar (cultures from lung), discrete fibrillar (e.g., cultures from skin), or punctate (some cultures from kidney) structures. The subunit sizes of cell-surface fibronectin and fibronectin soluble in medium appeared identical in sodium dodecyl sulfate-polyacrylamide gels. To explain the polymorphism of cell-surface fibronectin, there must be chemical differences among the fibronectins synthesized by different cell strains or factors in the cell layer which influence fibronectin binding and aggregation.     

Functional end-group polymers derived from free-radical chain transfer. I. Kinetic prediction of functionality

The kinetic scheme describing chain transfer in free-radical polymerizations, the Mayo equation, has been rearranged to yield the probability of generating a functional end group by chain transfer (e.g., to a disulfide). The prediction is that a mixture of functional and nonfunctional ends occurs. Examination of literature data shows a number of systems produce more functionality than predicted. Hence, the challenge to devise a new kinetic scheme to account for the increased functionality is made (e.g., by selective reaction of initiator with chain-transfer agent).