Orthogonality Relations and Supercharacter Formulas of U(m|n) Representations

In this paper we obtain the orthogonality relations for the supergroup U(m|n), which are remarkably different from the ones for the U(N) case. We extend our results for ordinary representations, obtained some time ago, to the case of complex conjugated and mixed representations. Our results are expressed in terms of the Young tableaux notation for irreducible representations. We use the supersymmetric Harish-Chandra-Itzykson-Zuber integral and the character expansion technique as mathematical tools for deriving these relations. As a byproduct we also obtain closed expressions for the supercharacters and dimensions of some particular irreducible U(m|n) representations. A new way of labeling the U(m|n) irreducible representations in terms of m + n numbers is proposed. Finally, as a corollary of our results, new identities among the dimensions of the irreducible representations of the unitary group U(N) are presented.Comment: 56 pages, LaTeX, changes only in the writing of the titl

Impact dynamics research facility for full-scale aircraft crash testing

An impact dynamics research facility (IDRF) was developed to crash test full-scale general aviation aircraft under free-flight test conditions. The aircraft are crashed into the impact surface as free bodies; a pendulum swing method is used to obtain desired flight paths and velocities. Flight paths up to -60 deg and aircraft velocities along the flight paths up to about 27.0 m/s can be obtained with a combination of swing-cable lengths and release heights made available by a large gantry. Seven twin engine, 2721-kg aircraft were successfully crash tested at the facility, and all systems functioned properly. Acquisition of data from signals generated by accelerometers on board the aircraft and from external and onboard camera coverage was successful in spite of the amount of damage which occurred during each crash. Test parameters at the IDRF are controllable with flight path angles accurate within 8 percent, aircraft velocity accurate within 6 percent, pitch angles accurate to 4.25 deg, and roll and yaw angles acceptable under wind velocities up to 4.5 m/s

The Large-NN Limit of the Two-Hermitian-matrix model by the hidden BRST method

This paper discusses the large N limit of the two-Hermitian-matrix model in zero dimensions, using the hidden BRST method. A system of integral equations previously found is solved, showing that it contained the exact solution of the model in leading order of large $N$.Comment: 19 pages, Latex,CERN--TH-6531/9

Impact data from a transport aircraft during a controlled impact demonstration

On December 1, 1984, the FAA and NASA conducted a remotely piloted air-to-ground crash test of a Boeing 720 transport aircraft instrumented to measure crash loads of the structure and the anthropomorphic dummy passengers. Over 330 time histories of accelerations and loads collected during the Full-Scale Transport Controlled Impact Demonstration (CID) for the 1-sec period after initial impact are presented. Although a symmetric 1 deg. nose-up attitude with a 17 ft/sec sink rate was planned, the plane was yawed and rolled 13 deg. at initial (left-wing) impact. The first fuselage impact occurred near the nose wheel well with the nose pitched down 2.5 deg. Peak normal (vertical) floor accelerations were highest in the cockpit and forward cabin near the nose wheel well and were approximately 14G. The remaining cabin floor received normal acceleration peaks of 7G or less. The peak longitudinal floor accelerations showed a similar distribution, with the highest (7G) in the cockpit and forward cabin, decreasing to 4G or less toward the rear. Peak transverse floor accelerations ranged from about 5G in the cockpit to 1G in the aft fuselage