On arithmetic and asymptotic properties of up-down numbers

Let $\sigma=(\sigma_1,..., \sigma_N)$, where $\sigma_i =\pm 1$, and let $C(\sigma)$ denote the number of permutations $\pi$ of $1,2,..., N+1,$ whose up-down signature $\mathrm{sign}(\pi(i+1)-\pi(i))=\sigma_i$, for $i=1,...,N$. We prove that the set of all up-down numbers $C(\sigma)$ can be expressed by a single universal polynomial $\Phi$, whose coefficients are products of numbers from the Taylor series of the hyperbolic tangent function. We prove that $\Phi$ is a modified exponential, and deduce some remarkable congruence properties for the set of all numbers $C(\sigma)$, for fixed $N$. We prove a concise upper-bound for $C(\sigma)$, which describes the asymptotic behaviour of the up-down function $C(\sigma)$ in the limit $C(\sigma) \ll (N+1)!$.Comment: Recommended for publication in Discrete Mathematics subject to revision

Retrieving time-dependent Green's functions in optics with low-coherence interferometry

We report on the passive measurement of time-dependent Green's functions in the optical frequency domain with low-coherence interferometry. Inspired by previous studies in acoustics and seismology, we show how the correlations of a broadband and incoherent wave-field can directly yield the Green's functions between scatterers of a complex medium. Both the ballistic and multiple scattering components of the Green's function are retrieved. This approach opens important perspectives for optical imaging and characterization in complex scattering media.Comment: 5 pages, 4 figure

ROSAT monitoring of persistent giant and rapid variability in the narrow-line Seyfert 1 galaxy IRAS 13224-3809

We report evidence for persistent giant and rapid X-ray variability in the radio-quiet, ultrasoft, strong Fe II, narrow-line Seyfert 1 galaxy IRAS 13224-3809. Within a 30 day ROSAT High Resolution Imager (HRI) monitoring observation at least five giant amplitude count rate variations are visible, with the maximum observed amplitude of variability being about a factor of 60. We detect a rise by a factor of about 57 in just two days. IRAS 13224-3809 appears to be the most X-ray variable Seyfert known, and its variability is probably nonlinear. We carefully check the identification of the highly variable X-ray source with the distant galaxy, and it appears to be secure. We examine possible explanations for the giant variability. Unusually strong relativistic effects and partial covering by occulting structures on an accretion disc can provide plausible explanations of the X-ray data, and we explore these two scenarios. Relativistic boosting effects may be relevant to understanding the strong X-ray variability of some steep spectrum Seyferts more generally.Comment: 14 pages, submitted to MNRA

Eddy current damper

A high torque capacity eddy current damper used as a rate limiting device for a large solar array deployment mechanism is discussed. The eddy current damper eliminates the problems associated with the outgassing or leaking of damping fluids. It also provides performance advantages such as damping torque rates, which are truly linear with respect to input speed, continuous 360 degree operation in both directions of rotation, wide operating temperature range, and the capability of convenient adjustment of damping rates by the user without disassembly or special tools

Non-destructive imaging of an individual protein

The mode of action of proteins is to a large extent given by their ability to adopt different conformations. This is why imaging single biomolecules at atomic resolution is one of the ultimate goals of biophysics and structural biology. The existing protein database has emerged from X-ray crystallography, NMR or cryo-TEM investigations. However, these tools all require averaging over a large number of proteins and thus over different conformations. This of course results in the loss of structural information. Likewise it has been shown that even the emergent X-FEL technique will not get away without averaging over a large quantity of molecules. Here we report the first recordings of a protein at sub-nanometer resolution obtained from one individual ferritin by means of low-energy electron holography. One single protein could be imaged for an extended period of time without any sign of radiation damage. Since ferritin exhibits an iron core, the holographic reconstructions could also be cross-validated against TEM images of the very same molecule by imaging the iron cluster inside the molecule while the protein shell is decomposed

Stationary phase slip state in quasi-one-dimensional rings

The nonuniform superconducting state in a ring in which the order parameter vanishing at one point is studied. This state is characterized by a jump of the phase by $\pi$ at the point where the order parameter becomes zero. In uniform rings such a state is a saddle-point state and consequently unstable. However, for non-uniform rings with e.g. variations of geometrical or physical parameters or with attached wires this state can be stabilized and may be realized experimentally.Comment: 6 pages, 7 figures, RevTex 4.0 styl