The extended quadratic residue code is the only (48,24,12) self-dual doubly-even code

An extremal self-dual doubly-even binary (n,k,d) code has a minimum weight d=4/spl lfloor/n/24/spl rfloor/+4. Of such codes with length divisible by 24, the Golay code is the only (24,12,8) code, the extended quadratic residue code is the only known (48,24,12) code, and there is no known (72,36,16) code. One may partition the search for a (48,24,12) self-dual doubly-even code into three cases. A previous search assuming one of the cases found only the extended quadratic residue code. We examine the remaining two cases. Separate searches assuming each of the remaining cases found no codes and thus the extended quadratic residue code is the only doubly-even self-dual (48,24,12) code.     

The Ups and Downs of Percent (and Some Interesting Connections)

Percent is a standardized ratio comparison that is often used to describe relative amounts of increase and decrease. In this paper, the nonsymmetric relationship between percent of increase and percent of decrease is explored in several ways. Beginning with a simple graphical representation of the relationship, the functional relationship is developed, with relative decrease expressed as a function of relative increase. Once expressed in the form f(x) = 100x/(100 + x), an immediate connection is made to two other topics commonly found within the study of rates—the work problem and the harmonic mean. Finally, successive percents of increase or decrease are shown to be everyday applications of the geometric mean. This deeper look at a common mathematical concept has uncovered rich structural relationships between topics that are often isolated in the curriculum.     

Transconductance and mobility of Si:B delta MOSFETs

Delta-doped MOSFETs have been fabricated in MBE-grown silicon using for the first time boron as the dopant within the delta layer. Current-voltage characteristics have been measured, and secondary ion mass spectrometry (SIMS) is used to confirm the location of the delta layer and the extent of layer broadening by diffusion during processing. Precise threshold voltages of the devices are difficult to determine since the devices (which all operate in depletion mode) take several volts to switch off. Transconductances of the devices have been measured, and it is shown how analysis of these results can yield estimates of the carrier mobility for transport along the delta layers despite the uncertainty in the threshold voltage. A clear transition is observed in the results which is attributed to the formation of a parasitic surface-channel field-effect transistor, providing conclusive evidence that the devices are conducting along a delta channel for part of the measured range of applied gate biases     

QCD sum rules: charmonium

The dimensiond=4 gluon condensateφ ₁ is determined from an analysis of charmonium, taking model dependent estimates ofd=6.8 condensates into account. ForS-waves, there is a compatibility region, where both these and model dependent higher state corrections to ground state dominance are small, enablingφ ₁ to be determined from a fit to the data. ForP-waves the estimated higher dimension contributions are large in the region of ground state dominance, and noφ ₁ determination is possible. Theφ ₁ value obtained from the fit to theS-wave ratios is 3 5 times bigger than that obtained by RRY using the plateau method. The methods are compared for the vector current. We show that the higher state correction used by RRY does not fit the data; and that the plateau method is much more sensitive to thed=6.8 condensates than the ratio used here. When reasonable estimates of both these and the higher state corrections are taken into account, there is compatibility between the two methods.     

The Silicon Backplane Design for an LCOS Polarization-Insensitive Phase Hologram SLM

Polarization-insensitivity is achieved in a reflective spatial light modulator by laying a quarter-wave plate (QWP) at the incident wavelength directly over the mirror pixels of a silicon backplane, and forming a nematic Freedrickcz cell over the QWP to modulate the reflected phase. To achieve the highest drive voltage from the available silicon process, a switched voltage common front electrode design is described, with variable amplitude square wave drive to the pixels to maintain constant root-mean-square drive and minimize phase fluctuations during the dc balance refresh cycle. The silicon has been fabricated and liquid-crystal-on-silicon cells both with and without the QWP assembled; applications include optically transparent switches for optical networks, beam steering for add-drop multiplexers for wavelength-division-multiplexing telecommunications, television multicast, and holographic projection.     

Dynamic digital holographic wavelength filtering

This paper describes the theory and results of a new generic technology for use in optical telecommunications and wavelength division multiplexing (WDM): dynamic digital holographic wavelength filtering. The enabling component is a polarization-insensitive ferroelectric liquid crystal (FLC) spatial light modulator (SLM) in conjunction with a highly wavelength-dispersive fixed diffractive element. The technology has been used to perform demultiplexing of single or multiple WDM signals, dynamic erbium doped fiber amplifier (EDFA) gain equalization and channel management, and used to tune an erbium-doped fiber laser (EDFL) functioning as a high power, very narrow linewidth WDM source