On the structure of non-full-rank perfect codes

The Krotov combining construction of perfect 1-error-correcting binary codes from 2000 and a theorem of Heden saying that every non-full-rank perfect 1-error-correcting binary code can be constructed by this combining construction is generalized to the $q$-ary case. Simply, every non-full-rank perfect code $C$ is the union of a well-defined family of $\mu$-components $K_\mu$, where $\mu$ belongs to an "outer" perfect code $C^*$, and these components are at distance three from each other. Components from distinct codes can thus freely be combined to obtain new perfect codes. The Phelps general product construction of perfect binary code from 1984 is generalized to obtain $\mu$-components, and new lower bounds on the number of perfect 1-error-correcting $q$-ary codes are presented.Comment: 8 page

A cusp electron gun for millimeter wave gyrodevices

The experimental results of a thermionic cusp electron gun, to drive millimeter and submillimeter wave harmonic gyrodevices, are reported in this paper. Using a "smooth" magnetic field reversal formed by two coils this gun generated an annular-shaped, axis-encircling electron beam with 1.5 A current, and an adjustable velocity ratio alpha of up to 1.56 at a beam voltage of 40 kV. The beam cross-sectional shape and transported beam current were measured by a witness plate technique and Faraday cup, respectively. These measured results were found to be in excellent agreement with the simulated results using the three-dimensional code MAGIC

On the form of growing strings

Patterns and forms adopted by Nature, such as the shape of living cells, the geometry of shells and the branched structure of plants, are often the result of simple dynamical paradigms. Here we show that a growing self-interacting string attached to a tracking origin, modeled to resemble nascent polypeptides in vivo, develops helical structures which are more pronounced at the growing end. We also show that the dynamic growth ensemble shares several features of an equilibrium ensemble in which the growing end of the polymer is under an effective stretching force. A statistical analysis of native states of proteins shows that the signature of this non-equilibrium phenomenon has been fixed by evolution at the C-terminus, the growing end of a nascent protein. These findings suggest that a generic non-equilibrium growth process might have provided an additional evolutionary advantage for nascent proteins by favoring the preferential selection of helical structures.Comment: 4 pages, 3 figures. Accepted for publication in Phys. Rev. Let

The HST Key Project on the Extragalactic Distance Scale XXVI. The Calibration of Population II Secondary Distance Indicators and the Value of the Hubble Constant

A Cepheid-based calibration is derived for four distance indicators that utilize stars in the old stellar populations: the tip of the red giant branch (TRGB), the planetary nebula luminosity function (PNLF), the globular cluster luminosity function (GCLF) and the surface brightness fluctuation method (SBF). The calibration is largely based on the Cepheid distances to 18 spiral galaxies within cz =1500 km/s obtained as part of the HST Key Project on the Extragalactic Distance Scale, but relies also on Cepheid distances from separate HST and ground-based efforts. The newly derived calibration of the SBF method is applied to obtain distances to four Abell clusters in the velocity range between 3800 and 5000 km/s, observed by Lauer et al. (1998) using the HST/WFPC2. Combined with cluster velocities corrected for a cosmological flow model, these distances imply a value of the Hubble constant of H0 = 69 +/- 4 (random) +/- 6 (systematic) km/s/Mpc. This result assumes that the Cepheid PL relation is independent of the metallicity of the variable stars; adopting a metallicity correction as in Kennicutt et al. (1998), would produce a (5 +/- 3)% decrease in H0. Finally, the newly derived calibration allows us to investigate systematics in the Cepheid, PNLF, SBF, GCLF and TRGB distance scales.Comment: Accepted for publication in the Astrophysical Journal. 48 pages (including 13 figures and 4 tables), plus two additional tables in landscape format. Also available at http://astro.caltech.edu/~lff/pub.htm K' SBF magnitudes have been update