C2 isomers of C84F40 and C84F44 are cuboid and contain benzenoid and naphthalenoid aromatic patches

A 1:1 mixture of C84F40 and C84F44, both derived from the D2(IV) isomer, has been isolated from the fluorination of [84]fullerene with either MnF3 or CoF3 at 500 degrees C. The 1D and 2D COSY 19F NMR spectra showed that each derivative is cuboid, having benzenoid rings at four of the six octahedral sites; the two remaining sites have naphthalenoid rings for C84F40, and two slightly offset benzenoid rings for C84F44. The benzenoid rings each have six adjacent sp3-hybridised carbon atoms whilst the naphthalenoid moieties have eight, thus facilitating full delocalisation. In terms of the number and size of aromatic patches, C84F44 is the most aromatic fullerene derivative yet isolated.     

Maximum packings ofK n with copies ofK 4 − e

For eachn, we determine the maximum number of pairwise edge disjoint copies ofK ₄ – e inK _n , and all possible graphs that arise from the unused edges.     

Experimental determination of the internal photoemission contribution to KLM Auger spectra of Na,Mg and Al

Photoemission from the 2p levels of the light metals excited by internally generated K_α1,2 X-rays has been observed, and the intensities compared with valence band to 2p intensity ratios obtained from X-ray photoemission spectroscopy. It is found that internal photoemission from the valence band contributes 0.5% of the intensity of the KL_2,3M Auger peak.     

Generalizations of the Sweedler Dual

As left adjoint to the dual algebra functor, Sweedler’s finite dual construction is an important tool in the theory of Hopf algebras over a field. We show in this note that the left adjoint to the dual algebra functor, which exists over arbitrary rings, shares a number of properties with the finite dual. Nonetheless the requirement that it should map Hopf algebras to Hopf algebras needs the extra assumption that this left adjoint should map an algebra into its linear dual. We identify a condition guaranteeing that Sweedler’s construction works when generalized to noetherian commutative rings. We establish the following two apparently previously unnoticed dual adjunctions: For every commutative ring R the left adjoint of the dual algebra functor on the category of R-bialgebras has a right adjoint. This dual adjunction can be restricted to a dual adjunction on the category of Hopf R-algebras, provided that R is noetherian and absolutely flat.     

The structure of the turbulent boundary layer over a mobile and deformable boundary

The structure of the velocity field above a propagating water wave of fixed frequency was investigated in order to evaluate the transport of wind momentum to water waves and the influence of a mobile and deformable boundary on the bursting cycle. The vertical and horizontal velocities were measured in a transformed Eulerian wave-following frame of reference with the aid of a cross hot film, in a wind-wave research facility at Stanford University.The mean velocity profiles have a log-linear form with a wake free-stream characteristic. The wave-coherent motion in the free-stream is irrotational; in the boundary layer, it has a strong shear behavior related to the wave-associated stress. The wave-induced velocity field and the wave-perturbed turbulence depend strongly on the ratio of the wave-speed to the mean free-stream velocity, c/U ₀.The presence of the propagating waves affects the bursting cycle, making the contribution of sweeps and ejections almost equal and dependent on the ratio c/U ₀. The magnitudes of the contribution of the bursting events are generally enhanced by the presence of water waves. The time interval between ejections or sweeps does not scale with either the inner and/or outer flow variables.This paper was presented at the Ninth Symposium on Turbulence, University of Missouri-Rolla, October 1–3, 1984     

A geminate recombination model for photoluminescence decay in plasma-deposited amorphous Si:H

We develop a model of geminate electron-hole recombination, including tunnelling and diffusion, to account for photoluminescence decay in amorphous semiconductors. The model correctly predicts the shape of the decay, the luminescence quantum efficiency, and the microscopic electron mobility.     

Time consistency and risk averse dynamic decision models: Definition,interpretation and practical consequences

This paper aims at resolving a major obstacle to practical usage of time-consistent risk-averse decision models. The recursive objective function, generally used to ensure time consistency, is complex and has no clear/direct interpretation. Practitioners rather choose a simpler and more intuitive formulation, even though it may lead to a time inconsistent policy. Based on rigorous mathematical foundations, we impel practical usage of time consistent models as we provide practitioners with an intuitive economic interpretation for the referred recursive objective function. We also discourage time-inconsistent models by arguing that the associated policies are sub-optimal. We developed a new methodology to compute the sub-optimality gap associated with a time-inconsistent policy, providing practitioners with an objective method to quantify practical consequences of time inconsistency. Our results hold for a quite general class of problems and we choose, without loss of generality, a CVaR-based portfolio selection application to illustrate the developed concepts.