Skein theory for SU(n)-quantum invariants

For any n>1 we define an isotopy invariant, _n, for a certain set of n-valent ribbon graphs Gamma in R^3, including all framed oriented links. We show that our bracket coincides with the Kauffman bracket for n=2 and with the Kuperberg's bracket for n=3. Furthermore, we prove that for any n, our bracket of a link L is equal, up to normalization, to the SU_n-quantum invariant of L. We show a number of properties of our bracket extending those of the Kauffman's and Kuperberg's brackets, and we relate it to the bracket of Murakami-Ohtsuki-Yamada. Finally, on the basis of the skein relations satisfied by _n, we define the SU_n-skein module of any 3-manifold M and we prove that it determines the SL_n-character variety of pi_1(M).Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol5/agt-5-36.ab

Automated Operations and Safety Data Collection and Usage in Contemporary Flight Operations Quality Audit Programs

Flight Operations Quality Audit (FOQA) programs are becoming more common to airlines of today. Flight data recording devices modified for repeated and daily data readouts have been dem-onstrating their unquestionable advantages in FOQA programmes. They demonstrate the interest of airlines, that use them, to transport people, cargo and mail in safe and efficient way. The paper will present general FOQA structure, historical developments in this field together with common obstacles when introducing FOQA to an airline. It also brings the latest data and understanding of benefits that FOQA has on airlines operation with potential applications of similar concepts to other means of transportation as well