Some remarks on compact constant mean curvature hypersurfaces in a halfspace of ℍ n+1

We consider embedded compact hypersurfacesM in a halfspace of hyperbolic space with boundaryM in the boundary geodesic hyperplaneP of the halfspace and with non-zero constant mean curvature. We prove the following. Let {M _n } be a sequence of such hypersurfaces withM _n contained in a disk of radiusr _n centered at a point P such thatr _n 0 and that eachM _n is a large. H-hypersurface,H > 1. Then there exists a subsequence of {M _n } converging to the sphere of mean curvatureH tangent toP at. In the case of smallH-hypersurfaces orH 1, if we add a condition on the curvature of the boundary, there exists a subsequence of {M _n } which are graphs. The convergence is smooth on compact subset of ³ .     

On the Classification of Flag-Transitive c.c*- Geometries

Let ( G) be a flag-transitive c.c*-geometry whose point-stabilizer is not an affine group. We list all known examples and show that, if (, G) is a minimal unknown example, then G is an almost simple group and the commutator subgroup G is a simple group of Lie type.     

Refinement of linear polymer crystal structures determined from electron diffraction data

The reliability of linear polymer structures determined by using electron diffraction data is investigated. The results of n-beam dynamical calculations and kinematic calculations which take account of crystal bending are compared with experimental structure factors for five published structures. In specific cases, both dynamical scattering and crystal bending effects are found to be important. Finally, guidelines are given for obtaining electron diffraction data which are optimal for structure solution.     

Number and length of attractors in a critical Kauffman model with connectivity one

The Kauffman model describes a system of randomly connected nodes with dynamics based on Boolean update functions. Though it is a simple model, it exhibits very complex behavior for "critical" parameter values at the boundary between a frozen and a disordered phase, and is therefore used for studies of real network problems. We prove here that the mean number and mean length of attractors in critical random Boolean networks with connectivity one both increase faster than any power law with network size. We derive these results by generating the networks through a growth process and by calculating lower bounds.     

Fermionic Linear Optics Revisited

We provide an alternative view of the efficient classical simulatibility of fermionic linear optics in terms of Slater determinants. We investigate the generic effects of two-mode measurements on the Slater number of fermionic states. We argue that most such measurements are not capable (in conjunction with fermion linear optics) of an efficient exact implementation of universal quantum computation. Our arguments do not apply to the two-mode parity measurement, for which exact quantum computation becomes possible.     

Acoustical Klein-Gordon equation: a time-independent perturbation analysis

The perturbation analysis of an ideal acoustical duct was first made by Rayleigh in 1878 and the result has since stood in the literature. However, the analysis is based on the assumption of potential and kinetic energy densities that remain constant as a change in cross section occurs, whereas, in fact, they may fluctuate significantly in comparison to the slowly varying "wave function," Psi(x,t), of the acoustical Klein-Gordon equation. The square of the time-independent eigenfunction, psi(2)(x), is directly proportional to the potential energy per unit length of fluid, and it is shown that it is precisely the perturbation in potential energy that defines correctly the eigenvalue shifts.     

Spatial unmasking of nearby pure-tone targets in a simulated anechoic environment

Detection thresholds were measured for different spatial configurations of 500- and 1000-Hz pure-tone targets and broadband maskers. Sources were simulated using individually measured head-related transfer functions (HRTFs) for source positions varying in both azimuth and distance. For the spatial configurations tested, thresholds ranged over 50 dB, primarily as a result of large changes in the target-to-masker ratio (TMR) with changes in target and masker locations. Intersubject differences in both HRTFs and in binaural sensitivity were large; however, the overall pattern of results was similar across subjects. As expected, detection thresholds were generally smaller when the target and masker were separated in azimuth than when they were at the same location. However, in some cases, azimuthal separation of target and masker yielded little change or even a small increase in detection threshold. Significant intersubject differences occurred as a result both of differences in monaural and binaural acoustic cues in the individualized HRTFs and of different binaural contributions to performance. Model predictions captured general trends in the pattern of spatial unmasking. However, subject-specific model predictions did not account for the observed individual differences in performance, even after taking into account individual differences in HRTF measurements and overall binaural sensitivity. These results suggest that individuals differ not only in their overall sensitivity to binaural cues, but also in how their binaural sensitivity varies with the spatial position of (and interaural differences in) the masker.