Field emission of individual carbon nanotubes in the scanning electron microscope

The field emission of individual multiwall carbon nanotubes grown by chemical vapor deposition was measured in a scanning electron microscope. By using a sharp anode, we were able to select one nanotube for measurements in carefully controlled conditions. Single nanotubes follow the Fowler-Nordheim law, and the dependence of the field enhancement with interelectrode distance and nanotube radius is in good agreement with the recent model of Edgcombe and Valdré. Our results suggest that only nanotubes with the highest field enhancement factors, i.e., at least 8x higher than those of the average nanotube population, contribute to the emitted current in usual large area measurements.     

Periodic Liénard-type delay equations with state-dependent impulses

Conditions are obtained for Liénard-type equations with delay and state-dependent impulses to admit an absolutely continuous periodic solution with first derivative of bounded variation (and consequently with Lebesgue integrable second derivative). The results are applied to Josephson's equation and the nonconservative forced pendulum equation.     

Hyperbolic manifolds with convex boundary

Let (M,∂M) be a 3-manifold, which carries a hyperbolic metric with convex boundary. We consider the hyperbolic metrics on M such that the boundary is smooth and strictly convex. We show that the induced metrics on the boundary are exactly the metrics with curvature K>-1, and that the third fundamental forms of ∂M are exactly the metrics with curvature K<1, for which the closed geodesics which are contractible in M have length L>2π. Each is obtained exactly once. Other related results describe existence and uniqueness properties for other boundary conditions, when the metric which is achieved on ∂M is a linear combination of the first, second and third fundamental forms.     

Hyperfine interactions in amorphous and nanocrystalline Fe80Ti7Cu1B12 alloy

⁵⁷Fe Mössbauer spectroscopy is used to elucidate the nature of the hyperfine interactions present in amorphous and nanocrystalline forms of Fe₈₀Ti₇Cu₁B₁₂ alloy. Two mutually independent distributions of hyperfine fields and one sextet of Lorentzian lines are employed to reproduce the broad (atoms in amorphous rest and interface zone) and narrow (ordered) parts of the spectra, respectively. The presented conclusions are derived from three-dimensional mapping of the hyperfine field distributions corresponding to both amorphous and interfacial spectral components. The individual distributions are decomposed into Gaussian components which characterize different types of hyperfine interactions.     

Computer-aided spectral assignment in nuclear magnetic resonance spectroscopy

The proton-carbon correlation spectra, HMBC (heteronuclear multiple bond correlation) and HMQC (heteronuclear multiple quantum correlation), respectively, provide direct and remote connectivity information with high sensitivity. Their combination enables carbon-carbon proximity relationships to be deduced, which are formally identical to those produced by a fictitious INADEQUATE-2D experiment, where correlations would be established exclusively between atoms linked by one or two bonds. The CASA program uses these relationships, as well as DEPT spectra and elementary chemical-shift considerations to assign the ¹³C spectrum of a compound if its structure is known or assumed. If the structure conflicts with the experimental data, no assignment is produced. The CASA program serves as an aid to either spectral assignment or structural elucidation.     

On Small Sumsets in (ℤ/2ℤ)<Superscript><Emphasis Type="Italic">n</Emphasis></Superscript>

It is proved that any subset of (/2)ⁿ, having k elements, such that (with c<4), is contained in a subgroup of order at most u^–1k where u=u(c)>0 is an explicit function of c which does not depend on k nor on n. This improves by a radically different method the corresponding bounds deduced from a more general result of I. Z. Ruzsa.     

Propriété de stabilité de la fonction extrémale relative

Nous donnons une caractérisation des domaines DX pour lesquels la fonction extrémale relative ^*(,E,D) a la propriété de stabilité pour tout ED, i.e. lim _k^*(,E,D _k )=^*(,E,D), ED. Ensuite, nous étudions la relation entre cette propriété et les enveloppes pluripolaires. Nous concluons par quelques remarques sur la propriété de stabilité lim _k^*(,E _k ,D)=^*(,E,D).