Microwave background constraints on inflationary parameters

We use a compilation of cosmic microwave anisotropy data (including the recent VSA, CBI and Archeops results), supplemented with an additional constraint on the expansion rate, to directly constrain the parameters of slow-roll inflation models. We find good agreement with other papers concerning the cosmological parameters, and display constraints on the power spectrum amplitude from inflation and the first two slow-roll parameters, finding in particular that $\epsilon_1 < 0.057$. The technique we use for parametrizing inflationary spectra may become essential once the data quality improves significantly.Comment: 6 pages LaTeX file with figures incorporated. Major revisions including incorporation of new datasets (CBI and Archeops). Slow-roll inflation module for use with the CAMB program can be found at http://astronomy.cpes.susx.ac.uk/~sleach/inflation

Test vectors for Rankin-Selberg LL-functions

We study the local zeta integrals attached to a pair of generic representations $(\pi,\tau)$ of $GL_n\times GL_m$, $n>m$, over a $p$-adic field. Through a process of unipotent averaging we produce a pair of corresponding Whittaker functions whose zeta integral is non-zero, and we express this integral in terms of the Langlands parameters of $\pi$ and $\tau$. In many cases, these Whittaker functions also serve as a test vector for the associated Rankin-Selberg (local) $L$-function.Comment: arXiv admin note: text overlap with arXiv:1804.0772

Design of an active helicopter control experiment at the Princeton Rotorcraft Dynamics Laboratory

In an effort to develop an active control technique for reducing helicopter vibrations stemming from the main rotor system, a helicopter model was designed and tested at the Princeton Rotorcraft Dynamics Laboratory (PRDL). A description of this facility, including its latest data acquisition upgrade, are given. The design procedures for the test model and its Froude scaled rotor system are also discussed. The approach for performing active control is based on the idea that rotor states can be identified by instrumenting the rotor blades. Using this knowledge, Individual Blade Control (IBC) or Higher Harmonic Control (HHC) pitch input commands may be used to impact on rotor dynamics in such a way as to reduce rotor vibrations. Discussed here is an instrumentation configuration utilizing miniature accelerometers to measure and estimate first and second out-of-plane bending mode positions and velocities. To verify this technique, the model was tested, and resulting data were used to estimate rotor states as well as flap and bending coefficients, procedures for which are discussed. Overall results show that a cost- and time-effective method for building a useful test model for future active control experiments was developed. With some fine-tuning or slight adjustments in sensor configuration, prospects for obtaining good state estimates look promising