On Representations of Semigroups Having Hypercube-like Cayley Graphs

The $n-dimensional hypercube, or n-cube, is the Cayley graph of the Abelian group Z2n. A number of combinatorially-interesting groups and semigroups arise from modified hypercubes. The inherent combinatorial properties of these groups and semigroups make them useful in a number of contexts, including coding theory, graph theory, stochastic processes, and even quantum mechanics. In this paper, particular groups and semigroups whose Cayley graphs are generalizations of hypercubes are described, and their irreducible representations are characterized. Constructions of faithful representations are also presented for each semigroup. The associated semigroup algebras are realized within the context of Clifford algebras

Evidence for 10^18-eV neutral particles from the direction of Cygnus X-3

Journal ArticleAnalysis of the cumulative Fly's Eye data reveals an excess of air showers from the direction of Cygnus X-3 at energies above 0.5 x 10^18 eV. No point source has previously been identified at such high energies. The probability of this excess arising as a chance clustering of isotropic cosmic rays is 6 . 5 x 10^-4 . The inferred signal flux is (2.0 ± 0.6) x 10&-17 particles/cm2 s. The Cygnus X-3 4.8-h periodicity is weakly present in the data

The structure of EAS at E 0.1 EeV

The ratio of extensive air showers (EAS) total shower energy in the electromagnetic channel (E em) to the size of the shower at maximum development (N max) from a direct measurement of shower longitudinal development using the air fluorescence technique was calculated. The values are not inconsistent with values based upon track length integrals of the Gaisser-Hillas formula for shower development or the known relation between shower energy and size at maximum for pure electromagnetic cascades. Using Linsley's estimates for undetected shower energy based on an analysis of a wide variety of cosmic ray data, the following relation for total shower energy E vs N max is obtained. The Gaisser Hillas implied undetected shower energy fractions

Proton-air inelastic cross section at S(1/2) = 30 TeV

The distribution of the maxima of high energy cosmic ray induced extensive air showers in the atmosphere was measured as a function of atmospheric depth. From the exponential tail of this distribution, it was determined that the proton-air inelastic cross section at 30 TeV center-of-mass energy to be 540 + or - 40mb

All sky Northern Hemisphere 10(15) EV gamma-ray survey

Flux limits in the range 10 to the minus 13th power-10 to the minus 12 power/sq cm/s have been obtained by observing Cerenkov flashes from small air showers. During 1983, a 3.5 sigma excess of showers was observed during the phase interval 0.2 to 0.3 of the 4.8h period of Cygnus X-3, but no excess was found in 1984 observations

500 TeV gamma rays from Hercules X-1

A signal (chance probability = .0002) with the 1.24 s period of Hercules X-1 has been observed using the Utah Fly's Eye. The signal's relatively long period and high shower energy conflict with some popular models of particle acceleration by pulsars. Optical and X-ray data suggest a picture in which energetic particles produce multi-TeV gamma rays by collisions with Hercules X-1's accretion disk

Limits on deeply penetrating particles in the 10(17) eV cosmic ray flux

Deeply penetrating particles in the 10 to the 17th power eV cosmic ray flux were investigated. No such events were found in 8.2 x 10 to the 6th power sec of running time. Limits were set on the following: quark-matter in the primary cosmic ray flux; long-lived, weakly interacting particles produced in p-air collisions; the astrophysical neutrino flux. In particular, the neutrino flux limit at 10 to the 17th power eV implies that z, the red shift of maximum activity is 10 in the model of Hill and Schramm

Energy calibration of the fly's eye detector

The methods used to calibrate the Fly's eye detector to evaluate the energy of EAS are discussed. The energy of extensive air showers (EAS) as seen by the Fly's Eye detector are obtained from track length integrals of observed shower development curves. The energy of the parent cosmic ray primary is estimated by applying corrections to account for undetected energy in the muon, neutrino and hadronic channels. Absolute values for E depend upon the measurement of shower sizes N sub e(x). The following items are necessary to convert apparent optical brightness into intrinsical optical brightness: (1) an assessment of those factors responsible for light production by the relativistic electrons in an EAS and the transmission of light thru the atmosphere, (2) calibration of the optical detection system, and (3) a knowledge of the trajectory of the shower

Arrival directions of cosmic rays of E .4 EeV

The anisotropy of cosmic rays observed by the Utah Fly's Eye detector has been studied. Emphasis has been placed on examining distributions of events in galactic coordinates. No statistically significant departure from isotropy has been observed for energies greater than 0.4 EeV (1 EeV = 10 to the 18th power eV). Results of the standard harmonic analysis in right ascension are also presented

Study of composition of cosmic rays with energy .7 E 3 Ee

The longitudinal shower development of extensive air showers (EAS) observed in the fly's eye is used to determine the distribution of X sub max, the depth in the atmosphere of the EAS maximum. Data and Monte Carlo simulations of proton and iron primaries are compared. A substantial contribution from light primaries is noted